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OFDM/FM frame synchronization for mobile radio data communication Warner, William D. 1991

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OFDM/FM FRAME SYNCHRONIZATION FOR MOBILE RADIO DATA COMMUNICATION By William D. Warner B. A. Sc., The University of Waterloo, 1986 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF A P P LI ED SCIENCE in T H E FACULTY OF G R A D U A T E STUDIES D E P A R T M E N T OF ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA March 1991 © William D. Warner, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of £L<£CT&ICAJ- £tJC/K)£:CR./fj£, The University of British Columbia Vancouver, Canada Date YtfocH- Z.1 '99/ DE-6 (2/88) Abstract A synchronization scheme enabling the use of OFDM/FM in a pure ALOHA environment over a mobile radio channel is proposed, implemented, and tested. The synchronization scheme encodes synchronization information in parallel with data in the same manner in which data is encoded in the OFDM/FM frame. The encoded synchronization informa-tion is in the form of tones, centered in reserved frequency sub-channels of the OFDM signal. The receiver uses a correlation detector, implemented in the frequency domain, to accurately acquire synchronization on a packet by packet basis. Experimental results indicate that BER performance with synchronization is achieved to within 1.5 dB of the performance achievable with ideal synchronization. ii Table of Contents Abstract ii List of Tables vi List of Figures vii Acknowledgement ix 1 Introduction 1 1.1 Mobile Data Communication 1 1.2 O F D M / F M for Mobile Radio Data Communication 3 1.3 Scope of Thesis 4 1.4 Organization of Thesis 4 2 OFDM Modulation, Implementation Configuration, FM Fading Channel 5 2.1 O F D M Modulation 5 2.1.1 Historical Perspective and Motivation 5 2.1.2 Basic Principles of Operation 6 2.2 Implementation Configuration 8 2.3 F M Fading Channel 10 2.3.1 Rayleigh Fading Channel 10 2.3.2 F M Transceiver Characteristics 10 3 Review of Current Synchronization Techniques 21 3.1 Purpose and Hierarchy of Synchronization 21 3.2 Serial Transmission 22 iii 3.2.1 Asynchronous Transmission 22 3.2.2 Synchronous Transmission '. 22 3.3 Parallel Transmission 25 4 Proposed Synchronization Technique 28 4.1 Synchronization Requirements 28 4.2 Basic Concept 30 4.3 Detailed Examination 33 4.3.1 Synchronization Signal Model 33 4.3.2 Three-phase Synchronization Acquisition 34 4.3.3 Synchronization Sub-Channel Selection 42 5 Experiments 44 5.1 Experimental Setup 44 5.1.1 Hardware 44 5.1.2 Pseudo-Random Bit Sequence Generator 55 5.1.3 Raised Cosine Weighting Function 56 5.1.4 OFDM Baseband Signal Spectrum 56 5.1.5 OFDM RF Signal Spectrum 58 5.1.6 Loop-Back Configuration 59 5.1.7 End-to-End Configuration 59 5.1.8 Received Data Analyzer 59 5.2 Experimental Results 63 5.2.1 Categorization of Results 63 5.2.2 Phase I Results 63 5.2.3 Phase II Results 66 5.2.4 Phase III Results 69 5.2.5 Integrated Results 71 iv 6 Conclusions 75 6.1 Conclusions 75 6.2 Topics for Further Research 76 Bibliography 77 A Models and Algorithms for Synchronization 83 A.l Synchronization Model 83 A.2 Frequency Domain Derivation of the Correlation Detector 85 A. 3 Fine Tune Algorithm 86 Appendices 83 B DFT Algorithms 88 B. l FFT Implementation 88 B.2 DFT Implementation 89 B.3 Sliding Window DFT 89 B. 4 Accumulated Round-Off Error for the Sliding Window DFT 91 C Digital Low Pass Filter 93 C. l Filter Requirements 93 C.2 UR vs. FIR 93 C.3 FIR Filter Design 95 D Modulating Signal Power Prediction 97 E Estimation of F M Channel Attack Time 100 v List of Tables 5.1 Experiment List Summary 63 5.2 Synchronization Sub-channel selection for 1024 block size 67 v i List of Figures 1.1 Typical Mobile Data Communication System 1 1.2 A sample plot of the received signal level 2 2.1 Transient Response of the ICOM-2ATs connected back-to-back 12 2.2 Transmitter Attack Time of ICOM-2AT 13 2.3 Estimated F M Channel Attack Time of ICOM-2AT 15 2.4 Receiver output power vs. IF SNR 16 2.5 Noise Power Distribution for modulating signal with constant power across spectrum 17 2.6 Noise Power Distribution for modulating signal with 10 dB per decade de-emphasis 18 2.7 Scatter plot of received data without channel equalization 19 2.8 Scatter plot of received data with channel equalization 20 2.9 Channel Equalization Transform of transmitted O F D M signal for 1024 sam-ple block size with lOdB per decade de-emphasis 20 4.1 Synchronization Block Diagram 35 4.2 Synchronization - Phase I 36 4.3 Synchronization - Phase II 37 4.4 Synchronization - Phase III 38 5.1 F M Fading Channel 45 5.2 Digital F M Channel 47 5.3 Tx and Rx Gain Units 50 5.4 Tx Switch 51 vi i 5.5 Mid-rise model of 8 level A/D quantization 53 5.6 A/D SNR versus Gaussian Standard Deviation 54 5.7 O F D M Baseband Signal Spectrum 57 5.8 O F D M R F Signal Spectrum 58 5.9 Discriminating among the four classifications of synchronization 62 5.10 Phase I performance in the absence of a transmitted signal 64 5.11 Phase I performance in the presence of a transmitted signal. Doppler rate is: / d=10Hz 64 5.12 Phase I performance in the presence of a transmitted signal. Doppler rates are: / d=20Hz and / d=50Hz 65 5.13 Phase II performance 67 5.14 Phase III performance - Absolute Results 69 5.15 Phase III performance - Relative to Ideal, fd = IQHz 70 5.16 Integrated System Synchronization Performance 71 5.17 Integrated System B E R Performance 72 5.18 Performance Loss Due to Synchronization 73 A. l Sync signal phasor diagram 86 B. l DFT calculations on sliding window 90 C. l Modified signal spectrum and L P F spectrum 94 C. 2 Interpolation filter impulse response 96 D. l O F D M Baseband Signal Generation 97 E . l Hardware Configuration to Estimate the Attack Time of the ICOM-2AT F M Channel 100 vi i i Acknowledgement I would like to thank all those who have helped and supported me during the course of my work on this thesis. Dr. Cyril Leung has spent countless hours with me discussing the merits of my ideas and has provided insightful advice regarding the problems I have faced. Pete McConnell of MDI provided some initial direction in researching the background of synchronization and assisted in making several RF measurements. I would like to acknowledge the financial assistance provided by NSERC in the form of a Post-Graduate Scholarship and funds from operating grant OGP0001731, by UBC in the form of a top-up award, and by the Science Council of British Columbia in the form of a GREAT award, sponsored by MDI. Finally, I would like to thank Lisa, my fianc6, for providing constant love and support and for reminding me of the important things in life. ix Chapter 1 Introduction 1.1 Mobile Data Communication Figure 1.1: Typical Mobile Data Communication System Reliable and efficient data communication between a base station and mobile users is of interest to many in the business and service industry. Examples of mobile user equipment currently in use are [1,2]: • The 7100-11FK mobile data terminal and the KDT 840 portable data terminal from Mobile Data International Inc. 1 Chapter 1. Introduction 2 • The GL1110 data link radio modem and GL4160A fax compatible radiotelephone for wide area mobile phone service from Glenayre Electronics. A system consisting of a base station interfaced to a central computer system and a multitude of mobile data terminals (MDT's) allows access by a mobile user to a central database. This capability is used by law enforcement agencies to obtain motor vehicle information or criminal record information while on patrol. MDT's are also beneficial to dispatch services such as taxi cabs and couriers. Figure 1.1 shows a typical mobile data communication system. HI in Distance (m) < n 0 1 2 3 4 10 i i i i i i i i i i I i i i i i i i i i i i i i i i i i i i I i i i i i 0 -m a> -o t "10 E < a> a. o -20 -30 -10 - -10 - -20 - -30 -40 '1'1'''1 ^ ''1'''''' ^ '''''''11 ^ '' 111111 p 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ^ f t n 1 * 1 1 • I *• •1 * *' • _4Q 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) Figure 1.2: A sample plot of the received signal level. The communication link is achieved through radio transceivers (transmitter/receiver). The processing of the received radio signals to recover the transmitted data sent to and from mobile sources is a challenging problem [3]. In an urban environment, radio signals transmitted by a stationary source are reflected and scattered by buildings and other Chapter 1. Introduction 3 objects. This results in a pattern of constructive and destructive interference forming a varying field strength. As the mobile moves through this interference pattern, the received signal level fluctuates. A similar effect occurs when a mobile transmits a signal to a stationary receiver. Figure 1.2, taken from Casas [4], was generated using the Rayleigh fading model. It shows the deep fades that are characteristic of the received signal. 1.2 OFDM/FM for Mobile Radio Data Communication Orthogonal Frequency Division Multiplexing (OFDM) has been proposed and investigated as an approach to the problem of fading [5,4]. OFDM is a modulation technique that frequency division multiplexes a serial data stream and transmits the data in parallel. This allows the baud rate to be reduced without decreasing the bit rate. The serial data stream is frequency mapped into many quadrature amplitude modulated1 sub-carriers [6]. Each transmitted symbol can convey hundreds or thousands of bits of data. Thus, the symbol duration can be increased by hundreds or thousands without decreasing the data rate. The increased duration of each symbol makes it less likely that the entire symbol will be severely faded. Signal fading results in cross-talk among the sub-channels of the OFDM signal and degrades performance. Cimini [5] investigated the use of OFDM Single Side Band (SSB) transceivers. Casas [4] also studied the use of OFDM. His work differed from Cimini's work in that narrow band Frequency Modulation (FM) transceivers were used. Both approaches had advan-tages: OFDM/SSB is more spectrally efficient and power efficient, but OFDM/FM does not suffer from effects of frequency offsets, and the system can be easily retrofitted to existing FM communications systems. A simplifying assumption made in [4,5] was that perfect symbol synchronization could be achieved. It is the purpose of this thesis to propose and evaluate a technique to achieve lsee section 2.1.2 Chapter 1. Introduction 4 this synchronization. 1.3 Scope of Thesis The OFDM/FM configuration used in [4] is selected. The motivating reason is the avail-ability of the actual equipment used by Casas [4] allowing direct comparison to his pre-viously established performance results. It is assumed that the only sources of signal degradation are additive white Gaussian noise and Rayleigh fading. The effects of log normal fading (shadow fading) are not considered. The main contributions of this thesis are: • proposal of an algorithm capable of providing good synchronization performance, • refinement of the synchronization algorithm to reduce computational complexity, • implementation of a prototype OFDM/FM system to measure the performance of the synchronization algorithm. 1.4 Organization of Thesis Chapter 2 provides background information on OFDM modulation, characteristics of the FM fading channel, and outlines the configuration of the implemented test system. Chapter 3 contains a review of some currently used synchronization techniques for serial and parallel data communication. Chapter 4 presents the proposed synchronization technique in detail and its similar-ities and differences to current techniques. Chapter 5 provides details of the test system, including parameter selection. Results of experiments conducted are presented and discussed. Chapter 6 summarizes the contributions of the thesis and recommends topics for further research. Chapter 2 OFDM Modulation, Implementation Configuration, FM Fading Channel 2.1 OFDM Modulation 2.1.1 Historical Perspective and Motivation Orthogonal Frequency Division Multiplexing (OFDM) is a member of a larger class of modulation schemes referred to as Multi-Carrier Modulation (MCM). M C M has also been referred to as Multi-Frequency Modulation (MFM) [7]. M C M , first used over 30 years ago [8], has been of continuing interest since, but has not moved beyond the realm of peripheral interest until recently [9]. One of the reasons for the recent interest in M C M is that the long symbol time, characteristic of M C M , produces a much greater immunity to impulse noise and fast fades [9]. MCM's greater immunity to fast fades has prompted researchers [4,5] to propose and investigate the use of O F D M as an approach to the problem of fading in the mobile radio environment. In M C M , when efficient use of bandwidth is not required, the most effective parallel system uses conventional F D M , in which the frequency sub-channel spectra do not overlap, and passband filters [5]. In mobile radio communication, however, spectrum is a precious commodity and efficient use of bandwidth is important [5]. In contrast to conventional F D M , the individual spectra of the O F D M sub-carriers overlap each other providing a better utilization of available bandwidth. Despite this overlap, complete separation of the signals by the receiver is possible due to the designed orthogonality of the sub-carriers [10]. The greater immunity of O F D M to the fast fades of the mobile radio environment re-sults from the effect of a fade being spread over all sub-carriers (assuming non-frequency 5 Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 6 selective fading) [9]. Instead of a few bits of data being severely distorted, all bits of data in the block are only slightly or moderately distorted. The distribution, or averaging, of noise over all sub-carriers results in demodulated data values distorted by noise with a distribution similar to Gaussian. This is in comparison to a bursty noise distribution that would result i f serial modulation techniques were used. The process of modulation and demodulation can be implemented quite simply by using the Discrete Fourier Transform (DFT). Computational requirements can be reduced using the Fast Fourier Transform (FFT) implementation of the DFT. This technique was originally proposed by [10] and later used in [9,4,5,11,12] 2.1.2 Basic Principles of Operation In O F D M , the sub-carrier frequencies are chosen to be spaced at the symbol rate, that is, i f the O F D M symbol duration is T seconds, the sub-carrier frequency spacing is 1/T Hz. With this frequency spacing, the sub-carriers are orthogonal when viewed over one symbol interval [6,10,13,5,4]. This allows modulation and demodulation using the DFT in its efficient F F T form [10]. During transmission of data, the sub-carriers are "keyed" by the stream of serial data. The incoming serial data is collected in blocks of K bits. To each sub-carrier, a smaller grouping of bits (usually 2 to 5) is assigned. These bits are used to set the phase and magnitude of the sub-carrier. Typically, a 2 m - Q A M constellation is used to encode the data into the phase and magnitude of the sub-carrier, where m is the number of bits assigned to the sub-carrier. From this perspective, O F D M can also be considered as Orthogonal Frequency Division Multiplexed Phase-Amplitude Shift Keying (OFDMPASK). For the purpose of this thesis, the more general term, O F D M , will be used. Conversion of the serial data to the modulating signal is actually performed by an N-point Inverse FFT. The m-bit groupings of data are encoded as complex values, a + jb, defining points in the 2 m - Q A M constellation. The complex encoded data values become Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 7 the data for the Inverse FFT, their location in the Inverse FFT data array corresponding to their assigned sub-carrier channel position in frequency. If specific sub-carriers are not used, the corresponding data values in the Inverse F F T data array are set to zero. Only the lower half of the data array is used to encode sub-carrier information. The upper half of the data array is encoded as the conjugate symmetry of the lower half. The purpose of this is to produce an N-sample real modulating signal when the Inverse FFT is performed. The real data samples generated by the Inverse F F T are converted to an analog waveform using the appropriate digital-to-analog (D/A) converters and reconstruction niters. The analog modulating signal can be transmitted directly as a baseband signal, or as in the case of mobile radios, used to modulate an RF transmitter. At the receiver, the reverse sequence of events occurs. The received baseband signal is sampled and converted to digital form. N consecutive samples are grouped to form an O F D M block. A n JV-point F F T is performed to determine the phase and magnitude of the sub-carriers. For each sub-carrier, the transmitted bit information is extracted by determining the location in the complex plane denned by the received sub-carrier and locating the nearest constellation point. Determination of the constellation point identifies the transmitted m-bit data sequence. Assuming the following conditions, the transmitted data can be recovered without error. • Ideal synchronization of O F D M frame. • No distortion of the magnitude or phase of the sub-carriers due to system hardware. • No degradation of the orthogonality of the sub-carriers due to fading and other sources of noise. The above ideal conditions are not realistically achievable. In this and the following Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 8 chapters, these problems are more thoroughly examined. In describing the basic principles of operation, it is assumed that the number of bits assigned to each sub-carrier is the same and that the total number of bits in the block is fixed. This is not a requirement of OFDM. As discussed in section 2.3.2 under Noise Power Distribution, the number of bits assigned to each sub-carrier can vary from one sub-carrier to the next. The performance of OFDM is dependent on the size of the FFT block used. When a larger block size is used, the effect of a fade is spread over a greater number of sub-channels, reducing the distortion in each sub-channel. Casas [4] studied the performance of OFDM for FFT block sizes of256, 512,1024, 2048 and 4096. Results showed improving performance with increasing block size. The performance of OFDM is also dependent on the rate of fading, a measure of the duration between fades and the duration of fades. The rate of fading is specified as the doppler rate, fj, and is defined by fi=f— (2-1) c where fc is the carrier frequency, v is the vehicle speed, and c is the velocity of propaga-tion. For OFDM/FM, Casas [4] examined the relation between block size, doppler rate and system performance. The product, Tfd, of the block duration, T, and the doppler rate, fd, was defined. Test conditions having equal Tfd values tended to produce similar performance. 