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Differentially detected GMSK systems in the presence of adjacent channel interference and nonlinearities Toor, Jagdeep S. 1994

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Differentially Detected GMSK Systems in the Presence of Adjacent Channel Interference and Nonlinearities by Jagdeep S. Toor B. A. Sc., The University of British Columbia, 1991 A THESIS SUBMiTTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA July 1994 © Jagdeep S. Toor, 1994  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 pemiission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  his  by  her  or  representatives.  It  is  understood  that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of  -  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  3  ,  J  Abstract In this thesis, the performance of differentially detected Gaussian Minimum Shift Keying (GMSK) systems operated in the presence of adjacent channel interference (ACT), modulation errors, amplifier nonlinearities and additive white Gaussian noise (AWGN) is investigated. We first evaluate by means of computer simulation the bit error rate (BER) per formance of conventional and decision feedback 1— and 2—bit differential receivers in the presence of static and Rayleigh faded ACT. The obtained BER performance evaluation results indicate that the decision feedback receivers outperform the con ventional differential receivers. For the static ACT channel, it was found that the best BER performance was achieved by the 2—bit decision feedback differential receivers. 3 and at a carrier-to-interference ratio C/IA, these receivers For example, at a BER= 1Cr resulted in gains in excess of 6 dB as compared to the conventional 2—bit differential receivers. For Rayleigh faded ACT channels, the BER performance evaluation results have indicated that the decision feedback differential receivers provide gains in the form of error floor reduction. Secondly, we have investigated, again by means of computer simulations, the effects on the BER of the cascade of an imperfect GMSK quadrature modulator followed by a nonlinear amplifier. We have considered a generic model for the imperfect modulator and have adopted two different sets of operating conditions (one typical and one extreme). In addition, we have considered two types of nonlinearities (one mild and one strong). For all the results obtained, it was found that the decision feedback differential receivers perform better than the conventional receivers for both typical and extreme values of the quadrature modulator errors as well as for both nonlinearities considered. It is also found that for the system operation under extreme operating conditions, the 1—bit decision feedback differential receiver outperforms all U  other receivers considered in this thesis. For example, it offers a gain of 8 dB over 2—bit decision feedback receiver at BER=10 3 and C/IA=20 dB. However, for system operation under typical operating conditions 2—bit decision feedback receiver has the best performance when compared to the other receivers considered in this thesis. Finally, in order to experimentally verify the effectiveness of the decision feed back differential receivers, we have designed, implemented and tested a prototype GMSK system. Various experimental BER performance evaluation results are re ported for receivers employing the 1—bit conventional and decision feedback dif ferential detection and operated in the presence of static and Rayleigh faded ACT. The obtained experimental BER results are in agreement with equivalent computer simulated BER results.  111  Table of Contents Abstract  ii  List of Tables  vii  List of Figures  viii  Acknowledgments  xiv  1  2  Introduction  1  1.1 Continuous Phase Modulation (CPM)  1  1.2 Interferences in Mobile Communication Systems  3  1.3 Detection of GMSK Scheme  4  1.4 Research Objectives of the Thesis  5  1.5 Thesis Organization  5  BER Performance Evaluation of GMSK Systems Employing Decision Feedback Receivers in ACI-AWGN Channels  7  2.1 Introduction  7  2.2 Communication System Model Description  7  2.2.1  Transmitter  2.2.2  Adjacent Channel Interference Model  11  2.2.3  Receiver Structures  14  7  2.3 Computer Simulation Results and Discussion  18  2.4 Summary  35 iv  3  BER Performance Evaluation of Non-ideal GMSK System Employing Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  36  3.1 Introduction  36  3.2 Imperfect Quadrature Modulator (QM) Model  .  .  .  3.3 Nonlinear Power Amplifier Model 3.4 Computer Simulation Results and Discussions  41 .  .  3.5 Summary 4  5  37  42 56  Design, Implementation, and Testing of a Prototype GMSK System  57  4.1 Introduction  57  4.2 Prototype GMSK System Model Description  57  4.3 GMSK Baseband Digital Synthesizer  59  4.4 Quadrature Modulator/Demodulator and Channel  65  4.5 DSP Based Decision-Feedback Receivers  67  4.6 Experimental Set-up and Measurements  70  4.7 SUMMARY  83  Conclusions and Some Suggestions for Future Research  84  5.1 Conclusions  84  5.2 Suggestions for Future Research  85  5.2.1  Generalization to other CPM Schemes V  85  5.2.2  Simultaneous use of 1— and 2—bit Decision Feedback Differential Receivers  85  5.2.3  Extension to Multilevel CPM Schemes  85  5.2.4  Further Development of Prototype GMSK System  .  .  85  References  86  Appendix A Program Listings  92  vi  List of Tables 1  The phase (in degrees) 6 k of 1 -bit and Vk of 2-bit differential detection of GMSK signal (BtT  2  =  0.3)  16  The error floors for conventional (C) and decision-feedback (DF) receivers in faded ACI-AWGN channel  26  3  The parameters used in generating the GLPF  61  4  All possible values of phase delay a (in degrees)  69  vii  List of Figures 1.1  The general block diagram of continuous phase modulation.  2.1  Block diagram of a GMSK transmitter. DE GLPF  2.2  =  Gaussian Low Pass Filter, FM  =  =  .  .  1  .  Differential Encoder,  Frequency Modulator.  7  .  (a) Pulse response of GLPF. (b) Power spectra of GMSK signals  2.3  10  Block diagram of the channel model which includes ACI (static or faded) and AWGN  12  2.4  Block diagram of fading signal, f(t), generator  13  2.5  Block diagram of (a) 1-bit conventional differential detector and (b) 2-bit conventional differential detector  2.6  Phase-state diagram for (a) 1-bit and (b) 2-bit differential detection  2.7  17  The block diagram of (a) 1-bit decision feedback receiver and (b) 2-bit decision feedback receiver  2.8  22  Computer generated spectrum of GMSK signal with two adjacent channel interferers  2.10  19  The level of C/IA (in dB) as a function of normalized channel spacing (Fm)  2.9  15  23  Eye-diagram of (a) 2—bit conventional differential receiver and (b) 2—bit decision feedback differential receiver at C/IA =15 dB with no AWGN present  24 vifi  2.11  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA  15 dB in a static  =  ACI-AWGN channel 2.12  27  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA  20 dB in a static  =  ACI-AWGN channel 2.13  28  Degradation in Eb/No at BER of 1O versus normalized channel spacing for 1-bit receivers in a static ACI-AWGN channel  2.14  Degradation in Eb/No at BER of 1O versus normalized channel spacing for 2-bit receivers in a static ACI-AWGN channel  2.15  co in a Rayleigh—faded  —  channel  31  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA  =  20 dB in a Rayleigh—faded  channel 2.17  32  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA  =  30 dB in a Rayleigh—faded  channel 2.18  30  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA  2.16  29  33  The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA channel  =  40 dB in a Rayleigh—faded 34  ix  3.1  Model of an imperfect Quadrature Modulator  3.2  Computer generated phase state-space diagrams of non-ideal  38  GMSK signal in the presence of QM errors: (a) typical values and (b) extreme values 3.3  40  GMSK Transmitter employing an imperfect quadrature modulator and a nonlinear power amplifier  3.4  41  Modelled characteristics of a Class A/B amplifier. (a) amplitude response (b) phase response  3.5  C/Ip ratio versus normalized channel spacing (Fm) for 1-bit receivers. QM errors: 10 d= 0 ( ’  3.6  —24 dB)  =  =  =  0.95, k  =  -24dB)  =  15°,  i. =  0.65, k  =  47  -12dB)  =  15°,  i =  0.65, k  =  48  -12dB)  49  The BER performance of non-ideal GMSK system with conventional (C) and decision feedback (DF) receivers at C/IA ACI-AWGN channel. QM errors: ( d 0  3.10  46  C/lA ratio versus normalized channel spacing (Fm) for 2-bit receivers. QM errors: ( d 0  3.9  0.95, k  C/l, ratio versus normalized channel spacing (Fm) for 1-bit receivers. QM errors: ( d 0  3.8  =  C/lA ratio versus normalized channel spacing (Fm) for 2-bit receivers. QM errors: ( d 0  3.7  43  = 150,  z  =  =  15 dB in static  0.65, k = -12dB).  .  50  The BER performance of non-ideal GMSK system with conventional (C) and decision feedback (DF) receivers at C/IA ACI-AWGN channel. QM errors: ( d 0 x  =  15°,  /. =  =  20 dB in static  0.65, k = -12dB).  .  51  3.11  Degradation of Eb/NO to achieve a BER of 10 versus normalized channel spacing for 1-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: ’ 10 d 0 ( =  3.12  0.95, k  i. =  -24dB)  =  52  Degradation of Eb/No to achieve a BER of 10 versus normalized channel spacing for 2-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: ( d 8  3.13  = °,  =  0.95, k  =  -24dB)  53  Degradation of Eb/NO to achieve a BER of 1O versus normalized channel spacing for 1-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: ( d 0  3.14  =  15°, z  =  0.65, k  =  -12dB)  54  Degradation of Eb/NO to achieve a BER of 10 versus normalized channel spacing for 2-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: ( d 0  =  15°,  t =  0.65, k  =  -12dB)  55  4.1  Block diagram of the implemented prototype GMSK system.  4.2  Flow chart for the implementation of the baseband transmission  .  algorithm  .  58  60  4.3  Impulse response of the GLPF with BtT  4.4  Illustration of how a output symbol of GLPF is generated  63  4.5  Functional block diagram of the implemented GMSK transmitter.  64  xi  =  0.3  62  4.6  Modulator, Demodulator and Channel Simulator  66  4.7  The block diagram of the ACI generation system  67  4.8  Functional block diagram of the DSP-based digital receiver..  4.9  The block diagram of a one-bit all digital decision feedback  .  68  .  receivers  69  4.10  Block diagram of the experimental set-up  70  4.11  I-channel eye-diagram at modulator input. Horizontal Axis: 0.1 msec/div, Vertical Axis: 1 V/div  4.12  71  The phase state-space diagram of the modulated GMSK signal. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div  4.13  71  The phase state-space diagram of the demodulated GMSK signal. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div  4.14  72  The spectrum of the GMSK signal at modulator output. Horizontal  Axis: 2 kHz/div, Vertical Axis: 10 dB/div, Center frequency  =  1.5  MHz 4.15  73  The spectrum of the GMSK signal at demodulator input. Horizontal Axis: 5 kHz/div, Vertical Axis: 10 dB/div, Center frequency  4.16  =  1.5 MHz  73  The spectrum of the desired signal along with two adjacent channel interferers at channel spacing of 7.8 kHz. Horizontal Axis: 5 kHz/div, Vertical Axis: 10 dB/div, Center frequency = 1.5 MHz. xli  .  74  4.17  The spectrum of the GMSK signal in AWGN channel. Horizontal Axis: 5 kHzldiv, Vertical Axis: 10 dB/div, Center frequency  =  1.5  MHz 4.18  75  The signal phase state-space at demodulator output after adding AWGN. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div  4.19  75  The BER performance of 1—bit decision feedback (DF) differential receiver in AWGN channel  4.20  77  The BER performance of 1—bit conventional (C) differential receiver in AWGN channel  4.21  78  The BER performance of the 1-bit decision feedback receiver in Rayleigh faded AWGN channel  4.22  79  The BER performance of the 1-bit conventional differential receiver in a Rayleigh faded AWGN channel  4.23  80  The BER performance of the 1-bit decision feedback (DF) and conventional (C) receivers in static ACI-AWGN channel at C/IA  =  10dB 4.24  81  The BER performance of the 1-bit decision feedback (DF) and conventional (C) receivers in static ACI-AWGN channel at C/IA 14dB  =  82  Xi”  Acknowledgments This thesis is dedicated to my sister, Gindu, whose support is beyond anyone’s imagination. I am indebted to my parents and my other sisters for their patience and moral support. I am enormously greateful to my supervisor, Dr. P. Takis Mathiopou los, for his support and continual guidance. Without his constant encouragement and valuable suggestions, the completion of this thesis would not have been possible. I would like to thank my fellow student, Dimitrios P. Bouras, for his help with the lab equipment.  xiv  Chapter 1 Introduction 1.1 Continuous Phase Modulation (CPM) Continuous Phase Modulation (CPM) represents a large class of modulated signals which have a continuous carrier phase and therefore exhibit a constant envelope [1]. A generic block diagram of how CPM signals can be generated is illustrated in Fig. 1.1. The information symbols, ak, are equiprobable and in general take values from the alphabet {±1, ±3,  ...,  ±(M-1)} where M is normally a power of 2 [2]. The pre  modulation filter is a low pass filter that bandlimits the input bit stream. The output of the pre-modulation filter, x(t), is modulated using a frequency modulator (FM) and the resulting CPM signal, s(t), can be expressed as .s(t)  =  0 cos [2irft + q(t)] A  (1.1)  and (t)  =  2h  f  x(r)dr  (1.2)  -00  where A 0 is the amplitude and h is the modulation index. It is clear from the above equation that the phase of a CPM signal is continuous in time and the envelope, A , 0 of the signal is constant. It is this property of the CPM signal that makes the CPM a,,  2ith Figure 1.1 The general block diagram of continuous phase modulation. 1  Chapter 1.  