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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 Systemsin the Presence of Adjacent ChannelInterference and NonlinearitiesbyJagdeep S. ToorB. A. Sc., The University of British Columbia, 1991A THESIS SUBMiTTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF ELECTRICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1994© Jagdeep S. Toor, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that pemiission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of-The University of British ColumbiaVancouver, CanadaDate 3 , JDE-6 (2/88)AbstractIn this thesis, the performance of differentially detected Gaussian Minimum ShiftKeying (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) performance of conventional and decision feedback 1— and 2—bit differential receiversin the presence of static and Rayleigh faded ACT. The obtained BER performanceevaluation results indicate that the decision feedback receivers outperform the conventional differential receivers. For the static ACT channel, it was found that the bestBER performance was achieved by the 2—bit decision feedback differential receivers.For example, at a BER= 1Cr3 and at a carrier-to-interference ratio C/IA, these receiversresulted in gains in excess of 6 dB as compared to the conventional 2—bit differentialreceivers. For Rayleigh faded ACT channels, the BER performance evaluation resultshave indicated that the decision feedback differential receivers provide gains in theform of error floor reduction.Secondly, we have investigated, again by means of computer simulations, theeffects on the BER of the cascade of an imperfect GMSK quadrature modulatorfollowed by a nonlinear amplifier. We have considered a generic model for theimperfect modulator and have adopted two different sets of operating conditions (onetypical 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 decisionfeedback differential receivers perform better than the conventional receivers for bothtypical and extreme values of the quadrature modulator errors as well as for bothnonlinearities considered. It is also found that for the system operation under extremeoperating conditions, the 1—bit decision feedback differential receiver outperforms allUother receivers considered in this thesis. For example, it offers a gain of 8 dB over2—bit decision feedback receiver at BER=103and C/IA=20 dB. However, for systemoperation under typical operating conditions 2—bit decision feedback receiver has thebest performance when compared to the other receivers considered in this thesis.Finally, in order to experimentally verify the effectiveness of the decision feedback differential receivers, we have designed, implemented and tested a prototypeGMSK system. Various experimental BER performance evaluation results are reported for receivers employing the 1—bit conventional and decision feedback differential detection and operated in the presence of static and Rayleigh faded ACT.The obtained experimental BER results are in agreement with equivalent computersimulated BER results.111Table of ContentsAbstract iiList of Tables viiList of Figures viiiAcknowledgments xiv1 Introduction 11.1 Continuous Phase Modulation (CPM) 11.2 Interferences in Mobile Communication Systems 31.3 Detection of GMSK Scheme 41.4 Research Objectives of the Thesis 51.5 Thesis Organization 52 BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channels 72.1 Introduction 72.2 Communication System Model Description 72.2.1 Transmitter 72.2.2 Adjacent Channel Interference Model 112.2.3 Receiver Structures 142.3 Computer Simulation Results and Discussion 182.4 Summary 35iv3 BER Performance Evaluation of Non-ideal GMSK SystemEmploying Decision Feedback Receivers in the Presence ofNonlinear Amplifiers 363.1 Introduction 363.2 Imperfect Quadrature Modulator (QM) Model . . . 373.3 Nonlinear Power Amplifier Model 413.4 Computer Simulation Results and Discussions . . 423.5 Summary 564 Design, Implementation, and Testing of a Prototype GMSKSystem 574.1 Introduction 574.2 Prototype GMSK System Model Description 574.3 GMSK Baseband Digital Synthesizer 594.4 Quadrature Modulator/Demodulator and Channel 654.5 DSP Based Decision-Feedback Receivers 674.6 Experimental Set-up and Measurements 704.7 SUMMARY 835 Conclusions and Some Suggestions for Future Research 845.1 Conclusions 845.2 Suggestions for Future Research 855.2.1 Generalization to other CPM Schemes 85V5.2.2 Simultaneous use of 1— and 2—bit Decision FeedbackDifferential Receivers 855.2.3 Extension to Multilevel CPM Schemes 855.2.4 Further Development of Prototype GMSK System . . 85References 86Appendix A Program Listings 92viList of Tables1 The phase (in degrees) 6k of 1 -bit and Vk of 2-bit differentialdetection of GMSK signal (BtT = 0.3) 162 The error floors for conventional (C) and decision-feedback (DF)receivers in faded ACI-AWGN channel 263 The parameters used in generating the GLPF 614 All possible values of phase delay a (in degrees) 69viiList of Figures1.1 The general block diagram of continuous phase modulation. . . . 12.1 Block diagram of a GMSK transmitter. DE = Differential Encoder,GLPF = Gaussian Low Pass Filter, FM = Frequency Modulator. . 72.2 (a) Pulse response of GLPF. (b) Power spectra of GMSKsignals 102.3 Block diagram of the channel model which includes ACI (static orfaded) and AWGN 122.4 Block diagram of fading signal, f(t), generator 132.5 Block diagram of (a) 1-bit conventional differential detector and (b)2-bit conventional differential detector 152.6 Phase-state diagram for (a) 1-bit and (b) 2-bit differentialdetection 172.7 The block diagram of (a) 1-bit decision feedback receiver and (b)2-bit decision feedback receiver 192.8 The level of C/IA (in dB) as a function of normalized channelspacing (Fm) 222.9 Computer generated spectrum of GMSK signal with two adjacentchannel interferers 232.10 Eye-diagram of (a) 2—bit conventional differential receiver and (b)2—bit decision feedback differential receiver at C/IA =15 dB withno AWGN present 24vifi2.11 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 15 dB in a staticACI-AWGN channel 272.12 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 20 dB in a staticACI-AWGN channel 282.13 Degradation in Eb/No at BER of 1O versus normalized channelspacing for 1-bit receivers in a static ACI-AWGN channel 292.14 Degradation in Eb/No at BER of 1O versus normalized channelspacing for 2-bit receivers in a static ACI-AWGN channel 302.15 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA — co in a Rayleigh—fadedchannel 312.16 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 20 dB in a Rayleigh—fadedchannel 322.17 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 30 dB in a Rayleigh—fadedchannel 332.18 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 40 dB in a Rayleigh—fadedchannel 34ix3.1 Model of an imperfect Quadrature Modulator 383.2 Computer generated phase state-space diagrams of non-idealGMSK signal in the presence of QM errors: (a) typical values and(b) extreme values 403.3 GMSK Transmitter employing an imperfect quadrature modulatorand a nonlinear power amplifier 413.4 Modelled characteristics of a Class A/B amplifier. (a) amplituderesponse (b) phase response 433.5 C/Ip ratio versus normalized channel spacing (Fm) for 1-bitreceivers. QM errors: (0d=10’ = 0.95, k = —24 dB) 463.6 C/lA ratio versus normalized channel spacing (Fm) for 2-bitreceivers. QM errors: (0d = = 0.95, k = -24dB) 473.7 C/l, ratio versus normalized channel spacing (Fm) for 1-bitreceivers. QM errors: (0d = 15°, i. = 0.65, k = -12dB) 483.8 C/lA ratio versus normalized channel spacing (Fm) for 2-bitreceivers. QM errors: (0d = 15°, i = 0.65, k = -12dB) 493.9 The BER performance of non-ideal GMSK system with conventional(C) and decision feedback (DF) receivers at C/IA = 15 dB in staticACI-AWGN channel. QM errors: (0d = 150, z = 0.65, k = -12dB). . 503.10 The BER performance of non-ideal GMSK system with conventional(C) and decision feedback (DF) receivers at C/IA = 20 dB in staticACI-AWGN channel. QM errors: (0d = 15°, /. = 0.65, k = -12dB). . 51x3.11 Degradation of Eb/NO to achieve a BER of 10 versusnormalized channel spacing for 1-bit conventional (C) anddecision feedback (DF) receivers in static ACI-AWGN channel.QM errors: (0d=10’ i. = 0.95, k = -24dB) 523.12 Degradation of Eb/No to achieve a BER of 10 versusnormalized channel spacing for 2-bit conventional (C) anddecision feedback (DF) receivers in static ACI-AWGN channel.QM errors: (8d = °, = 0.95, k = -24dB) 533.13 Degradation of Eb/NO to achieve a BER of 1O versusnormalized channel spacing for 1-bit conventional (C) anddecision feedback (DF) receivers in static ACI-AWGN channel.QM errors: (0d = 15°, z = 0.65, k = -12dB) 543.14 Degradation of Eb/NO to achieve a BER of 10 versusnormalized channel spacing for 2-bit conventional (C) anddecision feedback (DF) receivers in static ACI-AWGN channel.QM errors: (0d = 15°, t = 0.65, k = -12dB) 554.1 Block diagram of the implemented prototype GMSK system. . . 584.2 Flow chart for the implementation of the baseband transmissionalgorithm 604.3 Impulse response of the GLPF with BtT = 0.3 624.4 Illustration of how a output symbol of GLPF is generated 634.5 Functional block diagram of the implemented GMSK transmitter. 64xi4.6 Modulator, Demodulator and Channel Simulator 664.7 The block diagram of the ACI generation system 674.8 Functional block diagram of the DSP-based digital receiver.. .. 684.9 The block diagram of a one-bit all digital decision feedbackreceivers 694.10 Block diagram of the experimental set-up 704.11 I-channel eye-diagram at modulator input. Horizontal Axis: 0.1msec/div, Vertical Axis: 1 V/div 714.12 The phase state-space diagram of the modulated GMSK signal.Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div 714.13 The phase state-space diagram of the demodulated GMSK signal.Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div 724.14 The spectrum of the GMSK signal at modulator output. HorizontalAxis: 2 kHz/div, Vertical Axis: 10 dB/div, Center frequency = 1.5MHz 734.15 The spectrum of the GMSK signal at demodulator input.Horizontal Axis: 5 kHz/div, Vertical Axis: 10 dB/div, Centerfrequency = 1.5 MHz 734.16 The spectrum of the desired signal along with two adjacentchannel interferers at channel spacing of 7.8 kHz. Horizontal Axis:5 kHz/div, Vertical Axis: 10 dB/div, Center frequency = 1.5 MHz. . 74xli4.17 The spectrum of the GMSK signal in AWGN channel. HorizontalAxis: 5 kHzldiv, Vertical Axis: 10 dB/div, Center frequency = 1.5MHz 754.18 The signal phase state-space at demodulator output after addingAWGN. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div 754.19 The BER performance of 1—bit decision feedback (DF) differentialreceiver in AWGN channel 774.20 The BER performance of 1—bit conventional (C) differentialreceiver in AWGN channel 784.21 The BER performance of the 1-bit decision feedback receiver inRayleigh faded AWGN channel 794.22 The BER performance of the 1-bit conventional differentialreceiver in a Rayleigh faded AWGN channel 804.23 The BER performance of the 1-bit decision feedback (DF) andconventional (C) receivers in static ACI-AWGN channel at C/IA =10dB 814.24 The BER performance of the 1-bit decision feedback (DF) andconventional (C) receivers in static ACI-AWGN channel at C/IA =14dB 82Xi”AcknowledgmentsThis thesis is dedicated to my sister, Gindu, whose support is beyond anyone’simagination. I am indebted to my parents and my other sisters for their patience andmoral support. I am enormously greateful to my supervisor, Dr. P. Takis Mathiopoulos, for his support and continual guidance. Without his constant encouragement andvaluable suggestions, the completion of this thesis would not have been possible. Iwould like to thank my fellow student, Dimitrios P. Bouras, for his help with thelab equipment.xivChapter 1 Introduction1.1 Continuous Phase Modulation (CPM)Continuous Phase Modulation (CPM) represents a large class of modulated signalswhich 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 fromthe alphabet {±1, ±3, ..., ±(M-1)} where M is normally a power of 2 [2]. The premodulation filter is a low pass filter that bandlimits the input bit stream. The outputof the pre-modulation filter, x(t), is modulated using a frequency modulator (FM) andthe resulting CPM signal, s(t), can be expressed asand.s(t) = A0 cos [2irft + q(t)](t) = 2h f x(r)dr-00(1.1)(1.2)where A0 is the amplitude and h is the modulation index. It is clear from the aboveequation that the phase of a CPM signal is continuous in time and the envelope, A0,of the signal is constant. It is this property of the CPM signal that makes the CPMFigure 1.1 The general block diagram of continuous phase modulation.a,,2ith1Chapter 1. Introductionscheme a spectrally and power efficient modulation scheme. In general, the powerspectrum of the constant envelope signals is more compact than the power spectrumof the signals with non-constant envelope [3, 4]. In addition, the constant envelopesignals are less sensitive to amplifier nonlinearities, which allows the use of highlynonlinear amplifiers that are more power efficient than the linear amplifiers [3]. Onthe other hand, non-constant envelope signals suffer the spectral sidelobes regrowthand spreading due to amplifier nonlinearities, which in general degrades the bit errorrate (BER) performance [5, 6]. By choosing different pre-modulation filters and byvarying parameters h and M, a great variety of CPM schemes can be obtained. Forbinary communication systems, i.e., M=2, it is often assumed that h = 1/2 [2]. Thereare several premodulation filters which have been considered in the past which resultin 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 CPMscheme for mobile communication systems. More importantly, GMSK has beenadopted as the transmission standard for various wireless communication systems,including the Groupe Speciale Mobile (GSM), the Pan-European digital cellularnetwork [12], and Digital European Cordless Telecommunications (DECT) [13]. Inthis thesis, we will be dealing with exclusively the GMSK modulation scheme andits application to mobile communication.2Chapter 1. Introduction1.2 Interferences in Mobile Communication SystemsThere 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 CCIhave 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 thename implies, ACI is generated by interfering channels which are located adjacent,in frequency domain, to the information channel. In cellular systems, because ofthe frequency reuse structure of the communication system, ACT is less problematicinterference as compared to CCI. However, it still represents a non-negligible sourceof interference [21]. For other, noncellular type communication systems, ACI isperhaps a more important source of interference. This is especially true in bandwidthefficient frequency division multiple access (FDMA) communication systems in whichchannel spaceing is important to improve system capacity[22].Another type of distortion that sometimes is overlooked in constant envelopeschemes is the nonlinear distortion. Such distortion is typically due to the presenceof a nonlinear amplifier [23]. For an ideal constant envelope scheme nonlinearamplifications has little effects on the overall spectrum and system performance.However, when a non-ideally generated CPM signal, such as non-ideal GMSK, whichis not a constant envelope signal any more, is passed through a nonlinear amplifierspectral spreading occurs and the signal phase is distorted [24].3Chapter 1. Introduction1.3 Detection of GMSK SchemeGMSK signals can be detected by either coherent (see for example [11]), differential detection (see for example [25, 26]), or a limiter/discriminator detection(see for example [27]). Although in AWGN channel, coherent detection has thebest performance, in interference channels that is not necessarily true. In fact, inmobile communication channels, coherent detection suffers considerably because ofincreased acquisition time and poor performance including high error floors [28]. Onthe other hand, non-coherent detection schemes, as they do not require carrier recovery, have, in general, simpler receiver structures and exhibit lower error floors.One very promising non-coherent detection technique based upon the use of differential detectors with decision feedback has been proposed and evaluated in [29] forGMSK signals transmitted over an AWGN channel. The technique is based uponthe concept of employing a decision mechanism to significantly reduce the effect ofthe inherent intersymbol interference (ISI) associated with the differential detectionof GMSK signals. A generalization of this technique to include any CPM type ofsignal can be found in [30]. In a recent publication [31], the decision feedback differential receivers have been evaluated in the presence of static and faded CCI. Theobtained performance evaluations results have indicated that as compared to conventional differential receivers significant performance improvements in CCI channelsare possible. It is with these types of decision feedback differential receivers thatthe thesis is dealing with.4Chapter 1. Introduction1.4 Research Objectives of the ThesisMotivated by the above, this thesis deals with differentially detected GMSKsystems operating in the presence of ACT, AWGN and nonlinearities. Its researchobjectives are three-fold.1. To evaluate, by means of computer simulations, the BER perfonnance of 1— and2—bit conventional and decision feedback differential receivers for GMSK signalstransmitted over ACT and AWGN channels.2. To investigate the effects on the BER performance of the cascade of an imperfectGMSK modulator followed by a nonlinear amplifier.3. To design and implement a prototype GMSK system and evaluate its BERperformance in the presence of ACT and AWGN.1.5 Thesis OrganizationIncluding this introductory chapter, this thesis consists of five chapters and oneappendix. Its organization is as follows:Chapter 2 deals with the first objective of the thesis. It starts with an introductionin Section 2.1. Afterwards, a detailed description of the communication systemmodel under consideration is presented in Section 2.2. Computer simulationresults and discussions can be found in Section 2.3. The chapter is concludedwith a summary in Section 2.4.Chapter 3 covers the second objective of the thesis. A brief introduction ispresented in Section 3.1. Non-ideal GMSK modulator model is detailed in Section5Chapter 1. Introduction3.2, 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 summaryof the chapter appears in Section 3.5.Chapter 4 is concerned with thesis’ third objective. Again, the chapter startswith an introduction in Section 4.1 followed by an overview of the prototypeGMSK system in Section 4.2. A detailed description of the GMSK basebanddigital synthesizer is given in Section 4.3. The RE modulator/demodulator andthe channel are described in Section 4.4. Section 4.5 presents details of the DSP-based implementation of the decision feedback detector. The experimental set-upmeasurements and results are presented in Section 4.6 followed by a summaryof the chapter in Section 4.7.Chapter 5 presents conclusions of the thesis and some suggestions for futureresearch.Appendix A contains program listings for the implemented GMSK digital baseband synthesizer, the 1—bit conventional differential detector, the 1—bit decisionfeedback differential detector and the ACI generator.6Chapter 2 BER Performance Evaluationof GMSK Systems EmployingDecision Feedback Receivers inACI-AWGN Channels2.1 IntroductionThe subject of this chapter is the BER performance evaluation of 1— and 2—bitconventional and decision feedback receivers structures for GMSK systems operatedin 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 resultsare presented and discussed in Section 2.3 followed by a summary of the chapterin Section 2.4.2.2 Communication System Model Description2.2.1 TransmitterThe block diagram of the GMSK transmitter is shown in Fig. 2.1. The GMSKFigure 2.1 Block diagram of a GMSK transmitter. DE = DifferentialEncoder, GLPF = Gaussian Low Pass Filter, FM = Frequency Modulator.transmitter consists of a differential encoder (DE), a Gaussian Low Pass Filter (GLPF),2ith7Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsand a frequency modulator (FM). The differential encoding operation is required forthe 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]. Theinput of the differential encoder, ak, is the non-return-to-zero (NRZ) information bitstaken from the alphabet {± 1}. The information bits, aj, are equally probable andindependent and each has a duration of T seconds. As mentioned, for 1—bit differentialdetector a differential encoder is not needed, hence bk = c. For the 2—bit differentialdetection, the output of the differential encoder is given by [32]= —akbk..4. (2.1)The GLPF, which has a frequency transfer function of HT(f), is used to bandlimtthe input binary NRZ data waveform. The resulting signal x(t) can be written asx(t)=bg(t— kT) (2.2)withg(t) = hT(t) * p(t) (2.3)where * denotes a convolution, p(t) is a rectangular pulse of duration T and unityamplitude, and hy(t) is the impulse response of the GLPF, i.e., the inverse Fouriertransform of H7-(J). As well known, [25]hT(t) = =kiBtexp[—(kiBttYJ (2.4)where k1 5.336 and B is the 3-dB bandwidth of the GLPF. As shownin Fig. 2.1, at the output of the FM, the transmitted GMSK signal is s(t) and it can8Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsbe mathematically expressed ass(t) = A0 cos [2irft + (t)] (2.5)where A0 is a constant amplitude (which without any loss of generality will beassumed 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 whichis normalized so that f g(t)dt = . [2]. As customary, we will consider that h = 1/2so that the maximum phase change over one symbol duration, T, is ir/2. Furthermoreg(t) is given by [2]g(t) = {Q[k2BtT(_.