2.2 Implementation Configuration The implementation configuration chosen for the test system is based on a centralized packet radio broadcasting network. The characteristics of this type of network are [14]: • packet transmission Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 9 • reception by many or all stations • common transmission medium • one central controller, multiple nodes In the context of this thesis, the MDT, or mobile, is a node and the base station is the central controller. For the remainder of this thesis, the terms mobile and base station will be used. The MDI N C P 3000 Network Control Processor [2] is an example of a mobile data transmission system based on a centralized packet radio broadcasting network. Since all mobiles communicate with the central controller via a common medium, a Medium Access Control Protocol (MACP) is required to regulate the access to the channel. Packet radio networks typically use random access or contention techniques [14]. Con-tention techniques can be either slotted or un-slotted. In slotted systems, the receiver has a priori information as to when a data packet may arrive. In an un-slotted system, the receiver has no a priori information concerning the arrival times of data packets, which may arrive at random times. Implementation of a M A C P is beyond the scope of this thesis. The implemented system has one central controller and only one mobile. Transmission wil l occur in the direction of controller to mobile only. The mobile has no a priori information regarding arrival times of data packets. In many data transmission systems, packet lengths are allowed to vary during trans-mission [14]. Information is contained within the packet identifying its length. In this thesis, only fixed packet lengths of 1024 samples are allowed. Implementation of variable length packets is left for future work. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 10 2.3 F M Fading Channel The OFDM baseband signal is used to modulate an FM transmitter, thereby broadcasting the signal to the mobile (from the base station) or to the base station (from the mobile). Surrounding buildings and other structures create an interference pattern with areas of constructive interference and areas of destructive interference. Motion of the mobile through this interference pattern results in a received signal whose instantaneous power fluctuates greatly. This power fluctuation can be modelled by the Rayleigh fading model. A similar effect occurs for transmission from the mobile to the base station. It is important to know the characteristics of the fading channel and the hardware used in the implementation, since limitations on system performance can be imposed by either. The following sections describe these characteristics and how they affect the design and performance of the OFDM/FM system. 2.3.1 Rayleigh Fading Channel 2.3.2 F M Transceiver Characteristics Two ICOM-2AT transceivers [15] are used for the experimental work, one as the trans-mitter and one as the receiver. They were previously used by Casas in his initial study of OFDM/FM [4]. These are amateur radio hand-held transceivers. An operating frequency of 144.15 MHz was chosen. Transient Response When a modulating signal is input to the transmitter, a transition in modulating sig-nal power from zero to maximum power occurs causing transients in the transmitter. The magnitude of the transients are dependent on the abruptness of the transition and result in a temporary distortion of the transmitted signal and thus affects the signal at the receiver output. Likewise, when the receiver experiences abrupt changes in the Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 11 modulation of the received carrier signal, transients are generated, further distorting the receiver output signal. Transients in either the transmitter or the receiver result in a distorted received sig-nal. This distortion degrades' the orthogonality of the O F D M baseband signal. Therefore, it is important to allow transients to decay before decoding is performed. Casas ensured this by preceding the O F D M modulating signal with a periodic extension of the signal itself. The duration of this periodic extension was set excessively long to ensure that system transients were negligible when the received baseband signal was sampled for decoding. Note that the extension must be a periodic extension of itself, so that abrupt phase changes do not occur at the junction of the extension and the data block. In this thesis, the preceding periodic extension is referred to as the pre-extension. The pre-extension of the O F D M block manifests itself as overhead, reducing the sys-tem throughput. Thus, it is desirable to minimize the duration of the pre-extension. The transient response of the ICOM-2AT was measured for the combined effect of both the transmitter and receiver. A pulse was input to the transmitter and the output of the receiver was monitored. Monitoring of the signal was achieved using a Textronix 2232 digital storage oscilloscope triggered by the transmitter input pulse. Figure 2.1 gives the results of the transient response test. The lower trace shows the pulse input to the trans-mitter. The upper trace shows the resulting output from the receiver. Results are shown for 2 consecutive cycles with a repetition period of approximately 1.8 milliseconds. From the oscilloscope tracing, it appears that by the time the second pulse input occurs, the receiver output transients have faded significantly. To obtain a conservative estimate of the transient duration, the measured duration of 1.8 milliseconds is doubled and rounded up to the nearest integer. Therefore, the minimum duration of the pre-extension is set to 4 milliseconds. This corresponds to 32 samples at an 8 kHz sampling rate. For an O F D M block size of 1024 samples, this is approximately 3% overhead. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 12 T E K T R O N I X 2 2 3 2 A U 1 = 0 . 8 F0 .0I T R I ' 3 2 = E 1.141 A T = " . 8 1 E SflU A A ,/ / V "1 • i 1 1 1 „ n > 0 . 1 s\ U 0 . 5 1 J P L E 0 . 1 Dfns Figure 2.1: Transient Response of the ICOM-2ATs connected back-to-back. R a d i o A t t a c k Time Radio Attack Time is specified separately for transmitter and receiver [16,17,18]. • Transmitter Attack Time: time required to produce carrier power output after oper-ation of the transmitter control switch. • Receiver Attack Time: time required to produce audio power output after application of a modulated RF signal. The minimum standard for Transmitter Attack Time is for the carrier level to increase to 50% of its maximum power in less than 100 milliseconds [16,18]. The minimum stan-dard for Receiver Attack Time is for the audio power output to reach 90% of its rated power output in less than 150 milliseconds [17,18]. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 13 Radio attack time is a major source of transmission overhead. It imposes a lower limit on the time interval required between transmitted blocks. Larger time intervals are required for longer radio attack times. LEVEL REF -46DBM CEN AMKR -2.8DB AHKR TEK 497P FREQUENCY . 144.150 OMHZ 0.OOKHZ TIME/D1V 10MS/ ^ i i ki iA i hi 11" titt 1111 • i i i • i i i • i • • IrT f 1111 1111 M i l 1 M l • 1 1-t 1 • 11 i ' 1 -OBM -46 -56 -66 -76 -86 -96 -106 -116 -126 10DB/ VERTICAL DISPLAY 10DB RF ATTENUATION 0-1.8 FREQ RANGE INT REF OSC 1KHZ RESOLUTION BANDWIDTH Figure 2.2: Transmitter Attack Time of ICOM-2AT Following the measurement procedures standardized by the Electronic Industries As-sociation (EIA) [16,17,18], the transmitter attack time for the ICOM-2AT was measured. For the measurement, a spectrum analyzer was used to monitor the carrier power in-stead of connecting a linear peak carrier detector to the vertical plates of an oscilloscope as specified in the EIA standard. The result is shown in figure 2.2. The transmitter at-tack time was measured to be approximately 75 milliseconds. The equipment necessary to measure the receiver attack time was not available, hence the measurement was not performed. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 14 A third parameter of interest, not defined by EIA standards, is the combined attack time for the Transmitter-Receiver system. The motivation for this measurement is that the response of the receiver to the transmitter during its power-on transition phase is not indicated by the EIA measurements. It may be possible that the receiver is sensitive enough to the presence of a carrier that it meets its specified criteria before the trans-mitter reaches its specified criteria. For purposes of this thesis, this measurement will be referred to as the FM Channel Attack Time. The F M Channel Attack Time is defined as the time required to produce audio power output from the receiver after application of a modulating signal to the transmitter and operation of the transmitter control switch. The measurement procedure is similar to that of the receiver attack time. Since the required equipment was not available, the measurement was not performed. A measure-ment procedure to estimate the true F M channel attack time is detailed in Appendix E . The result of the F M channel attack time estimate is shown in Figure 2.3. The conclusion from the experiment is that the F M Channel Attack Time for the ICOM-2AT transmitter-receiver system is approximately 80 milliseconds. Receiver Output Power When the receiver squelch is disabled, the audio output power of the ICOM-2AT receiver is greater in the absence of a modulated or un-modulated carrier than in the presence of a carrier. Figure 2.4 plots the receiver audio output power in the presence ..of O F D M modu-lated and un-modulated carriers at various IF S N R levels. The receiver output power approaches a maximum as the IF S N R level decreases. The receiver output power ap-proaches a minimum as the IF S N R level increases. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 15 T E K T R O N I X 2 2 3 2 T R I i a 2 = ' .9U A T = 8 8 . 8 n s SfW P L E 2 8 ms Figure 2.3: Estimated FM Channel Attack Time of ICOM-2AT Noise Power Distribution If an OFDM modulating signal, whose power is distributed evenly over its spectrum, is transmitted over the FM channel, the baseband SNR of the received signal is not constant over its spectrum. Figure 2.5 shows this effect for the channel condition of IF SNR = lOdB and fj = 10 Hz. Since the signal mean is constant over the band, the uneven distribution of noise power results in varying SNR over the sub-channels of the received signal. The trend shown in the figure 2.5 indicates that the SNR improves in the higher frequency sub-channels. This corresponds to the results of Casas [4], who noted that the lower sub-channels experienced higher BERs relative to the higher sub-channels, the effect becoming more pronounced at lower IF SNR levels. Casas determined that de-emphasizing the modulating signal by lOdB per decade tended to equalize the BERs of Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 16 •10 ~| i i i 1 1 1 i 1 r m 33. w o o. S Q. •20 -Carrier without modulation Carrier with modulation -40 1 1 1 1 1 1 1 1 1 1 I I ' ' ' I i . . . ' •25 0 25 50 75 IFSNR (dB) Figure 2.4: Receiver output power vs. IF SNR the received signal sub-channels. The results of applying lOdB/decade de-emphasis to the modulating signal is shown in figure 2.6. The distribution of the noise power has flattened, giving a more constant SNR over the band. To maximize the attainable bit rate at a given error rate and SNR, Bingham [9] has indicated that the optimum power distribution should be calculated by a "water-pouring" procedure that is similar to that of Gallager [19]. Alternatively, BERs can be equalized over the sub-channels by employing a technique known as adaptive loading [9]. In this technique, more bits are assigned to the sub-channels with higher SNR and fewer bits are assigned to the sub-channels with lower SNR. To achieve optimal BER performance, a combination of adaptive power distribution and adaptive loading should be used [19,20]. To maintain similarity to the system in [4], the method of lOdB per decade de-emphasis is employed. The implementation is simple and yields reasonably good results [4]. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 17 IFSNR = 10dB, fd«10Hz 1 1 1 I 128 256 384 Sub-Channel Number 512 8 •5 z 1E-01 1E-02 IFSNR-10dB, fd-10Hz 1E-03 ~I I r ' I 1 1 1 _l I I I L. 100 1000 Sub-Channel Number Figure 2.5: Noise Power Distribution for modulating signal with constant power across spectrum Channel Hardware Equalization In Figure 5.2, a block diagram of the OFDM/FM data transmission system is presented. Several blocks have been grouped together and labelled as a Digital FM channel. This channel accepts a stream of serial digital data. The data is processed to generate digital data denning the OFDM baseband modulating signal. The digital OFDM signal is passed through a D/A converter and appropriate analog reconstruction niters and gain units to yield an analog OFDM signal suitable for modulating an FM transmitter. At the receiving end, the inverse functions occur in the reverse order. The hardware comprising the digital FM channel, specifically the analog components, introduce phase and amplitude distortions. These phase and amplitude variations must be accounted for when decoding the OFDM signal (note: with 4-QAM encoding, ampli-tude equalization is not important since only the phase is used in the decoding process, however, when decoding larger constellations, such as 16-QAM, amplitude equalization becomes important.) To measure the compensation required, a training procedure is performed in which Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 18 c n o 2 0.5 0.4 0.3 02 0.1 0 IFSNR-IOdB, fd = 10Hz T T 12B 256 384 Sub-Channel Number 512 a % a. o z IFSNR = 10dB, fd-10Hz 1E-01 p 1 1 1 1—i—i—i—r 1E-02 -1E-03 1000 Sub-Channel Number Figure 2.6: Noise" Power Distribution for modulating signal with 10 dB per decade de-emphasis known blocks of data are transmitted and received. The received data blocks are com-pared to the transmitted data blocks to determine the mathematical transformation re-quired to counteract the phase and magnitude distortions. To eliminate the necessity of synchronizing the transmitter and receiver, a loop-back configuration is employed in which only one modem, the base station, is used for both transmission and reception. Using a loop-back configuration will introduce error into the training sequence since the receiver characteristics of the mobile may differ from the receiver characteristics of the base station. Therefore, an end-to-end training sequence would be preferable. However, the loop-back configuration appears to give reasonable results and is simple to implement. It is, therefore, the chosen method. The effect of channel equalization is shown in Figures 2.7 and 2.8. Both figures are scatter plots of Q A M encoded data extracted from a received O F D M signal with a channel condition of: IF SNR = 15dB and no fading. In Figure 2.7, no channel equalization has been performed. Figure 2.8 is identical to Figure 2.7 except that channel equalization has been performed. It can be seen that with channel equalization, the received Q A M encoded data is clustered around the four Q A M constellation points. Without channel Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 19 equalization, the data is scattered and the signal points are not evident. 1 ~1 •• - 1 o qL o o o o o ° o O CD * ° o o § ° • 1 1 1 1 I &o o <5° ° >o o CD cfsScfo^o0 ° CP & C P 8 ^ ° o ^ % ° o 0 ^ o0o o^o 0 aS. S o o°oO^ o ooQo $ °© o O 1 1 1 1 o° o o 0 ° 0 ° o o o 0 o OD r-j CD OcO o ^ « ° o ° o ° o 3 <oo <S> 9§ oo° 1 1 1 1 -0.5 0 0.5 In-Phase Figure 2.7: Scatter plot of received data without channel equalization The training procedure was performed for the IC0M-2AT based digital FM channel. The results for 10 transmissions of OFDM blocks generated from random data are av-eraged and are shown in Figure 2.9. The training procedure was performed periodically over the course of experimentation with no significant visible changes in the equalization transform. However, with analog components, drift is inevitable. A practical system might employ an adaptive equalization vector to compensate for this drift. Chapter 2. OFDM Modulation, Implementation Configuration, FM Fading Channel 3 3 H •o flj 3 O 0.5 -0.5 -0.5 0.5 In-Phase Figure 2.8: Scatter plot of received data with channel equalization 8 2.8 2.3 1.6 1.3 0.6 0.3 •02 -0.7 •1.2 -1.7 •22 -2.7 •32 ~i—i—I—i—i—i—I—i—i—r Magnitude Phase - 0.75 (B 0.5 2 - 0.25 S12 OFDM sub-channel index Figure 2.9: Channel Equalization Transform of transmitted OFDM signal for 1024 sample block size with lOdB per decade de-emphasis. Chapter 3 Review of Current Synchronization Techniques In this chapter several synchronization techniques currently used in data communica-tions are examined. Although OFDM is a parallel transmission scheme, the examination extends to both parallel and serial techniques. 