Introduction  scheme a spectrally and power efficient modulation scheme. In general, the power spectrum of the constant envelope signals is more compact than the power spectrum of the signals with non-constant envelope [3, 4]. In addition, the constant envelope signals are less sensitive to amplifier nonlinearities, which allows the use of highly nonlinear amplifiers that are more power efficient than the linear amplifiers [3]. On the other hand, non-constant envelope signals suffer the spectral sidelobes regrowth and spreading due to amplifier nonlinearities, which in general degrades the bit error rate (BER) performance [5, 6]. By choosing different pre-modulation filters and by varying parameters h and M, a great variety of CPM schemes can be obtained. For binary communication systems, i.e., M=2, it is often assumed that h  =  1/2 [2]. There  are several premodulation filters which have been considered in the past which result in various CPM schemes. Some of the well known schemes are MSK [7], TFM [8], GTFM [9], Duobinary FSK [10], and GMSK [11]. Because of its excellent spectral properties and simple implementation structure, Gaussian Minimum Shift Keying (GMSK) has been perhaps the most popular CPM scheme for mobile communication systems. More importantly, GMSK has been adopted as the transmission standard for various wireless communication systems, including the Groupe Speciale Mobile (GSM), the Pan-European digital cellular network [12], and Digital European Cordless Telecommunications (DECT) [13]. In this thesis, we will be dealing with exclusively the GMSK modulation scheme and its application to mobile communication.  2  Chapter 1.  Introduction  1.2 Interferences in Mobile Communication Systems There are numerous interferences encountered in mobile communication systems, including fading, co-channel interference (CCI) and adjacent channel interference (ACT) (see for example [14, 15, 16]). Over the last decade or so, fading and CCI have been very extensively investigated both in terms of modelling (see for example [16, 17]) in terms of performance of various modulation schemes  ( see for example  [18, 19, 20]). On the contrary, ACI has received considerably less attention. As the name implies, ACI is generated by interfering channels which are located adjacent, in frequency domain, to the information channel. In cellular systems, because of the frequency reuse structure of the communication system, ACT is less problematic interference as compared to CCI. However, it still represents a non-negligible source of interference [21]. For other, noncellular type communication systems, ACI is perhaps a more important source of interference. This is especially true in bandwidth efficient frequency division multiple access (FDMA) communication systems in which channel spaceing is important to improve system capacity[22]. Another type of distortion that sometimes is overlooked in constant envelope schemes is the nonlinear distortion. Such distortion is typically due to the presence of a nonlinear amplifier [23].  For an ideal constant envelope scheme nonlinear  amplifications has little effects on the overall spectrum and system performance. However, when a non-ideally generated CPM signal, such as non-ideal GMSK, which is not a constant envelope signal any more, is passed through a nonlinear amplifier spectral spreading occurs and the signal phase is distorted [24]. 3  Chapter 1.  Introduction  1.3 Detection of GMSK Scheme GMSK signals can be detected by either coherent (see for example [11]), dif ferential detection (see for example [25, 26]), or a limiter/discriminator detection (see for example [27]). Although in AWGN channel, coherent detection has the best performance, in interference channels that is not necessarily true. In fact, in mobile communication channels, coherent detection suffers considerably because of increased acquisition time and poor performance including high error floors [28]. On the other hand, non-coherent detection schemes, as they do not require carrier re covery, have, in general, simpler receiver structures and exhibit lower error floors. One very promising non-coherent detection technique based upon the use of differ ential detectors with decision feedback has been proposed and evaluated in [29] for GMSK signals transmitted over an AWGN channel. The technique is based upon the concept of employing a decision mechanism to significantly reduce the effect of the inherent intersymbol interference (ISI) associated with the differential detection of GMSK signals. A generalization of this technique to include any CPM type of signal can be found in [30]. In a recent publication [31], the decision feedback dif ferential receivers have been evaluated in the presence of static and faded CCI. The obtained performance evaluations results have indicated that as compared to conven tional differential receivers significant performance improvements in CCI channels are possible. It is with these types of decision feedback differential receivers that the thesis is dealing with.  4  Chapter 1.  Introduction  1.4 Research Objectives of the Thesis Motivated by the above, this thesis deals with differentially detected GMSK systems operating in the presence of ACT, AWGN and nonlinearities. Its research objectives are three-fold. 1.  To evaluate, by means of computer simulations, the BER perfonnance of 1— and 2—bit conventional and decision feedback differential receivers for GMSK signals transmitted over ACT and AWGN channels.  2.  To investigate the effects on the BER performance of the cascade of an imperfect GMSK modulator followed by a nonlinear amplifier.  3.  To design and implement a prototype GMSK system and evaluate its BER performance in the presence of ACT and AWGN.  1.5 Thesis Organization Including this introductory chapter, this thesis consists of five chapters and one appendix. Its organization is as follows: Chapter 2 deals with the first objective of the thesis. It starts with an introduction in Section 2.1. Afterwards, a detailed description of the communication system model under consideration is presented in Section 2.2.  Computer simulation  results and discussions can be found in Section 2.3. The chapter is concluded with a summary in Section 2.4. Chapter 3 covers the second objective of the thesis. A brief introduction is presented in Section 3.1. Non-ideal GMSK modulator model is detailed in Section 5  Chapter 1.  Introduction  3.2, followed by the description of the nonlinear amplifier model in Section 3.3. Numerical results and discussions are presented in Section 3.4 and a summary of the chapter appears in Section 3.5. Chapter 4 is concerned with thesis’ third objective. Again, the chapter starts with an introduction in Section 4.1 followed by an overview of the prototype GMSK system in Section 4.2. A detailed description of the GMSK baseband digital synthesizer is given in Section 4.3. The RE modulator/demodulator and the channel are described in Section 4.4. Section 4.5 presents details of the DSPbased implementation of the decision feedback detector. The experimental set-up measurements and results are presented in Section 4.6 followed by a summary  of the chapter in Section 4.7. Chapter 5 presents conclusions of the thesis and some suggestions for future research. Appendix A contains program listings for the implemented GMSK digital base band synthesizer, the 1—bit conventional differential detector, the 1—bit decision feedback differential detector and the ACI generator.  6  Chapter 2 BER Performance Evaluation of GMSK Systems Employing Decision Feedback Receivers in ACI-AWGN Channels 2.1 Introduction The subject of this chapter is the BER performance evaluation of 1— and 2—bit conventional and decision feedback receivers structures for GMSK systems operated in the presence of static and faded ACI-AWGN environment. This chapter consists of four sections including this introduction. In Section 2.2, we describe the model of the GMSK system. Numerous computer simulation results are presented and discussed in Section 2.3 followed by a summary of the chapter in Section 2.4.  2.2 Communication System Model Description 2.2.1 Transmitter The block diagram of the GMSK transmitter is shown in Fig. 2.1. The GMSK  2ith Figure 2.1 Block diagram of a GMSK transmitter. DE = Differential Encoder, GLPF = Gaussian Low Pass Filter, FM = Frequency Modulator.  transmitter consists of a differential encoder (DE), a Gaussian Low Pass Filter (GLPF), 7  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  and a frequency modulator (FM). The differential encoding operation is required for the 2-bit or higher detector so that the hard decisions on the differential detector output (see Figs. 2.5 and 2.7) reflect the decisions on the true input data sequence [32]. The input of the differential encoder,  is the non-return-to-zero (NRZ) information bits  ak,  taken from the alphabet {± 1}. The information bits, aj, are equally probable and independent and each has a duration of T seconds. As mentioned, for 1—bit differential detector a differential encoder is not needed, hence bk  =  c. For the 2—bit differential  detection, the output of the differential encoder is given by [32] =  (2.1)  —akbk..4.  The GLPF, which has a frequency transfer function of HT(f), is used to bandlimt the input binary NRZ data waveform. The resulting signal x(t) can be written as x(t)  bg(t  —  kT)  (2.2)  =  with g(t) where  *  =  hT(t)  *  p(t)  (2.3)  denotes a convolution, p(t) is a rectangular pulse of duration T and unity  amplitude, and hy(t) is the impulse response of the GLPF, i.e., the inverse Fourier  transform of H -(J). As well known, [25] 7 hT(t) where k 1  =  =kiBtexp[—(kiBttYJ  (2.4)  5.336 and B is the 3-dB bandwidth of the GLPF. As shown  in Fig. 2.1, at the output of the FM, the transmitted GMSK signal is s(t) and it can 8  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  be mathematically expressed as s(t)  =  0 cos [2irft + (t)] A  (2.5)  where A 0 is a constant amplitude (which without any loss of generality will be assumed to be equal to 1), f is the carrier frequency and (t)  2rh  =  bkf g(r  —  kT)dr.  (2.6)  In the above equation h is the modulation index and g(t) is the pulse response which is normalized so that  f  g(t)dt  =  .  [2]. As customary, we will consider that h  =  1/2  so that the maximum phase change over one symbol duration, T, is ir/2. Furthermore g(t) is given by [2] g(t)  =  —  {Q[k B 2 tT(_.  Q[k B 2 tT(.  —  where k 2  =  bandwidth of GLPF and  )] }  (2.7)  7.547, B,T is the normalized (to symbol duration) 3-dB  Q(.)  is the well known Q-function given by [33]  Q(y)  =  fexp  (--)  dw.  (2.8)  The plots of g(t) along with the corresponding power spectrum of GMSK signals with BT as a parameter are illustrated in Fig. 2.2. As it can be seen from this figure and is well known, the performance of GMSK system is very sensitive to the BT product of the GLPF. For our purpose in this thesis we have considered the specification of the Groupe Special Mobile (GSM), the Pan-European cellular network, system where a B T 1  =  0.3 has been adopted [34]. 9  Chapter 2.  BER Pe,fonnance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Chwinth  (MSK)  _____  B,T  0.5  ___—  B,T  0.3  g(t)/2T  0.25 B,T0.2  °T4TT:T8T9T  (a)  j  : ac_  1.0  ).$  IO)4AJ.1ZtD FIcqucNç  (b)  Figure 2.2 (a) Pulse response of GLPF. (b) Power spectra of GMSK signals. [11]  10  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI.AWGN Channels  2.2.2 Adjacent Channel Interference Model Assuming that the mt interfering signal, im(t), is of the same modulation format as the useful GMSK signal, s(t) (see Eq. 2.5), then it can be represented as  im(t) =  0 B  COS  [2ir(fc +  fm)t  + Om + cfm(t)].  (2.9)  In the above equation, B 0 is the constant amplitude of the interferer,fm is the difference in the frequency allocation of the two carriers,  m 9  denotes the lack of carrier phase  coherence between s(t) and im(t) and is assumed to be uniformly distributed over (0, 2r]. Furthermore, 4m(t) is given by  m(t) =  2Th  cif g(7  iT  —  Tm)d7  (2.10)  where c are independent and equiprobable bits taking values from the alphabet {±l }, h1/2,  Tm  is timing offset between s(t) and im(t) which is assumed to be uniformly  distributed over the time interval [0, 1). In general, there are two adjacent channel interferers which contribute most significantly to the degradation in performance of digital communication systems. Both of them are located adjacent (in frequency domain) to the channel through which the information signal is transmitted [35]. Based upon this, in this thesis we have considered the channel model which is illustrated in a block diagram in Fig. 2.3.  It consists of two interfering signals, namely the upper interferer (UI), i(t),  and the lower interferer (LI), ij(t), as well as the information signal s(t). It will be assumed that both interferers are symmetrically (in frequency domain) located around 11  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in Ad-AWON Channels  the carrier frequency f of the information signal channel. In this respect, the carrier frequency of the i(t) is f  + fm,  whereas the carrier frequency of the ij(t) is f  -  fm.  f(t) i(t)  i(t)  Upper Interferer (UI)  r(t)  s(t) Information Signal (IS) n(t)  i,(t)  Lower Interferer (LI)  Switch selection (1 or2)  Figure 2.3 Block diagram of the channel model which includes ACI (static or faded) and AWGN. 12  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  Furthermore, and as illustrated in Fig. 2.3, we will consider the case where all three signals (i.e., i(t), s(t) and ij(t)) could be faded. A block diagram of how the fading signal,f(t), is generated is shown in Fig. 2.4 [36]. In this figure, nj(t) and nQ(t) are independent white Gaussian noise processes that are filtered by two fading filters having the same transfer function HF(J). The complex summation of the outputs of the fading filters is modulated by  f1  to generate the fading signal. In the channel  model under consideration, f 1 is f, fc+fm orfc—fm. The transfer function of the fading filters, HF(f), determines the type of fading, e.g. rectangular [37], Gaussian [38] and land-mobile [14]. In this thesis, land mobile model is considered. The fading filter transfer function of this model is given by [14] 1 for 0 HF(f)  Ifi  fD  (2.11)  =  10 elsewhere and the corresponding autocorrelation function by Rf(r)  =  (2.12)  (2lrfDr). 