—— Q[k2BtT(. )] } (2.7)where k2 = 7.547, B,T is the normalized (to symbol duration) 3-dBbandwidth of GLPF and 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 signalswith BT as a parameter are illustrated in Fig. 2.2. As it can be seen from thisfigure and is well known, the performance of GMSK system is very sensitive tothe BT product of the GLPF. For our purpose in this thesis we have consideredthe specification of the Groupe Special Mobile (GSM), the Pan-European cellularnetwork, system where a B1T = 0.3 has been adopted [34].9Chapter 2. BER Pe,fonnance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Chwinth(MSK)_____ B,T 0.5g(t)/2T___— B,T 0.30.25B,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]10Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI.AWGN Channels2.2.2 Adjacent Channel Interference ModelAssuming that the mt interfering signal, im(t), is of the same modulation formatas the useful GMSK signal, s(t) (see Eq. 2.5), then it can be represented asim(t) = B0 COS [2ir(fc + fm)t + Om + cfm(t)]. (2.9)In the above equation, B0 is the constant amplitude of the interferer,fm is the differencein the frequency allocation of the two carriers, 9m denotes the lack of carrier phasecoherence between s(t) and im(t) and is assumed to be uniformly distributed over (0,2r]. Furthermore, 4m(t) is given bym(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 uniformlydistributed over the time interval [0, 1).In general, there are two adjacent channel interferers which contribute mostsignificantly to the degradation in performance of digital communication systems.Both of them are located adjacent (in frequency domain) to the channel throughwhich the information signal is transmitted [35]. Based upon this, in this thesis wehave 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 beassumed that both interferers are symmetrically (in frequency domain) located around11Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in Ad-AWON Channelsthe carrier frequency f of the information signal channel. In this respect, the carrierfrequency of the i(t) is f + fm, whereas the carrier frequency of the ij(t) is f - fm.LowerInterferer (LI)Figure 2.3 Block diagram of the channel model which includes ACI (static or faded) and AWGN.f(t)i(t)i(t)UpperInterferer (UI)s(t)InformationSignal (IS)r(t)i,(t)n(t)Switchselection(1 or2)12Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsFurthermore, and as illustrated in Fig. 2.3, we will consider the case where allthree signals (i.e., i(t), s(t) and ij(t)) could be faded. A block diagram of how thefading 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 filtershaving the same transfer function HF(J). The complex summation of the outputs ofthe fading filters is modulated by f1 to generate the fading signal. In the channelmodel under consideration, f1 is f, fc+fm orfc—fm. The transfer function of the fadingfilters, HF(f), determines the type of fading, e.g. rectangular [37], Gaussian [38] andland-mobile [14]. In this thesis, land mobile model is considered. The fading filtertransfer function of this model is given by [14]1 for 0 Ifi fDHF(f) = (2.11)1 0 elsewhereand the corresponding autocorrelation function byRf(r) =J0(2lrfDr). (2.12)n/i)eflQ(t) eJ(’t)Figure 2.4 Block diagram of fading signal, fit), generator.13Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsIn the above equations, J0 is the zero order Bessel function of the first kind andfD isthe fading bandwidth (or maximum Doppler frequency) given byfD— (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 Gaussiannoise, n(t), in our channel model. n(t) is white in the sense that it has a constantdouble-sided power spectral density of NJ2.2.2.3 Receiver StructuresAs it was mentioned in Chapter 1, this thesis will be investigating the performanceof noncoherent GMSK receivers employing 1— and 2—bit differential detectors. Wewill be referring to these receivers as “conventional receivers”. It will be explainedlater on in this section that by employing decision feedback to these conventionalreceivers, significant performance improvements are possible. We will be referring tothese proposed receivers as “decision feedback receivers”. For both sets of receiversthe received signal r(t) must be first filtered by a detection receive filter, HRQ9, whichis typically a 4th order bandpass Butterworth filter [29, 31]. For such a filter it canbe easily found that the resulting SNR is given by [31]F 2(tSNR— 214N0c rTwhere Eb is the transmitted bit energy, Br is a double-sided 3—dB bandwidth of the4th-order Butterworth filter, c 1.026 and a(t) is the normalized signal amplitude14Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsafter 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 conventionalreceivers are shown in Fig. 2.5 (a) and (b), respectively. The signal r(t) presentat the input of the receive filter consists of four components,— f s(t) + iuçt) + ii(t) + n(t) (without fading) 2 16r— sf(t) + i(t) + i((t) + n(t) (with fading). )As well known [25], for the 1-bit differential detector, the output of the receive filteris multiplied by its own version that is delayed by a symbol time, T, and phase shiftedby 900. In the 2-bit differential detector, the output of the receive filter is multipliedd,(t) d1(kT) A_ar(t)kT(a)r(t)d.c. bias(b)Figure 2.5 Block diagram of (a) 1-bit conventional differentialdetector and (b) 2-bit conventional differential detector.15Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsby its version that is delayed by 2T. Without including the effects of interference andnoise, d1(kT) and d2(kT) can be expressed as follows [29]:d1(kT) sin (‘6k), (2.17)d2(kT) = cos (/.Wk) (2.18)whereLS.6k = (2.19)= (2.20)with°k-j = J g(r — jT)dT, (2.21)kT-TVk_f = f g(r — jT)dr. (2.22)kT-2TThe values of °k.j and Vk..J for BT = 0.3 are tabulated in Table 1. In this Table, 6, V0,and V1 represent the signal and all other terms represent the intersymbol interference(1ST) caused by pulse shaping [29]. From Table 1 and using Eqs. 2.19 and 2.20,the phase states, 0k and zVk for B1T = 0.3 are calculated and plotted in Fig. 2.6.&2 S-i 6 °i 02 630.2 15.9 57.8 15.9 0.2 —V_2 Vi V0 Vi V2 V30.2 16.2 73.6 73.6 16.2 0.2Table 1 The phase (in degrees) 0k of 1-bit and Vk of 2-bit differential detection of GMSK signal (BET = 0.3)16Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsThe phase states are all possible changes in phase over one symbol interval for 1—bitreceiver 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 thisPhase States: AOk89.6•-.57.8‘,26.0decisionthreshold.-26.04•—- -57.8-89.6Phase States: AVk114.8-/147.2w-147.2-114.8decisionthreshold\ 32.41T0,‘ -32.4(a)Before Decision FeedbackAfter Decision Feedback(b)Figure 2.6 Phase-state diagram for (a) 1-bit and (b) 2-bit differential detection.Phase States:73.7decisiondecisionPhase States: AVw threshold/_147.2/-147.2\ 32.4.-threshold/ -41.9-73.7To,.:32.4/17Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI.AWGN Channelsscheme works is that it introduces a phase delay, we will call it the feedback phase, inthe signal delay branch of the conventional receivers. This feedback phase is relatedto the 1ST. The feedback phases for 1—bit and 2—bit receivers are given, respectively,as [29]0 = bk_18i + bk_262 (2.23)2bkV + 2bk_3V3 if bk_3 and bk_14bk_2= 2b_V if bk_1= bk_3 and bk_1 bk_2 2 242bk_3V3 if bk_1 bk_3 and bk_1= bk_20 if bk1= bk....3 and bk_1= bk....2The block diagram of the 1-bit and 2-bit decision feedback receivers are shown inFig. 2.7 (a) and (b), respectively. After applying the decision feedback, the resultingphase states, which will be referred to as Mk and IVkDF, are calculated usingEqs. (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 awayafter applying the decision feedback. This results in a greater eye opening and BERimprovements are expected. It is also noticeable that no dc bias is required for 2-bitdetector when decision feedback is applied.2.3 Computer Simulation Results and DiscussionThe communication system described in the previous section have been realizedby means of computer simulations using the BloSim software [39]. In particular,we have simulated and evaluated the performance of both conventional and decisionfeedback GMSK systems operated in the presence of static and faded ACI-AWGNchannels. Monte Carlo error counting techniques were employed to obtain the various18Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsAa5(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 levelsto achieve confidence interval of at least 90% for all simulation results [40]. Aspreviously 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 digitalcellular network. The BrT product of the receive filter, HR(f), was chosen to be equalto 0.97 for all the receivers employing 1—bit differential detectors and 0.85 for all thereceivers employing 2—bit differential detectors. The reason for these choices wasthat it was found through computer simulations that these values are near-optimal atBER=103 in an AWGN channel.As discussed in Section 2.2.2, we have simulated two adjacent channel interferers,r(t)(a)19Chapter 2. BER Performance Evaluadon of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsone on each side of the desired channel. It was assumed that both of these interfererswere also GMSK signals with B1T = 0.3 and having the same power as the desiredsignal. According to Eq. 2.9, for the interfering signals, their carrier phase (6m)and timing (Tm) have been randomized. However, it is worthwhile to note that themost important parameter influencing the BER performance is the overall interferencepower, which greatly depends on the channel spacing, and the actual power of theinterfering signals (but not °m or Tm).In general, the carrier-to-adjacent-interference ratio (C/IA) is defined as the ratiobetween the average power of the desired information signal (PDJS) and average powerof the adjacent interfering signals (PAlS), both measured at the output of HR(f). Usingthe decibel as a convenient means of comparing performance we thus haveC/IA (dB) = 10 log10 PDIS (dB). (2.25)PAlSAs we have considered that the power of both interferers is same as the desiredsignal and, for a given B1T, C/IA will be controlled by changing the channel spacingfrequency fm. It is convenient to introduce the parameter, Fm, which will be referredto as normalized (to the rate of transmission) channel spacing, asFm = fmT (Hz/bits/sec). (2.26)Equivalently, Fm refers to the channel spacing in Hz at a bit rate of 1 bitJsec. Itis also clear that the smaller Fm becomes, i.e., the more closer the adjacent channelinterferers are to the main channel, higher C/IA is introduced.20Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsBy means of computer simulation, we have calculated the amount of C/IA whichis 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 runningaverage of square of the signal samples. For example, the average power of thedesired signal would bePDS = (s[n]) (2.27)where s[n] are the samples of the desired signal and N is the size of running averagewindow. The obtained results for C/IA versus Fm are illustrated in Fig. 2.8. We notethat the results are different for 1— and 2—bit receivers. This is solely due to the factthat the BrT of two types of receivers are different. It should also be mentioned thatthe C/IA ratio is independent of the operating SNR and fading.A typical spectrum, generated by means of computer simulation and whichincludes two adjacent channel interferers with Fm = 1.5 and the desired signal, isillustrated 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 isevaluated in both static and faded