3.1 Purpose and Hierarchy of Synchronization The purpose of synchronization is to provide a frame of reference from which something or someone, a receiver, is able to correctly extract information from a signal that it has received from a sender. In computer data communications, the process of synchronization occurs at one or more layers of abstraction. In many ways, the multi-layered process, or hierarchy of synchronization, is similar to the syntactic structure of the text of this thesis. Consider processing this text, from which all punctuation has been removed and the capitals be-ginning each sentence suppressed: • individualcharacterscaneasilybeidentifiedbutitwouldbeverydifficultifnotimpossibl etoaccuratelyinterpretthemeaningofthetext • Individual characters can easily be identified, but it would be very difficult, if not impossible, to accurately interpret the meaning of the text. Reinserting the spaces allows the reader to easily identify each word. However, it is still likely that errors in interpretation will be made. Reinserting punctuation further simplifies the interpretation process and fewer errors are likely to occur. 21 Chapter 3. Review of Current Synchronization Techniques 22 In computer data communications, the implementation of synchronization may differ from the syntax of this text, but the concepts are similar. 3.2 Serial Transmission Serial transmission of digital data can be achieved with either digital or analog signals [14]. For analog signalling, synchronization begins with carrier synchronization followed by bit synchronization. For digital signalling, synchronization begins with bit synchro-nization. Two methods are common for digital signal synchronization, one for asynchronous transmission and the other for synchronous transmission [14]. 3.2.1 Asynchronous Transmission In asynchronous transmission, bits are sent one character at a time, with characters ranging in size from 5 to 8 bits. The receiver resynchronizes at the start of each character, and must maintain synchronization within each character. This technique is simple, but it requires a start and stop bit for each character. This results in 2 to 3 bits of overhead per character. Higher levels of synchronization are employed to group characters into messages. 3.2.2 Synchronous Transmission A more common technique, used in demanding applications, is synchronous transmission. It provides more efficient communication than asynchronous transmission. To improve efficiency, blocks of characters or bits are transmitted without start or stop symbols. Synchronization within the block is accomplished by exploiting coding schemes that have embedded clocking information, such as biphase encoding, or using the carrier to maintain synchronization for analog signals. Synchronizing to the block requires the detection of the start and end of the block. To achieve start detection, each block begins with a Chapter 3. Review of Current Synchronization Techniques 23 preamble bit pattern. This is a unique bit pattern that the receiver will recognize as the start of the block. To achieve end detection, either a postamble bit pattern is used at the end of the block, or control information is included within the block to indicate its length. In a noisy environment, bit errors during transmission are likely to occur. If one or more of the bits in the preamble are in error, the receiver will not detect the start of the block and the data will be lost. Barker [21] first examined the problem of detecting synchronization patterns in a noisy channel. Current techniques are based on his initial work. Barker's technique is based on the cross-correlation function, defined as: where Xk and ijk are the sampled values of two signals, and M is the number of signal data samples used in estimating the cross-correlation. Generally speaking, the cross-correlation function measures the similarity between two sets of data. Synchronization patterns are prefixed to the data to be transmitted. During transmission, the synchroniza-tion pattern may be corrupted by errors. A receiver, implementing the cross-correlation function, measures the similarity between the expected synchronization pattern and the received signal pattern. If a high measure of similarity is detected, then it is likely that the synchronization pattern has been detected. Although correlation detection has been shown to be sub-optimal [22], it provides good performance and is still used. The effectiveness of this method depends on the selection of the synchronization, or preamble, pattern. The ideal preamble pattern will have an auto-correlation defined as: where K is a finite value whose magnitude depends on the magnitude of the signal x(n), M-\ Rxy(n) = XkVn+k (3.1) otherwise (3.2) Chapter 3. Review of Current Synchronization Techniques 24 and a cross correlation (with random data) denned as: Rxy(n)= 0, alln. (3-3) Since the initial work by Barker, much work has been focused on finding synchroniza-tion patterns having the desired autocorrelation and cross correlation properties. In practice, these two conditions cannot be achieved exactly; however, preamble pat-terns of various lengths have been discovered that provide excellent results [23]. The first set of synchronization patterns were discovered by Barker. These patterns, now known as Barker sequences [21], have the property that the maximum absolute value of the autocorrelation sidelobes is M = 1. Unfortunately, there are only a total of 8 known Barker sequences, ranging from 2 bits to 13 bits in length. More recently, Linder performed a brute force computer search to find synchronization sequences of length up to 40 with good correlation properties. Barker sequences are a subset of Linder sequences [23]. It should be noted that a synchronization sequence that is optimal for one application is not necessarily optimal in general. For example, Maury and Styles found a set of optimal synchronization sequences for deep space telemetry, but, as Wu [23] pointed out, for digital satellite communications, sequences exist that exhibit better correlation properties than the Maury and Styles sequences. Radar tracking systems [24] using pulse compression are similar. The transmitted signal is a carefully selected signal having an auto-correlation function with low side-lobes. The receiver picks up the reflected signal and uses a matched filter to detect the known pattern and determine the time duration from transmission of the signal until reception. The oldest, and best known, type of pulse compression code (PCC) is the chirp. Basically, the chirp is a sinusoid whose frequency is linearly increased throughout the duration of the signal. Binary phase coding is the second most common type of PCC. Of the family of binary phase codes, Barker codes are the most frequently used, primarily because they achieve sidelobes that are relatively small compared to other binary codes. Chapter 3. Review of Current Synchronization Techniques 25 In binary phase codes, the transmitted signal is divided into a number of segments of equal duration. The phase of each segment is switched between two binary values in accordance with a predetermined code sequence. Frank codes [24], a family of polyphase codes closely related to the chirp and Barker codes, are also used. Frank codes are ba-sically a digital version of the analog chirp [24]. These codes, and many others used in radar tracking systems, all seem to have one common element: the characteristics of the signal change during the duration of the signal (eg. the changing frequency in the chirp). 3.3 Pa ra l l e l Transmiss ion The area of synchronization for parallel transmission has received much less attention compared to serial transmission. This is largely due to the greater use of serial trans-mission schemes in past years. Most of the devised schemes are designed to maintain correct timing when slight deviations of timing are present. Also, many of the techniques accumulate information from consecutive baud intervals to improve timing estimates. When Weinstein and Ebert [10] first proposed the use of the DFT in data transmission systems based on F D M , they recognized the need for synchronization, and indicated that "one or several channels of the transmitted signal can readily be utilized for this purpose". However, they did not investigate the details of implementing such a system, nor did they indicate expected levels of performance of such a technique. Hirosaki, whose work followed Weinstein and Ebert's by ten years, took a different approach to synchronization [25,12,26]. Although his work revolved around a slightly different M C M system: Orthogonally Multiplexed Q A M (OQAM), the conditions under which synchronization is applied are similar. Rather than using pilot tones to determine timing deviations, dual automatic equalizers were employed. The dual automatic equal-izer is a slightly modified version of the complex automatic equalizer used in conventional Chapter 3. Review of Current Synchronization Techniques 26 single channel Q A M systems. Hirosaki showed that dual automatic equalizers, with ap-propriately spaced tapped delay lines, can equalize not only the transmission channel distortions, but the timing deviations and demodulating carrier phase deviations as well. One equalizer is employed for each sub-channel of the O Q A M signal. During reception of an O Q A M signal, an estimate of the timing deviation is determined by each sub-channel equalizer. The timing deviation estimates from each sub-channel are averaged together. The adjustment of the equalizer coefficients is continuous but response to deviations oc-curs over several baud intervals. Deviations in timing can be adjusted for only when the deviation in timing is slower than the loop tracking speed of the automatic equalizers. Following his previous work, Hirosaki joined with others to design a 19.2 Kbps voice-band data modem based on his OQAM technique [13]. To achieve the desired data throughput, a 128 point Q A M constellation had to be used. It was determined that with the large constellation, it would not be possible to track phase and gain hits using the data channels. Therefore, two pilot tones were used for synchronization. As in Hirosaki's previous work, adaptive equalizers were used on each of the data and timing channels. Paralleling the work of Hirosaki, Keasler studied the use of M F M techniques in voice band telephone modems [27,11]. His work was based on O F D M , similar to that of We-instein and Ebert [10]. Correlation detection is employed at the receiver to extract, or demodulate, the information contained in the various sub-carriers. Synchronization tim-ing information is provided by transmitting a pair of unmodulated sub-carriers in two reserved sub-channels. The two reserved sub-channels are identified as timing channels. The correlation process used in demodulation produces vectors indicating the phase of the sub-carriers in the timing channels. During demodulation of a received O F D M signal, the timing channel correlation vectors are monitored. When the monitored vectors are identical in phase, the proper correlation interval is established and synchronization is achieved. In addition, the relation between the timing channel phase in adjacent baud times is employed to correct for frequency offset. Chapter 3. Review of Current Synchronization Techniques 27 Another orthogonal M F M based transmission scheme using pilot tones for synchro-nization was designed and marketed by the Telebit Corporation [28]. The product was a telephone modem, able to achieve up to 12000 bps over a dial up line with a simultaneous 300 bps reverse channel. To obtain the high level of data throughput, the modem used 64 sub-channels with 5 bits of data encoded in each sub-channel. To provide synchroniza-tion, one of the sub-channels was reserved. Unlike previous systems, however, timing information was provided by pulsing the channel with a carrier. That is, the timing channel cyclically transmitted at full intensity for one epoch (baud interval), off for two, on for one, off for two, etc. The amplitude of the received timing channel was used as an amplitude reference to counteract gain hits. The beginning and end of transmissions of the timing channel was used to establish the time boundaries for each epoch. Timing accuracy was maintained by fine tuning the time boundary estimates over consecutive frames. A novel synchronization technique for differentially encoded M F M signals was re-cently developed by Moose [7]. The technique is similar in concept to synchronous serial transmission. Synchronization is achieved by inserting a known sync baud at the begin-ning of a packet of data bauds in a transmission. The receiver synchronizes to the sync baud using a matched filter and must maintain accurate timing for the remaining data bauds. Matched filter detection is performed on the received analog signal. Once syn-chronization has been established, the analog signal is sampled to allow data decoding in the digital domain. Chapter 4 Proposed Synchronizat ion Technique This chapter presents the proposed synchronization technique for O F D M signals. The synchronization requirements are first denned. The basic concept is then presented, followed by a detailed examination of the synchronization process. 4.1 Synchroniza t ion Requirements The synchronization requirements can be separated into two categories: (1) conditions under which synchronization must operate (2) the probability of synchronization error. The designed implementation is a pure A L O H A based mobile radio communication network using F M transceivers. The requirements under this category are: • The available spectrum being very restricted, the bandwidth overhead must be min-imized. • Due to the pure A L O H A implementation, each frame has to be synchronized inde-pendently. • Due to the fading nature of the mobile radio channel, the synchronization procedure cannot use a simple energy detector to provide synchronization. • The synchronization procedure must be relatively immune to phase and amplitude distortions induced by the channel noise. The probability of synchronization error can be grouped into four sub-categories. • Probability of false alarm is the probability that the synchronization algorithm de-tects the presence of a data block when none is present. 28 Chapter 4. Proposed Synchronization Technique 29 • Probability of miss detection is the probability that the synchronization algorithm does not detect the presence of a data block when one is present. • Probability of bad synchronization is the probability that the synchronization al-gorithm detects the presence of a data block when one is present, but, does not correctly synchronize. This occurs when enough distortion of the signal occurs to prevent proper synchronization, but not enough distortion to cause a miss detection. • Probability of correct synchronization is the probability that the synchronization algorithm detects the presence of a data block when one is present and correctly synchronizes to the data block. Within the category of correct synchronization, the degree of accuracy can range from excellent to poor. During experimentation, the accuracy of the synchronization procedure wil l be determined indirectly through B E R measurements. Channel noise and fading imposes a lower limit on the achievable BER. When synchronization is poor, the resulting error in the time frame of reference causes a rotation of the decoded Q A M phasor. The magnitude of this rotation increases for the higher frequency sub-channels. Thus, ideal synchronization minimizes the B E R for a given block. Comparing the B E R achieved using the synchronization procedure with the ideal B E R provides an indication of the accuracy of the synchronization procedure. Prior to experimentation, desired synchronization performance levels are established. The primary motivation in establishing the performance goals is to define levels of syn-chronization performance such that the resulting inaccuracy of the synchronization pro-cedure is not the major contributing factor limiting the achievable BER. That is, the achievable B E R should be limited by the O F D M modulation technique, not the synchro-nization procedure. The minimum requirements for the probabilities of false alarm, miss detection and Chapter 4. Proposed Synchronization Technique 30 bad synchronization are set equal to the B E R of the O F D M system given ideal synchro-nization. This should result in a measured B E R that does not exceed two times the B E R given ideal synchronization. The required probability of good synchronization is not specified; it is simply the probability that one of the three denned errors does not occur. With better synchronization performance, system performance would be improved only marginally, due to the limiting BER. One last concern regarding the synchronization algorithm is that i f it is too complex and too computationally expensive, it will not be practical. 