0 J  n/i)  e e  flQ(t)  Figure 2.4 Block diagram of fading signal, fit), generator. 13  J(’t)  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  In the above equations, J 0 is the zero order Bessel function of the first kind andfD is the fading bandwidth (or maximum Doppler frequency) given by  fD—  (2.13)  where v denotes the vehicle speed,f is the carrier frequency and c is the speed of light. Finally, as illustrated in Fig. 2.3, we have included the additive white Gaussian noise, n(t), in our channel model. n(t) is white in the sense that it has a constant double-sided power spectral density of NJ2.  2.2.3 Receiver Structures As it was mentioned in Chapter 1, this thesis will be investigating the performance of noncoherent GMSK receivers employing 1— and 2—bit differential detectors. We will be referring to these receivers as “conventional receivers”. It will be explained later on in this section that by employing decision feedback to these conventional receivers, significant performance improvements are possible. We will be referring to these proposed receivers as “decision feedback receivers”. For both sets of receivers the received signal r(t) must be first filtered by a detection receive filter, HRQ9, which is typically a 4th order bandpass Butterworth filter [29, 31]. For such a filter it can be easily found that the resulting SNR is given by [31]  SNR—  F  2(t  c rT 0 N  214  where Eb is the transmitted bit energy, Br is a double-sided 3—dB bandwidth of the 4th-order Butterworth filter,  c  1.026 and a(t) is the normalized signal amplitude 14  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  after the signal is filtered [25], i.e., a(t)  =  /{hR(t)  *  cos [ç(t)]} 2 + {hR(t)  *  sin [(t)]} . 2  (2.15)  In 2.15, hR(t) is the inverse Fourier transform of HR(f). Conventional Receivers: The block diagrams of the 1— and 2—bit conventional receivers are shown in Fig. 2.5 (a) and (b), respectively. The signal r(t) present at the input of the receive filter consists of four components, r  —  —  f s(t) + iuçt) + ii(t) + n(t)  sf(t) + i(t) + i((t) + n(t)  (without fading) (with fading).  2 16 )  As well known [25], for the 1-bit differential detector, the output of the receive filter is multiplied by its own version that is delayed by a symbol time, T, and phase shifted by  900.  In the 2-bit differential detector, the output of the receive filter is multiplied d,(t)  r(t)  (kT) 1 d  A  a  kT  (a)  r(t)  d.c. bias  (b) Figure 2.5 Block diagram of (a) 1-bit conventional differential detector and (b) 2-bit conventional differential detector.  15  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  by its version that is delayed by 2T. Without including the effects of interference and noise, d (kT) and d 1 (kT) can be expressed as follows [29]: 2 (kT) 1 d  (kT) 2 d  sin  =  k), 6 (‘  (2.17)  cos (/.Wk)  (2.18)  where LS.6k  =  (2.19)  =  (2.20)  with  J f  °k-j =  g(r  —  jT)dT,  (2.21)  jT)dr.  (2.22)  kT-T  Vk_f  =  g(r  —  kT-2T  The values of °k.j and Vk..J for BT = 0.3 are tabulated in Table 1. In this Table, 6, V , 0 and V 1 represent the signal and all other terms represent the intersymbol interference (1ST) caused by pulse shaping [29]. the phase states, &2  k 0  From Table 1 and using Eqs. 2.19 and 2.20,  and zVk for B T 1  0.2  S-i 15.9  2 V_ 0.2  =  0.3 are calculated and plotted in Fig. 2.6.  6  02  63  57.8  °i 15.9  0.2  Vi  0 V  Vi  2 V  3 V  16.2  73.6  73.6  16.2  0.2  Table 1 The phase (in degrees)  k 0  —  of 1-bit and Vk of 2-bit differential detection of GMSK signal (BET = 0.3) 16  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  The phase states are all possible changes in phase over one symbol interval for 1—bit receiver and over two symbol duration for 2—bit receiver. Decision Feedback Receivers: The decision feedback scheme proposed in [29] reduces much of the ISI and the receivers are simple to implement. The way this Phase States:  AOk  AVk  Phase States:  89.6 •-.57.8  decision threshold  114.8/  ‘,26.0  32.4  \  147.2w  1  decision threshold  T0  .-26.0  -147.2  ,‘ -32.4  4 •—-  -114.8  -57.8  -89.6  Before Decision Feedback  Phase States:  Phase States:  AVw  decision threshold  73.7 /_  \  147.2 /  decision threshold  -  To ,.:32.4  -147.2 /  32.4  .  -41.9  /  -73.7  After Decision Feedback (a) Figure 2.6 Phase-state diagram  (b)  for (a)  1-bit and (b) 2-bit differential detection. 17  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI.AWGN Channels  scheme works is that it introduces a phase delay, we will call it the feedback phase, in the signal delay branch of the conventional receivers. This feedback phase is related to the 1ST. The feedback phases for 1—bit and 2—bit receivers are given, respectively, as [29] 0 V + 2bk_ 2 2bk V3 3 =  2b_V V3 3 2bk_ 0  =  (2.23)  bk_18i + bk_262  if if 1 bk_ = if bk_ 1 if bk = 1  bk_ 3 3 bk_ 3 bk_ 3 bk....  and and and and  4 bk_ 1 bk_ 2  bk_ bk_ 1 2 = bk_ 1 bk_ 2 = bk.... 1 bk_ 2  2 24  The block diagram of the 1-bit and 2-bit decision feedback receivers are shown in Fig. 2.7 (a) and (b), respectively. After applying the decision feedback, the resulting phase states, which will be referred to as Mk and IVkDF, are calculated using Eqs. (31) to (38) of [29] and plotted in Fig. 2.6. As can be seen in this figure, the phase states that were closer to the decision threshold are moved further away after applying the decision feedback. This results in a greater eye opening and BER improvements are expected. It is also noticeable that no dc bias is required for 2-bit detector when decision feedback is applied.  2.3 Computer Simulation Results and Discussion The communication system described in the previous section have been realized by means of computer simulations using the BloSim software [39]. In particular, we have simulated and evaluated the performance of both conventional and decision feedback GMSK systems operated in the presence of static and faded ACI-AWGN channels. Monte Carlo error counting techniques were employed to obtain the various 18  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels A  5 a r(t)  (a)  (b) Figure 2.7 The block diagram of (a) 1-bit decision feedback receiver and (b) 2-bit decision feedback receiver.  BER performance evaluation results. At least 100 error are counted at all BER levels to achieve confidence interval of at least 90% for all simulation results [40]. As previously mentioned, for the simulated GMSK transmitter, we have chosen BT  =  0.3, as this is the recommended value for the GSM system, the Pan-European digital cellular network. The BrT product of the receive filter, HR(f), was chosen to be equal to 0.97 for all the receivers employing 1—bit differential detectors and 0.85 for all the receivers employing 2—bit differential detectors. The reason for these choices was that it was found through computer simulations that these values are near-optimal at 3 in an AWGN channel. BER=10 As discussed in Section 2.2.2, we have simulated two adjacent channel interferers, 19  Chapter 2.  BER Performance Evaluadon of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  one on each side of the desired channel. It was assumed that both of these interferers T 1 were also GMSK signals with B  =  0.3 and having the same power as the desired  signal. According to Eq. 2.9, for the interfering signals, their carrier phase and timing  (Tm)  (6m)  have been randomized. However, it is worthwhile to note that the  most important parameter influencing the BER performance is the overall interference power, which greatly depends on the channel spacing, and the actual power of the interfering signals (but not  °m  or  Tm).  In general, the carrier-to-adjacent-interference ratio (C/IA) is defined as the ratio between the average power of the desired information signal (PDJS) and average power of the adjacent interfering signals (PAlS), both measured at the output of HR(f). Using the decibel as a convenient means of comparing performance we thus have  C/IA (dB)  =  10 log 10  PDIS PAlS  (dB).  (2.25)  As we have considered that the power of both interferers is same as the desired signal and, for a given B T, C/IA will be controlled by changing the channel spacing 1 frequency fm. It is convenient to introduce the parameter, Fm, which will be referred to as normalized (to the rate of transmission) channel spacing, as  Fm  =  fmT  (Hz/bits/sec).  (2.26)  Equivalently, Fm refers to the channel spacing in Hz at a bit rate of 1 bitJsec. It is also clear that the smaller Fm becomes, i.e., the more closer the adjacent channel interferers are to the main channel, higher C/IA is introduced. 20  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  By means of computer simulation, we have calculated the amount of C/IA which is introduced as a function of Fm for both 1— and 2—bit differential detector receivers. To compute C/IA,  PDJS  and  PAlS  are calculated at the output of the receive filter.  In computer simulations, the average power of a signal is determined as a running average of square of the signal samples. For example, the average power of the desired signal would be (s[n])  PDS =  where  s[n]  (2.27)  are the samples of the desired signal and N is the size of running average  window. The obtained results for C/IA versus Fm are illustrated in Fig. 2.8. We note that the results are different for 1— and 2—bit receivers. This is solely due to the fact that the BrT of two types of receivers are different. It should also be mentioned that the C/IA ratio is independent of the operating SNR and fading. A typical spectrum, generated by means of computer simulation and which includes two adjacent channel interferers with Fm = 1.5 and the desired signal, is illustrated in Fig. 2.9. In this figure frequency axis is normalized to the bit rate (1/I) and F is the normalized carrier frequency of the desired signal. The performance of 1-bit and 2-bit decision feedback differential receivers is evaluated in both static and faded ACI-AWGN channels. Figs. 2.11 and 2.12 illustrate the obtained BER performance evaluation results of the decision feedback receivers for static ACI at C/IA  =  15 dB and 20 dB, respectively. In the same figures, the  performance of conventional 1-bit and 2-bit differential receivers, operated in the same environment, is also given for comparison. It is clear from these results that 21  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  the decision feedback differential receivers outperform the conventional differential receivers. For example, as can be seen from Fig. 2.11, the 2-bit decision feedback differential receiver results in a gain of more than 6 dB as compared to the 2-bit conventional differential detector at BER of iO. The gain of 1-bit decision feedback differential receiver over the 1-bit conventional differential detector is more than 11  55 50 45 40  35 30 25 20 15 10 5 0 -5  0.5  1  Normalized Channel Spaceing Figure 2.8 The level of 074 (in dB) as a  2  1.5  (ii,)  (Hz/bitlsec)  function of normalized channel spacing 22  (Fm).  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  dB at BER of 1 O. The computer simulated eye-diagrams given in Fig. 2.10 also give a clear explanation of why improvements in performance take place. The eye opening for the 2—bit decision feedback differential receiver is significantly bigger than the one for the 2—bit conventional differential receiver. By reducing Fm, the equivalent C/IA decreases, i.e., the ACI increases. However,  —10  I  —20  —30  —40  —50  —60  fT (HzJbits/sec) Figure 2.9 Computer generated spectrum of GMSK signal with two adjacent channel interferers. 23  Chapter 2.  BER Performance Evaluation of GMSK System$ Employing  Decision Feedback Receivers in ACI-AWGN Channels  at the same time, we have an increase in the spectral efficiency. Similar to [41], we  0  2  4  6  10  8  12  14  16  (a)  ——  —  —  —-—--.—-  — —  -  --  --  —  -  —--.—-.---  — -r  -  -  -  -  -  -  ----..  .----.----  —.  -  -.—.-  —  0  2  4  6  8  10  -...  12  14  (b) Figure 2.10 Eye-diagram of (a) 2—bit conventional differential receiver and (b) 2—bit decision feedback differential receiver at C/IA =15 dB with no AWON present. 24  16  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  define spectral efficiency,  ,  as the inverse of Fm, i.e.,  (bits/sec/Hz).  (2.28)  Clearly from Fig. 2.8, there is one-to-one correspondence between  and an equivalent  T and the type and bandwidth 1 C/IA. This correspondence depends upon the choice of B of the receive filter HR(fl. By means of computer simulation, we have evaluated the degradation (in dB) of the 0 JN (at BER 1 E  =  l0) as a function of Fm for the 1—bit and 2—bit differential  conventional and decision feedback GMSK receivers.  The degradation, for all  receivers, is measured with respect to the Lb/N 0 that is required by 2—bit decision feedback differential receiver to achieve BER  =  . 3 i0  The obtained results are  summarized in Figs. 2.13 and 2.14. In both of these figures, one more horizontal axis is included which represent the equivalent  .  