ACI-AWGN channels. Figs. 2.11 and 2.12 illustratethe obtained BER performance evaluation results of the decision feedback receiversfor static ACI at C/IA = 15 dB and 20 dB, respectively. In the same figures, theperformance of conventional 1-bit and 2-bit differential receivers, operated in thesame environment, is also given for comparison. It is clear from these results that21Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsthe decision feedback differential receivers outperform the conventional differentialreceivers. For example, as can be seen from Fig. 2.11, the 2-bit decision feedbackdifferential receiver results in a gain of more than 6 dB as compared to the 2-bitconventional differential detector at BER of iO. The gain of 1-bit decision feedbackdifferential receiver over the 1-bit conventional differential detector is more than 1125201000.5Normalized Channel Spaceing (ii,) (Hz/bitlsec)Figure 2.8 The level of 074 (in dB) as a function of normalized channel spacing (Fm).555045403530155-51 1.5 222Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsdB at BER of 1 O. The computer simulated eye-diagrams given in Fig. 2.10 alsogive a clear explanation of why improvements in performance take place. The eyeopening for the 2—bit decision feedback differential receiver is significantly biggerthan the one for the 2—bit conventional differential receiver.By reducing Fm, the equivalent C/IA decreases, i.e., the ACI increases. However,—10—20I —30—40—50—60fT (HzJbits/sec)Figure 2.9 Computer generated spectrum of GMSK signal with two adjacent channel interferers.23Chapter 2. BER Performance Evaluation of GMSK System$ EmployingDecision Feedback Receivers in ACI-AWGN Channelsat the same time, we have an increase in the spectral efficiency. Similar to [41], we0 2 4 6 8 10 12 14 160 2 4 6 8 10 12 14 16(a)—-— ———-—--.—- ——- -- -—--.—-.--- --- — -— -r - --.----.---- ----.. —. - -.—.-— -...-(b)Figure 2.10 Eye-diagram of (a) 2—bit conventional differential receiver and (b) 2—bitdecision feedback differential receiver at C/IA =15 dB with no AWON present.24Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channelsdefine 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 equivalentC/IA. This correspondence depends upon the choice ofB1Tand the type and bandwidthof the receive filter HR(fl.By means of computer simulation, we have evaluated the degradation (in dB) ofthe E1JN0 (at BER = l0) as a function of Fm for the 1—bit and 2—bit differentialconventional and decision feedback GMSK receivers. The degradation, for allreceivers, is measured with respect to the Lb/N0 that is required by 2—bit decisionfeedback differential receiver to achieve BER = i03. The obtained results aresummarized in Figs. 2.13 and 2.14. In both of these figures, one more horizontal axisis included which represent the equivalent . The performance results for both 1—bitand 2—bit differential receivers indicate, as expected, that for every value of Fm, thedecision feedback receivers outperform the conventional ones. It was also found thatthe performance of the 2—bit decision feedback differential receivers is always betterthan 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 introducedby the ACI is small. For these values of Fm, the corresponding values of C/IA areabout 20 dB. Equivalently, by reducing the Fm to 1.0 one can achieve an overallspectral efficiency of 1 bit/sec/Hz.25Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWON ChannelsFigs. 2.15 — 2.18 illustrate the BER performance of the proposed receivers ina 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 andconventional 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 resultshave been also reported in [27, 26, 42, 43]. Furthermore, the decision feedbackreceivers offer reduction in the error floors. This is also true in the presence of fadedACI-AWGN environment, as can be seen in Figs. 2.16 through 2.18. The error floorsat various C/IA levels and maximum normalized Doppler frequencies (JDT) has beentabulated in Table 2.RECEIVER TYPEfDT CII(dB)1-bit C 1-bit DF 2-bit C 2-bit DF0.03 20 0.02 0.013 0.061 0.0350.003 20 0.0095 0.0085 0.027 0.0750.03 30 0.0 13 0.008 0.055 0.030.003 30 0.0019 0.0014 0.004 0.00140.03 40 0.011 0.0075 0.05 0.030.003 40 0.00028 0.002 0.0011 0.0003Table 2 The error floors for conventional (C) and decision-feedback (DF) receivers in faded ACI-AWGN channel.26-411IIt’)_-,kJC’) H. h h0BitError RateProbabilityI--.-.ICCCCCBitErrorRateProbabilityT1c vt’) p00U U. —C.0000S. ‘1Chapter 2. BER Performance Evaluation of GMSK Systems Employing.5)Decision Feedback Receivers in ACI-AWGN Channels2015105NormalizedChannelSpacing (F 0(Hz/bit/see) 0.5SpectralEfficiency (TI) I(bits/sec/Hz) 2 1 0.67Figure 2.13 Degradation in Eb/No at BER of iO versus normalizedchannel spacing for 1-bit receivers in a static ACI-AWGN channel.1 1.5 20.529Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsSpectralEfficiency (Ti)(bits/sec/Hz) 2Figure 2.14 Degradation in Eb/No at BER of 1O versus normalizedchannel spacing for 2-bit receivers in a static ACI-AWGN channel.1 0.67 0.530tx, h 1% C)w-IoCi I.’BitErrorRateProbabilityK0Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsEb/No [cm]Figure 2.16 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 20 dB in a Rayleigh—faded channel.i2010—110-210.310.4100jEEEEEEEEEEEi:E:EEEE—-__-——---——--—%—I.•..‘4%:+:‘------ --A- -% A —z : : : : : ::: :: : : : : ::::: ::: ::: ::: :::: : =:2-bit DF A2-bitC I -—: 1-bitDF ——--A——-— : : = = = = = I = = I = =:: 1-bitC----+---- ::: :: ::: ::: —__ii.ui.ii. -—f T=O.003fDT= 0.0310 20 30 40 50 6032Chapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN ChannelsEb/No [dB]60Figure 2.17 The BER performance of GMSK system with conventional anddecision-feedback receivers at C/IA = 30 dB in a Rayleigh—faded channel.010100 10 20 30 40 5033IIGo p n II — IC) ILIBitErrorRateProbability— o— CCC C t) C 00IC 0 CChapter 2. BER Performance Evaluation of GMSK Systems EmployingDecision Feedback Receivers in ACI-AWGN Channels2.4 SummaryBy means of computer simulations, the performance of 1-bit and 2-bit decisionfeedback and conventional differential receivers has been evaluated for GMSK signaltransmitted over static and faded ACI-AWGN channels. The obtained results indicatethat the decision feedback receivers perform better than the conventional differentialreceivers. The BER improvements are more significant for the static ACI-AWGNchannel. For the faded ACI-AWGN channel, reductions in error floors have beenobserved.35Chapter 3 BER Performance Evaluation ofNon-ideal GMSK System EmployingDecision Feedback Receivers in thePresence of Nonlinear Amplifiers3.1 IntroductionIn this chapter the performance of conventional and decision feedback 1— and2—bit differential detector receivers is evaluated when a non-ideal GMSK signal ispassed through nonlinear power amplifier. The non-ideal GMSK signal is a resultmodulator deficiencies. As mentioned previously, it was shown in [24] that thedeficiencies in a modulator will produce envelope variations and phase distortion in theGMSK signal. It was also shown in [24] that, when the imperfect GMSK modulatoris cascaded with a nonlinear RF amplifier, spectral spreading and in-band distortionwill occur. However, the BER performance of the decision feedback differentialreceivers 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 quadraturemodulator is described in Section 3.2. Two nonlinear amplifier models are describedin Section 3.3. In Section 3.4, BER computer simulation results are presented anddiscussed followed by a summary of the chapter in Section 3.5.36Chapter 3. BER Performance Evaluation of Non-ideoj GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiers3.2 Imperfect Quadrature Modulator (QM) ModelAmong the various methods for generating GMSK signals, such as phase-lockedloops [11], direct digital synthesis [44], and quadrature modulator (QM) [1], theQM approach seems to be the most flexible and preferred method [1]. With theQM method, there are two signals generated digitally in baseband which are usuallyreferred to as I- and Q-channel. These signals carry the phase information of theGMSK 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 theappropriate RF carrier frequency. Mathematically, it is very easy to show that aGMSK signal can be represented by a QM signal. From Eq. 2.5, s(t) can berewritten as ( assuming A4, = 1)s(t) = i(t) cos 27rft — q(t) sin 2irft(3.1)wherei(t) = cos 4(t)(3.2)q(t) = sin qf(t).Using complex envelope notation [45], the complex envelope of the GMSK signal isb(t) = i(t) + jq(t). (3.3)Clearly, the magnitude of b(t) isIb(t)I = V/j2(t) +q2(t) = 1, (3.4)as it is expected from a constant envelope scheme.37Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence ofNonlinear AmplifiersTheoretically, a QM does not introduce any signal distortion to the GMSKsignal. However, in practice, non-ideal components (for example local oscillators)in the QM will result in signal distortions, including signal imbalances and offsetsbetween the I- and Q-channels. In the past, such distortions occurring in QM havereceived attention for several applications, including radar signal processing [46]and digital communication systems [47]. In a more recent paper [24], the effectsof 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 thechannels, (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 ass’(t) = [k + Li(t — rd)] cos (2irft) — q(t) sin (27rft) (3.5)where Td is the differential time delay which is related to the differential phase errorki(t)cos(2içtt)q(t)Figure 3.1 Model of an imperfect Quadrature Modulator.38Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiersas [24]= 1rT (3.6)Using Eqn. 3.4, the complex envelope of s’(t), b’(t), is given asb’(t) = k + I. cos q(t — Td) + j sin 4(t). (3.7)Furthermore, s’(t) can be represented ass’(t) = Re{bl(t)e32t}(3.8)= Re{ b’(t) ej’(t) efBt }where Re{’} represents real part of {‘}, I • I represents absolute value of•. Ib’(t)Iand qV(t) are given byIb’(t)I v’{k + cos(t — rd)]2 + sin2 (t)} (3.9)cii’(t) = tan1[k + zScosqf(t — Td)] (3.10)Finally, from Eq. 3.8, the imperfectly generated GMSK signal can be expressed ass’(t) ={[k + cosç(t — rd)]2 + sin2—1 1 sin4(t) . )cos 2irft+tank+zcoscS(t—rd)It is evident from the above equation that the phase of the GMSK signal is distortedand the envelope is no longer constant. Clearly, for k = 0, z = 1, and rd = 0, s’(t)becomes the ideal GMSK signal s(t) (see Eq. 2.5).For the purpose of this thesis, we have considered two sets of values for modellingthe imperfections of the QM. Following [24], for the first set, which will be referred39Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiersto as “typical values”, °d = l, L = 0.95, k = —24 cIB. For the second set, which isreferred to as “extreme values”, 9d = 15°, = 0.65, k = -12dB. As illustrated bythe phase state-space diagrams in Fig. 3.2, the distortion which is introduced to thetransmitted GMSK signal by the extreme values is much more prominent comparedto the distortion caused by the typical values.