4.2 Basic Concept Synchronization techniques currently available for serial or parallel modulation schemes are inadequate for use in M F M based communication systems in a pure A L O H A mobile radio environment. Serial techniques are inherently unsuitable because of channel fading. The fading causes burst errors that would make it difficult to detect the synchronization preamble. Also, the complexity of the transmitter and receiver would be increased in order to support both serial mode for synchronization and parallel mode for data transfer. Current parallel techniques rely on at least one assumption that contradicts the syn-chronization requirements: • Hirosaki's [25,12,26] technique described in section 3.3 requires adaptive equalizers for each sub-channel. A typical O F D M signal may have up to one thousand or more sub-channels. The resulting complexity and amount of processing make the technique impractical. A modified version of Hirosaki's technique [13] uses only two reserved sub-channels for timing control. Unfortunately, in this version and in Hirosaki's original version, the technique can only handle slight deviations in timing, and the accuracy of timing is obtained over several baud periods through use of a feedback loop. That is, the technique assumes that synchronization has Chapter 4. Proposed Synchronization Technique 31 already been established and that only fine tuning has to be performed and can be executed over consecutive baud intervals. Neither of these assumptions are valid in a pure A L O H A environment. • Keasler's system [27], using the difference in phase between the un-modulated car-riers of two reserved sub-channels, has merit. However, the technique is sensitive to phase errors. As the channel noise increases, the phase errors introduced to the two reserved sub-channels (as well as to all data channels) also increase. There-fore, it is possible that when the data frame is ideally synchronized, the two reserved sub-channels will have a large phase error. When the synchronization procedure modifies the time reference to minimize the phase error in the two reserved sub-channels, the remaining data sub-channels will experience an increased BER. Therefore, the sensitivity of Keasler's system to phase noise makes it unsuitable for the mobile radio environment. • The method employed by the Telebit Corporation [28] is not useful for two reasons: 1) accurate detection of the start and stop of a baud interval (epoch) is required, but, due to the frequent fades of the received mobile radio signal, this is not possible; 2) inaccuracies in timing are averaged out over consecutive baud intervals; however, in a pure A L O H A environment each baud is independent and timing information from one baud interval is not useful in synchronizing to another baud. • Moose's [7] system is designed for use in mobile satellite communications and is relatively immune to the problem of fading. Moose's system, however, uses a syn-chronization baud preceding a packet of data bauds. Synchronization is not achieved on individual bauds, and since the technique uses all available sub-channels, data cannot be transmitted in the synchronization baud. Therefore, Moose's technique is not suitable. The proposed solution utilizes two basic concepts: Chapter 4. Proposed Synchronization Technique 32 1. A number of the sub-channels of the O F D M signal are reserved for synchronization tones. 2. At the receiver, a correlation detector is used to detect the synchronization signal imbedded in the O F D M signal and indicate synchronization timing. Both concepts are used in current systems. The novel aspects of the proposed system are the way in which the concepts are combined and the method for implementation. The transmitter encodes the reserved synchronization tone sub-channels with known phases and amplitudes. The remaining sub-channels are encoded with data as outlined in section 2.1.2. To the synchronization algorithm of the receiver, the received signal can be interpreted as a sync baud (as in [7]) imbedded in noise, where the noise is a combi-nation of channel noise distorting the O F D M signal, and the signal components of the data sub-channels. Typically, to keep transmission overhead at a minimum, the number of reserved sub-channels is small compared to the number of available sub-channels. Re-sulting from this is a very poor SNR 1 . For example, i f 10% of the available sub-channels are reserved, the perceived SNR will be -9.54dB. For a correlation detector to work, the SNR would have to be much larger [29]. However, recall that the O F D M sub-channels are orthogonal; in a properly implemented correlation detector the noise components due to the data sub-channels would cancel, resulting in a much higher effective SNR. The only degradation to the effective SNR would result from degradations to the orthogonality of the O F D M sub-channels caused by fades and channel noise. Similar to Moose's system, this technique does not rely on time-domain detection of the start of the data block and is therefore relatively insensitive to channel fading. Unlike Moose's system, however, synchronization is achieved separately for each block, so that the technique wil l work in a pure A L O H A environment. 'In this interpretation of signal and noise, assuming negligible channel noise and equal distribution of power among the sub-channels, the SNR would be denned as: SNR = 101og10 n o " o f synchronization sub-channels 0 1 0 no. of data sub-channels Chapter 4. Proposed Synchronization Technique 33 Error performance of the technique can be controlled by altering the number of syn-chronization sub-channels. For a given number of synchronization sub-channels, error performance can be optimized through judicious selection of sub-channels. 4.3 Detailed Examination 4.3.1 Synchronization Signal Model In Appendix A, a model of the synchronization signal is presented. To reduce the complex-ity, simplifying assumptions are made. The derived model is periodic and has infinite duration. The auto-correlation of the synchronization signal model also has these two characteristics. Periodicity: Each sub-carrier of an O F D M signal is sinusoidal and has an integer number of periods in the frame interval. Therefore, each sub-carrier is periodic over the frame interval. The synchronization signal is comprised of a number of phase and amplitude encoded sub-carriers. Therefore, the synchronization signal is also periodic over the frame interval. Depending on the specific sub-channels used for synchronization, it is possible for the synchronization signal to be periodic over a duration that is less than the frame period. The minimum periodic duration of the synchronization signal is the lowest common periodic duration of the synchronization sub-carriers. This wil l not be less than the period of the highest synchronization sub-channel (which has the smallest period), and will not exceed the frame duration. Infinite Duration: In the model, the synchronization signal is assumed to be of infinite duration and is therefore band-limited. Auto-correlation: In Appendix A, the synchronization model derivation shows that, as-suming an infinite duration received synchronization signal, the modelled auto-correlation Chapter 4. Proposed Synchronization Technique 34 functions of the received signal and the reference signal are also periodic and band-limited. The period of the auto-correlation is equal to the period of the synchronization signal. The maximum frequency component of the auto-correlation is equal to the maxi-mum frequency component of the synchronization signal. 4.3.2 Three-phase Synchroniza t ion Acqu i s i t i on A three phase synchronization acquisition procedure is used: 1. Phase I detects when an O F D M signal is present by monitoring the power in the received signal. It does not attempt to acquire synchronization, but does determine a rough estimate of the location of the signal. 2. Phase II uses a correlation detector to extract the synchronization information from the received signal and to acquire synchronization to within ± \ of the sample period. This is considered as coarse synchronization. 3. Phase III provides fine tuning of Phase II synchronization by accurately locating the local peak of the correlation detector implemented in Phase II. Figure 4.1 presents a block diagram of the synchronization data processing steps. Phase I - Energy Detect ion In Figure 2.4 it can be seen that the audio output power of the receiver is larger in the absence of a carrier and smaller in the presence of a carrier. In an A L O H A mobile radio environment, a transmitter only generates a carrier when transmitting data; therefore, i f no transmitters are transmitting data, there will not be a carrier for a receiver to detect. Referring to Figure 4.1, Phase I monitors the power level of the received signal. When the power level drops below a threshold, phase I concludes that an O F D M signal is present and phase II of synchronization is initiated. Chapter 4. Proposed Synchronization Technique 35 Rx Signal A/D Data Start Phasei A Phase I Power Estimation Start Phase H Main Data Buffer Phase II Coarse Synchronization Sync Index Start Phase HI 1 Phase III Fine Synchronization Figure 4.1: Synchronization Block Diagram Figure 4.2 provides greater detail on the operation of Phase I. The received data is stored in Data Buffer I prior to power estimation. The data buffer will keep a record of the most recent values. When a new data value is received from the A/D converter, it is loaded into the Data Buffer I and the oldest data value in the buffer is discarded. Each time a new data value is received, the power of the received signal is estimated and compared to the reference threshold. The power of the signal is estimated by determining the power of the data in Data Buffer I. The equation used to calculate the power is: N - l »'=0 (4.1) where x, are the data samples and N is the number of samples used in the estimate and the size of Data Buffer I. The accuracy of this estimate is dependent on the number of data samples used [30]. Given this, it might seem reasonable to use a very large number of data samples, as this would enable the receiver to determine the presence of a carrier more reliably. However, using a data set that is larger than the OFDM data frame would reduce its ability to determine the location of the OFDM data frame. This, in turn, would Chapter 4. Proposed Synchronization Technique 36 Data Buffer I Dala Reference Threshold Sun Phase I 1 1 Power Power ^ Threshold Start Estimator Estimate Detector Phase II Enable Figure 4.2: Synchronization - Phase I make it necessary for phase II to work under more difficult conditions. Therefore, a compromise is made; the number of data samples used to estimate the signal power is set equal to the number of samples in the OFDM frame. Determination of an appropriate threshold is achieved experimentally. If the thresh-old is set too high, the probability that the power estimate falls below the threshold when no carrier is present will be too high. This will result in a high probability of false alarm and a high probability of incorrect synchronization. If the threshold is set too low, the probability that the power estimate will not fall below the threshold when a carrier is present will be too high. This will result in a high probability of miss detection. Phase II - Coarse Synchronization Referring to Figure 4.1 and with more detail in Figure 4.3, following the detection of an OFDM signal and rough determination of its location, phase II is used to acquire synchro-nization alignment to within ± 1 sample period. This is considered coarse synchronization because it is unacceptable for decoding of the OFDM data. Consider the data sub-carrier Chapter 4. Proposed Synchronization Technique 37 Sync Reference EQ Data Data Buffer II Start Phase II EI Data Data Index Calculator Matched Filter Interpolating Filter Peak Detector Peak Location ; Initialize 'Start Stop Delay Start; Phasem Figure 4.3: Synchronization - Phase II corresponding to 2 kHz, the center of the OFDM baseband signal. At a sampling rate of 8 kHz, an alignment error of ± \ of a sampling period will result in a phase error of ±45 degrees. This is unacceptable for QAM decoding. For the data sub-carriers corresponding to higher frequencies in the OFDM signal, the phase errors will be even greater. Similar to Phase I, the received A/D sampled data values are temporarily stored in Data Buffer II. When Phase II begins, the last data value stored in Data Buffer I will also be the last data value stored in Data Buffer II. Initially, and each time a new data value is received, a correlation detector is used to determine the correlation of the data in the buffer and the reference synchronization signal. The reference synchronization signal is a copy of the transmitted synchronization signal. The minimum size required for Data Buffer II is equal to the number of data samples used by the correlation detector. The output of the correlation detector is input into an interpolating filter to provide a higher rate of samples. A peak detector monitors the output of the interpolating filter and keeps track of the location of the peak value. Operation of the peak detector is controlled by a start/stop signal. The peak detector resets and begins operation when Chapter 4. Proposed Synchronization Technique 38 Data EQDala Start Phase ID" FFT Hardware Optimal Equalizer Synchronizer Start Phase I i Figure 4.4: Synchronization - Phase III phase II processing starts. A fixed time later, peak detection is halted. The peak location indicated by the detector corresponds to the point of synchronization. The Data Index Calculator converts the output of the Peak Locator to an index pointer that identifies the location, in the Main Data Buffer, of the synchronized data block. The control signal that halts operation of the peak detector also initiates phase III of synchronization. The correlation detector and the interpolation filter are described in greater detail below. Correlation Detector The correlation detector calculates the correlation between the data in Data Buffer II and the reference synchronization signal. -J Often, correlation detectors are implemented in the time domain. However, in the OFDM system, time domain implementation may lead to difficulty in implementation. Recall, from Channel Hardware Equalization in section 2.3.2, that the received signal is phase and amplitude distorted due to analog filtering and the FM channel. This distortion must be compensated for before the results of the correlation detector can be used. One Chapter 4. Proposed Synchronization Technique 39 technique is to pass the received data values through an equalization filter prior to stor-ing them in Data Buffer II. Another technique is to use a phase and amplitude distorted version of the reference synchronization signal. The first technique has the advantage of being adaptable and the disadvantage of increasing the computational load. The second technique does not increase the computational load, but it is not easily adaptable, an im-portant consideration i f the transfer function of the hardware drifts. To provide adaption in the second technique would require an analysis of the change in transfer function and its effect on the transmitted signal. The phase and amplitude distorted version of the transmitted signal would then have to be regenerated. A third technique is proposed that allows flexibility and adaptability without dramat-ically increasing the computational load: the correlation detector is implemented in the frequency domain. At first thought, it might seem that the transformation of the data to the frequency domain is computationally expensive. However, a special routine can be used that is order N, compared to order N log JV for the F F T and order N2 for the DFT. This routine, called the DFT update routine, is described in the following paragraphs and is derived in Appendix B . Using the DFT update routine, the data in the phase II data buffer is processed to extract the phase and magnitude (in phasor form) of the sync tone sub-channels. To compensate for known phase and magnitude distortions, the received sync tone phasors are multiplied by equalization phasors, determined using a training sequence as described in section 2.3.2. The equalized phasors and the synchronization reference phasors are used to calculate the correlation detector output. The equation defining the frequency domain implemen-tation of the correlation detector, developed in Appendix A, is given as: Y^n^SiQri (4.2) t=l where s, is the equalized phasor of the ith sync tone of the received signal, r,- is the phasor of the ith sync tone of the reference signal, j is the number of synchronization tones used, Chapter 4. Proposed Synchronization Technique 40 0 is the dot product, and K is a constant. The DFT update routine achieves a reduction in computational complexity by updating the spectral estimates based on previous estimates, rather than by recalculating the spectral estimates, and by only updating the spectral estimates for the specific frequencies required. This is an ideal situation for the correlation detector which only requires the spectral information for the synchronization tones. From Appendix B , the DFT update equation is Xn+1(k) = [Xn(k) - x(n) + x(n + N)}expjZ& (4.3) where Xn(k) is the spectral information of the kth sub-channel with the trailing edge of the data window positioned at the nth data sample, x(n) is the nth data sample and N is the block size of the DFT/FFT. The equation is simple: from the previous spectral estimate, the newly received data value is added, the oldest data value is subtracted and the result is multiplied by a phase shift. When phase II is initiated, a previous spectral estimate does not exist. Therefore, the sync tone spectral information of the received data is calculated using a DFT or F F T 2 . Following this, the spectral estimates are updated using equation 4.3. A drawback of the DFT update routine is that round-off errors propagate and are accumulated at each invocation of the routine. Therefore, the DFT/FFT should be used periodically to recalculate the spectral estimates. Appendix B contains an analysis of the accumulated error and discusses how often the spectral estimates should be recalculated. Interpolat ion F i l t e r The correlation detector provides correlation results for the re-ceived O F D M sync signal and the reference synchronization signal. These