The performance results for both 1—bit  and 2—bit differential receivers indicate, as expected, that for every value of Fm, the decision feedback receivers outperform the conventional ones. It was also found that the performance of the 2—bit decision feedback differential receivers is always better than the performance of the equivalent 1—bit decision feedback differential receiver. One other interesting observation from Figs. 2.13 and 2.14 is that for values of Fm> 1.0 (for 2—bit receivers) and Fm> 1.1 (for 1—bit receivers), the degradation introduced by the ACI is small. For these values of Fm, the corresponding values of C/IA are about 20 dB. Equivalently, by reducing the Fm to 1.0 one can achieve an overall spectral efficiency of 1 bit/sec/Hz. 25  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWON Channels  Figs. 2.15  —  2.18 illustrate the BER performance of the proposed receivers in  a Rayleigh faded ACI-AWGN channel at C/IA  —,  00  (no ACT) and C/IA  =  20, 30,  and 40 dB. Fig. 2.15 illustrates the BER performance of decision feedback and conventional receivers in Rayleigh faded AWGN channel with no ACT. In this figure, we observe that the 1-bit receivers outperform the 2-bit receivers. Similar results have been also reported in [27, 26, 42, 43]. Furthermore, the decision feedback receivers offer reduction in the error floors. This is also true in the presence of faded ACI-AWGN environment, as can be seen in Figs. 2.16 through 2.18. The error floors at various C/IA levels and maximum normalized Doppler frequencies (JDT) has been tabulated in Table 2. fDT  CII(dB)  0.03  RECEIVER TYPE 1-bit C  1-bit DF  2-bit C  2-bit DF  20  0.02  0.013  0.061  0.035  0.003  20  0.0095  0.0085  0.027  0.075  0.03  30  0.0 13  0.008  0.055  0.03  0.003  30  0.0019  0.0014  0.004  0.0014  0.03  40  0.011  0.0075  0.05  0.03  0.003  40  0.00028  0.002  0.0011  0.0003  Table 2 The error floors for conventional (C) and decision-feedback (DF) receivers in faded ACI-AWGN channel.  26  t’)  C’)  h  H.h  kJ  _-,  II  11  -4  0  -.  C  C C  I-  Bit Error Rate Probability C  -.  I  C  00  —  C.  U.  U  p  vt’)  T1 c  0  0 0  Bit Error Rate Probability 0  ‘1  S.  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  20  15  10  .  5)  5  Normalized Channel Spacing (F (Hz/bit/see) Spectral Efficiency (TI) (bits/sec/Hz)  0  0.5  1  1.5  2  1  0.67  0.5  I  2  Figure 2.13 Degradation in Eb/No at BER of iO versus normalized channel spacing for 1-bit receivers in a static ACI-AWGN channel.  29  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  Spectral Efficiency (Ti) (bits/sec/Hz)  2  1  0.67  Figure 2.14 Degradation in Eb/No at BER of 1O versus normalized channel spacing for 2-bit receivers in a static ACI-AWGN channel. 30  0.5  I  w  Ci  -  C)  I.’  o  1%  h  tx,  0  Bit Error Rate Probability  K  BER Performance Evaluation of GMSK Systems Employing  Chapter 2.  Decision Feedback Receivers in ACI-AWGN Channels  10  0  jEEEEEEEEEEEi:E:EEEE 10  —1 —-  __  -——--  f T=O.003  -——--—%—I.•..  i 2  ‘4%  10  :+:‘------ --A-  -2  z  : :  : :  :: :: :  : :  % A  : :  fDT= 0.03  : :  :::: ::: ::: ::: 10  .3  :  A 2-bit DF 2-bitC I 1-bitDF ——--A——-— 1-bitC----+----  :: __ii.ui.ii.  10  -  —  :::: : =: -—  : : = = = = = I = = ::: :: ::: :::  I  = =  —  -—  .4  0  10  20  30  40  50  Eb/No [cm] Figure 2.16 The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA = 20 dB in a Rayleigh—faded channel. 32  60  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  10  10  0  0  10  30  20  40  50  Eb/No [dB] Figure 2.17 The BER performance of GMSK system with conventional and decision-feedback receivers at C/IA = 30 dB in a Rayleigh—faded channel. 33  60  I  I  IL  IC)  —  II  n  p  Go  0  0 C  C  0  t) C  C  C  —  C  C  o  —  Bit Error Rate Probability  I I  Chapter 2.  BER Performance Evaluation of GMSK Systems Employing  Decision Feedback Receivers in ACI-AWGN Channels  2.4 Summary By means of computer simulations, the performance of 1-bit and 2-bit decision feedback and conventional differential receivers has been evaluated for GMSK signal transmitted over static and faded ACI-AWGN channels. The obtained results indicate that the decision feedback receivers perform better than the conventional differential receivers. The BER improvements are more significant for the static ACI-AWGN channel. For the faded ACI-AWGN channel, reductions in error floors have been observed.  35  Chapter 3 BER Performance Evaluation of Non-ideal GMSK System Employing Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  3.1 Introduction In this chapter the performance of conventional and decision feedback 1— and 2—bit differential detector receivers is evaluated when a non-ideal GMSK signal is passed through nonlinear power amplifier. The non-ideal GMSK signal is a result modulator deficiencies. As mentioned previously, it was shown in [24] that the deficiencies in a modulator will produce envelope variations and phase distortion in the GMSK signal. It was also shown in [24] that, when the imperfect GMSK modulator is cascaded with a nonlinear RF amplifier, spectral spreading and in-band distortion will occur. However, the BER performance of the decision feedback differential receivers under consideration has not yet been investigated under such distortions. Hence, this is the subject of this chapter. After this brief introduction, the model of the imperfect GMSK quadrature modulator is described in Section 3.2. Two nonlinear amplifier models are described in Section 3.3. In Section 3.4, BER computer simulation results are presented and discussed followed by a summary of the chapter in Section 3.5. 36  Chapter 3.  BER Performance Evaluation of Non-ideoj GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  3.2 Imperfect Quadrature Modulator (QM) Model Among the various methods for generating GMSK signals, such as phase-locked loops [11], direct digital synthesis [44], and quadrature modulator (QM) [1], the  QM approach seems to be the most flexible and preferred method [1]. With the QM method, there are two signals generated digitally in baseband which are usually referred to as I- and Q-channel. These signals carry the phase information of the GMSK signals to be transmitted, and can be generated by means of a look-up tables [1]. These two I- and Q-channels are then modulated by means of a QM to the appropriate RF carrier frequency. Mathematically, it is very easy to show that a GMSK signal can be represented by a QM signal. rewritten as  , 4 ( assuming A  =  1)  s(t)  =  i(t) cos 27rft  —  From Eq.  2.5, s(t) can be  q(t) sin 2irft (3.1)  where i(t)  =  cos 4(t)  q(t)  =  sin qf(t).  (3.2) Using complex envelope notation [45], the complex envelope of the GMSK signal is b(t)  =  i(t) + jq(t).  (3.3)  Clearly, the magnitude of b(t) is  Ib(t)I  =  (t) 2 V/j2(t) + q  =  as it is expected from a constant envelope scheme. 37  1,  (3.4)  BER Performance Evaluation of Non-ideal GMSK System Employing  Chapter 3.  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  Theoretically, a QM does not introduce any signal distortion to the GMSK signal. However, in practice, non-ideal components (for example local oscillators) in the QM will result in signal distortions, including signal imbalances and offsets between the I- and Q-channels. In the past, such distortions occurring in QM have received attention for several applications, including radar signal processing [46] and digital communication systems [47]. In a more recent paper [24], the effects of QM deficiencies on a signal have been identified as a differential phase error (Od), amplitude imbalance (LS), and local oscillator breakthrough and DC offsets (k). Mathematically, it is convenient to group all the error terms together in one of the channels, (e.g., the I-channel). Therefore, following [24] and as illustrated in Fig. 3.1, the distorted GMSK signal s’(t) can be mathematically expressed as  s’(t)  where  Td  =  [k + Li(t  —  rd)] cos (2irft)  —  q(t) sin (27rft)  (3.5)  is the differential time delay which is related to the differential phase error k  i(t)  cos(2içtt)  q(t)  Figure 3.1 Model of an imperfect Quadrature Modulator. 38  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  as [24] = 1rT  (3.6)  Using Eqn. 3.4, the complex envelope of s’(t), b’(t), is given as  b’(t)  =  k+  I.  cos q(t  —  Td)  + j sin 4(t).  (3.7)  Furthermore, s’(t) can be represented as s’(t)  =  =  Re{bl(t)e32t} ej’(t) efBt  Re{ b’(t)  where Re{’} represents real part of {‘}, I  •  (3.8)  }  I represents absolute value of•.  Ib’(t)I  and qV(t) are given by  Ib’(t)I  v’{k  cii’(t)  =  + cos(t  1 tan  —  2 rd)]  [k + zScosqf(t  (3.9)  + sin 2 (t)}  (3.10) Td)]  —  Finally, from Eq. 3.8, the imperfectly generated GMSK signal can be expressed as s’(t)  ={[k + cosç(t cos 2irft+tan  —  —1  2 rd)]  2 + sin  1  .  sin4(t) k+zcoscS(t—rd)  )  It is evident from the above equation that the phase of the GMSK signal is distorted and the envelope is no longer constant. Clearly, for k becomes the ideal GMSK signal  s(t)  =  0, z  =  1, and  rd =  0, s’(t)  (see Eq. 2.5).  For the purpose of this thesis, we have considered two sets of values for modelling the imperfections of the QM. Following [24], for the first set, which will be referred 39  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  to as “typical values”,  °d  = l, L =  referred to as “extreme values”,  0.95, k  d = 9  =  15°,  —24 cIB. For the second set, which is =  0.65, k  =  -12dB. As illustrated by  the phase state-space diagrams in Fig. 3.2, the distortion which is introduced to the transmitted GMSK signal by the extreme values is much more prominent compared to the distortion caused by the typical values.  —1  —0.5  0  0.5  1.5  (a)  —0.4  —0.2  0  0.2  0.4  0.6  0.8  (b) Figure 3.2 Computer generated phase state-space diagrams of non-ideal GMSK signal in the presence of QM errors: (a) typical values and (b) extreme values. 40  1  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  3.3 Nonlinear Power Amplifier Model The block diagram of the complex baseband equivalent of the GMSK transmitter, which employes the imperfect QM described in the previous section as well as a nonlinear power amplifier (PA), is shown in Fig. 3.3. In our computer simulations, the signals are represented by the time samples of their baseband complex envelope so that the input to the nonlinear PA is b’(t). Therefore, the model of the nonlinear PA must operate on the samples of b’(t). Volterra series representation of nonlinearities is one such technique that is commonly used to model nonlinear PA for computer simulations [48]. This model is very simple to implement and requires very few numerical computations to be realized. As derived in [49], for a complex envelope input, b”(t), the output of the fifth order Volterra series model can be expressed as  b”(t)  =  1+ b’(t)(G  1b’(t)1 5 G ) 1b’(t)1 + 4 3 G 2  (3.12)  where G ,G 1 3 and G 5 are constant complex coefficients. However, relationship is only valid if b’(t) has a narrowband (with respect to the carrier frequency f) spectrum. Therefore, we assume that b’(t) exhibits this property. The values of complex coefficients G , G 1 3 and G 5 are determined by amplitudeto-amplitude modulation (AM-AM) and amplitude-to-phase modulation (AMPM) responses of the nonlinear PA. Among the various values for the coeffi  Figure 3.3 GMSK Transmitter employing an imperfect quadrature modulator and a nonlinear power amplifier. 41  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  cients of Eq.  3.12, as in [47], we have selected G 1  =  1, G 2  =  O.0479L  —  2.816 rad and (73= O.00102L0.39 rad. The AM-AM and AM-PM characteristics of this model are calculated and plotted in Fig. 3.4. Typically these AM-AM and AM-PM characteristics represent a class A/B amplifier. It should be pointed out that a class A/B amplifier is considered as a “mildly nonlinear”. This is because, as illustrated in Fig. 3.4 (a), its amplitude response is not very nonlinear. Perhaps the most nonlinear PA amplitude response is that of a hardlimiter (HL). Mathematically, the output of the HL is given by  1/’(t)  (3.13) =  The HL has been used in the past for simulating the effects of an extremely highly nonlinear amplifier, for example for satellite communication systems [41]. In this thesis, both amplifier models will be considered.  3.4 Computer Simulation Results and Discussions In this section, computer simulation BER performance results of a 1—bit and 2—bit conventional differential receivers and decision feedback differential receivers are presented. As in Chapter 2, the BTproduct of the GLPF is 0.3 and the modulation index, h, is 0.5. The forth order Butterworth filter is used as a receive filter and its BrT product is equal to 0.97 and 0.85 for all receivers employing 1-bit and 2-bit differential detection respectively. The channel model used in the simulations is ACI-AWGN which is described in Chapter 2. There are two interferers, one on each side of the desired channel, having the same power as the desired signal. These 42  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Ainpl(fiers  r  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  I I I I I  0.5  1  1.5  2  2.5  3  3.5  2.5  •••I•  2  I I C. I I 1.5 -————I I I I I —  1  I I I I  I I I I -1  I I  -  0.5  L  c0  4  Vi (a) C  I I I  1  I I  I I  I  -0.05 .————L.  I  •0 Ct ‘—4  5)  -0.1  I -‘I  -  I I -0.15 -————I I I I -0.2  I 44  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 1.5  I 2  I I I I -1————-1——— 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 2.5  I 3  I 3.5  -  -0.25  I I I I I  —0  0.5  I 1  4  Vi Figure 3.4 Modelled characteristics of a Class A/B amplifier. (a) amplitude response (b) phase response.  43  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  interferers are GMSK signals generated independently from the desired information signal and their carrier phase and symbol timing are randomized. Since the nonlinearities cause spectral spreading, new C/IA versus Fm curves needed to be computed. Figs. 3.5  —  3.8 show the new C/IA versus Fm curves for  the non-ideal GMSK system. The C/IA curves for the ideal GMSK system are also included in the figures for reference. As it can be seen in Figs. 3.5 and 3.6, the C/IA  curves for non-ideal GMSK system with typical values of QM errors are almost same as the ideal GMSK system. This indicates that spectral spreading is negligible for these values of QM errors. However for extreme values of QM errors, C/IA drops significantly, especially when HL is employed. This is due to spectral spreading caused by extreme nonlinearities [24]. Figs. 3.9 and 3.10 illustrate typical BER performances of the various receivers under investigation for a static ACI with C/IA  =  15 and 20 dB, respectively. For all  systems, it has been assumed that a QM with extreme values of QM errors and a HL are employed. From both figures, it is clear that the decision feedback differential receivers perform better than the conventional differential receivers, with the 1—bit decision feedback differential receiver performing the best. For example, as can be seen from Fig. 3.10, the 1-bit decision feedback differential receiver has a gain of 8 dB over the 2-bit decision feedback differential receiver at BER  =  i0. It is  interesting to note that if the C/IA decreases, the performance limitations appear in the form of error floors. The decision feedback receivers offer significant error floor reductions. For example, at C/IA of 15 dB the 1-bit decision feedback differential 44  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  receiver exhibits an error floor at BER  =  , whereas the one-bit conventional 3 1.4x10  differential receiver has an error floor at BER Figs. 3.11  —  =  . 