—0.2 0 0.2 0.4 0.6 0.8(b)Figure 3.2 Computer generated phase state-space diagrams of non-ideal GMSKsignal in the presence of QM errors: (a) typical values and (b) extreme values.1.5—1 —0.5 0 0.5(a)—0.4 140Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiers3.3 Nonlinear Power Amplifier ModelThe block diagram of the complex baseband equivalent of the GMSK transmitter,which employes the imperfect QM described in the previous section as well as anonlinear 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 envelopeso that the input to the nonlinear PA is b’(t). Therefore, the model of the nonlinear PAmust operate on the samples of b’(t). Volterra series representation of nonlinearitiesis one such technique that is commonly used to model nonlinear PA for computersimulations [48]. This model is very simple to implement and requires very fewnumerical computations to be realized. As derived in [49], for a complex envelopeinput, b”(t), the output of the fifth order Volterra series model can be expressed asb”(t) = b’(t)(G1+G31b’(t)12+G51b’(t)14) (3.12)where G1, G3 and G5 are constant complex coefficients. However, relationship is onlyvalid 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 G1, G3 and G5 are determined by amplitude-to-amplitude modulation (AM-AM) and amplitude-to-phase modulation (AM-PM) responses of the nonlinear PA. Among the various values for the coeffiFigure 3.3 GMSK Transmitter employing an imperfect quadrature modulator and a nonlinear power amplifier.41Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifierscients of Eq. 3.12, as in [47], we have selected G1 = 1, G2 = O.0479L —2.816 rad and (73= O.00102L0.39 rad. The AM-AM and AM-PM characteristicsof this model are calculated and plotted in Fig. 3.4. Typically these AM-AM andAM-PM characteristics represent a class A/B amplifier. It should be pointed outthat a class A/B amplifier is considered as a “mildly nonlinear”. This is because, asillustrated in Fig. 3.4 (a), its amplitude response is not very nonlinear. Perhaps themost nonlinear PA amplitude response is that of a hardlimiter (HL). Mathematically,the output of the HL is given by1/’(t)=(3.13)The HL has been used in the past for simulating the effects of an extremely highlynonlinear amplifier, for example for satellite communication systems [41]. In thisthesis, both amplifier models will be considered.3.4 Computer Simulation Results and DiscussionsIn this section, computer simulation BER performance results of a 1—bit and2—bit conventional differential receivers and decision feedback differential receiversare presented. As in Chapter 2, the BTproduct of the GLPF is 0.3 and the modulationindex, h, is 0.5. The forth order Butterworth filter is used as a receive filter and itsBrT product is equal to 0.97 and 0.85 for all receivers employing 1-bit and 2-bitdifferential detection respectively. The channel model used in the simulations isACI-AWGN which is described in Chapter 2. There are two interferers, one on eachside of the desired channel, having the same power as the desired signal. These42Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Ainpl(fiers2.5 r I2 •••I•— I I I I I II I I I I I IC. I I I I I II I I I I I I1.5-————I -1I I I I I II I I I I II I I I I II I I I I I1 -I I I I I II I I I I II I I I I II I I I I I I0.5 I I I I I Ic L___L___I.___ ___0 0.5 1 1.5 2 2.5 3 3.5 4Vi(a)C I I 1I I II I I-0.05 .————L.I I I-0.1 - -‘I 44•0Ct‘—4 I I I I I5) I I I I I I-0.15-————I -1————-1———I I I I I II I I I I I II I I I I I I-0.2-I I I I I II I I I I I II _•••••_•__I I I I I I-0.25 I I II I I I I I II I I I I I I—0 I I I I I I0.5 1 1.5 2 2.5 3 3.5 4ViFigure 3.4 Modelled characteristics of a Class A/B amplifier. (a) amplitude response (b) phase response.43Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiersinterferers are GMSK signals generated independently from the desired informationsignal and their carrier phase and symbol timing are randomized.Since the nonlinearities cause spectral spreading, new C/IA versus Fm curvesneeded to be computed. Figs. 3.5 — 3.8 show the new C/IA versus Fm curves forthe non-ideal GMSK system. The C/IA curves for the ideal GMSK system are alsoincluded in the figures for reference. As it can be seen in Figs. 3.5 and 3.6, the C/IAcurves for non-ideal GMSK system with typical values of QM errors are almost sameas the ideal GMSK system. This indicates that spectral spreading is negligible forthese values of QM errors. However for extreme values of QM errors, C/IA dropssignificantly, especially when HL is employed. This is due to spectral spreadingcaused by extreme nonlinearities [24].Figs. 3.9 and 3.10 illustrate typical BER performances of the various receiversunder investigation for a static ACI with C/IA = 15 and 20 dB, respectively. For allsystems, it has been assumed that a QM with extreme values of QM errors and a HLare employed. From both figures, it is clear that the decision feedback differentialreceivers perform better than the conventional differential receivers, with the 1—bitdecision feedback differential receiver performing the best. For example, as can beseen from Fig. 3.10, the 1-bit decision feedback differential receiver has a gainof 8 dB over the 2-bit decision feedback differential receiver at BER = i0. It isinteresting to note that if the C/IA decreases, the performance limitations appear inthe form of error floors. The decision feedback receivers offer significant error floorreductions. For example, at C/IA of 15 dB the 1-bit decision feedback differential44Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiersreceiver exhibits an error floor at BER = 1.4x103,whereas the one-bit conventionaldifferential receiver has an error floor at BER = 1.5x102Figs. 3.11 — 3.14 illustrate the degradation in Eb/No (at BER = icr3) versusnormalized channel spacing (Fm) and spectral efficiency (n). The degradation, for allreceivers, is measured with respect to the Eb/No that is required by an ideal GMSKsystem, employing 2—bit decision feedback receiver, to achieve BER = iO. Theplots for the ideal GMSK system (i.e., without any QM errors) are also included forcomparison purposes. First of all, it is clear from simulation results that the decisionfeedback differential receivers outperform the conventional differential receivers inall the situations considered. It is interesting to note that in all the plots there is avalue of Fm below which the required Eb/No to achieve a BER of i03 increasesdrastically, 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. Followingthese figures, the degradations caused by the nonlinearities (i.e., QM errors andnonlinear PA) are relatively small (about 1 dB) when Fm > FmC. However, whenFm < FmC, the degradations caused by the nonlinearities are much higher for theconventional differential receivers than the equivalent degradations for the decisionfeedback differential receivers.For extreme values of QM errors, as illustrated in Figs. 3.13 and 3.14, theFmC of the conventional differential receivers is much higher than the equivalentFm” of the decision feedback differential receivers. For example, as can be seenin Fig. 3.13, the Fm” is 1.25 and 1.5 for 1—bit decision feedback receiver and 1—bit45Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiersconventional receiver, respectively, when employing a HL. If one views the FmC as anabsolute minimum Fm at which the system can operate, then the system employinga decision feedback receiver will allow narrower channel spacing. Hence, betterspectral efficiency will be achieved.--. -.Non-ideal GMSK + Hard Limite - - - - - - - - - - - -Non-ideal GMSK ÷ Class AB - - - -•- - - -Ideal GMSKI I•I I••I•I 1•11•11• ——,,p —1,-------, , ‘0’, r’ “-—--—- -‘,‘ #‘:::‘*:E::::z::::::::::::z:1 1.5Normalized Channel Spacing (Fm) (Hz/bit/sec)Figure 3.5 C’L4 ratio versus nonnalized channel spacing (Fm)for 1-bit receivers. QM errors: (9d=1°, A = 0.95, k = —24 dB).5550454035302520151050-50.5 246Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiers50454035302520151050Normalized 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 =55-50.5 1 1.5 247Chapter 3. BER Performance Evoluo.tion of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiers2015100Normalized Channel Spacing ( Fm) (Hz/bit/see)Figure 3.7 C/IA ratio versus normalized channel spacing (Fm)for 1-bit receivers. QM errors: (9d = 15°, z = 0.65, k = -12dB).555045403530255-50.548Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear AmplifiersNormalized 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).5550454035302520151050: = : = : = = : = = = = = : :Non-ideal GMSK + Hard Limite X- - - -Non-ideal GMSK + Class AB - - - - - - - - -IdeaIGMSK: : : : : : : ;:: : -: .-E-50.5 1 1.5 249—-eCCBitError RateProbabilityC-a CI C0I:IQH -a 11• Iot II o() UI g-a 0 1’)0 U) 0 0 UI C..————TT711EEEEHHEEEEHEHEEEFz::EEEEEEEE“1jT------,----,---II-----------IIIIII-x--------------II--“------4---H_----I-----t----———--—)———--.—————II———--————-—I-—-———-II——-“———-..—--‘-o•.11.0.0U PC’JI..o•II-‘aBitErrorRateProbability0Chapter 3. BER Performance Evaluation ofNon-ideal GMSK System Employing30CIINormalizedChannelSpacing(F) 0(Hz/bit/see) . 0.5Decision Feedback Receivers in the Presence ofNonlinear Amplifiers40352520151051SpectralEfficiency(ri) I I(bits/secfllz) 21.5 20.67Figure 3.11 Degradation of E,1N0 to achieve a BER of versus normalizedchannel spacing for 1-bit conventional (C) and decision feedback (DF) receiversin static ACI-AWGN channel. QM errors: (Od=1°, = 0.95, k = -24dB).0.552Chapter 3. BER Performance Evaluation of Non-ideal GMSK System Employing15C10Decision Feedback Receivers in the Presence of Nonlinear Amplifiers205NormalizedChannelSpacing(F) 0(Hz/bit/see) 0.5SpectralEfficiency(fl) I(bits/sec/Hz)—p- 2 0.67Figure 3.12 Degradation of E,1N0 to achieve a BER of iO versus normalizedchannel spacing for 2-bit conventional (C) and decision feedback (DF) receiversin static ACI-AWGN channel. QM errors: (Od = 1°, A = 0.95, k = -24dB).1 0.553Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingeC30Decision Feedback Receivers in the Presence of Nonlinear Amplifiers252015105NormalizedChannelSpacing(F) 0(Hz/bitlsec) 0.5SpectralEfficiency(rl)(bitslsecIHz)— 2 1Figure 3.13 Degradation of Eb/N0 to achieve a BER of i- versus normalizedchannel spacing for 1-bit conventional (C) and decision feedback (DF) receivers instatic ACI-AWGN channel. QM errors: (Od = 15°, = 0.65, k = -12dB).0.67 0.554Chapter 3. BER Performance Evaluation of Non-ideal GMSK System Employing‘0•035Decision Feedback Receivers in the Presence of Nonlinear Amplifiers302015105NormalizedChannelSpacing() 0(Hz/bitfsec) 0.5SpectralEfficiency(r) I(bits/sec/Hz)—— 2 0.67Figure 3.14 Degradation of E,,/N0 to achieve a BER of 10 versus normalizedchannel spacing for 2-bit conventional (C) and decision feedback (DF) receivers instatic ACI-AWGN channel. QM errors: (Od = 15°, = 0.65, k = -12dB).1 0.555Chapter 3. BER Performance Evaluation of Non-ideal GMSK System EmployingDecision Feedback Receivers in the Presence of Nonlinear Amplifiers35 SummaryIn this chapter, the performance of decision-feedback and conventional differentialreceivers has been evaluated for the typical and extreme values of QM errors. Thenonlinear amplifier is modelled as a class MB amplifier and a hardlimiter. The non-ideal GMSK signals are transmitted over static ACI-AWGN