results are snapshots, spaced at intervals equal to the sample period, of the continuous time cor-relation. If the width of the expected correlation detector output peak is less than the sample period, the peak may not appear in the output of the correlation detector. This 2Depending on the number of sub-channels of interest, the D F T may be faster than the F F T . The D F T routine can be modified to calculate the spectral information for specific sub-channels. Chapter 4. Proposed Synchronization Technique 41 possibility can be avoided by recalling that the auto-correlation of the synchronization signal is band-limited. Therefore, the correlation detector output will be band-limited, and can be passed through a digital interpolation filter to obtain more frequent snapshots of the signal and reduce the possibility of missing the correlation peak. In Appendix C, a 63 tap finite impulse response low pass filter is derived that provides interpolated data values at four times the original data rate. This is sufficient to insure that the peak is detected to within 95% of its actual value. Phase III - Fine Synchronization Referring to Figures 4.1 and 4.4, fine synchronization is performed following the comple-tion of coarse synchronization. Due to the discrete nature of phase II, coarse synchronization can only be obtained to within ± 1 of a sample period. This degree of accuracy, however, results in large phase errors for the higher frequency sub-channels and, therefore, is inadequate. Phase III uses a closed-form equation to provide fine synchronization by accurately determining the location of the local maximum of the correlation detector output from Phase II. In addition, phase III demodulates the OFDM signal and extracts the encoded data. Since phase II achieves sync to within ± 1 of a sample period, it is guaranteed that the data frame will be aligned within the un-weighted pre-extension of the OFDM data frame. Therefore, an FFT can be performed on the received data block without loss of information. Following the FFT computations, all sub-channels of the OFDM signal are equalized to compensate for the known phase and magnitude distortions. Optimal syn-chronization is performed on this final set of data. The algorithm, derived in Appendix A, calculates the time shift that maximizes the correlation with the reference synchro-nization signal. The required phase shift for each sub-channel is then calculated and applied. Chapter 4. Proposed Synchronization Technique 42 4.3.3 Synchronization Sub-Channel Selection Selection of the sub-channels of the O F D M signal which should be reserved for synchro-nization is critical to the performance of the synchronization algorithm. As with matched filter and correlation filter synchronization techniques for serial com-munications, different synchronization signals produce different side lobe patterns with local correlation peaks occurring away from the synchronization location. The variation of the side-lobe patterns results in differing synchronization performance. The ideal cor-relation function for serial techniques, equations 3.2 and 3.3, are also ideal for O F D M . As previously indicated, the assumption of infinite duration signals allows the output of the correlation "detector in phase II of synchronization to be modelled by the correlation of the infinite duration O F D M signal with one period of itself. The resulting correlation signal has a period equal to the period of the synchronization signal. In phase II of synchronization, the output of the correlation detector is monitored for a fixed period of time. If this period of time is greater than the synchronization period, two occurrences of the synchronization peak may be detected which will cause synchronization errors. Therefore, the selection of synchronization tones must have a period greater than the duration of phase II. The duration of phase II, however, is dependent on the ability of phase I to detect the location of the data frame. For this reason, the selection of sync tones cannot be made until analysis of Phase I synchronization has been completed. Given that the duration of the minimum synchronization period has been determined through analysis of Phase I results, selection of synchronization sub-channels can pro-ceed. Ideally, the combination of J sub-channels that has a period greater than the minimum required and the minimum side-lobe levels of all possible sub-channel combi-nations is to be determined. The value of J , the number of sub-channels used, must also be determined. In general, as J increases, the minimum attainable side-lobe level will decrease and Phase II performance will improve. Previous work on designing sinusoidal signals with desired correlation properties Chapter 4. Proposed Synchronization Technique 43 could not be located, and a theoretical development was not readily apparent. Therefore, a computer search was used to determine the best combinations. This brute force technique has been used previously in designing synchronization patterns for serial communications [23]. An accurate theoretical prediction of the number of sub-channels required to meet synchronization performance requirements was unavailable. Experimentation was used: the number of sub-channels was increased until suitable performance was obtained. Initially, a brute force search to select 4 from the 256 available sub-channels, was performed on a SUN SPARC Station 1. With 80% CPU utilization, the search took approximately 7 days to complete. As the number of desired sub-channels is increased, the number of possible combinations increases factorially. It is estimated that selecting 5 from the 256 available sub-channels will take 350 days to complete. To be of any practical use, the search time must be greatly reduced. Two simplifica-tions were found and implemented. 1. Results from the initial experiments were examined and a pattern was found. In all cases, each of the 4 sub-channels selected had an integer (or close to an integer) number of periods in the minimum required periodic duration. Therefore, the search space was reduced to include only those sub-channels that had an integer number of periods in the minimum required periodic duration. 2. The search was divided into several consecutive steps, each step building on the results of the previous step. In each step, the selected sub-channels from the pre-vious step are kept and an additional 3 sub-channels are selected that provide the smallest sidelobes. Because of the above simplifications, the resulting set of sub-channels may not be optimal. However, a larger set of synchronization tones can be used to compensate for this sub-optimality. Chapter 5 Experiments This chapter describes the experimental setup used to measure the performance of the proposed synchronization system. The results of the experiments are also presented. 5.1 Experimental Setup 5.1.1 Hardware Analog FM fading channel A block diagram depicting the implementation of an F M fading channel is given in in Figure 5.1. The implementation is that used by Casas [4]. A baseband signal is used to modulate an ICOM-2AT narrow-band F M transmitter. Transmission occurs over a co-axial cable link to provide isolation from external electromagnetic interference and to allow control of signal fading and SNR levels. The R F output of the transmitter is passed through a Rayleigh fading channel simulator. The simulator [31], provides for Doppler rate selection of 2 Hz to 126 Hz in increments of 2 Hz. The output from the Rayleigh fading channel simulator is passed through a step-wise variable attenuator (Kay model no. 437A) and combined with the output of an RF noise source using a power split-ter/combiner (Mini-Circuits model no. ZSC-2-1). The Kay attenuator allows levels of 0 dB to 102.5 dB attenuation, in increments of 0.5 dB, to be selected. A power amplifier (Mini-Circuits model no. ZHL-2-8) is used as the R F noise source. To prevent amplifi-cation of any stray signals present in the environment, the input to the amplifier was terminated with a 50Q, shielded load. The output of the power combiner is connected to 44 Chapter 5. Experiments 45 Signal Flow \ ICOM-2AT Transmitter 144.15 MHz QAM Modulator Baseband Modulating Signal Power Splitter/Combiner Mini-Circuits Model ZSC-2-1 RF Attenuator Kay Model 437A -Q 0 0 o Q P a Z P — C ICOM-2AT Receiver Fading Channel Control / Baseband Demodulated Signal Rayleigh Fading ..CMnnelSirriuJator.. Power Amplifier Mini-Circuits Model ZHL-2-8 Figure 5.1: FM Fading Channel the antenna input of the ICOM-2AT receiver. The recovered baseband signal is monitored via the audio output jack of the receiver. The SNR of the RF signal seen by the receiving ICOM-2AT is difficult to measure. However, as in [4], the RF SNR can be approximated by measuring the IF SNR within the ICOM-2AT receiver. The IF SNR level is controlled by varying the attenuation setting of the Kay step attenuator. Increasing the attenuation level reduces the signal power and thus decreases the IF SNR. Conversely, a decrease in the attenuation level results in an increased IF SNR. For the setup of Figure 5.1, Casas calibrated the IF SNR level resulting in an equation relating the attenuation level and the IF SNR: IF SNR (dB) = 75(dB) - attenuation (dB) (5.1) The IF SNR measurement procedure, as detailed in [4,32,33,34], was reproduced and equation (5.1) shown to be accurate. Chapter 5. Experiments 46 Dig i t a l F M channel The digital F M channel, shown in Figure 5.2, is comprised of the analog F M fading channel shown in Figure 5.1, and additional hardware and software which allows the input of data to the transmitter to be in digital form, and for the output of data from the receiver to be in digital form. The O F D M modulating technique is imbedded within the hardware and software of the digital F M channel. The generation of the O F D M signal is shared between the host computer and spe-cial Digital Signal Processing (DSP) hardware. The host computer is an I B M PC/AT compatible. Residing on the bus internal to the host is a DSP56001 Processor Board from Spectrum Signal Processing of Burnaby, Canada [35]. This is a specialized signal processing board based on Motorola's DSP56001 digital signal processor. Connected to this board, and also residing on the host's internal bus, is a 4-channel I/O board which provides Digital-to-Analog (DIA) and Analog-to-Digital (AID) conversion. The I/O board is also from Spectrum Signal Processing [36]. Da ta Input At the transmitting end serial digital data, in binary form, is accepted. The data is Q A M encoded, grouped into blocks and converted to parallel. Software De-emphasis The blocks of data received from the data input serial to par-allel converter are interpreted as frequency domain information from which the O F D M baseband signal is constructed. The Q A M encoding of data results in equal energy in each of the frequency components of the O F D M signal. De-emphasis of the encoded data by 10 dB per decade is provided in software to improve the performance of the system (see Noise Power Distribution in section 2.3.2). O F D M Signa l Generat ion The sampling frequency of the system is set at 8 kHz, the Nyquist 1 frequency corresponding to a maximum signal frequency of 4 kHz. In the 1The Nyquist rate is defined as twice the maximum frequency of the signal [37]. Chapter 5. Experiments 47 QAM Encoding Serial Digital Data Input Serial Digital Data Output Serial iS to Parallel Data Flow Software De-emphasis QAM Decoding Parallel to Serial X o Inverse FFT a. Vi a Parallel to Serial FM Fading Channel Tx Switch DSP Gain LPF + HPF Filler D/A Conversion LPF Filter Tx Gain Rx Gain Channel Equalization FFT Serial 1 2? to DSP Parallel DSP DSP Gain A/D Conversion Figure 5.2: Digital F M Channel Chapter 5. Experiments 48 experiments, 256 frequency sub-channels between 1 kHz and 3 kHz are used to carry data and synchronization information. A n inverse F F T is used to construct the O F D M signal with these characteristics from the Q A M encoded data. To implement this, an inverse F F T block size of 1024 is used. Within this block, data elements from 0 to 127 and from 384 to 511 are set to zero. The Q A M encoded data is transfered to data elements 128 to 383. Data elements 512 to 1023 are denned to be the complex conjugates of elements 0 to 511. Performing an inverse F F T on this data results in a signal with no complex component. Data element 128 in the constructed data block corresponds to the 1 kHz frequency sub-channel of the O F D M signal. Data element 384 corresponds to the 3 kHz frequency sub-channel. Following the application of the inverse FFT, the resulting block of data is converted back to serial form. This serial digital data represents the O F D M modulating signal in digital form. D / A L o a d i n g Fac tor Prior to D/A conversion, the amplitude of the signal is modified to optimize the loading factor (LF) [38], defined as: _ Peak amplitude ^ RMS amplitude' Correct choice of the loading factor maximizes the SNR following D/A conversion. Also affected by the loading factor is F M transmitter performance. Frequency deviation in a F M transmitter is controlled by the amplitude of the modulating signal. To prevent frequency deviations from exceeding the allowed limit, the F M transmitter clips the am-•s, plitude of the modulating signal. According to Jakes [3], the optimal loading factor for voice signals over F M channels is: L F = 3.16 2 . This level was used in [4]. However, the characteristics of the O F D M baseband signal differ from voice signals. The O F D M baseband signal has a Gaussian distribution, while human speech is often modelled with a Laplace, or more accurately with a Gamma distribution [39]. Jayant [38] provides an 2Jakes specifies the Peak to RMS power ratio to be 10 dB, which corresponds to LF = 3.16 Chapter 5. Experiments 49 analysis of optimal loading factor for A/D conversion. The process of D/A conversion fol-lowed by reconstruction filtering is different from A/D conversion, with the distortions of each process affecting the signal characteristics differently. Therefore, Jayant's analysis of optimal loading factor may not be precise for D/A conversion. However, the analysis provides a reasonably good estimate of the optimal D/A loading factor. The analysis of the optimal A/D loading factor3 identified L F « 4.0 to be the optimal loading factor for A/D conversion. A loading factor of 4.0 is selected for D/A conversion. It is achieved by applying a software gain to the O F D M signal. In the fixed point implementation of the DSP56001, the magnitude of the data is bounded by ±1.0 4 . When the magnitude of a number exceeds ±1.0, it is limited to ±1.0. Thus, multiplying a set of data by a scalar value greater than 1.0 will increase the RMS value of the data but wil l not increase the peak magnitude beyond ±1.0. Multiplication of data by a factor greater than 1.0 can be done by realizing that shifting the data to the left by one bit is equivalent to multiplying by two. The RMS value of the O F D M signal data generated by the inverse F F T is approxi-mately 1.1 x 1 0 - 2 (refer to Appendix D for derivation)5. To achieve a loading factor of 4.0, assuming a peak of 1.0, the signal must have an RMS value of 0.25. This can be obtained by multiplying the signal data by 22.7. For ease of implementation, a factor of 32 is chosen. This can be implemented by shifting all data values 5 bits to the left. The DSP56001 properly saturates to ±1.0 when this value is exceeded during bit shifting [40]. The effect of choosing a multiplying factor that is larger than optimal wil l decrease the loading factor resulting in an increase in overload distortion. However, the effect on overall performance appears to be negligible6. 3see A/D Loading Factor in this section. 4 Actually, +1.0 cannot be represented in the fixed point architecture of the DSP56001. The largest positive value is 0.9999998. 'This is a representation internal to the DSP. No units are associated with this number. 