2 1.5x10  3.14 illustrate the degradation in Eb/No (at BER  normalized channel spacing (Fm) and spectral efficiency  (n).  =  ) versus 3 icr  The degradation, for all  receivers, is measured with respect to the Eb/No that is required by an ideal GMSK system, employing 2—bit decision feedback receiver, to achieve BER  =  iO. The  plots for the ideal GMSK system (i.e., without any QM errors) are also included for comparison purposes. First of all, it is clear from simulation results that the decision feedback differential receivers outperform the conventional differential receivers in all the situations considered. It is interesting to note that in all the plots there is a value of Fm below which the required Eb/No to achieve a BER of i0 3 increases drastically, we will refer to this value as the “critical” Fm, Fm’. Figs. 3.11 and 3J2 show the results for typical values of QM errors. Following these figures, the degradations caused by the nonlinearities (i.e., QM errors and nonlinear PA) are relatively small (about 1 dB) when Fm Fm  < FmC,  > FmC.  However, when  the degradations caused by the nonlinearities are much higher for the  conventional differential receivers than the equivalent degradations for the decision feedback differential receivers. For extreme values of QM errors, as illustrated in Figs.  3.13 and 3.14, the  FmC  of the conventional differential receivers is much higher than the equivalent  Fm”  of the decision feedback differential receivers. For example, as can be seen  in Fig. 3.13, the Fm” is 1.25 and 1.5 for 1—bit decision feedback receiver and 1—bit 45  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  conventional receiver, respectively, when employing a HL. If one views the FmC as an absolute minimum Fm at which the system can operate, then the system employing a decision feedback receiver will allow narrower channel spacing. Hence, better spectral efficiency will be achieved.  55 50  Non-ideal GMSK + Hard Limite Non-ideal GMSK ÷ Class AB Ideal GMSK  45  -  -  -  -•-  -  - -  -  -  --.  -.  -  -  -  -  -  -  -  -  -  -  I I•I I••I•I 1•11•11•  —  —  ,,  40 1,  35  p  —  -------  ,  ,  ‘  0’  ,  30  r’ “ -—-  -  ‘  ,‘  #‘  25 20 15 10 5 0 -5  :::‘*:E::::z::::::::::::z: 0.5  1  1.5  Normalized Channel Spacing (Fm) (Hz/bit/sec) Figure 3.5 C’L 4 ratio versus nonnalized channel spacing (Fm) for 1-bit receivers. QM errors: ( d=1°, A = 0.95, k = —24 dB). 9  46  2  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  55 50 45 40  35 30  25 20 15 10  5 0  -5  0.5  1  1.5  2  Normalized Channel Spacing ( i) (Hz/bit/sec) Figure 3.6 C/IA ratio versus normalized channel spacing (Fm) for 2-bit receivers. QM errors: (Li = l, A = 0.95, k = 47  Chapter 3.  BER Performance Evoluo.tion of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  55 50 45 40 35 30 25 20 15 10 5 0 -5  0.5  Normalized Channel Spacing ( Fm) (Hz/bit/see) Figure 3.7 C/IA ratio versus normalized channel spacing (Fm) for 1-bit receivers. QM errors: ( d = 15°, z = 0.65, k = -12dB). 9 48  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  := : = :== : = = = = =: :  55 50  Non-ideal GMSK + Hard Limite Non-ideal GMSK + Class AB IdeaIGMSK  45  X-  -  - -  -  -  - -  - -  -  -  -  40 35  ::: : ::: ;: :  30 25  E -: .-  20 15 10 5 0 -5  0.5  1  1.5  Normalized Channel Spacing (i) (Hz/bitlsec) Figure 3.8 C/IA ratio versus normalized channel spacing (Fm) for 2-bit receivers. QM errors: (Sd = 15°, = 0.65, k = -12dB). 49  2  ()  g  UI  o  II  Iot  11•  -a  H  I:IQ  UI C  0  0  U)  1’) 0  0  -a  C  -  - -  -  -  -  -  -  --  “  — —  —  -  -  -  -  -  -“  —  -  — — — —  -  --“  -  -  EEEEE  z::  EEEEHH  ..  -  -  -  -  -  -  —-..  I  -  -  ——  —  —  — —  -  —)— I ——  -I-  --  -  -  -----  -  I I  -,-  — —  -  -  -  -  -  -  -  I —I-—-— I  -.———  -t-  —  —  —  -  -  —  —  -  -  -  -4---  --  I I  -  T --  -,-  -  EH  —  C  EEE  j 1  EEEEH  —  C  Bit Error Rate Probability  I  H_  I  I  xI  II  EEEF  C  TT711  I  C  -a  0  -e  —  -‘  o•  o•  .  -‘a  II  .  JI  U PC’  .0.0  .11  -  0  Bit Error Rate Probability  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  40  35  30 C  25  I  I  20  15  10  5 Normalized Channel Spacing(F) (Hz/bit/see) Spectral Efficiency(ri) (bits/secfllz)  0 .  0.5 I  1  1.5  2  0.67  0.5  I  2  Figure 3.11 Degradation of E,1N versus normalized 0 to achieve a BER of channel spacing for 1-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: (Od=1°, = 0.95, k = -24dB). 52  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  20  15 C  10  5  Normalized Channel Spacing(F) (Hz/bit/see)  0 0.5  Spectral Efficiency(fl) I (bits/sec/Hz) —p- 2  1  0.67  Figure 3.12 Degradation of E,1N 0 to achieve a BER of iO versus normalized channel spacing for 2-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: (Od = 1°, A = 0.95, k = -24dB). 53  0.5  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  30  25 e  C  20  15  10  5 Normalized Channel Spacing(F) (Hz/bitlsec)  0  0.5  Spectral Efficiency(rl)  (bitslsecIHz) —  2  1  0.67  Figure 3.13 Degradation of Eb/N 0 to achieve a BER of i- versus normalized channel spacing for 1-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: (Od = 15°, = 0.65, k = -12dB).  54  0.5  Chapter 3.  BER Performance Evaluation  of Non-ideal  GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  35  30 ‘0  20  15  •0  10  5 Normalized Channel Spacing() (Hz/bitfsec)  0  Spectral Efficiency(r)  0.5 I  (bits/sec/Hz) ——  2  1  0.67  Figure 3.14 Degradation of E,,/N 0 to achieve a BER of 10 versus normalized channel spacing for 2-bit conventional (C) and decision feedback (DF) receivers in static ACI-AWGN channel. QM errors: (Od = 15°, = 0.65, k = -12dB).  55  0.5  Chapter 3.  BER Performance Evaluation of Non-ideal GMSK System Employing  Decision Feedback Receivers in the Presence of Nonlinear Amplifiers  35 Summary In this chapter, the performance of decision-feedback and conventional differential receivers has been evaluated for the typical and extreme values of QM errors. The nonlinear amplifier is modelled as a class MB amplifier and a hardlimiter. The nonideal GMSK signals are transmitted over static ACI-AWGN channel. The results have shown that the decision-feedback receivers overwhelmingly outperform conventional differential receivers under severe GMSK transmitter nonlinearities. The degradations due to nonlinearities are smaller for decision feedback receivers which makes them more robust.  It is also found that the decision-feedback receivers performance  improvements are more significant for narrower channel spacing, hence they provide better spectral efficiency.  56  Chapter 4 Design, Implementation, and Testing of a Prototype GMSK System 4.1 Introduction In this chapter the design, implementation and testing of a prototype GMSK system employing 1—bit conventional and decision feedback differential receivers will be presented. The performance of the modem will be evaluated in the presence of AWGN and ACT. The obtained BER performance results will be compared with equivalent results which have been obtained by means of computer simulation. Following this introduction, the chapter is organized as follows. An overview of the prototype GMSK system is given in Section 4.2. In Section 4.3, the details of the Digital Signal Processor (DSP) based GMSK baseband generator are presented. The RE modulator, the channel and the RE demodulator are described in Section 4.4. Section 4.5 gives the details of the DSP-based implementation of the decisionfeedback receivers.  Experiment measurements and BER performance evaluation  results are presented in Section 4.6 and a summary of the chapter is given in Section 4.7.  4.2 Prototype GMSK System Model Description The block diagram of the implemented GMSK system is illustrated in Fig. 4.1. It consists of a transmitter, an RE quadrature modulator, the channel and an RE quadrature demodulator. 57  Chapter 4.  Design, Implementation, and Testing of a Pmtorype GMSK System  The transmitter and the receiver are implemented in software. Both the transmitter and the receiver utilize TMS32OC3O Digital Signal Processor (DSP) system boards which reside in a Host PC. The transmitter generates baseband I- and Q-channel of the GMSK signal. The baseband I- and Q-channels are then modulated using the 1.5 MHz RF quadrature modulator to produce a GMSK signal that can be transmitted through the communication channel. In the channel, AWGN, ACT, and Rayleigh fading distort the transmitted signal. The RF demodulator down converts the RE signal to its baseband I- and Q-channels. The receiver DSP board samples the incoming signal and processes the samples to determine the transmitted bit. It should be noted that the only reason 1.5 MHz RE modulator/demodulator are used is because of their availability in the Communications Lab. In next few sections, the different modules of the system will be described in detail.  I-channel  TMS32OC3O  (Transmitter)  C  TMS32OC3O DSP card  Channel (AWGN, AU & Fading) I-channel 1(t)  (Receiver)  q(t) Q-channel  Ri? Demodulator  p  Figure 4.1 Block diagram of the implemented prototype GMSK system.  58  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  4.3 GMSK Baseband Digital Synthesizer There exists many different techniques for generating a GMSK signal among which the FM modulator is perhaps the simplest one [50]. However, the disadvantage of this technique is that the phase of the carrier can not be controlled accurately. For a prototype system, it seems that the most effective implementation solution is the Baseband Digital Synthesizer (BDS), which allows precise control of the phase of the signal. It was therefore decided to design the transmitter based upon this technique. The transmitter is implemented in software on a DSP platform which consists of a Spectrum TMS32OC3O DSP system board and software development tools for an IBM PC [51]. The TMS32OC3O DSP boards were chosen due their availability and excellent software support. For a prototype system, the software DSP design is more suitable because it allows one to make changes in parameters and software algorithms in a fraction of time required for a hardware update. The transmitter digitally generates the baseband I- and Q-channels of the GMSK signal.  The flowchart shown in Fig.  4.2 describes the baseband transmission  algorithm. The program uses an Interrupt Service Routine (ISR) which is executed when the interrupt is enabled. Interrupt is enabled by the on-chip timer/counter. The counter value is set to 200 which corresponds to the timer period of 24 psec [51]. For this value of the period and considering 8 Samples-Per-Symbol (SPS), the Baud rate is  Baud rate =  T  =  (8  *  24psec)  =  5208 symbols/sec.  (4.1)  Clearly for the GMSK system the baud rate is same as the bit rate because one symbol represents one bit. Every time the ISR is executed, the SPS counter is checked. If a 59  Chapter 4.  Design, Implementation, and Testing of a Pmtotype GMSK System  new symbol is required, it is fetched out from the GLPF output look-up-table (LUT). The index to the LUTs of I and  Q is computed and the samples of I and Q are fed  to the D/A convertors. The TSR also checks if the sample number of the symbol is four. If it is, a pulse is output to the digital port. We will call this pulse the SYNC signal and it used by the receiver for symbol synchronization. At the end, program control returns from the TSR and waits for the next interrupt.  Compute index of I and Q LUTs and output I,Q to DIA  Figure 4.2 Flow chart for the implementation of the baseband transmission algorithm.  60  Chapter 4.  Design, Implementation, and Testing of a Pmtoiype GMSK System  Duration of the impluse response window  3T  Samples Per Symbol (SPS)  8  Number of samples in the impluse response window (N)  8 x3  =  24  Table 3 The parameters used in generating the GLPF.  The GLPF output LUT is generated upon initialization of the transmitter. It is generated using the GLPF impulse response, hT(t), given in Eqn. 2.4. By normalizing the time, t, with the symbol duration (7), hT(t) becomes hT(t/T)  i=kiBtTexp[_(kiBT(t/T))2]  where, as previously stated, k 1  = 1rVf  (4.2)  5.336 and BT is the normalized 3 cIB  bandwidth of the GLPF. For B T of 0.3, impulse response of the GLPF is plotted in 1 Fig. 4.3. It is clear from this plot that hT(1i7’) “dies out” outside the time interval [-1.5, 1.5] and therefore it can be truncated at these points without any “signal loss”. This truncating is required to digitally generate the GLPF output table. After truncating and sampling (8 times per symbol) hTfr./T), we have impulse response window of length 8x3=24 samples. The parameters used in generating the GLPF output table are summarized in Table 3. The GLPF output samples are generated by convolving the impulse response window with all possible NRZ input symbol sequences. Since duration of the impulse response window is 3T, there are 2(3+1)=16 distinct NRZ sequences, hence 16 distinct output symbols. NRZ sequences are generated internally by the program and they are made up of combinations of +l and ‘-1’ symbols. Mathematically, the output of a GLPF can be described as y[n]  =  x[n]h[O] +x[n— 1]h[1] +...x[n —N— 1]h[N— 1] 61  (4.3)  Chapter 4.  