channel. The results haveshown that the decision-feedback receivers overwhelmingly outperform conventionaldifferential receivers under severe GMSK transmitter nonlinearities. The degradationsdue to nonlinearities are smaller for decision feedback receivers which makes themmore robust. It is also found that the decision-feedback receivers performanceimprovements are more significant for narrower channel spacing, hence they providebetter spectral efficiency.56Chapter 4 Design, Implementation, and Testingof a Prototype GMSK System4.1 IntroductionIn this chapter the design, implementation and testing of a prototype GMSKsystem employing 1—bit conventional and decision feedback differential receiverswill be presented. The performance of the modem will be evaluated in the presenceof AWGN and ACT. The obtained BER performance results will be compared withequivalent results which have been obtained by means of computer simulation.Following this introduction, the chapter is organized as follows. An overview ofthe prototype GMSK system is given in Section 4.2. In Section 4.3, the details ofthe Digital Signal Processor (DSP) based GMSK baseband generator are presented.The RE modulator, the channel and the RE demodulator are described in Section4.4. Section 4.5 gives the details of the DSP-based implementation of the decision-feedback receivers. Experiment measurements and BER performance evaluationresults are presented in Section 4.6 and a summary of the chapter is given in Section4.7.4.2 Prototype GMSK System Model DescriptionThe 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 REquadrature demodulator.57Chapter 4. Design, Implementation, and Testing of a Pmtorype GMSK SystemThe transmitter and the receiver are implemented in software. Both the transmitterand the receiver utilize TMS32OC3O Digital Signal Processor (DSP) system boardswhich reside in a Host PC. The transmitter generates baseband I- and Q-channel ofthe GMSK signal. The baseband I- and Q-channels are then modulated using the 1.5MHz RF quadrature modulator to produce a GMSK signal that can be transmittedthrough the communication channel. In the channel, AWGN, ACT, and Rayleighfading distort the transmitted signal. The RF demodulator down converts the RE signalto its baseband I- and Q-channels. The receiver DSP board samples the incomingsignal and processes the samples to determine the transmitted bit. It should be notedthat the only reason 1.5 MHz RE modulator/demodulator are used is because of theiravailability in the Communications Lab.In next few sections, the different modules of the system will be described indetail.I-channelTMS32OC3O__________(Transmitter) Channel(AWGN, AUC TMS32OC3O & Fading)DSP card I-channel1(t) Ri? Demodulator p(Receiver) q(t)Q-channelFigure 4.1 Block diagram of the implemented prototype GMSK system.58Chapter 4. Design, Implementation, and Testing of a Prototype GMSK System4.3 GMSK Baseband Digital SynthesizerThere exists many different techniques for generating a GMSK signal amongwhich the FM modulator is perhaps the simplest one [50]. However, the disadvantageof this technique is that the phase of the carrier can not be controlled accurately. Fora prototype system, it seems that the most effective implementation solution is theBaseband Digital Synthesizer (BDS), which allows precise control of the phase of thesignal. It was therefore decided to design the transmitter based upon this technique.The transmitter is implemented in software on a DSP platform which consists ofa Spectrum TMS32OC3O DSP system board and software development tools for anIBM PC [51]. The TMS32OC3O DSP boards were chosen due their availability andexcellent software support. For a prototype system, the software DSP design is moresuitable because it allows one to make changes in parameters and software algorithmsin a fraction of time required for a hardware update.The transmitter digitally generates the baseband I- and Q-channels of the GMSKsignal. The flowchart shown in Fig. 4.2 describes the baseband transmissionalgorithm. The program uses an Interrupt Service Routine (ISR) which is executedwhen the interrupt is enabled. Interrupt is enabled by the on-chip timer/counter. Thecounter value is set to 200 which corresponds to the timer period of 24 psec [51]. Forthis value of the period and considering 8 Samples-Per-Symbol (SPS), the Baud rate isBaud 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 symbolrepresents one bit. Every time the ISR is executed, the SPS counter is checked. If a59Chapter 4. Design, Implementation, and Testing of a Pmtotype GMSK Systemnew 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 fedto the D/A convertors. The TSR also checks if the sample number of the symbol isfour. If it is, a pulse is output to the digital port. We will call this pulse the SYNCsignal and it used by the receiver for symbol synchronization. At the end, programcontrol returns from the TSR and waits for the next interrupt.Compute index ofI and Q LUTs andoutput I,Q to DIAFigure 4.2 Flow chart for the implementation of the baseband transmission algorithm.60Chapter 4. Design, Implementation, and Testing of a Pmtoiype GMSK SystemDuration of the impluse response window 3TSamples Per Symbol (SPS) 8Number of samples in the impluse response window (N) 8 x 3 = 24Table 3 The parameters used in generating the GLPF.The GLPF output LUT is generated upon initialization of the transmitter. It isgenerated using the GLPF impulse response, hT(t), given in Eqn. 2.4. By normalizingthe time, t, with the symbol duration (7), hT(t) becomeshT(t/T) i=kiBtTexp[_(kiBT(t/T))2] (4.2)where, as previously stated, k1= 1rVf 5.336 and BT is the normalized 3 cIBbandwidth of the GLPF. For B1T of 0.3, impulse response of the GLPF is plotted inFig. 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”. Thistruncating is required to digitally generate the GLPF output table. After truncatingand sampling (8 times per symbol) hTfr./T), we have impulse response window oflength 8x3=24 samples. The parameters used in generating the GLPF output tableare summarized in Table 3.The GLPF output samples are generated by convolving the impulse responsewindow with all possible NRZ input symbol sequences. Since duration of the impulseresponse window is 3T, there are 2(3+1)=16 distinct NRZ sequences, hence 16 distinctoutput symbols. NRZ sequences are generated internally by the program and theyare made up of combinations of +l and ‘-1’ symbols. Mathematically, the outputof a GLPF can be described asy[n] = x[n]h[O] +x[n— 1]h[1] +...x[n —N— 1]h[N— 1] (4.3)61Chapter 4. Design, Implementation, and Testing of a Prototype GMSK Systemwhere 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 samplesof the impulse response. As illustrated in Fig. 4.4, the output of GLPF is a functionof 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 are0.40.30.20.1Figure 4.3 Impulse response of the GLPF with B1T = 0.3.10.90.80.70.60.50t/T62Chapter 4. Design, Implementation, and Testing of a Prototype GMSK Systemcosine 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 modstands for the well known math function modulo. The result of mod2ir is always inthe range [0, 27r). The output of GLPF is normalized so that the maximum changein phase over one symbol interval, T, is ir/2. The index, P,, is calculated asF,, FIX[Nj * 44n]/(2r)j (4.5)where NL is the size of the I- and Q-channel LUTs. FIX[•] is a built-in TMS32OC3Oassembler function which converts a floating point number to integer number.Impulse Response Window___________ ___________ __________ConvolveT T T T and— — -— ShiftPast Three Symbols CurrentSymbolFigure 4.4 Illustration of how a output symbol of GLPF is generated.63Chapter 4. Design, Implementation, and Testing of a Prototype GMSK SystemThe values stored in the I- and Q-channels LUTs are given bynI, = ND cos 2ir—/ (4.6)= ND Sin (27r!\ Njwhere 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 blockdiagram of the transmitter is shown in Fig. 4.5. The input bit stream is convertedfrom serial-to-parallel to generate an address of the appropriate output symbol inthe GLPF output LUT. The samples, y[n], of the output symbol are fed to the IndexGenerator to calculate P, as described above. P, indicates the location of I and Q,which are clocked out to D/As.Input Bit StreamFigure 4.5 Functional block diagram of the implemented GMSK transmitter.64Chapter 4. Design, Implementation, and Testing of a Prototype GMSK System4.4 Quadrature Modulator/Demodulator and ChannelA block diagram of the hardware implemented RF modulator/demodulator andthe realization of the channel is shown in Fig. 4.6. With the exception of the ACIimplementation, which has been realized by the author of this thesis, the design andimplementation of the modulator/demodulator and the channel simulator were done byD. P. Bouras and documented in [36]. The modulator and demodulator are designedto operate at the carrier frequency of 1.5 MHz. Upon entering the modulator, thecarrier is divided into its inphase and quadrature components by a 900 splitter. Thesecomponents are then mixed with I and Q components of the baseband signals andsummed by a signal combiner. The resulting 1.5 MHz RF signal is amplified and fedto the 3-way RF signal combiner along with two adjacent channel interferers.The adjacent channel interferers are independent GMSK signals that are generatedusing frequency modulators (FM). The reason for adopting to this approach is thatby using FM options on HP8656B and M12022 signal generators, we can easilychange the channel spacing by changing the frequency of the outputs of the signalgenerators. It should be noted, however, that such an approach would not generatean exact GMSK signal as the QM approach. The block diagram of the ACI generatoris given in Fig. 4.7. Referring back to Fig. 2.1, the equiprobable and independentinformation bits, a, are generated inside the Host PC and the GLPF is realizedin software on TMS32OC3O system board. The output of the GLPF is frequencymodulated using the FM inputs available on HP8656B and M12022 signal generators.65.1Qq(t)MixerChapter 4. Design. Implementation. and Testing of a Pmtotype GMSK SystemThe channel module allows the fading to be simulated by the use of Digital FadingSimulator presented in [52]. Upon entering the channel module, the signal is dividedinto its inphase and quadrature components by a 900 splitter. These components arethen mixed with inphase and quadrature components of the fading signal. WhiteI Upper ACT Lower ACTi( ‘x’ Generator L Generatori(t)c1ml.5 MHZ 3-way RF Combinerq(t)Mixer ooMODULATOR Splitter 1Fading\7,/J SimulatorDEMODULATOR4i(t)00490°Roofing—i-—— 200 kHzBPFI WHITE NOISECHANNELFigure 4.6 Modulator, Demodulator and Channel Simulator66Chapter 4. Design, Implementation, and Testing of a Prototype GMSK SystemGaussian is also added to the signal from a White Gaussian Noise Generator whoseband coverage is 6 kHz to 25 MHz. A wideband (200 kHz) roofing filter, with acenter frequency of 1.5 MHz, is used to limit the noise.The demodulator takes the received RF modulated carrier and splits it into itsinphase and quadrature components, which are then coherently mixed down to thebaseband