6Phase III testing with LF = 22.7 resulted in BER performance similar to testing with LF = 32 Chapter 5. Experiments 50 Figure 5.3: Tx and Rx Gain Units Gain and Filtering The output signal of the D/A converter has a measured RMS level of 620 millivolts. The signal contains high frequency components which are replicas of the desired frequency spectrum at multiples of the sampling frequency. This characteristic of D/A conversion is compensated for using a reconstruction filter. This is a low pass filter with a cutoff frequency usually set equal to half of the sampling rate. In the experimental setup, an S^-order Butterworth low pass filter with a cutoff fre-quency of 4 kHz is used. As a precaution, an 8th order high pass filter with a cutoff frequency of 100 Hz is used to remove any unexpected DC component from the signal. Krohn-Hite filters (Model no. 3342) are used. The desired level for the modulating signal is 6 millivolts (RMS). The attenuation provided by the Tx Gain unit, the filters and the Tx switch reduce the signal level from Chapter 5. Experiments 51 On/Off Control 50k n -AAr luH From Krohn-Hite Filler To microphone input of ICOM-2AT 50ft InF SI - Manual Switch S2 - Voltage Controlled Switch Figure 5.4: Tx Switch 620 millivolts (RMS) to the desired level. The circuit for the Tx Gain unit, shown in Figure 5.3, is designed to additionally provide a high input impedance and a low output impedance. Tx Switch The Tx switch, shown in Figure 5.4, serves a dual purpose. It provides the last stage of attenuation required to reduce the level of the modulating signal to the desired level. It also provides a means to turn the FM transmitter on and off. Within the ICOM-2AT transceiver, a load detector is attached to the microphone input. When a load is detected, the transmitter's Push To Talk (PTT) is enabled. When the load is removed, PTT is disabled. The Tx switch is an electronically controlled switch that when closed provides a 25 kn load on the line connected to the transmitter microphone input, and when open presents an open circuit to the microphone input. When the switch is closed, the attenuated OFDM signal is gated to the switch output. The electronic control of the switch allows the FM transceiver to be turned on and off by the DSP hardware at the times appropriate for data transmission. For the ICOM-2ATs, a trigger advance of 80 milliseconds is used. That is, the PTT is enabled 80 milliseconds Chapter 5. Experiments 52 prior to the start of data transmission by the DSP. This allows adequate time for the transmitter to power-up (see Radio Attack Time in Section 2.3.2). Receiver Sect ion The components of the receiver section perform the inverse functions to the transmitter section in the reverse order. A n t i - A l i a s i n g F i l t e r s A 16th-order Butterworth low pass filter with a cutoff frequency of 4 kHz is used to remove all frequencies above 4 kHz. At an A/D sampling rate of 8 kHz, any frequency components above 4 kHz will be aliased down into the 0 to 4 kHz range. Therefore, these frequencies are removed from the signal. R x G a i n A n Rx gain of 2.4 is used to achieve a signal level of 620 millivolts (RMS). For A/D sampling with a signal input range of ±2.5 volts, this corresponds to a loading factor of 4.0. A / D L o a d i n g Factor Following the analysis in Jayant [38], the optimal A/D loading factor for zero mean, gaussian distributed signals, when considering the SNR following conversion, can be calculated. The optimal loading factor minimizes the sum of the gran-ular error variance, o^ , , and the overload error variance, CT2 , ,, thus maximizing 1 granular Hoverload the SNR of the A/D conversion. Granular error arises because the A/D converter has a finite number of sample values and thus cannot exactly represent the signal level. Over-load error arises due to the magnitude limitation of the A/D converter. The equation for total error variance is given as: <72 = CT2 + CT2 (5 3) 1 1 granular Q overload ^ ' where Agranular = E / (* " Vk)2Px(x)dx + 2 / (x - yLfPx(x)dx (5.4) k=2 Jxk Jx*< Chapter 5. Experiments 53 Y, Digital Output • Y 8 - -Y 7 - -Y 6 - --Xol X2 X3 X4 H — I — I — h -X6 X7 X8 Xol Y3 • Y2 - f Y l X, Analog Input Note: Xol = Xoverload Figure 5.5: Mid-rise model of 8 level A/D quantization and 9 overload = 2 f (x- yL)2Px(x)dx (5.5) ' ^overload In equations 5.4 and 5.5, Px(x) is the Probability Density Function (PDF) of the signal input to the quantizer, and X is the number of discrete levels of the A/D converter. The x variables and y variables, corresponding to the continuous input signal and the quantized output signal, are identified in Figure 5.5. The variable Peak Amplitude in equation 5.2 corresponds the variable xoverioaj in equations 5.4 and 5.5. The variable RMS amplitude corresponds to the variable ax, the standard deviation of the PDF Px(x). Figure 5.6 shows the A/D conversion SNR as a function of the standard deviation of a Gaussian signal and the bit resolution of the A/D converter. For all curves, i o u e r j o a d = 1-0. and the loading factor is equal to the reciprocal of the standard deviation. For 8-bit A/D conversions, an SNR level of 40dB is obtained when the loading factor is 4.0. For each curve, there is a point where the SNR level begins to drop off dramatically as the loading factor is increased. This is the loading factor at which the overload distortion becomes Chapter 5. Experiments -| 1 r~ -i 1 r -i i 1-60 -12 bit ADC 0-11 bit ADC • -10 bit ADC m-9 bit ADC *-8 bit ADC -J \ L_ _l I L-0.1 02 03 Std. Dev. of Gaussian Signal Figure 5.6: A/D SNR versus Gaussian Standard Deviation 04 Chapter 5. Experiments 55 dominant [38]. A loading factor of 4.0 is chosen. Rx Software Gain In the transmitter, a software gain of 32 was applied to the signal to modify the loading factor. In the receiver, a software gain of 1/32 is applied to counteract this. Without this gain, processing of the data by the DSP will result in saturation and, therefore, distortion of the received data. Data Recovery The serial data from the Rx Software Gain section is grouped into blocks and converted to parallel. An FFT is then performed on this data to recover the transmitted QAM encoded data. Channel Equalization The hardware comprising the digital FM channel distorts the amplitude and phase of the signal by a fixed amount. Equalization is performed to compensate for this distortion. Determination of the proper equalization is made through a training sequence procedure (see Channel Hardware Equalization in Section 2.3.2). Data Output The parallel data, following equalization, is converted back to serial form and QAM decoded to recover the transmitted bit sequence. 5.1.2 Pseudo-Random Bit Sequence Generator A Pseudo-Random Bit Sequence (PRBS) generator is used to generate the binary bit stream injected into the digital FM channel. The PRBS generator is implemented as a shift register with feedback. The generator polynomial, taken from [41], generates a maximal length sequence of period 2 2 3 - 1. The PRBS generator was implemented in the host computer. Chapter 5. Experiments 56 5.1.3 Raised Cosine Weighting Function Transmission of the OFDM signal block is preceded by a 32 sample periodic extension, called the pre-extension, of the OFDM signal to allow time for transients to dissipate (see Transient Response in Section 2.3.2) and is followed by a 32 sample periodic extension, called the post-extension. An improvement is made to further reduce the transient power at the start of the OFDM data. The first 16 samples of the pre-extension and the last 16 samples of the post-extension are weighted by a raised cosine function. This provides a smooth transition in signal power from zero to full power during transmission of the pre-extension and from full to zero power during transmission of the post-extension. Since transient magnitudes are dependent on the abruptness of the signal transition, the weighting function, which provides a smoother transition, should reduce the magnitude of the transients. The purpose of weighting the post-extension is to reduce the effect of transients on an immediately following OFDM signal block. 5.1.4 OFDM Baseband Signal Spectrum Figure 5.7 shows the spectral plot of the OFDM baseband signal following D/A con-version and reconstruction filtering. Due to the resolution bandwidth limitation of the Tektronix 497P spectrum analyzer, it is not possible to distinguish individual frequency sub-channels. However, it can be seen that only sub-channels in the frequency range from 1 kHz to 3 kHz are used. The power distribution among the sub-channels is not constant; lower frequency sub-channels have more power than higher frequency sub-channels. This is due to the soft-ware de-emphasis of 10 dB per decade. The spectral plot also indicates the presence of signal content above 5 kHz. Recall that D/A conversion results in replicas of the desired spectrum at multiples of the sampling frequency. Ideally, the reconstruction filter removes these higher frequency components. Chapter 5. Experiments 57 LEVEL REF 10DBM FREQUENCY CEN 3.OOKHZ SPAN/D1V 500HZ TEK 497P -L -. . . 1 1 1 1 1 1 1 1 i i i i I I I I " ii i i i i i i i M M M M t i l l 1 1 1 1 1 1 1 1 i i i i I I I I i l l i i I I I I I I I I II . i i . 1 1 1 1 V OBM 10 -10 -20 -30 -40 -50 -BO -70 10DB/ VERTICAL DISPLAY 40DB RF ATTENUATION 0-1. B INT FREO REF RANGE OSC 3HZ 100HZ VIDEO RESOLUTION FILTER BANDWIDTH Figure 5.7: OFDM Baseband Signal Spectrum Chapter 5. Experiments 58 LEVEL FREQUENCY SPAN/D1V REF 14DBM CEN 144.150MHZ 10KHZ 10DB/ 50DB 0-1.8 INT 30HZ 1KHZ VERTICAL RF FREO REF VIDEO RESOLUTION DISPLAY ATTENUATION RANGE OSC FILTER BANDWIDTH Figure 5.8: OFDM RF Signal Spectrum In practice, it is impossible to remove them completely. The signal above 5 kHz is the portion of the replicas that the reconstruction filter was unable to remove. 5.1.5 OFDM RF Signal Spectrum The Department of Communications (DOC) in Canada and the Federal Communications Commission (FCC) in the U.S.A. strictly regulate RF emissions. Included in these reg-ulations are specifications on the out-of-band emission attenuation for FM transmitters [42,43]. Figure 5.8 shows the spectral image of the ICOM-2AT transmitter RF output when modulated by a typical OFDM signal. Superimposed on the spectral plot is the spectral hat that indicates the maximum signal power output of the transmitter. Exami-nation of the spectral plot indicates that the ICOM-2AT transmitters are well within the Chapter 5. Experiments 59 guidelines. 5.1.6 Loop-Back Configuration During the training sequence and in several phases of experimentation, perfect synchro-nization is assumed. This is achieved with a loop-back configuration. In this configura-tion, the host and its internal DSP processor board act as both transmitter and receiver. The clock that is used to trigger D/A conversion for the transmitter also triggers A/D conversion for the receiver. The design of the implemented DSP software allows simul-taneous operation of transmit and receive functions. 5.1.7 End-to-End Configuration In the final test of the synchronization technique, the receiver must be unaware of trans-mitter timing. This is provided by the end-to-end configuration. In this configuration, A/D sampling and data recovery by the receiver is performed using a second host, with a DSP processor board and I/O board, operating independently of the transmitter. While it is possible to install both sets of DSP boards in the same host and have the host perform the necessary functions for both transmitter and receiver, the DSP boards are installed in separate hosts. This is to reassure outside observers that the transmitter and receiver are functioning independently! 5.1.8 Received Data Analyzer In the experiments, five performance indicators are measured to indicate synchronization performance: • Bit Error Rate (BER) • Probability of false alarm • Probability of miss detection Chapter 5. Experiments 60 • Probability of bad synchronization • Probability of correct synchronization In the loop-back configuration only the B E R needs to be determined. Since ideal synchronization is obtained in the loop-back configuration, the remaining performance measures are meaningless. The B E R is determined by comparison of the transmitted bit sequence with the received bit sequence. In the end-to-end configuration, all performance indicators are required. To provide B E R testing, the receiver's host is designed to generate a PRBS bit stream identical to that generated by the transmitter's host. Comparison by the receiving host of the generated bit stream and the received bit stream yields the BER. Determination of the other performance indicators is more difficult. When a block of bits are received, they are compared to the expected data and a B E R for that block, referred to as the block BER, is determined. If the block B E R is small, then it is un-likely that an error in synchronization has occurred since the expected block B E R with synchronization in error is 0.5. B E R threshold levels are used to classify whether a block is the result of correct synchronization. The design of Phase III experiments provides information used to determine the B E R thresholds. During Phase III testing, the host monitors the block B E R for ideal synchronization and keeps track of the maximum block B E R experienced during each experiment. This measured B E R provides a lower bound on the setting of the B E R threshold. If the threshold is set below this bound, it is likely that during end-to-end testing, a block that is correctly synchronized wil l be classified as bad. In practice, the B E R threshold levels are set between the measured maximum block BERs and 0.5. This provides a safety margin to ensure that mis-classification of synchronization errors is unlikely. If a data block is determined to be in synchronization error, there are three possibili-ties: 1. The block is the result of a false alarm. Chapter 5. Experiments 61 2. A transmitted block was missed and the received block is a subsequently transmitted block. 3. The received block corresponds to the transmitted block, but due to inaccuracies in synchronization, the number of bit errors is large. To differentiate among the possibilities, the receiver keeps a buffer of the expected data blocks. The received data block is compared to each block in the data buffer until a match is found or the limits of the buffer are exceeded. When a match is found, the position of the match within the buffer is examined. Knowledge of the location of the previous match, the number of blocks received since that are in error, and the location of the current match allow for determination of which error has occured and if the error has occured consecutively. It should be noted that it is not possible to differentiate between the case of a false alarm followed by a miss and the case of a bad sync. In this instance, the error is classified as a bad sync. Figure 5.9 illustrates the occurence and detection of each synchronization classifica-tion. In each illustrated situation, the expected blocks are blocks n, n+l, n+2, etc., and the received blocks are blocks k, k+1, k+2, etc. • In the case of a false alarm, block k is matched with block n, block k+1 is matched with block n+l, and block k+3 is matched with block n+2. Note that no match is found for received block k+2, but matches are found for each of the expected blocks. Received block k+2 is the result of a false alarm. • In the case of a miss sync, each of the received blocks are matched with expected blocks. However, no match is found for expected block n+2. The block that should have been matched with block n+2 was not detected, thus a miss sync has occurred. • In the case of a bad sync, block k is matched with block n, block k+1 is matched with block n+l and block k+4 is matched with block n+4. Received blocks k+2 and Chapter 5. Experiments 62 False Alarm Miss Sync block n matches block k blockn _^  matches block k block n+l block k+1 block n+l block k+1 block n+2 *— block k+2 block n+2 block k+2 block n+3 block k+3 block n+3 block k+3 block n+4 block k+4 block n+4 block k+4 • • • • • • • • • • • • Expected Data Received Data Blocks Blocks Expected Data Received Data Blocks Blocks Bad Sync Correct Sync block n ^ matches block k block n — matches block k block n+l — block k+1 block n+l block k+1 block n+2 block k+2 block n+2 — block k+2 X— block n+3 block k+3 block n+3 block k+3 block n+4 block k+4 block n+4 block k+4 • • • • • • • • • • • • Expected Data Received Data Blocks Blocks Expected Data Received Data Blocks Blocks Figure 5.9: Discriminating among the four classifications of synchronization Chapter 5. Experiments 63 IF SNR Phase I Phase II Phase III Integrated lOdB 15dB 20dB 25dB X Y Z X . _ X . _ X Y Z X Y . X Y _ X . _ X _ _ X Y _ X Y _ X Y _ X Y . X Y _ X . _ X Y _ X Y . X : / d=10Hz Y : fd=20] Hz Z: / d=50Hz Table 5.1: Experiment List Summary k+3 are not matched with blocks n+2 and n+3 as expected. Received blocks k+2 and k+3 are classified as bad syncs. • In the case of correct sync, all received blocks are matched with their respective expected block. 5.2 Exper imenta l Results 5.2.1 Categorizat ion of Results Experiments were conducted to measure, separately, the performance of each phase of synchronization. Experiments were also conducted for the integrated system. Table 5.1 summarizes the list of experiments conducted. The interpretation of the table is as follows: for Phase I with IF SNR = lOdB, experiments were made for doppler rates of 10Hz, 20Hz, and 50Hz; for Phase I with IF SNR = 15dB, experiments were only performed for a doppler rate of 10Hz. Additional to this list is the test for probability of False Alarm, which is independent of the IF SNR and doppler rate. Results from the experiments are presented in graphical form. The estimated mean and 95% confidence intervals [44] are identified. 