where  Design, Implementation, and Testing of a Prototype GMSK System  y[nJ is the output sample, x[n] is the current input sample, x[n-1] to x[n-N-1]  are past N-i input samples of the NRZ sequence and h[O] to h[N-1] are N samples of the impulse response. As illustrated in Fig. 4.4, the output of GLPF is a function of the present input symbol as well as the past three input symbols. As mentioned in Chapter 3, the baseband I- and Q-channels of GMSK signal are  1  0.9  0.8  0.7  0.6  0.5  0.4  0.3  0.2  0.1  0  t/T Figure 4.3 Impulse  response of the GLPF with B T = 0.3. 1 62  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  cosine and sine, respectively, of the signal phase  qf’(t).  Hence, the index, P,, of I-  and Q-channels LUTs is computed by first calculating the digitized phase 44n] as  [n]= {(:;s)Y[n_]}mod2  (4.4)  where h is the modulation index and is set to 0.5, SPS is equal to eight, and mod stands for the well known math function modulo. The result of mod2ir is always in the range [0, 27r). The output of GLPF is normalized so that the maximum change in phase over one symbol interval, T, is ir/2. The index, P,, is calculated as  F,,  FIX[Nj  *  44n]/(2r)j  (4.5)  where NL is the size of the I- and Q-channel LUTs. FIX[•] is a built-in TMS32OC3O assembler function which converts a floating point number to integer number.  Impulse Response Window  T —  T  —  T -  T —  Past Three Symbols  Current Symbol  Figure 4.4 Illustration of how a output symbol of GLPF is generated.  63  Convolve and Shift  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  The values stored in the I- and Q-channels LUTs are given by I,  =  n  ND cos 2ir— /  =  ND Sin  (4.6)  (27r! \ Nj  where ND is the normalization factor for the D/A to give an output of 3 volts peak. Notice that P takes the values 0 up to NL-1. After this detailed description of transmission algorithm, a functional block diagram of the transmitter is shown in Fig. 4.5. The input bit stream is converted from serial-to-parallel to generate an address of the appropriate output symbol in the GLPF output LUT. The samples, y[n], of the output symbol are fed to the Index Generator to calculate P, as described above. P, indicates the location of I and which are clocked out to D/As.  Input Bit Stream  Figure 4.5 Functional block diagram of the implemented GMSK transmitter. 64  Q,  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  4.4 Quadrature Modulator/Demodulator and Channel  A block diagram of the hardware implemented RF modulator/demodulator and the realization of the channel is shown in Fig. 4.6. With the exception of the ACI implementation, which has been realized by the author of this thesis, the design and implementation of the modulator/demodulator and the channel simulator were done by D. P. Bouras and documented in [36]. The modulator and demodulator are designed to operate at the carrier frequency of 1.5 MHz. Upon entering the modulator, the carrier is divided into its inphase and quadrature components by a components are then mixed with I and  Q  900  splitter. These  components of the baseband signals and  summed by a signal combiner. The resulting 1.5 MHz RF signal is amplified and fed to the 3-way RF signal combiner along with two adjacent channel interferers. The adjacent channel interferers are independent GMSK signals that are generated using frequency modulators (FM). The reason for adopting to this approach is that by using FM options on HP8656B and M12022 signal generators, we can easily change the channel spacing by changing the frequency of the outputs of the signal generators. It should be noted, however, that such an approach would not generate an exact GMSK signal as the QM approach. The block diagram of the ACI generator is given in Fig. 4.7. Referring back to Fig. 2.1, the equiprobable and independent information bits, a, are generated inside the Host PC and the GLPF is realized in software on TMS32OC3O system board. The output of the GLPF is frequency modulated using the FM inputs available on HP8656B and M12022 signal generators. 65  Chapter 4.  Design. Implementation. and Testing of a Pmtotype GMSK System  The channel module allows the fading to be simulated by the use of Digital Fading Simulator presented in [52]. Upon entering the channel module, the signal is divided into its inphase and quadrature components by a 900 splitter. These components are then mixed with inphase and quadrature components of the fading signal. White  I i(  i(t)  Upper ACT Generator  ‘x’  L  Lower ACT Generator c1m  l.5 MH  Z  3-way RF Combiner  q(t) Mixer  o  MODULATOR  o  Splitter  \7,/J  Fading Simulator  DEMODULATOR Mixer 4  i(t) Roofing  00 4  90°  —i-—— 200 kHz BPF  Q 1 . I  WHITE NOISE  q(t)  CHANNEL Figure 4.6 Modulator, Demodulator and Channel Simulator  66  1  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  Gaussian is also added to the signal from a White Gaussian Noise Generator whose band coverage is 6 kHz to 25 MHz. A wideband (200 kHz) roofing filter, with a center frequency of 1.5 MHz, is used to limit the noise. The demodulator takes the received RF modulated carrier and splits it into its inphase and quadrature components, which are then coherently mixed down to the baseband signals. This coherent conversion to baseband signals is necessary just because our differential detector is designed to operate on baseband signals. It is important note that this coherent demodulation does not “compensate” at all the interference introduced in the channel.  In fact, the interference appears totally  “uncompensated” at the demodulated baseband I- and Q-channels. The baseband I- and Q-channels are then passed through Low Pass Filter (LPF) and fed to the DSP card for baseband differential detection. HP8656B  GLPF output  Upper Interferer  TMS32OC3O DSP Board  2ith (Digital GLPFs)  GLPF output  j  M12022 ii  Lower Interferer  Figure 4.7 The block diagram of the ACI generation system.  4.5 DSP Based Decision-Feedback Receivers The functional block diagram of the implemented 1—bit differential receiver is shown in Fig. 4.8. The reason for implementing only 1—bit receiver is that it is easier to implement (compared to 2—bit redceiver) and our purpose for this exercise 67  Chapter 4.  Design, Implementation, and Testing of a Pmtotype GMSK System  is only to experimentally verify the effectiveness of decision feedback algorithm. The analog baseband I- and Q-channels provided by the RF demodulator must be first filtered by the receive filters which are 4th order Butterworth filters similar to the one implemented in computer simulations. These filters are provided on the TMS32OC3O system board and they have unity gain and their cut-off frequency can be varied  according to the plug-in register pack [51]. A/D conversions are triggered by the SYNC signal provided by the transmitter for symbol synchronization. The digital output of A/D convertors is processed by the decision feedback algorithm which is implemented in software. The program uses an TSR triggered by the SYNC signal. The decision feedback algorithm is the heart of the receiver. Its implementation is based on the block diagram shown in Fig. 4.9. The baseband differential detection algorithm takes current samples of I- and Q-channels, time delayed samples, and sine and cosine values of the phase delay (a) as its inputs. The phase delay for 1-bit  Figure 4.8 Functional block diagram 68  of the DSP-based digital receiver.  Chapter 4.  Design, Implementation, and Testing of a Pmtotype GMSK System  decision-feedback receiver is given by (4.7) where 0 is given by Eqn. 2.23 and repeated here for readers’ convenience, 0  = b_0  (4.8)  + bk_202.  All possible values of a are calculated using Eqn. 4.7 and tabulated in Table 4. The output of the differential detection algorithm is used for deciding the received bit. If PHASE DELAY FOR ONE-BIT RECEIVER bk_i, bk_.2  01 (deg)  -1, -1  15.9  0.2  73.9  -1, 1  15.9  0.2  74.3  1, -1  15.9  0.2  89.8  1, 1  15.9  0.2  90.2  02  (deg)  a (deg)  Table 4 All possible values of phase delay a (in degrees).  Baseband Differential Detection Q-channe, Algorithm I-channe  I  sin  (a)  j2  cos (a)  Addressing  Figure 4.9 The block diagram of a one-bit all digital decision feedback receivers  69  LjC  Chapter 4.  Design. Implementation. and Testing of a Prototype GMSK System  it is greater than zero the received bit is ‘1’ and ‘0’ otherwise.  4.6 Experimental Set-up and Measurements This section describes the experimental set-up used to evaluate the prototype GMSK system. It also presents the signal measurements and obtained BER per formance evaluation results of 1-bit decision-feedback differential receiver and 1-bit conventional differential receiver. The block diagram of the experimental set-up is shown in Fig. 4.10. In addition to the equipment shown, a Tektronix 2232 oscil  Figure 4.10 Block diagram of the experimental set-up. 70  Chapter 4. Design, Implemenkition, and Testing of a Prototype GMSK System  Figure 4.11 I-channel eye-diagram at modulator input. Horizontal Axis: 0.1 msec/div, Vertical Axis: I V/div.  loscope was used to monitor the baseband signals. The I-channel eye-diagram at the input of the RF modulator is shown in Fig. 4.11. The signal has an amplitude of 3V peak, as discussed in Section 4.3. This is the maximum output voltage of D/A convertors on the TMS32OC3O DSP card. The operation of DIA convertors at maximum output voltage minimizes the quantization errors [51]. The phase state-  Figure 4.12 The phase state-space diagram of the modulated GMSK signal. Horizontal Axis: 1 V/div. Vertical Axis: 1 V/div.  71  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  Figure 4.13 The phase state-space diagram of the demodulated GMSK signal. Horizontal Axis: 1 V/div, Vertical Axis: I V/div.  space diagram of the modulated signal is depicted in Fig. 4.12. It is evident from this figure that the transmitted GMSK signal has constant envelope and continuous phase. Without any channel interference introduced, the phase state-space diagram of the demodulated signal is shown in Fig. 4.13. The non-ideal components of the modulator and the demodulator cause slight phase shift and amplitude distortion. The peak voltage of the demodulator output signals is almost 2.5V when the modulator inputs has amplitude of 3V. Referring back to Section 4.3, we have designed the GMSK BDS for B T 1  =  03  and Baud rate was set to 5208 symbols/second. At these values of B T and Baud 1 rate, we expect the 3-dB bandwidth, B , to be 1  B  =  =  0.3 x 5208  72  =  1.6kHz.  (4.9)  Chapter 4.  Design, Implementation, and Testing of a Prototype (3MSK System  As can be seen from the signal spectrum shown in Fig. 4.14, B 1 is indeed close to  Figure 4.14 The spectrum of the GMSK signal at modulator output. Horizontal Axis: 2 kHzjdiv, Vertical Axis: 10 dB/div, Center frequency = 1.5 MHz.  1.6 kHz. After the signal passed through the 3—way combiner, the fading modulator and the noise summer, without any fading and noise introduced, the spectrum of the signal at the demodulator input is illustrated in Fig. 4.15. The distortion introduced by the channel simulator hardware is evident in this figure. As mentioned in Section 4.4, the adjacent channel interferers are generated using FM options of two signal generators, namely HP8656B and M12022. The interferers are then combined using a  Figure 4.15 The spectrum of the GMSK signal at demodulator input. Horizontal Axis: 5 kHz/div, Vertical Axis: 10 dBldiv, Center frequency = 1.5 MHz.  73  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  Figure 4.16 The spectrum of the desired signal along with two adjacent channel interferers at channel spacing of 7.8 kHz. Horizontal Axis: 5 kHzjdiv, Vertical Axis: 10 dBfdiv, Center frequency = 1.5 MHz.  3—way RF combiner and the spectrum of the combined signal is depicted in Fig. 4.16. It is intresting to note that the spectrum of the lower interferer, which is generated by M12022, is significantly different than the desired signal, whereas the spectrum of the upper interferer, which is generated by HP8656B, is not so different than the desired signal. These discrepancies are mainly due to the quality of the FM moudulators of the respective signal generators and, as stated previously, the fact that FM method is not the best method to generate GMSK signals. The spectrum of the received GMSK signal in AWGN channel is presented in Fig. 4.17 and corresponding phase state-space is shown in Fig. 4.18. The experimental BER performance results for 1-bit conventional and decision feedback receivers are obtained with various channel conditions. The BER results for receivers operating in AWON channel are depicted in Figs. 4.19 and 4.20. There is only small deviation (0.5— 1 dB at BER  =  10  3)  from the computer simulations. These  deviations are attributed primarily to the non-ideal RF modulator and demodulator. 74  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  Figure 4.17 The spectrum of the GMSK signal in AWON channel. Horizontal Axis: 5 kHzjdiv, Vertical Axis: 10 dB/div, Center frequency = 1.5 MHz.  The BER results for the conventional and decision feedback receivers in an AWON and Rayleigh fading channel for two values of fDT are presented in Figs. 4.21 and 4.22, respectively. The close agreement between the experimental and the computer simulated BER results is evident. Figs. 4.23 and 4.24 illustrate the BER performance of the implemented receivers in static ACI-AWGN channel at C/IA  =  10 and 14 dB. It is clear from Fig. 4.23  Figure 4.18 The signal phase state-space at demodulator output after adding AWGN. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div.  75  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  that the decision feedback differential receiver provides significant reductions in error floors, as predicted by computer simulation results in Chapter 2. In Fig. 4.24 with C/IA  =  14 dB, the decision feedback receiver has a gain of almost 6 dB as compared  to the conventional differential receiver at BER  76  =  iO.  I  0  C  -a  C  C  = --  ——-  —--  ---  —  —— -  ———  z  -a  -  -  -  ——--  —---  ----  —  =  C  -a  --  -  ——-  —--  ---  —  —  -  ——-  ——-  ---  —--  —  —  :t :[::  C  -a  —-1I11 1• ur-  z=  C  Bit Error Rate Probability  ,.  