signals. This coherent conversion to baseband signals is necessary justbecause our differential detector is designed to operate on baseband signals. It isimportant note that this coherent demodulation does not “compensate” at all theinterference introduced in the channel. In fact, the interference appears totally“uncompensated” at the demodulated baseband I- and Q-channels. The basebandI- and Q-channels are then passed through Low Pass Filter (LPF) and fed to the DSPcard for baseband differential detection.GLPF output HP8656B Upper InterfererTMS32OC3ODSP Board(Digital GLPFs)2ithGLPF output j M12022 ii Lower InterfererFigure 4.7 The block diagram of the ACI generation system.4.5 DSP Based Decision-Feedback ReceiversThe functional block diagram of the implemented 1—bit differential receiver isshown in Fig. 4.8. The reason for implementing only 1—bit receiver is that it iseasier to implement (compared to 2—bit redceiver) and our purpose for this exercise67Chapter 4. Design, Implementation, and Testing of a Pmtotype GMSK Systemis only to experimentally verify the effectiveness of decision feedback algorithm. Theanalog baseband I- and Q-channels provided by the RF demodulator must be firstfiltered by the receive filters which are 4th order Butterworth filters similar to the oneimplemented in computer simulations. These filters are provided on the TMS32OC3Osystem board and they have unity gain and their cut-off frequency can be variedaccording to the plug-in register pack [51]. A/D conversions are triggered by theSYNC signal provided by the transmitter for symbol synchronization. The digitaloutput of A/D convertors is processed by the decision feedback algorithm which isimplemented in software. The program uses an TSR triggered by the SYNC signal.The decision feedback algorithm is the heart of the receiver. Its implementationis based on the block diagram shown in Fig. 4.9. The baseband differential detectionalgorithm takes current samples of I- and Q-channels, time delayed samples, andsine and cosine values of the phase delay (a) as its inputs. The phase delay for 1-bitFigure 4.8 Functional block diagram of the DSP-based digital receiver.68Chapter 4. Design, Implementation, and Testing of a Pmtotype GMSK Systemdecision-feedback receiver is given bywhere 0 is given by Eqn. 2.23 and repeated here for readers’ convenience,0 = b_0 + bk_202.(4.7)(4.8)All possible values of a are calculated using Eqn. 4.7 and tabulated in Table 4. Theoutput of the differential detection algorithm is used for deciding the received bit. IfPHASE DELAY FOR ONE-BIT RECEIVERbk_i, bk_.2 01 (deg) 02 (deg) a (deg)-1, -1 15.9 0.2 73.9-1, 1 15.9 0.2 74.31, -1 15.9 0.2 89.81, 1 15.9 0.2 90.2Table 4 All possible values of phase delay a (in degrees).I-channeIFigure 4.9 The block diagram of a one-bit all digital decision feedback receiversQ-channe,BasebandDifferentialDetectionAlgorithmj2AddressingLjCsin (a) cos (a)69Chapter 4. Design. Implementation. and Testing of a Prototype GMSK Systemit is greater than zero the received bit is ‘1’ and ‘0’ otherwise.4.6 Experimental Set-up and MeasurementsThis section describes the experimental set-up used to evaluate the prototypeGMSK system. It also presents the signal measurements and obtained BER performance evaluation results of 1-bit decision-feedback differential receiver and 1-bitconventional differential receiver. The block diagram of the experimental set-up isshown in Fig. 4.10. In addition to the equipment shown, a Tektronix 2232 oscilFigure 4.10 Block diagram of the experimental set-up.70Chapter 4. Design, Implemenkition, and Testing of a Prototype GMSK Systemloscope was used to monitor the baseband signals. The I-channel eye-diagram atthe input of the RF modulator is shown in Fig. 4.11. The signal has an amplitudeof 3V peak, as discussed in Section 4.3. This is the maximum output voltage ofD/A convertors on the TMS32OC3O DSP card. The operation of DIA convertors atmaximum output voltage minimizes the quantization errors [51]. The phase state-Figure 4.11 I-channel eye-diagram at modulator input. Horizontal Axis: 0.1 msec/div, Vertical Axis: I V/div.Figure 4.12 The phase state-space diagram of the modulatedGMSK signal. Horizontal Axis: 1 V/div. Vertical Axis: 1 V/div.71Chapter 4. Design, Implementation, and Testing of a Prototype GMSK SystemFigure 4.13 The phase state-space diagram of the demodulatedGMSK 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 fromthis figure that the transmitted GMSK signal has constant envelope and continuousphase. Without any channel interference introduced, the phase state-space diagramof the demodulated signal is shown in Fig. 4.13. The non-ideal components of themodulator and the demodulator cause slight phase shift and amplitude distortion. Thepeak voltage of the demodulator output signals is almost 2.5V when the modulatorinputs has amplitude of 3V.Referring back to Section 4.3, we have designed the GMSK BDS for B1T = 03and Baud rate was set to 5208 symbols/second. At these values of B1T and Baudrate, we expect the 3-dB bandwidth, B1, to beB = = 0.3 x 5208 = 1.6kHz. (4.9)72Chapter 4. Design, Implementation, and Testing of a Prototype (3MSK SystemAs can be seen from the signal spectrum shown in Fig. 4.14, B1 is indeed close toFigure 4.14 The spectrum of the GMSK signal at modulator output. HorizontalAxis: 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 modulatorand the noise summer, without any fading and noise introduced, the spectrum of thesignal at the demodulator input is illustrated in Fig. 4.15. The distortion introducedby the channel simulator hardware is evident in this figure. As mentioned in Section4.4, the adjacent channel interferers are generated using FM options of two signalgenerators, namely HP8656B and M12022. The interferers are then combined using aFigure 4.15 The spectrum of the GMSK signal at demodulator input. HorizontalAxis: 5 kHz/div, Vertical Axis: 10 dBldiv, Center frequency = 1.5 MHz.73Chapter 4. Design, Implementation, and Testing ofa Prototype GMSK SystemFigure 4.16 The spectrum of the desired signal along with two adjacent channel interferers at channel spacingof 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 byM12022, is significantly different than the desired signal, whereas the spectrum of theupper interferer, which is generated by HP8656B, is not so different than the desiredsignal. These discrepancies are mainly due to the quality of the FM moudulators ofthe respective signal generators and, as stated previously, the fact that FM method isnot the best method to generate GMSK signals.The spectrum of the received GMSK signal in AWGN channel is presented inFig. 4.17 and corresponding phase state-space is shown in Fig. 4.18.The experimental BER performance results for 1-bit conventional and decisionfeedback receivers are obtained with various channel conditions. The BER results forreceivers operating in AWON channel are depicted in Figs. 4.19 and 4.20. There isonly small deviation (0.5— 1 dB at BER = 10 3) from the computer simulations. Thesedeviations are attributed primarily to the non-ideal RF modulator and demodulator.74Chapter 4. Design, Implementation, and Testing of a Prototype GMSK SystemFigure 4.17 The spectrum of the GMSK signal in AWON channel. HorizontalAxis: 5 kHzjdiv, Vertical Axis: 10 dB/div, Center frequency = 1.5 MHz.The BER results for the conventional and decision feedback receivers in an AWONand Rayleigh fading channel for two values of fDT are presented in Figs. 4.21 and4.22, respectively. The close agreement between the experimental and the computersimulated BER results is evident.Figs. 4.23 and 4.24 illustrate the BER performance of the implemented receiversin static ACI-AWGN channel at C/IA = 10 and 14 dB. It is clear from Fig. 4.23Figure 4.18 The signal phase state-space at demodulator output afteradding AWGN. Horizontal Axis: 1 V/div, Vertical Axis: 1 V/div.75Chapter 4. Design, Implementation, and Testing of a Prototype GMSK Systemthat the decision feedback differential receiver provides significant reductions in errorfloors, as predicted by computer simulation results in Chapter 2. In Fig. 4.24 withC/IA = 14 dB, the decision feedback receiver has a gain of almost 6 dB as comparedto the conventional differential receiver at BER = iO.76CC-a C-a C-a CC0Bit ErrorRateProbability-a C-a C,I-t I I0zz==z=:t:[::,.———LILLLL{I—-—-1I11—hRTP11—--—-1•ur---——-1-I-i-i-n10LLLLLflI-rflh1TFI—---—--—--l4I41-II-------------—--—---—--——-I.TpTJ——-——--——-——-I ‘IiCBitError RateProbability0I-’ 0I 0L.)0f IBitErrorRateProbabilityC0I0‘TI00,.cBitErrorRateProbabilityC0I I ‘IChapter 4. Design, Implementation, and Testing of a Prototype GMSK SystemEb/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.1 1-bitDF A1 1-bitC—110-210.310%,ZEEEEEEZEE:zz\S\-410 -15 25 35 45 5581oQ.t’.)1100ZQ S.CCU’BitErrorRateProbabilityCC•100C U’Chapter 4. Design, Implementation, and Testing of a Pmtotype GMSK System4.7 SUMMARYA prototype GMSK system was designed, implemented and tested on aTMS32OC3O based DSP platform. The obtained test results are in close agreement with computer simulations. The BER performance results, obtained for 1-bitconventional and decision feedback receivers operating in static ACI-AWGN channel,verify significant improvements provided by decision feedback receivers.83Chapter 5 Conclusions and Some Suggestionsfor Future Research5.1 ConclusionsIn this thesis, the BER performance of 1— and 2—bit conventional and decisionfeedback differential receivers was evaluated for the detection of GMSK signal in thepresence of Ad, modulator errors, amplifier nonlinearities, and AWGN. The BERperformance results for conventional and decision feedback differential receivers ofGMSK signals has been obtained for static and faded ACI-AWGN channel by meansof computer simulations. It has been found that the decision feedback receivers alwaysprovide better performance when compared to the conventional differential receivers.The gains are more significant for static ACI-AWGN channel. For faded ACI-AWGNchannel, the decision feedback differential receivers provide error floor reductions.The obtained BER performance results for the system with an imperfect modulatorand a nonlinear amplifier indicate that for extreme modulator errors, 1—bit decisionfeedback differential receiver out performs all other receivers that are considered.For typical modulator errors, 2—bit decision feedback differential receiver has thebest performance.Finally, a prototype GMSK system was designed, implemented and tested. Theexperimental results verified the effectiveness of decision feedback receivers.84Chapter 5. Conclusions and Some Suggestions for Future Research5.2 Suggestions for Future Research5.2.1 Generalization to other CPM SchemesThis thesis has dealt exclusively with GMSK signals. However, as it was shownin [30], the decision feedback receivers can be applied to any CPM scheme. It wouldbe therefore of interest to investigate the performance of more generalized CPMscheme in the presence of ACI.5.2.2 Simultaneous use of 1— and 2—bit DecisionFeedback Differential Receivers.As it was shown in [29, 30], by employing a combination of 1— and 2—bitdecision feedback differential receivers, further performance improvements have beenobtained for the AWGN channel. By using such combinations of receiver structures(or perhaps employing even higher order differential detectors), further performanceimprovements are to be expected for the ACI and CCI channel.5.2.3 Extension to Multilevel CPM SchemesIn order to increase the bandwidth efficiency, multilevel CPM can be employed.It will be therefore of interest to investigate the performance of such modulationschemes in the presence of interference and/or nonlinearities.5.2.4 Further Development of Prototype GMSK System1J Optimization of the transmitter by reducing the size of LUTs.D Optimization of the receiver processing speed.85References[1] 3. B. Anderson, T. Aulin, and C. E. Sundberg, Digital Phase Modulation. NewYork: Plenum Press, 1986.