5.2.2 Phase I Results Phase I experimentation measures two performance indicators: Chapter 5. Experiments 64 1E+00 ^ 1E-01 tr E < <D ra 3 1E-02 -1E-03 I 1 1 1 1 1 1 1 i I I i i i i 0.35 04 0.45 0.5 Threshold Figure 5.10: Phase I performance in the absence of a transmitted signal. Detection Location Prior to Sync (in Sample Periods) Figure 5.11: Phase I performance in the presence of a transmitted signal. Doppler rate is: /<i=10Hz Chapter 5. Experiments 65 250 Detection Location Prior to Sync (in Sample Periods) Figure 5.12: Phase I performance in the presence of a transmitted signal. Doppler rates are: / d=20Hz and / d=50Hz • probability of False Alarm • ability of Phase I to determine location of O F D M data frame Figure 5.10 shows the performance of Phase I in the absence of a transmitted signal. From this, the probability of false alarm for a range of threshold levels can be predicted. During testing, 50000 trials were performed for each indicated threshold level. One trial represents the transmission and reception of one O F D M data block. During each trial, no R F carrier is present. The power of the demodulated baseband signal received from the F M receiver is estimated using 1024 samples of the received signal. Power estimation continues each time a new sample is received and concludes when a total of 1024 additional samples have been received. A false alarm is detected i f any of the 1025 power estimations has a value less than the specified threshold. The trend is an increase in the probability of False Alarm with increasing threshold level. For thresholds of 0.375 and lower, no false alarm errors were detected. Later, in this section, it is shown that Chapter 5. Experiments 66 threshold levels of 0.15, 0.18, 0.21 and 0.25 are selected for IF SNR levels of 25db, 20db, 15db and lOdb respectively. These thresholds are below the level for which false alarms were detected. Figures 5.11 and 5.12 show the performance of Phase I in the presence of a transmitted O F D M signal. The results are used to interpret the ability of Phase I to determine the location of the O F D M data frame. Two sets of curves appear. The curves rising to the right give the probabilities that the estimated signal power drops below the threshold prior to that location. The horizontal axis indicates the location of detection prior to the start of the O F D M frame. The second set of curves (rising to the left) is generated by subtracting the first set from 1.0. They represent the probabilities that the estimated signal power does not drop below the threshold prior to that location. The thresholds used for each IF SNR level is determined experimentally. The goal is to reduce the probability of detection occurring after the point of synchronization to satisfy the specified probability of miss sync. At the same time, the probability of detection at a point well before synchronization is to be reduced, since this will improve the conditions under which Phase II must operate. The results of these experiments are used to determine the required duration of Phase II. For a given IF SNR, the location at which the curve rising to the right equals the required synchronization performance is determined. The distance from this location to the point of synchronization indicates the necessary duration of Phase II. This process is repeated for each IF SNR level. For the experimental results of Figure 5.11, a duration of 700 sample periods is sufficient to meet the required synchronization performance for all IF SNR levels of interest. Figure 5.12 shows the effect of increasing the doppler rate. Increasing the doppler rate reduces the necessary duration of Phase II. 5.2.3 Phase II Results Chapter 5. Experiments 67 1E+00 i 1 1 1 1 1 1 1—i 1 1—i 1 r 1E-01 — 1E-02 .O O 1E-03 1E-04 15 sync tones, fd=10Hz 0-18 sync tones, fd=10Hz e-21 sync tones, fd=10Hz &-21 sync tones, fd=20Hz a-required performance B-1E-05 ... i J i i i i i ' • ' 15 20 IF SNR (dB) 25 Figure 5.13: Phase II performance Number of Sync Tones Selected Sub-channels (cumulative) 3 162 246 312 6 170 310 358 9 176 214 256 12 206 230 370 15 132 190 224 18 140 234 372 21 184 276 344 Table 5.2: Synchronization sub-channel selection. O F D M block size is 1024, therefore available sub-channels are [0,512]. Of these, only [128,384] are used. Chapter 5. Experiments 68 Phase II experimentation measures the ability of Phase II to correctly detect the correlation detector output peak corresponding to correct synchronization and to ignore the sidelobes of the correlation detector output. Figure 5.13 displays the performance of Phase II as a function of the IF SNR level for a number of synchronization tones and doppler rates. Three curves appear for the doppler setting of 10Hz, corresponding to the use of 15,18, and 21 synchronization tones. The sub-channels used for synchronization are listed in Table 5.2. The selection of sub-channels was determined using the computer search algorithm presented in Section 4.3.3. The list of selected sub-channels in Table 5.2 is cumulative. For example, the sub-channels selected for 6 sync tones are {162, 246, 312,170, 310, 358}. Comparing these curves with the reference curve indicating the required performance (also shown in the figure), it is apparent that the specified requirements can be met using 15 sync tones. Also appearing in Figure 5.13 is a performance plot for 21 synchronization tones and a doppler rate of 20Hz. The effect of increasing the doppler rate from 10Hz to 20Hz results in a 2dB improvement for the case of 21 sync tones. Chapter 5. Experiments 69 1E+00 1E-01 1E-02 rr LU m 1E-03 1E-04 1E-05 i i I i ]j I i r~—1 j I i i i | i i Asymptote for fd «= 10 Hz fd = 10 Hz e-fd = 20 Hz -O A £> A 0 5 10 15 20 Number of Synchronization Tones Figure 5.14: Phase III performance - Absolute Results 5.2.4 Phase III Results Phase III experimentation measures the ability of the fine tune synchronization algorithm to accurately locate the position of synchronization. This ability is measured indirectly by determining the BER resulting from fine tune synchronization and comparing with the BER that could be obtained if ideal synchronization is achieved. Figures 5.14 and 5.15 present the experimental results. In Figure 5.14, the dotted curves represent the best achievable BER for a doppler rate of 10Hz, obtained when ideal synchronization is achieved. Figure 5.15 displays the same data as 5.14, but as a ratio of actual BER compared to the BER for ideal synchronization. Except for the case of IF SNR=25dB, the relative results are quite similar. Also shown is the BER performance requirement curve. In general, fine tune synchronization improves as the number of synchronization tones is increased. The rate of improvement is greatest when the number of tones is small, and decreases as the number of tones increases. When Chapter 5. Experiments 70 1 1 1 -i—r—|—i—i—i—i—|—i—i—i—i—|—i—i— IF SNR - 25dB -1 1 1 —<s> -IF SNR - 20dB -— & IF SNR = 15dB - B IF SNR » 10dB -— e Requirement -•\ Ideal sync — -^ ^ ^ 0 -1 1 1 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 L_ | 0 5 10 15 20 Number of Synchronization Tones Figure 5.15: Phase III performance - Relative to Ideal, fd = 10Hz 6 or more synchronization tones are used, performance of the fine tune synchronization algorithm exceeds the requirements. The effect of increasing the doppler rate is shown in Figure 5.14 by the dashed lines. Minimal improvement results for IF SNR = lOdB. The degree of improvement increases with increasing IF SNR. For IF SNR = 25dB, increasing the doppler rate from 10Hz to 20Hz reduces the B E R by a factor of 3 when 7 or more synchronization tones are used. Integrated testing, presented in the following section, uses 21 synchronization tones for phase II, and uses all of them again for phase III. The performance of phase III using these synchronization tones is identified by the solid triangles in Figures 5.14 and 5.15. Chapter 5. Experiments 71 1E+00 1E-01 2 1E-02 0) u c >. w n g 1E-03 0. 1E-04 1E-05 10 15 20 25 IF SNR (dB) Figure 5.16: Integrated System Synchronization Performance 5.2.5 Integrated Results The results of the integrated system tests are given in Figures 5.16, 5.17, and 5.18. For each test case, 100,000 trials were conducted. Figure 5.16 shows the performance of the synchronization algorithm with respect to the probability of bad synchronization, the probability of missed synchronization and the probability of false alarm. For IF SNR levels of 15dB or more, no false alarms were detected. For 25dB IF SNR and 20Hz doppler rate, no synchronization errors at all were detected. The results show that the achieved synchronization performance is better than the specified requirements. For lOdB IF SNR and 10Hz doppler, this margin is approximately 4dB. An increase in the doppler rate to 20Hz improves performance by an additional 4dB. Figure 5.17 shows the resulting BER performance. Two sets of curves appear. One set indicates BER when only correctly synchronized OFDM blocks are considered. The Chapter 5. Experiments 72 T — i — i — i — | — i — i — i — i — r required BER performance B : 1E-01 BER, fd=10Hz A-BER, fd=20Hz » adjusted BER, fd=10Hz 6-adjusted BER, fd=20Hz -0- = perfect sync BER, fd=10Hz a : perfect sync BER, fd=20Hz 0 rr LU CO 1E-05 J I I I I I L 10 15 J—i— I i i i i L 20 25 IF SNR (dB) Figure 5.17: Integrated System B E R Performance second set of curves has been adjusted to indicate B E R performance when incorrectly syn-chronized O F D M blocks are included. In adjusting the B E R it is assumed that incorrectly synchronized blocks have a block B E R of \ . The specified B E R requirements are met by both the adjusted and unadjusted B E R measurements. For a 10Hz doppler rate, B E R performance more than 1.5dB better than the specified requirements. A n additional 1.5dB performance gain is obtained when the doppler rate is increased to 20Hz. The specification of synchronization performance in section 4.1 is somewhat arbitrary, so that comparison of actual performance with the specified requirements is a bit artificial. To provide a better indication of the achieved synchronization performance, the BER versus IF SNR curves are converted to B E R versus E b / N 0 . The conversion from IF SNR to E b / N 0 is performed using the relationship (5.6) Chapter 5. Experiments 73 1E+00 1E-01 -1E-02 -rr LU m 1E-03 1E-04 1E-05 -i—i—i i—i—i—i—I—i—i—i—i—i—i—i—i—r adjusted BER, fd=10Hz ideal, fd=10Hz adjusted BER, fd=20Hz ideal, fd=20Hz [Casas89], fd=20Hz - - E 3 - -—A— —i—i—I—i I I i I I I I i i ' I 20 25 30 Eb/No (dB) -~0~-35 Figure 5.18: Performance Loss Due to Synchronization where B is the IF noise bandwidth, and R is the bit rate. The IF noise bandwidth of the IC0M-2AT receiver was measured to be B = 14.9kHz [4]. In the current implementation, a maximum of 256 data sub-channels are used, each transmitting 2 data bits per block. Since 21 sub-channels are reserved for synchroniza-tion, the actual number of data sub-channels is 235. Therefore, the data rate is 470 bits per block. Accounting for the overhead of the pre-extension and post-extension, the block rate is 7.35 blocks per second. Thus, the overall bit rate is 3456 bits per second. Expressed in dB units, EJ. 14900 g^(dB) = SNR (dB) + 10 log ^ ^ ( d B ) (5.7) which can be simplified to |^(dB) = SNR (dB) + 6.35(dB) 1N0 (5.8) Figure 5.18 shows the adjusted BER results versus the calculated values of E b / N 0 . Chapter 5. Experiments 74 The ideal performance curves are also shown to provide a reference from which the per-formance loss due to synchronization is measured. The ideal curves are determined based on the assumptions of ideal synchronization and no overhead required for synchronization information or for periodic extensions. Thus, the ideal bit rate is 4000 bits per second. The ideal B E R values are obtained from Phase III experimental results. The results obtained by Casas [4] for a doppler rate of 20Hz and assumption of ideal synchronization are shown. These results allow comparison with the measured results of this thesis. The curves in Figure 5.18 show that for both the 10Hz and 20Hz doppler rate, the use of synchronization results in a B E R performance that is approximately 1.5dB worse than the B E R performance with ideal synchronization. Increasing the doppler rate from 10Hz to 20Hz results in a 2dB improvement in B E R performance. The conditions of 20Hz doppler rate and ideal synchronization are comparable to the conditions for the displayed results from [4] and so are the performance curves. Chapter 6 Conclusions 6.1 Conclusions O F D M / F M is a multi-carrier modulation technique for use with F M transceivers. It has previously been proposed for data communication over mobile radio channels. A new synchronization technique has been proposed enabling the use of O F D M / F M in a pure A L O H A environment. The synchronization technique utilizes the O F D M modulation principles, thus reducing its sensitivity to signal fades which occur on the mobile radio channel. A simple model for synchronization was developed and used in selecting the operating parameters of the synchronization algorithm. Determination of the optimal parameters is a difficult and unsolved problem. A simple algorithm was proposed to select a good set of parameters. The proposed synchronization algorithm relies on frequency domain analysis of the received signal and extensively uses the F F T implementation of the DFT. A modified ver-sion of the DFT was used that performs significantly faster than the F F T in its intended application. A n analysis is provided denning the limitations of the modified DFT. A n experimental O F D M / F M system was implemented using unmodified commercial V H F F M radio equipment, a fading channel simulator, and commercially available DSP processors. A three phase synchronization procedure, based on the proposed synchro-nization model, was implemented. Test procedures were devised to separately measure the performance of each phase and to measure the performance of the integrated syn-chronization algorithm. Performance results from each phase were used to adjust the 75 Chapter 6. Conclusions 76 operating parameters of the other phases. Final experimental results indicated that the B E R performance of the system implementing the proposed synchronization algorithm is only 1.5 dB worse than the B E R performance achievable given ideal synchronization. 6.2 Topics for Further Research The current technique for determining which sub-channels should be reserved for syn-chronization is sub-optimal. No analysis has been done to determine how sub-optimal the current selection is, nor has any analysis been done to determine the effect of this sub-optimality on the performance of the synchronization algorithm. If it is determined that a significant improvement in performance can be obtained through better selection of synchronization sub-channels, work should proceed in formulating an improved selection process. Differential encoding of data has been previously proposed as a way to circumvent the need to perform channel equalization. Synchronization, however, will still be required. Modifications of the proposed technique may yield a synchronization algorithm capable of operating with differentially encoded data. Phase I of the synchronization algorithm does not exploit OFDM's insensitivity to signal fades. Replacing Phase I with a variation of Phase II, where the output of the Phase II correlator is threshold detected, may provide improved performance. The modulating signal levels into the F M transmitter are based on values suitable for the human voice. The characteristics of an O F D M signal are different from those of human voice. 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Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1975. [49] P. J . Bloom, "High-quality digital audio in the entertainment industry," IEEE ASSP Magazine, pp. 2-25, Oct. 1985. Bibliography 82 [50] F. J . Harris, "On the use of windows for harmonic analysis with the discrete fourier transform," Proceedings of the IEEE, vol. 66, pp. 51-83, Jan. 1978. [51] R. W. Schafer and L . R. Rabiner, "A digital signal processing approach to interpola-tion," Proceedings of the IEEE, vol. 61, pp. 692-702, June 1973. Appendix A Models and Algorithms for Synchronization A.1 Synchronization Model The OFDM signal contains a synchronization signal that is composed of a number of tones located in reserved sub-channels of the OFDM signal. The OFDM signal has a finite duration and is preceded and followed by a weighted periodic extension of itself. Therefore, the synchronization signal also has finite duration and is preceded and followed by a weighted periodic extension of itself. From this, it follows that the synchronization signal is deterministic and can be represented as N. s(t) = We(t)J2M^it) (A.l) :=1 where, Nt = number of synchronization tones u>i = angular frequency of the ith synchronization tone W„(t) = weighting function A correlation detector, implementing the correlation equation /+ O0 sr(t + r)r(T)dT (A.2) -oo can be used in a receiver to measure the similarity between the received signal, sr(t), and a known reference signal, r-(r). The reference signal is similar to the synchronization signal (equation A.l), except that it does not have the weighted periodic extensions. The 83 Appendix A. Models and Algorithms for Synchronization 84 N. (A.3) reference signal is denned as r(r) = Wr(r)^sin(u>;r) t'=i where i, JVs,and u>,- are as above and Wr(r) is a window function equal to unity over a width equal to the duration of the OFDM signal, not including the periodic extensions, and zero elsewhere. In the absence of channel distortions, the received signal will be identical to the transmitted signal and, therefore, can be modelled by equation (A.l). However, channel degradations cause phase and magnitude distortions in the received signal. Considering phase distortions only, the model of the received signal can be written as N. sr(t) = iy,(f)^sin(w,i + ^) (A.4) i=i where V ; is the phase noise term. From equations (A.2), (A.3), and (A.4), the output of the correlation detector is given by -oo N. N, Wr(r)Ws(t + r) ^ sin(u>,r) £ sin(uj(t + r) + if, A «'=i j-i dr (A.5) Denning T to be the symbol duration of the OFDM signal, Wr(r) = 1 for r = [0,T], and zero elsewhere, (A.5) becomes Jo N. N. W8(t +T)J2 sin(w,-r) ^  sin(wj(t + r) + Vi) x'=l j=l dr (A.6) The solution to (A.6) is not readily apparent. If it is assumed that the weighting function, W„(t), is unity everywhere, (A.6) can be further simplified, yielding Jo N. N. sin(cj.r) ^ sin(uj(t + r) + ipj) i=l j=l dr. (A.7) As defined in section 2.1.2, each synchronization tone has an integral number of periods in the interval [0,T]. Therefore, / sin(u;,'T) s'm(ujj(t + r) + ipi)dr = £ cos(w:i + fa), i = j i ^ j (A.8) Appendix A. Models and Algorithms for Synchronization 85 Substituting (A.8) into (A.7) gives rp N. Kr*M = -y)cos(fa;.