LLLLLflI  I.TpTJ  l4I41-II  rflh1TFI  0  LILLLL{I  C  hRTP11 1-I-i-i-n1  z  C,  -a 0  I  I  -t  I  0  L.) 0  0  I-’  C  Bit Error Rate Probability 0  ‘Ii  I  I  0  Bit Error Rate Probability C 0  I  f  00  ,.  c  ‘TI  Bit Error Rate Probability C 0  ‘I  I  I  Chapter 4.  Design, Implementation, and Testing of a Prototype GMSK System  —1  10  1 1-bitDF 1 1-bitC %  10  A  ,  -2  ZEEEEEEZEE  :zz \  10  \  .3  10  S  -4 -  15  35  25  45  Eb/No [dB] Figure 4.23 The BER performance of the 1-bit decision feedback (DF) and conventional (C) receivers in static ACI-AWGN channel at C/IA = 10 dB. 81  55  00  t’.)  Q  S.  ZQ  11  .  o  0  U’  C  U’  C  C  Bit Error Rate Probability C  C 0  •1  Chapter 4.  Design, Implementation, and Testing of a Pmtotype GMSK System  4.7 SUMMARY A prototype GMSK system was designed, implemented and tested on a TMS32OC3O based DSP platform.  The obtained test results are in close agree  ment with computer simulations. The BER performance results, obtained for 1-bit conventional and decision feedback receivers operating in static ACI-AWGN channel, verify significant improvements provided by decision feedback receivers.  83  Chapter 5 Conclusions and Some Suggestions for Future Research 5.1 Conclusions In this thesis, the BER performance of 1— and 2—bit conventional and decision feedback differential receivers was evaluated for the detection of GMSK signal in the presence of Ad, modulator errors, amplifier nonlinearities, and AWGN. The BER performance results for conventional and decision feedback differential receivers of GMSK signals has been obtained for static and faded ACI-AWGN channel by means of computer simulations. It has been found that the decision feedback receivers always provide better performance when compared to the conventional differential receivers. The gains are more significant for static ACI-AWGN channel. For faded ACI-AWGN channel, the decision feedback differential receivers provide error floor reductions. The obtained BER performance results for the system with an imperfect modulator and a nonlinear amplifier indicate that for extreme modulator errors, 1—bit decision feedback differential receiver out performs all other receivers that are considered. For typical modulator errors, 2—bit decision feedback differential receiver has the best performance. Finally, a prototype GMSK system was designed, implemented and tested. The experimental results verified the effectiveness of decision feedback receivers. 84  Chapter 5.  Conclusions and Some Suggestions for Future Research  5.2 Suggestions for Future Research 5.2.1 Generalization to other CPM Schemes This thesis has dealt exclusively with GMSK signals. However, as it was shown in [30], the decision feedback receivers can be applied to any CPM scheme. It would be therefore of interest to investigate the performance of more generalized CPM scheme in the presence of ACI.  5.2.2 Simultaneous use of 1— and 2—bit Decision Feedback Differential Receivers. As it was shown in [29, 30], by employing a combination of 1— and 2—bit decision feedback differential receivers, further performance improvements have been obtained for the AWGN channel. By using such combinations of receiver structures (or perhaps employing even higher order differential detectors), further performance improvements are to be expected for the ACI and CCI channel.  5.2.3 Extension to Multilevel CPM Schemes In order to increase the bandwidth efficiency, multilevel CPM can be employed. It will be therefore of interest to investigate the performance of such modulation schemes in the presence of interference and/or nonlinearities.  5.2.4 Further Development of Prototype GMSK System 1J  Optimization of the transmitter by reducing the size of LUTs.  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VT-39, pp. 205—2 12, Aug. 1990.  91  Appendix A Program Listings •  GMSK digital baseband synthesizer  •  1—bit conventional differential detector  •  1—bit decision feedback differential detector  •  Generator of two adjacent channel interferers  92  File: Date:  ‘  START START ISR START START START START START START START START START  .init  ***  1’’  ‘  .stack”, 400k  Program Section at address ODOk  STACK .u$ect  .data irpluse response of the Gaussian filter .float 0.0013 .float 0.0038 .float 0.0104 .float 0.0255 .float 0.0565 .float 0.1133 .float 0.2055 .float 0.3372 .float 0.5004 .float 0.6716 .float 0.8152 .float 0.8950 .float 0.8886 .float 0.7979 .float 0.6480 .float 0.4759 .float 0.3161 .float 0.1899 .float 0.1032 .float 0.0507 .float 0.0225 .float 0.0091 .float 0.0033 .float 0.0011 *** Stack in BLOCKO at 809800k ‘‘  Data Section at address 30000  .word .word .word .word .word .word .word .word .word .word .word .word  .sect  “‘  * aci.asin * 9 Oct. 1993 Use: ‘generate two independent gaussian filtered * for adjacent channel interference purpose  Interrupt Vectors at address 0  BESET INTO INTl 1812 1873 XINT0 RINTO XINT1 RINT1 TINTO 71871 DINT  * * *  *  aci.asm  *  804080k 804001k 808042h 00808030k 00008038k 00000601k 000086CTh  START:  .set .set et  CODES DUAL ONCRIP  30000k 809c00k  LDI OPRIMCTL, ARO  LDP CODES LDI 8STACKADDR,SP  Set up primery bus wait states  ;get the page of stored adress :set up stack pointer  the following code Sets up the stack pointer and initializes DSP hardware as outlined in the user’s annual  0  ;start address of DUAL aem ;end address of DUAL(-BANK3) ;start address of onchip RAM1  .word .word .word  DOBISTART DUALEND RAM1  030000k 033300k 0809cOOk  ;esid 33210  start of the data ;end of data—31910  Thit or 2bit used for 2bit encoding  :pOinter to iirpluse response pointer to data window pointer to waveform tabel  ;scaling factor  Timer period — 6.6 usec samples per syso1 Hunkers of samples in Fib window  ;FSX/DX/CLKX PORT CONTROL Tiierl control register Tiamrl period register  Primery bus control Expansion bus control  IMP RES .word 0809cOOh WINDOW .word 809c32h WAVETIiBLE .word 809c64h P0EV BIT1 .set 809d00h .set 009d81h DIF_ENC PBEVBIT2 .set 009d02h BIT_COUNT .set 809d03k SET FLAG .set 009d04k TABLE .set 009d05h DATAEND1 .set 809d06h DATAEND2 jet 809d07h CURE 80001 et 809d08k CURE 80802 -set 809d09h .set BO9dOak INDEX1 INDEX2 .set 8O9dObh BEADY FLAG 30001k .set VDATAI .word 30010h EDATAI .word 31910h V1)ATA2 .word 31911k .word 33210k EDATA2  constants in the program COUNT .word 200 SPS .set 0 WIN SIZE jet 24 READY .set 11 DACRES .float 1500.0  ADCBANA .set ADCRANB .set ;SERIALO .word TIMECTL .word PERIOD .word RSTCTRL .word SETCTRL .word  .text STACK ADDR .word STACK PRIMCTh .word 00800064k EXPCTL .word 00008068k PRIMWD .word 00000800k LEANT .word 00008000k  :set digital output to  Set up expansion bus wait-states.  STI  RU, *1106+4  **ea* ***** ** cnn ** ***a*** ***** ****** cc ***a na******* Clear the DUAL sesory (30000 to 33300) ODUALSTART,R6 101 $DUAIEND,R7 101 106,107 SUBI 0,100 WI 106,1106 101 107 PETS  * *********** *  This portion of the code changes the wave table into integer table and shift the values to upper 16 bits.  ‘**************************a**************c********c****c*************** This portin of the code calls MAKE_SIN to wake a tahel of all possible sasples; GLOBAL PEGS. :R3,R4,R5,1R3 these should not be aodified by calls $NAVETRBI,E, 1103 101 6,105 ; a counter for total I of nystola 101 -1.0,104 1,0021 102 SPS,R3 WI BUILD_WIN CALL NO? CALL MAKE_SIN NO? l.U,R4 ID? BUILD_WIN CALL NO? 525,103 101 CALL KAKE_STN NO? ocresEnt the counter 1,105 MDI SPS,R5 CMPI 10021 BNZ NO? CALL FIXIT NO? FINISB BR  :  ,  ;********************************a**a*********a**********************a** This portion of the code roves IMP RES data given above, ; to on chip 101141 at $809c00 ; 101 ODUALSTART, 1100 P101141,1101 101 *M044R0 102 WIN_SIZE PETS *110044,100 102 RU, *Ml.f4. (I 571’ NO?  101 @E)TCTL,ARO 101 OEPEND,R0 571 R0,*ARO 101 OSLRIALO, MO 1.01 2h,R0 £71 R0.*ARO  101 @PRIMWD,R0 57! R0,M0  PETS  WI RPTB LDF M?TF FIX lET! ;SUBI ISP  €WXVETABLE, AR? 127,RC FINSB *M7,R7 ODACBES,R7 R1,R7 1550,10? 3,R7 16,10? 10?, 9J744 571  101  525-1 RU,*MU4.f SPS-l J,*,fl+f 525-1 fl*MU44.  initialize registers  --  1,103 MAlE_SIN SUBI BGTU NO? NO? NO? PETS  ;result of FIR is in RU  This portion of the code finds FIR of two vectors of length  $WINOOW, 1100 $INP_PES,1R1 WIN_SIZE, BK NIN_SIZE-2,RC FIR RO, Q,p,34-f LOT WI 101 LOT CALL 572  This portion of the code creates the gunk syirhol. INPUTS: 1R3 (location in rem wher sysbol to be located), R3(sps), R4(new bit) OUTPUTS :1103 (location of next sysi) KNEE_SIN: UNINUON, 1100 LOT WIN SIZE-l,RC WI load in new value 104,100 102 STUFF CALL  P275 STE RPTS STE lETS STF PETS  This portion of the code builds the window INPUTS: R5(systol $ 0-?) BUILD_WIN: UWINDOW, 1100 101 -l.O,RU LOP -1.0,101 LDF -l.O,R2 LDF l,R5 TSTB LDFNE 1.O,RO 2,RS TSTB LDFNE 1.O,Rl 4,R5 TSTB LOFNE l.U,R2  FINSU  FIXIT  C  BETH IDF  101 STI 101 STI SI! £01 STI 101 STI 101 511 STI 101  0,1(1 R7,@SET_FIAG -1,1(7 R7,0PREVHIT1 R7,)PREVBIT2 1,1(7 R7,00IF_ENC 32,1(5 R5,001T COUNT 0,1(3 R3,@INDEX1 R3,01N01X2 SPS,R4  :set the counter for sasples per UN  ;initialize 1(3 for index  :type of encoding UNit or 2bit :bit count 12-global  Here we initialize the variables used in the intrupt service routine. ARO,A1(l,A1(5,AR4,R4,R5 are global CODES ID? TWIT: :address of the data word 11(0—global @VDATAL,AR0 101 €VDATA2,1R1 101 0EDATAL,1B2 101 @EDATA2,A1(3 IDI ;set a pointer to the ainewave table 101 @WAVETADIE,AB4 INAVETADLE,A1(S 101 *ARO++,RO :get the first data word and lncreant 101 *11(1+41(1 101 ONCHI? ID? RO, @CUBR_NORD1 STI STI Rl, @C0RR’ORD2 LOX 11(4,1(7 :pointer to the beginning of table R7,UTABLE STI 10! 11(2,1(7 STI R7,@DATAEND1 11(3,1(7 101 STI R7,UDATAEND2  if ready start otherwise wait keep checking if ready  save the old value stuff in the new one  This portion of code is used to stuff a value at the first location of a vector and shift the older values down by one. INPUTS: AR0{vector pointer),RC)vector size), R0{new value)  IIPTF3 *pj(0*f(fl,*0fl144W%,R0 ;initialize RU ;initialize 1(2 IDE 0.0,1(2 BETS RC flpy3’3 *M044U) tA1(14-f(l) %, 1(0 II ADDF3 1(0,1(2,1(2 ;Add last prduct R0,R2,R0 ADDF I RETS  DONE *31(,pJ R0,*A1k04f II STF 1(1,1(0 DONE LDF BETS DUAL FINISH: LOP III )REAOYFLAS,R7 CNPI 1(11(01,1(7 Bill FINISH  STUFF  FUN  N. INPUTS : AJ(0{addrl),Afl{addr2),HK(N),RC{N-2), OUTPUTS: RU(result)  NENHIT:  wait for intrupts here  :enable intrupt for tiaerl ;set the global intrupt OlE in ST  ID? 101 Bill LOX ID! STI STI  USET_FLAG,R7 GETOUT @TAHLE,1R4 @TAHLE,ARS SPS,R4 UCUBR_NORDI,RN @CURRNHRD2,R2 R0,R1 1(2,1(3 1,1(1 1,1(3 -1,1(0 R0,UCURR_N0R01 -1,1(2  101 HNZ 101 ID! 101 ID! 1.0! ID! ID! AND AND 1.SH STI LSH  output bit in 1(1,1(3  :reset sarple counter  ;check if the flag Ia set if aet,getout :reset table pointer  NO PLUSE OUTPUT  :if end of nyitol get new bit  output to the channel  :point to beginning of the syitol  Intrupt service routine 11(0—current address, current word, —new bit, R5— 32 bit count R4—sps, these are global registers for ISR  DEAD  2,IE 2000b,ST  ONCUP PSETyIAG,B7 GETOOT AR4+4,R7 t *BE5.ff,1( R7,PADCHANA R6,0ADCHANB CODES LOP 0511(1110,11(3 £0! ONCHI? ID? 2LR6 ID! *11(3 1(6, SN 1,1(4 SUB! NENHIT BE 4,1(4 CUll’! GETOUT Hill 6H,R6 ID! 1(6,9.1(3 STI GETOUT: HR ISR RET!  ISR:  DEAD: HR  OR OR  Here we set up Tinerl control registers and period registers CODES ID? OTINECTI,1R7 101 ORSTCTRI,R7 101 R7,*1R7 STI €PUNIOD,AR6 101 @COUNT,R6 IDI R6,*1R6 STI USETCTBIOR7 ID! R7,*1R7 STI  Co 0’  SETFIPkG: 101 STI  ;if yes do two bit enc ;index of wave table  DDIF_ENC,R7 l,R7 RLR1 BIRD B112_ENC  INDEX  101 ‘ISTA LDINZ LDINE BE NO? BR  ;reset bit count  BR  32,R5 *AR0++,RO *ARlf4,J R0,@CURRW0001 R2,OCURRW0002 @DATAEND1,ARO SETFLAG ODATAEND2,ARI SETFLAG INC_BIT  ONCRIP R0,@CURRWORD1 R2,DCURRWORD2  ENC_BI’!  BR  l,Ri R7,RDET_FLAG CODES OVDATA1,ARO DVDATA2,AR1 *A,R044 RO  ;find index of wave tabel  INDEX  check if end is reached  ;check if end is reached  ;get the new word  ;bk__ak*bk_1  €PREVBITl,P7 R7 R7,Rl Rl,€PREV Bill DPREVBfi2,R7 Ri R7,R3 R3,DPREVBIT1  101 NEGI MElt STI 101 NEGI MPh $71  ;bk__ak*bk_l  Thit diff. encoding ;if yes, no encoding  ONCRIP l,R1 -1,R1 1,R1 1,R3 -l,R3 1,R3 ;is it ‘1’ ;if not if yes :is it ‘1’ ;if not if yes  lf 32nd bit reached get newword  decrewant the bit count  ID? TSTB t.DIZ LOIRE ISlE IDlE LDINZ  R2, @CURRWORD2 l,R5 ENC_BIT REWORD  ID? 101 101 101 101 ID? STI STI  101 101 IDI STI STI CMPI BE CMPI BE BR  BIT2ENC:  INC_BIT:  ill SUBI BNZ BE  *  Pile: Date: Use:  BR .end  .word .word .word .word .word .word .word .word .word .word .word .word  START START RCV START START START START START START START START START  **  .usect “.stack”, 40Db Progra,s Section at address ODOh  STACK  *** Stack in BIOCKO at 809800h  Data Section at address 30000  RESET INTO INTl INT2 INT3 KINTO RINTO XINT1 RINT1 TINTO TINT1 DINT  “  ***  *  *  *  ddl.asm  ;update the table pointer  ;store the index in 100  ;update the table pointer  ddl.asn 9 Oct. 1993 ‘1-bit conventional differential detector  TOU’!  8,R7 R7,R0,IRO RO,DINDEX1 *AR4++(IRO) ,R7 8,R7 07,02,100 R2,€INDEX2 *AJ5++(100),R7  LDI MPYI3 STI LOP LDI HP113 STI LOP ;store the index in 100  ;convert to bit ‘0’ or ‘1’ Rl,Rl 0,RJ. ;‘O’ if Ri was ‘—1’, unchanged otherwise ;convert to bit ‘0’ or ‘1’ R3,R3 ‘0’ if Ri was ‘-1’, unchanged otherwise 0,03 OINDEX1,R0 INDEX2,R2 ;mke space for new bit l,R0 Ofh,R0 ;use only 4 LIDs of 03 01,03 ;stuff in new bit ;jake space for new bit 1,02 Ofh,R2 ;use only 4 LSBS of 03 03,02 ;stuff in new bit  IDI IDIN 101 IDIN 11)1 101 LID AND OR ISO AND OR  *** Interrupt Vectors at address 0 .global .bss .global cinit .sect “.init’  * *  I  INDEX:  CD C)  .word 604000h .word 804001h .wørd 808042h  .set .word .word .word  030001h 030000h 033300h 0809c00h  START:  ONCE  CODES DUAL  3000Db 809c00h  809d00h 809d01h 809d02h 809d03h  :1 sasple of previous syirbol  ;start address of DUAL sm ;end address of DUAL(—BANK3} :start address of onchip RAI41  sauples per synbol Nuners of sasples in FIR window  Prmnnry bus control Expansion bus control  Clear the DUAL sanory (30000 to 33300) LOT DUALST3RT,R6 UDURLEND,R7 LDI SUBI R6,R7 O,RO WI  :set CLXO serial port as outout  Set up expansion bus wait-states.  WI NECT1,ARO LDI 8EWD,R0 STI R0,*ARO  WI OSERIALO,ARO LDI 2h,R0 STI RH, *ARO  Set up primry bus wait states  :get the page of stored adress ;set up stack pointer  LDI NPRINCTL,ARO WI €PRINWD, RH STI R0,AR0  LOP CODES LDI @S’!ACK_ADDR,SP  the following code sets up the stack pointer and initializes DSP hardware as outlined in the user’s sanual  .set .set .set  ;program variables READIFLAG .set SERIALQ .set .set I_SMP_T .set Q_SMP_T  ;output data word 030010h RCVVATA  READY FLAG DUALSIART DUALEND RAM1  .set 8 SF5 WIN SIZE .set 24 .set 11 READY  constants in the program  ADCHANA1 ADCHEABL SERIALO  .text STACK_ADDR .word STACK PRIMCTL .word 00808064h EERCTL .word 00808060h PRINWD .word 00000800h EWD .word 00000000h  R6,AR6 R7 00, *+4  FLOAT RO,R4 FLOAT Rl,R5  LOP LDI WI LOT WI ASH ASH  ;read channel A :read channel B  intrupt service routine  GETOUT: RETI .end  LDThE 2h,06 WIGT 6h,R6 WI SERThLO.AR3 STI R6,*AR3  WY t_S?€’_T,R2 LDF Q_SNP_T,R3 STY 04,HI_SMP_T STY R5,00_SHP_T HPYF 04,03 HP!F 05,02 SERF R3,R2  LDP ONCEIP  ;output the received bit to the andem tester  ;keep the current saiples :for next tue ;t_SMP (0) *Q5 (7) ;Q_SMP (0) tI_SW (7)  :get the previous aaiples  ;at this point R4 and R5 contain the current I,Q sasples  RCV:  ;wait here for intrupts  ;enable intrupt for tiserl :set the global intrupt GIE in ST  CODES OADCHANAL,A0O HADCUANB1,AR1 *J0R0 •AR1,Rl -16,00 -16,Rl  2,1K 2000h,ST  CODES ORCVDATh,A02 @SERIALO,AR3 ONCAIP AR3,R7 R7,OSERIALO 0,07 R7,I_SMP_T R7,HQ_S)j  WAIT HER!: BR WAIT_BEBE  OR OR  LDP WI WI LOP WI 511 LDF STY STY  Here we initialize the intrupt routine variables  WI OPTS STI  dfl.asm  dfl.asm 21 Feb 1993 ‘1—bit decision feedback detection’  .word .word .word .word .vord .word .vord .word .word .word .word .word  STAR’! START RCV START START START START START START START START START  .float .float .float .float .float .float .float .float  0.277314653296 0.270600445468 -0.27060045987 -0.277314653306 0.960779154159 0.962691746429 0.962691746423 0.960779154156  “.  stack”, 400h  .word 804000h .word 804001h .word 808042h  .set  8  constants in the program  IIDCBANA1 ADcBANB1 SERIALO  .text STACK_ADDR .word STACK PRI!4CTI. .word 00808064h EIPCTI, .word 00808060h PRINWD .word 00000800h EXPWD .word 00000000h  SPS  ***  Program Section at address ODOh  .usect  Stack in BIOCKO at 809800h  STACK  CCC  ***  Data Section at address 30000 *** .data :cosine and sine valued of the phase delay alpha  OESET INTO INTl INT2 INT3 XIN’!O RINTO XINT1 RINT1 TINTO TINT1 DINT  .sect “.init  Interrupt Vectors at address 0  .word .word .word  030000h 033300h 0809c00h  IDP CODES 101 €SThCK_ADDR,SP  sanples per syithol  Prianry bus control Expansion bus control  ;  Clear the DUAL amsory (30000 to 33300) NDUIiLSTART,R6 ID! @DUIiLEND, R7 ID1 SUB! R6,R7 ID! 0,R0 R6,0R6 IDE RPTS R7 SI! RO, *AR6++  CCC  ******C** CC *  ;set CLXO serial port as output  Set up expansion bus wait-states.  Set up prinary bus wait states  ;get the page of stored adress ;set up stack pointer  mve the data from DUAL (30000) to ONCRIP (809c00) IDE ODUIiLSTART,ARO IDI ORN41,AR1 IDF *ARO++, RO OPTS 8 1DF *AR014, RO II SIP RO,CAR1H.  *****************C ********C*  IDI €SERIALO,ARO IDE 2h,R0 STI R0,*ARO  101 NEXPC’!L,ARO IDE OEXPWD,R0 STI R0,*ARO  CC  ;current Q saiple stored here ;I saiple of previous syshol :0 previous nrz bit one before previous  ;cos values of theta stored here sin””  ;start address of DUAL 1mm ;end address of DUAL{—BANK3) :start address of onchip RADIi  Nurhers of sasples in FIR window  the following code sets up the stack pointer and initializes DSP hardware as outlined in the user’s wanual  :sin theta  .  START:  30000h 809c00h  0  CODES DUAL 08CM!? .set .set .set  809c00h 809c04h 809d00h 809d01h 809d02h 809d03h 809d04h 809d05h  ;program variables AUX1 .word AUX2 .word RZADYFIAG .set SERIALO .set .set I_SMP_T -set Q_SMP_T .set BK1 -set BK2  ;output data RCVDATA .word 030010h  JUAISTART DUALEND RAII1  101 @PRIMCTL,ARO IDI OPRINWD,R0 STI R0,*ARO  I  .set 24 .set 11  ;cos theta  **CC** **C C **** * * ** *** *** *C*** CC *C** **C *********CC***C*C**** C  *  C  File: Date: Use:  ****************C*******************************************  C  I  WIN_SIZE LEADY  CODES 81,DCHANA1, ARC €ADCHANB1,AR1 *1.J0R0 *ARl,Rl -16,R0 -16,Rl  FLOAT RO FLOAT Rl  LDP LDI WI LDI LDI ASH ASH :read channel A ;read channel B  WI @BKL,R2 LDI DBK2,R3 STI R2,CBK2 LSH l,R2 OR R3,R2 LDI 02,IRO LDF *+ARO(IN0)p, LDF *+1J1(fl0)R3 LDF 8I_SMF_1,R4 LDF QOSMPI,R5 SIT R0,CISMPT SIT Rl, CQSMPT MPIT3 R4,R2,R6 MPYF3 R5,R3,R7 SURF R7,R6 MPYF R5,R2 MPYF R4,R3 ADDF3 R2,R3,R7 MF’IF R6,R0  WI CAUX1, ARC WI CAUK2,ARi LDP 014CH1P  ;wait for intrupts  :enable intrupt for tlixmrl :set the global intrupt OlE in ST  :R7-isag :ISMP(0)*reel  ;R6—reel :iang  :keep the current sanples ;for next tine ;reei  ;auxl aux2  ;bk(2j—bk)l]  ;pointer to cos theta pointer to sin theta  at this point RD and Ri contain the current 1,0 sasples  RCV:  BR WAIT_HERE  2,IE 2000h,ST  OR OR  WAIT_HERE:  0,R7 R7,NISMPT R7,80SMPT 0,R7 R7, OBK1 R7,80K2  LDF SIT SIT !DI 511 $11  Here we initialize the intrupt routine variables LDP CODES LDI 8RCVDATA,.AR2 WI OSERIALO,AR3 LDP ONCHIF LDI AR3,R7 STI R7,@SERIALO  RETI .end  File: Date: Use: gmsktx.asia ii March 1994 ‘Gmsk transmitter’ *  *  .vord .word .word .word .word .word .word .word .word .word .word .word  ‘  START START ISR START START START START START START START START START  .init’  .float .float .float .float .float .float .float .float .float .float .fjoat  0.0013 0.0038 0.0104 0.0255 0.0565 0.1133 0.2055 0.3372 0.5004 0.6716 0.8152  .data ispluse response of the GLPF  Data Section at address 30000  RESET INTO INTl 1572 1573 XINTO RINTO XINT1 DISh TINTO TINT1 DINT  .sect  .include table.asn .glohal .bss .global cinit Interrupt Vectors at address 0  ***  ***  ************************************************  *  *  gznsktx.asm  bk(11—bk(0)  ;output the received bit to ndem tester  :0_SOP (0) *jq ;this is dd  ************************************************  *  I  GETOUT:  158 2,R6 571 R6,CBK1  LDThE 2h,R6 IDIGT 6h,R6 WI @SERIELO,AR3 STE R6,*AR3  WRIT R7,R1 ZsDDF R0,R1  CD CD  -usect  -stack”,400h  **  ;FSX/DXICLYJC PORT CONTROL Tiserl control register Tismrl period register  IMP PES -word 0809cOOh ;pointer to ispluse response WINDOW -word 809c32h ;pointer to NRZ sequence WAVETABLE word 809c64h pointer to 6111 output table DIP EWC 80940Db set lbit or 2bit P0EV BIT -set 809d02ft used for 2bit encoding SET_FLAG -set 009d04h TABLE -set 809d05h PEASE 809d07h -set storage for pbade phi COS_POINTER -set 809d00h SIN_POINTER -set 809d09h SERIALO -set GO9dOah SIN POINTER -set BO9dObh NOD VALUE1 -set OO9dOch MOD VALUE2 -set BO9dOdh  constants in the program COUNT -word 200 Tirer period — 24 riicrosec SI’S 8 -set saaples per systol WIN_SIZE -set 24 Wurhers of saxples in FIR window Nt -set 10000 size of sin and cos tables MOD1 -float 2-0 HOD2 -float -2-0 00104 -float 0.7SlOSlO6e-3 DA’IPES -float 32751-0 1 volt—l09l7, 3 volt—32751-0 ARAB! -set 11  804000h 80400lh 808042h 0080803Gb 00008038h 00000603h 000006CTh  ADCEANA ADCED21B SERIALO TIMECTL PERIOD RSTCTRL SETCTRL  -set -set -word -word -word -word -word  Prirery bus control Expansion bus control  -text STACK ADUR -word STACK PRIWDTI -word 00800064h EXPCTL -word 0080806Gb PRD4WD -word 0000000Db ETYWD -word 00000000h  Program Section at address ODOb  STACK  ***  -float 0-0950 -float 0-8886 -float 0-7979 -float 0-6480 -float 0-4759 -float 0-3161 -float 0-1099 -float 0-1032 -float 0-0507 -float 0-0225 -float 0-0091 -float 0-0033 -float 0-0011 Stack in BLOCKO at 809880b -word 30010h  0 30000h 809c00b  :start address of DUAL sam ;end address of DUAL(—BANK3) ;start address of onchip RAM1 only part of rasil  start of the data  ;set digital output to 0  : Set up expansion bus wait-states  Set up prinnry bus wait states  Clear the DUAL aesory (30000 to 33300) tEl @DUALSTART, R6 WI @DUALEWD,R7 CALL CLEAR ;  This portion of the code adjusts the sine and cosine tables in table-asm- So that the valoas can be output to 0/As  This portion of the code auves IMP_PBS data ,given above, to on chip RAND. at $809c00 WI PDUALSTART, ARO WI €RANLAR1 ARO+-f,R0 WY OPTS WIN_SIZE AR0H-,R0 t WY ATtll-f RO, t I) STY WUP ;  :  ;*******************C*******************************C*******************  code initializes OWCEIP aerory OO9cOO-OO9cff €RAM1,R6 IRAHEND,R7 R6,R7 0,RQ R6,AR6 R7 R0,*AR6If  WI PSERIAL0, ARO LDI 22h,R0 STI R0,*ARO  WI 0EBPCTL,ARO LDI 0EKPND,RU STI RO, *7ffi0  WI OPRIOKTL,AR0 WI 0PRIMWD,R0 STI R0,*ARO  LOP CODES ;get the page of stored adress LDI GSTACKADDR,SP ;set up stack pointer  the following code sets up the stack pointer and initializes DSP hardware as outlined in the user’s annual  -set -set -aet  The following WI WI SUEZ WI LU! OPTS STY  START:  CODES DUAL ONCRIP  DUALSTIRT -word 030000b DUALEND .word 03330Db KOHl -word 0809c00h -word Bo9cffh RAMEND  VDATA  I-a  0 0  LOOPL  ;adjust the output voltage  0,R7 R7,05E1_PLAG R7,0SINPOINIER 0.0,07 initial pbase R7,@PBASE -1,07 R7,0PREV OTT 1,07 R7,00IP_ENC :type of encoding lbit or 2bit  of the code is initializes the variables of TSR CODES 0WAVETABLE,AR1 :set a pointer to the wave table OCOS TABLE, 002 @SINTABLE,AR3 OSERIALO,004 OMOO1,R7 0NO02,R6 ONCHIP R7,0MOOVA1UEI. R6,IMOOVALUE2 001,07 07, ITABLE ;pointer to the beginning of table AR2,R7 R7,ICOS POINTER AR3,R7 R7,0STN POINTER 004,07 R7,ISERTALO  CODES @COS_TABLE,0R7 OSINTABLE,0R6 NL-l,RC FINSR1 *Rp77j7 *00606 000CRES,R7 600COZS,R6 Ri R6 16,R7 l6,R6 R7,*AR74f R6,*RR64f  This portin of the code calls MAKE_SIN to ante a tabel of all possible sasples: GLOBAL PEGS. :03,04,05,003 these sbould not be andified by calls LOP CODES LOT IWAVETABLE,AR3 LOT 0,05 a counter for total I of sysbols LOP —l.0,R4 LOT SPS,R3 CALL BUILD_WIN HOP CALL MAKE_SIN HOP  LOT SIT SIT LOP SIP LOT SIT LOT SIT  this portion LOP LOT LOT LOT LOT LOP LOP LOP SIP SIP LOT SIT LOT SIT LOT SIT LOT SIT  FTNSB1:  LDP LOl LOI LOI RPTB LOP LOF MPIP HPYF FIX FIX LSU 1,511 511 $71  incresent the counter  MAIN_ROUTINE  1,05 SPS,R5 LOOP1  SPS,R3 MORE SIN  1.0,04 BUILD_WIN  SPS-l R0, A 1 RO++ SPS-l 01, *00014 SPS-l P2,*000+4  SOOT BOlD NOP WOO NOP PETS  LOT LOT LOT LOT CALL MPh RHO SIP  1,03 MAZE_SIN  ONINOOW, 000 0INP_RES,AR1 NIN_STZE,BK WIN_SIZE-2,RC FIR @NOBN,R0 RU R0,ThR3+f  ;result of FIR is in 00 norsnlize the filter output  This portion of the code creates the GLUT’ output syrbol. INPUTS: 0R3{location in an wher systol to be located), R3{sps), R4{new bit) OUTPUTS :003 1 location of next sysi) MAKE SIN: LOT ININOON, 000 LOT WTN_STZE-l,RC LOP 04,00 load in new value CALL STUFF  ******************************************************  OPTS SIP OPTS SIP OPTS SIP PETS  LOl ONINOOW, 000 LOP —1.0,00 initialize registers LOP -1.0,01 LOP -1.0,02 7510 1,05 LOIRE l.O,R0 7510 2,05 LOFNE 1.0,01 7510 4,05 LOIRE 1.0,02  INPUTS: R5{systol I 0-7) BUILD_WIN:  This portion of the code builds NRZ sequences  * ** ********** ******* * ** * * * * *** ** * *** **** I  LOP CALL HOP LOI CALL NOP ROOT GiPI 0HZ HOP BR  I-a  0 I-A  DONE RPTB *MUR1 WF RU,9R01-f II STY Rl,RU WF NETS  save the old value stuff in the new one  This portion of code is used to stuff a value at the first location of a vector and shift the older values down by one. INPUTS: ARO{vector pointer),RC{vector size), RU{new value)  MPYF3 *ARU++(l),*ARl4f(l)%,RU ;initialize RH WY O.U,R2 ;initialize R2 NETS RC ppy *ARU44(l),*APd4f(l)%,RQ II ADDFS RO,E2,R2 RO,R2,RO ADDF ;Add last prduct BETS  2, IN  OR  ;enable intrupt for tinerl  HNAVETABLE, Ml :set a pointer to the wavetable UVDATA,ARO U,R3 ;initialize RI for index U,R4 ;set the counter for sasples per aye OOffh,BK  LDI LU! LDI LDI LU!  Here we set up Tiserl control registers and period registers BEGIN_IRENS: CODES WP NTDIECTE,AR7 WI @RSTCTRLRI LDI E7,*AR7 STI @PETUOD,AR6 LDI @COUNI,R6 WI R6,*AR6 SI! USETC’rEi,Ri LDI RT,*AR7 SI!  This section clears sesory chunks specified by ARO -->AR1 CLEAR: SUB! R6,R7 WIN 1, Ri RN DEAD WI O,RO LDI R6,ARU RPTS R7 STI RU, ‘ARD++ NETS  DONE  STUFF  FIR  This portion of the code finds FIR of two vectors of length N. INPUTS : ARU{addrl),AR1{addr2),BK{N),RCIN-2), OUTPUTS: RO{result)  OR Z000b,ST  :aet the global intrupt GIN in ST  WP WI BNZ DIP! HZ  ONUBIP €SET LAG, Ri GETOUT if first sanple get new bit O,R4 NENBIT  Intrupt service routine Ri-new bit, Ri— wave table index AR1—pointer to wavetable R4—aps, these are global registers for ISR  BR DEAD  NENBIT:  GETOHI:  LDP ED! ED! WI  BET!  SUB!  ED! ED! DPI LDIEQ SI!  ;if end of systol get new bit  ;aend a pluse to the receiver once every sasple  UNCUIP : reset the sysbol counter SPS, R4 @TABLE,AR1 ;reset the table pointer @SERIALO,AR3  l,R4  PSERIALO,AR3 22H,R6 8,E4 62h,R6 R6,CAR3  TRANSMIT: LUF ARl++,Ri ;point to GLPF output sysbol t END Ri RND RI •**C*** PHASE ACCUMULATOR **C******** U,RS LUF LUF @PHASE,R6 : get preivious phase END R6 ;integrate ADDF R7,R6 END R6 END R6 (phase)ind 2pi operation LDFN @MO7LUE1,R5 01FF €MUD_VALUE1,R6 WFG’F €MOD VALUE2,R5 ADDF R5,R6 END R6 STY ;store the phase for next Use R6, €PBASE MUTT O.5,R6 FLOAT NL,R5 R5,R6 WIT FIX R6 R6,IR1 WI R6, €SYM_POINZR STE €COS_POINIER,AR6 WI WI )SINPOINTER,AR1 LU! +AR6(IR1),R6 t *+M7(Bl)R7 ED! ;output I sasple SI! RH, NAUCHANA :output 0 sasple R7,@ADCHANB SI!  ISR:  DEAD:  t’3  0  INDEX:  WI WIN ISO AND OR IDI HEllS LDF BR .end  BIT2_ENC:  INC_BIT:  WI STI WI AND WE  ØPREVBIT,R7 Ri Ri,Rl R1,@PREV BIT  :bk__ak*bk_i  differentaily encode the bit l,Rl is it ‘1’ -i,Ri :1.1 not i,Ri. if yesi @DIFENC,R7 Wit diff. encoding LR7 Ri,R1 ;if yes no encoding BIT2_ENC ;if yes do two bit enc INDEX ;index of the systol in 61ff output table  ;msk the bit to be transriitted bit is in Ri  ;output a pluse to the mden tester to get a bit  Ri,Ri ;convert to bit ‘0’ or ‘1’ 0001 :‘O’ if Ri was ‘-1’, unchanged otherwise i,R3 ;snke space for new bit Ofh,R3 ;use only 4 ISB5 of 003 Ri.R3 ;stuff in new bit 8,R7 R7,R3,IRO ;store the index in ThO *Mi++(IN0) ,Ri ;update the table pointer TRANSMIT  WI NEGI MPYI 571  75Th WIZ JIDIND WI 75Th WIND BZ BR  26b,R6 R6, t JJ3 *AN3R1 0800h,Rl -ll,Rl  Ia  ca  C  

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