-t+tfc).' . (A.9) From W3(t) as denned in section 5.1.3, the use of the simplifying assumption is valid when the correlation interval is within 16 sample periods of the true synchronization position, since then Ws(t) is unity over the range of integration. Therefore, (A.9) provides reasonably accurate results in the region of interest. In regions farther away from the true synchronization position, WB(t) is not unity over the range of integration. Hence, (A.9) is less accurate further away from the true synchronization position. A.2 Frequency Domain Derivation of the Correlation Detector Given the spectral information of the sinusoidal components of a received periodic signal, it is possible to implement the correlation detector in the frequency domain. Consider two phasors, P r and Ps, in the complex plane shown in Figure A. l , rep-resenting a single sinusoidal component of the received signal and a single sinusoidal component of the same frequency in the reference signal. The phasors can be denned as Pr = kxert* (A.10) Ps = k2e^' (Al l ) Let <pr = utr and <p8 = ut,, where u is the angular frequency of the two sinusoids and t is time. The angle between the phasors is 6 = u>(ts - tr). The dot product of Pr and Ps is Pr-P„ = \Pr\\P,\COS 0 = kik2 COs(u(ts - tr)) - KCOs(w(t r - *,)) (A12) where K,ki,k2 are scalar constants. Letting r = tr - ts, (A.12) can be re-written as Pr • Pa = K cos(u>r). (A.13) Appendix A. Models and Algorithms for Synchronization 86 Imaginary Figure A.1: Sync signal phasor diagram For synchronization signals with multiple sinusoidal components, the dot products of each signal/reference phasor pair are summed. The result is an equation that, with K = ^, is identical to the synchronization model (equation A.9). Therefore, a time domain correlation detector can be realized in the frequency domain as the sum of the dot products of the corresponding received synchronization signal and reference signal phasors. A.3 Fine Tune Algorithm It is assumed that synchronization is achieved when the output of the synchronization cor-relation detector is maximum. Using the synchronization model, equation (A.9), TZrSr(t) is maximized when the condition w,f + Vi; = 0 is satisfied for all N, synchronization tones. Due to the presence of the phase noise term, Vi» it is unlikely that a value oft can be found to satisfy this condition. However, the value off that maximizes the correlation can be determined. Equation (A.9) is modified to include the variable Af, a time adjustment factor, yielding rp N. Kr.r(t) = 2 E C 0 S M * + A*) + V>.0 (A.14) Appendix A. Models and Algorithms for Synchronization 87 In equation (A.9), the term (uit+ipi) represents the phase difference between the received signal synchronization components and the corresponding reference synchronization com-ponents. Therefore, equation (A.14) can be re-written as rp N. ftr.r(*) = «" £ c o s ( ^ .A< + Bi) (A.15) 1 t = i where 0,-A(w,-i 4- tpi) is the phase difference. The time axis shift, At, that maximizes the correlation, can be determined by setting the derivative of 1ZrSr(t) equal to zero and solving for At , yielding 0 = dUrd^ = - £ w,- sm(w.-A< + e{) (A. 16) « = i or, N. 0 = £w,-sin(w,-At + Oi). (A.17) The objective of the algorithm is to make the phase difference between the received sync signal and the reference as small as possible. That is, (w,-A< + Oi) —• 0 for all synchronization tones. Assuming that the phase differences are small, we can use the small angle approximation, sin 9 « 6, in (A.17), to obtain N. 0 « £ w , ( w , A t + Oi) (A.18) « ' = i or A<*-3^ r- (A.i9) For a fixed set of synchronization tones, let constant j3 be defined as 1 Then AT, A t « ^ w ^ . (A.21) i=i Appendix B DFT Algorithms This appendix presents three DFT algorithms used in this thesis for generating the OFDM baseband signal, decoding the OFDM baseband signal and acquiring frame synchroniza-tion during reception of an OFDM transmission. Also included is an analysis of the accumulated roundoff error for the third DFT algorithm. B.l F F T Implementation Generation of the OFDM baseband signal is performed by an inverse DFT. Decoding of the received OFDM signal is performed by a DFT. To reduce computational requirements, the DFT block size is chosen to be 2". This allows use of the very efficient Fast Fourier Transform (FFT) algorithm [45,46] The implemented FFT is based on the program fftr2a.asm, obtained through Dr. BuB, Motorola's DSP electronic bulletin board. The basic algorithm is the decimation-in-time (DIT), radix 2 FFT algorithm using 24 bit fixed-point arithmetic with a sine-cosine lookup table for the FFT coefficients. The algorithm is very restricted in its operation. It provides only the basic FFT for a fixed block size determined at compile time. Modifications were made to improve its flexibility. The following added features are run-time selectable through software control. • forward/inverse FFT • scale/noscale by N • variable block size, 2" where n=l,2,3,...,15. 88 Appendix B. DFT Algorithms 89 This is a general purpose complex valued F F T algorithm. It was chosen because of its simplicity and flexibility. Although it is much faster than a DFT, it is not as fast as many optimized F F T algorithms. Improvements in speed can be obtained by using higher radix algorithms and other techniques discussed in [45] B.2 DFT Implementation If spectral information is required for only a few subchannels, it is more efficient to perform a DFT for those selected frequencies than to perform an FFT. Two DFT algorithms were considered, the direct calculation algorithm and the 2 n d or-der Goertzel algorithm [46]. The Goertzel algorithm uses fewer mathematical operations than direct calculation and is faster on a general purpose computer. However, due to the parallel bus structure of the Motorola DSP56001, the direct calculation algorithm is both simpler to implement and is faster. The direct calculation algorithm was used in this work. B.3 Sliding Window DFT During the establishment of frame sync, the data window on which the DFT is performed is shifted by increments of one data sample. At each window position, the DFT is used to calculate the spectral information for the sync tones. When the window is shifted, most of the samples remain the same, except for their position within the window. This can be used to formulate an algorithm which updates the spectral estimates based on estimates from the previous window position. The result is a much faster algorithm. Figure B . l illustrates the sliding window concept. X0(k) and Xi(k) represent the spectral information for two consecutive window positions. Appendix B. DFT Algorithms 90 Xi(k) 1 Xo(k) 1 Sample instances 0 1 2 3 4 5 6 7 8 ' N-3 N-2 N - l N n Figure B.l: DFT calculations on sliding window Using the definition of the DFT equation [45], X0(k) can be expressed as N-l X0(k) = * (n)e-^ . (B.l) n=0 Similarly, JTi(*0 = ^ x W e " * * * ^ (B.2) n=l which can be re-written as X^k) = jr x ( n ) e - ^ (B.3) n=l The summation term in B.3 is the same as that in B.l , except for the range of the variable of summation. Expanding (B.3) yields Xx(k) = [X0(k) - x(0)e° + x(N)e~''2iek] (B.4) Equation B.4 can be further simplified and written in general terms as Xn+i(k) = [Xn(k) - x(n) + x(n + N)). (B.5) Appendix B. DFT Algorithms 91 B.4 Accumulated Round-Off Error for the Sliding Window DFT Since the sliding window DFT algorithm updates spectral estimates from one window position to the next, round-off error accumulates and progressively degrades the accuracy of the estimate. To ensure that the degradation will not be significant, an analysis of accumulated round-off error is performed. The sliding window DFT (equation B.5) can be rewritten symbolically as the product of two complex terms, Xn+1(k) = (a + jb)(c + jd) = (ac-bd) + j(bc+ad) (B.6) The Motorola DSP56001 is capable of performing the multiplications and additions in (B.6) within its arithmetic logic unit without incurring round-off errors. Round-off occurs only when intermediate or final results are transfered to data memory. From [47], the round-off errors can be modelled as additive noise with variance a], CT2, where o -2p O] = = — (B-7) and p is the word size, in bits, of the data memory. The round-off error variance for each frequency component for a given update is a 2 = a? + al = t—. (B.8) Assuming that the round-off noise does not add coherently from one update to the next, the variance of the round-off noise for K consecutive upates is °l = ^ — (B.9) The FFT implemented on the Motorola DSP56001 results in a round-off error given by °FFT = i £ L - f = (B.10) where N is the FFT block size. If the round-off error of an FFT is used as an upper allowable limit, the maximum number of updates, K, can be calculated as 'K21~2p _ (N - l)2X~2P^ ( B Appendix B. DFT Algorithms 92 Solving for K, K = N-1. (B.12) For a DFT block size of N = 1024 samples, the maximum number of updates that could be performed before round-off error becomes a factor is 1023. Appendix C Digital Low Pass Filter As discussed in section 4.3.2 a digital Low Pass Filter (LPF) is used to oversample (or interpolate) a band-limited input signal. C.l Filter Requirements For this implementation, the input signal is specified as a signal with a maximum, fre-quency of 3 kHz which is sampled at a rate of 8 kHz. A n oversampling factor of 4 is required. The standard method requires insertion of three zero's in the data stream for every data sample of the signal to be interpolated. The sample rate then becomes 4 x 8 kHz = 32 kHz. The addition of zeros in the data stream does not affect the shape of the spectrum below 4 kHz. The spectrum of the modified signal is periodic with period 8 kHz, not 32 kHz as with signals sampled normally at 32 kHz. The aliased signal components between 4 kHz and 28 kHz must be filtered out. To accomplish this without filtering out any of the frequencies below 3 kHz, the transition band of the designed filter must be from 3 kHz to 5 kHz. This results in a transition bandwidth of 2 kHz. Normalizing 32 kHz to 2n radians, the transition bandwidth is specified as TT /8. Figure C . l shows the spectrum of the signal modified with zero insertion and the spectrum of the required L P F . C.2 IIR vs. FIR The filter can be designed as either an Infinite Impulse Response (IIR) or Finite Impulse Response (FIR) filter. IIR filters have the advantage of superior amplitude response at the 93 Appendix C. Digital Low Pass Filter 94 X'(f) 1 H(f) 1 -i i t i ' i ' 1 i ' i 8 16 24 a) Modified signal spectrum • Digital LPF X / i i—:—r---1-"1 i—:—p-== n—L-u-i — — F » f ' • t ' 32 frequency (kHz) • •• —•—i—•—•— i—•—>—i—•—•—i—•—•—t—•—•—i—•— 1 i • — • — i — • — • m~ 8 16 24 32 frequency (kHz) b) Digital LPF spectrum Figure C.l: Modified signal spectrum and LPF spectrum. expense of non-linear phase [48]. FIR filters, however, have exactly linear phase and are often preferred for interpolation. A common example of FIR filters used for interpolation are Compact Disk (CD) audio systems [49]. For this implementation, an FIR design was chosen. Two basic techniques to design FIR filters are an iterative design method and the window method [48]. The iterative design method tends to give better results at the cost of increased design complexity and is normally implemented on a computer. The window method is straightforward in its application and can provide quite reasonable results. The window technique was used in this project. Appendix C. Digital Low Pass Filter 95 C.3 FIR Filter Design The first step in designing an FIR filter using the window technique is to approximate the ideal infinite impulse response with a finite impulse response. For LPF's, the ideal response is the sinc(a:) = (s'mx)/x function. The finite impulse response approximation to this is simply a truncated (windowed) version of the sinc(a;) function. The process of truncation results in a smearing of the filter's frequency response [48]. The extent of smearing can be reduced by increasing the size of the truncation window and/or modifying the window with a weighting function. Extensive analysis has been done in the design of windows [50]. In the present design, a Hanning window was chosen. The transition width of the Hanning window is equal to 8ir/Nw, where Nw is the number of samples in the window. As discussed in section C.l the maximum allowable transition band is 7r/8. Therefore, JV„, = 64. If Nw is even, the filter will impose a phase shift equal to a non-integral number of sample periods resulting in a filter that will not preserve the samples of the original sequence [51]. However, if N is odd the filter will have a phase shift equal to an integer number of sample periods and, therefore, will preserve the original samples. In this case, an immediate processing reduction of 25% can be achieved, since only 3 interpolated values between the original samples have to be calculated. Choosing N = 63, results in always having 16 samples of the original data sequence and 47 added zeros in the window [51]. Further reduction in processing can be realized by noting that the zero samples of the signal do not contribute to the output of the filter. As a result, only the contributions of the 16 samples from the original data sequence have to be determined. For the Hanning window, the window weights are given by The unweighted filter coefficients of the approximated ideal LPF are given by the sampled 1 — cos( N - l ' \ 2irn ) • (C.l) Appendix C. Digital Low Pass Filter 96 (s'mx)/x function centered at n = 32: = I n M n - a ) ] u>c(n - a) where u>c = TT/4 is the filter cutoff frequency, and a = (JV — l)/2 is the phase delay. The unit impulse response of the FIR linear-phase causal filter of length N is h(n) = hci(n)w(n). (C.3) Expanding we can obtain h(n) = s inMn-a) ] [ l-cos(fe)] (C.4) 2uc(n — a) Figure C.2 illustrates the truncated ideal LPF impulse response, the weights of the Hanning window, and the impulse response of the implemented filter. 1.5 0.5 -B o -0.5 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Ideal L PF Hanning Window Implemented filter 5 I i i i i i I I I I I i i i i i i i i i i 0 31 62 Figure C.2: Interpolation filter impulse response. Appendix D Modulating Signal Power Prediction PRBS ^ QAM Construct Encoding Spectrum IDFT Figure D . l : O F D M Baseband Signal Generation Figure D . l shows the basic steps in the generation of an O F D M baseband signal. A pseudo random bit sequence is Q A M encoded, interpreted as frequency domain information and a congugate symmetric spectrum is constructed. The spectrum data values are denoted by Xk- The O F D M baseband signal is generated by performing an inverse F F T on the encoded data, Xk. The resulting baseband signal data values are denoted by x,-. If the Q A M constellation points are denned as ± 1 ± j, the mean of Xk wil l be nx = 0 and the variance wil l be ax = 2. Due to the properties of the IDFT, a;, can be approximated by a Gaussian random variable. The mean of x, is then given by N-l ax = E [x^ = E jr t,  x*w~ ik which can be reduced to N-l (D.l) (D.2) fc=0 97 Appendix D. Modulating Signal Power Prediction 98 However, E [Xk] = p-x = 0. Substuting into D.2 and simplifying, we get px = 0. The variance of a;, is given by However, Therefore, a\ = E [ z , < ] - | E M | 2 = E JV-l JV-l jr E Kir-" • 1 £ xrw" 1 k=0 1 1=0 •JV-l N-l E E E XkXtw-w-1) .fc=o ;=o JV-l N - l fc=0 /=0 A/2 for k A' — ^ 2 0 for k = N - I, k < f 0 otherwise N - l r2 _ m = 0 (D.3) (D.4) (D.5) (D.6) Let M be the number of subchannels used. For the subchannels not used, X,- = 0 and E[XmX^|subchannel m not used] = 0. Therefore, (D.6).can be simplified and written as 2 2 M 2 °x = -xT°X (D.7) In summary, the statistics of the digital O F D M baseband signal can be expressed as f-x = 0 2 2 M 2 (D.8) (D.9) Appendix D. Modulating Signal Power Prediction 99 where N is the size of the IDFT, M is the number of sub-channels used, and o\ is the variance of the Q A M encoded data. In the implemented system, Q A M encoding is Xk = ±0.35 ± 0.35j. If the effect of the lOdB per decade de-emphasis is ignored, the mean is \xx = 0 and the variance is o\ = 0.245. The number of sub-channels containing data is M = 256, and the size of the IDFT is N = 1024. Therefore, the variance of the data following processing by the IDFT is 2 x 256 10242 o\ = 1.2 x 10 - 4 (D.10) and the standard deviation is ox = 1.1 x I O - 2 . (D. l l ) > Appendix E Estimation of FM Channel Attack Time Digital Storage Oscilloscope Tektronix 2232 Voltage Controlled Switch FM Channel (no fading) B Trigger Signal Figure E . l : Hardware Configuration to Estimate the Attack Time of the IC0M-2AT F M Channel. Figure E . l shows the hardware configuration used to estimate the F M channel attack time for the ICOM-2AT transmitter/receiver system. The baseband input to the F M channel is connected to a 50 kft termination via a voltage controlled switch. When a control voltage of zero volts is applied to the switch, the F M channel input leads are open circuited resulting in no R F carrier transmission by the F M transmitter. When the switch is closed by applying a positive +5 volt levle at the control input, a 50 kQ load is applied to the F M channel input leads causing the F M 100 Appendix E. Estimation of FM Channel Attack Time 101 transmitter to emit an R F carrier. In the absence of an R F carrier, and with squelch turned off, the baseband output of the F M receiver is noise. In the presence of an R F carrier, the baseband output of the F M receiver is the recovered transmitted signal. Since the transmitted signal is zero volts DC, the recovered signal should be zero volts DC plus noise incurred due to the F M channel. The output of the F M channel is captured with a digital storage oscilloscope. Trigger-ing of the oscilloscope is provided by the control signal used to trigger F M transmission. The following details the procedure for estimating the F M channel attack time. 1. Connect the F M channel, voltage controlled switch, and the digital storage oscillo-scope as in Figure E . l . 2. Trigger the oscilloscope on the rising edge of input B . 3. Adjust the oscilloscope to the appropriate voltage and time base settings. This will be approximately 1 to 5 Volts per division vertically and 20 milliseconds per division horizontally. 4. Set trigger signal to zero volts. 5. Set oscilloscope for single trace and arm the trigger mechanism. 6. Set trigger signal to +5 volts DC. 7. Examine oscilloscope tracing and measure the duration from the rising edge of the trigger signal to the location where the noise output of the F M channel has diminished to its final level. This measurement provides an estimate of the F M channel attack time. 


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