[2] C. B. Sundberg, “Continuous phase modulation,” IEEE Comm. Mag., vol. 24,pp. 25—38, Apr. 1986.[3] T. S. Rappaport, “The wireless revolution,” IEEE Comm. Mag., pp. 52—7 1, Nov.1991.[4] J. B. Anderson and C. B. Sundberg, “Advances in constant envelope codedmodulation,” IEEE Comm. Mag., pp. 36—45, Dec. 1991.[5] K. Feher, Advanced Digital Communications. New Jersey: Prentice-Hall, 1987.[6] J. S. Seo and K. Feher, “SQAM: a new superposed QAM modem technique,”IEEE Trans. Comm., vol. COM-33, pp. 296-300, Mar. 1985.[7] S. Pasupathy, “Minimum shift keying: a spectrally efficient modulation,” IEEEComm. Mag., vol. 17, pp. 14—22, July 1979.[8] F. Jager and C. B. Dekker, “Tamed frequency modulation, a novel methodto achieve spectrum economy in digital transmission,” IEEE Trans. Comm.,vol. COM-26, pp. 534—542, May 1978.[9] K. S. Chung, “General tamed frequency modulation and its applications for mobileradio communications,” IEEE .1. Sel. Areas Comm., vol. SAC-2, pp. 487—497,July 1984.86[10] G. S. Deshpande and P. H. Wittke, “Correlative encoded digital FM,” IEEETrans. Comm., vol. COM-29, pp. 156—162, Feb. 1981.[11] K. Murota and K. Hirade, “GMSK modulation for digital mobile radiotelephony,” IEEE Trans. Comm., vol. COM-29, pp. 1044-1050, July 1981.[12] K. Raith and J. Uddenfeldt, “Capacity of digital cellular TDMA systems,” IEEETrans. Veh. Tech., vol. VT-40, pp. 323—331, May 1991.[13] D. J. Goodman, “Second generation wireless information networks,” IEEE Trans.Veh. Tech., vol. VT-40, pp. 366—371, May 1991.[14] W. C. Jakes, Microwave Mobile Communications. New York: Wiley, 1974.[15] W. C. Y. Lee, Mobile Communication Engineering. New York: McGraw Hill,1982.[16] R. S. Kennedy, Fading Dispersive Communication Channels. New York:McGraw Hill, 1966.[17] H. Hashemi, “The indoor radio propagation channel,” IEEE Proc., vol. 81,pp. 943—968, July 1993.[18] D. Makrakis, P. T. Mathiopoulos, and D. P. Bouras, “Optimal decoding ofcoded PSK and QAM signals in correlated fast fading channels and AWGN:A combined envelope, multiple differential and coherent detection approach,”IEEE Trans. Comm., vol. COM-42, pp. 63—77, Jan. 1994.[19] F. Edbauer, “Performance of interleaved trellis-coded differential 8-PSK modulation over fading channels,” IEEE .1. Se!. Areas Comm., vol. SAC-7, pp. 1340—871346, DEC. 1989.[20] D. P. C. Wong and P. T. Mathiopoulos, “Nonredundant error correctionanalysis and evaluation of differentially detected piI4-shift DQPSK systems in acombined CCI and AWGN environment,” IEEE Trans. Veh. Tech., vol. VT-41,pp. 35—48, Feb. 1992.[211 W. C. Y. Lee, Mobile Cellular Telecommunication Systems. New York: McGrawHill, 1989.[22] I. Kom, “Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference,” IEEE Trans. Veh. Tech., vol. VT-40, pp. 461—471, May 1991.[23] S. Ariyavisitakul and T. Liu, “Characterizing the effects of nonlinear amplifierson linear modulation for digital portable radio,” IEEE Trans. Veh. Tech., vol. VT-39, pp. 383—389, Nov. 1990.[24] A. E. Jones, T. H. Wilkinson, and J. 0. Gardiner, “Effects of modulatordeficiencies and amplifier nonlinearities on the phase accuracy of GMSKsignalling,” lEE Proc. -I, vol. 140, pp. 157—163, Apr. 1993.[25] M. K. Simon and C. C. Wang, “Differential detection of Gaussian MSK in amobile radio environment,” IEEE Trans. Veh. Tech., vol. VT-33, pp. 307—320,Nov. 1984.[26] S. M. Elnoubi, “Analysis of GMSK with differential detection in land mobilechannels,” IEEE Trans. Veh. Tech., vol. VT-35, pp. 162—167, May 1986.88[27] S. M. Elnoubi, “Analysis of GMSK with discriminator detection in land mobilechannels,” IEEE Trans. Veh. Tech., vol. VT-35, pp. 71—76, May 1986.[28] K. Hirade, “Error-rate performance of digital FM with differential detection inland mobile channels,” IEEE Trans. Veh. Tech., vol. VT-28, pp. 204—212, Aug.1979.[29] A. Yongacoglu, D. Makrakis, and K. Feher, “Differential detection of GMSKusing decision feedback,” IEEE Trans. Comm., vol. COM-36, pp. 641—648,June 1988.[30] D. Makrakis and P. T. Mathiopoulos, “Differential detection of corelativeencoded continuous phase modulation schemes using decision feedback,” lEEProc., vol. 1-138, pp. 473—480, Oct. 1991.[311 S. Shin and P. T. Mathiopoulos, “Differentially detected GMSK signals in CCIchannels for mobile cellular telecommunication systems,” IEEE Trans. Veh.Tech., vol. VT-42, pp. 289—293, Aug. 1993.[32] S. Ogose and K. Murota, “Differentially encoded GMSK with 2-bit differentialdetection,” Trans. IECE Japan, vol. 364-B, pp. 248—254, April 1981.[33] 3. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering.New York: Wiley, 1965.[34] A. D. Kucar, “Mobile radio: An overview,” IEEE Comm. Mag., pp. 72—85,Nov. 1991.[35] V. K. Varma and S. C. Gupta, “Performance of partial response CPM in the89presence of adjacent channel interference and Gaussian noise,” IEEE Trans.Comm., vol. COM-34, pp. 1123—1131, November 1986.[36] D. P. Bouras, “Optimal decoding of PSK and QAM in frequency nonselectivefading channels,” Master’s Thesis, University of B.C., Sept. 1991.[37] D. R. Hummels and F. W. Ratcliffe, “Calculations of error probability for MSKand OQPSK systems operating in a fading multipath environment,” IEEE Trans.Comm., vol. COM-30, pp. 112—120, Aug. 1981.[38] P. A. Bello, “Aeronautical channel characterization,” IEEE Trans. Comm.,vol. COM-21, pp. 548—563, May 1973.[39] D. G. Messerschmitt, “A tool for structured functional simulation,” IEEE .1. Se!.Areas Comm., vol. SAC-2, pp. 137—147, Jan. 1984.[40] M. C. Jeruchim, “Techniques for estimating the bit error rate in the simulationof digital communication systems,” IEEE J. Se!. Areas Comm., vol. SAC-2,pp. 153—170, Jan. 1984.[41] T. Le-Ngoc and K. Feher, “Performance of LJF-OQPSK modulation schemesin a complex interference environment,” IEEE Trans. Comm., vol. COM-31,pp. 137—144, Jan. 1983.[42] S. M. Elnoubi, “Analysis of GMSK with two-bit differential detection in landmobile channels,” IEEE Trans. Comm., vol. COM-35, pp. 237—240, Feb. 1987.[43] I. Korn, “GMSK with frequency-selective Rayleigh fading and cochannelinterference ,“ IEEE.!. Se!. Areas Comm., vol. SAC-lO, pp. 506—515, Apr. 1992.90[44] A. Kopta, S. Budisin, and V. Jovanovic, “New universal all digital CPMmodulator,” IEEE Trans. Comm., vol. COM-35, pp. 458—462, Apr. 1987.[45] J. G. Proakis, Digital Communications. New York: McGraw-Hill, 2nd ed., 1989.[46] M. I. Skolnik, Introduction to Radar Systems. New York: McGraw-Hill, 1980.[47] M. Faulkner and T. Mattsson, “Specttral sensitivity of power amplifiers toquadrature modulator misalignment,” IEEE Trans. Veh. Tech., vol. VT-41,pp. 516—525, Nov. 1992.[48] T. A. H. Wilkenson and P. A. Matthews, “Assessment of UHF power amplifierlinearisation by measurement and simulation,” lEE Proc. 5th mt. Conf MobileRadio, pp. 60—64, Dec. 1989.[49] T. T. Ha, Solid-State Microwave Amplifier Design. New York: John Wiley andSons, 1981.[50] H. Hirono, T. Mild, and K. Murota, “Multilevel decision method for band limteddigital FM with Limter Discriminator Detection,” IEEE J. Sel. Areas Comm.,pp. 498—506, July 1984.[51] SPECTRUM Signal Processing Inc., The TM5320C30 System Board TechnicalReference Manual, May 1991.[52] E. Casas and C. L. S. Leung, “A simple digital fading simulator for mobileradio,” IEEE Trans. Veh. Tech., vol. VT-39, pp. 205—2 12, Aug. 1990.91Appendix A Program Listings• GMSK digital baseband synthesizer• 1—bit conventional differential detector• 1—bit decision feedback differential detector• Generator of two adjacent channel interferers92aci.asm*File:aci.asin**Date:9Oct.1993**Use:‘generatetwoindependentgaussianfiltered**foradjacentchannelinterferencepurpose*InterruptVectorsataddress0“‘.sect‘.initBESET.wordSTARTINTO.wordSTARTINTl.wordISR1812.wordSTART1873.wordSTARTXINT0.wordSTARTRINTO.wordSTARTXINT1.wordSTARTRINT1.wordSTARTTINTO.wordSTART71871.wordSTARTDINT.wordSTARTDataSectionataddress30000***.datairpluseresponseoftheGaussianfilter.float0.0013.float0.0038.float0.0104.float0.0255.float0.0565.float0.1133.float0.2055.float0.3372.float0.5004.float0.6716.float0.8152.float0.8950.float0.8886.float0.7979.float0.6480.float0.4759.float0.3161.float0.1899.float0.1032.float0.0507.float0.0225.float0.0091.float0.0033.float0.0011***StackinBLOCKOat809800k‘‘STACK.u$ect‘.stack”,400k.textSTACKADDR.wordSTACKPRIMCTh.word00800064kEXPCTL.word00008068kPRIMWD.word00000800kLEANT.word00008000kADCBANA.set804080kADCRANB.set804001k;SERIALO.word808042hTIMECTL.word00808030kPERIOD.word00008038kRSTCTRL.word00000601kSETCTRL.word000086CThconstantsintheprogramCOUNT.word200SPS.set0WINSIZEjet24READY.set11DACRES.float1500.0IMPRES.word0809cOOhWINDOW.word809c32hWAVETIiBLE.word809c64hP0EVBIT1.set809d00hDIF_ENC.set009d81hPBEVBIT2.set009d02hBIT_COUNT.set809d03kSETFLAG.set009d04kTABLE.set009d05hDATAEND1.set809d06hDATAEND2jet809d07hCURE80001et809d08kCURE80802-set809d09hINDEX1.setBO9dOakINDEX2.set8O9dObhBEADYFLAG.set30001kVDATAI.word30010hEDATAI.word31910hV1)ATA2.word31911kEDATA2.word33210kPrimerybuscontrolExpansionbuscontrol;FSX/DX/CLKXPORTCONTROLTiierlcontrolregisterTiamrlperiodregisterstartofthedata;endofdata—31910;esid33210;startaddressofDUALaem;endaddressofDUAL(-BANK3);startaddressofonchipRAM1;getthepageofstoredadress:setupstackpointerSetupprimerybuswaitstatesTimerperiod—6.6usecsamplespersyso1HunkersofsamplesinFibwindow;scalingfactor:pOintertoiirpluseresponsepointertodatawindowpointertowaveformtabelThitor2bitusedfor2bitencodingDOBISTARTDUALENDRAM1CODESDUALONCRIP.word030000k.word033300k.word0809cOOk.set0.set30000ket809c00kthefollowingcodeSetsupthestackpointerandinitializesDSPhardwareasoutlinedintheuser’sannualSTART:LDPCODESLDI8STACKADDR,SPLDIOPRIMCTL,ARO1’’ProgramSectionataddressODOk101@PRIMWD,R057!R0,M0101@E)TCTL,ARO101OEPEND,R0571R0,*ARO101OSLRIALO,MO1.012h,R0£71R0.*ARONO?CALLFIXITNO?BRFINISBSetupexpansionbuswait-states.:setdigitaloutputtoocresEntthecounterFIXIT101€WXVETABLE,AR?WI127,RCRPTBFINSBLDF*M7,R7M?TFODACBES,R7FIXR1,R7lET!1550,10?;SUBI3,R7ISP16,10?FINSU57110?,9J744PETSThisportionofthecodebuildsthewindowINPUTS:R5(systol $0-?)BUILD_WIN: 101UWINDOW,1100LOP-l.O,RULDF-1.0,101LDF-l.O,R2TSTBl,R5LDFNE1.O,ROTSTB2,RSLDFNE1.O,RlTSTB4,R5LOFNEl.U,R2P275525-1STERU,*MU4.fRPTSSPS-lSTEJ,*,fl+flETS525-1STFfl*MU44.PETSinitializeregistersThisportionofthecodecreatesthegunksyirhol.INPUTS:1R3(locationinremwhersysboltobelocated),R3(sps),R4(newbit)OUTPUTS:1103 (locationofnextsysi)KNEE_SIN: LOTUNINUON,1100WIWINSIZE-l,RC102104,100loadinnewvalueCALLSTUFFLOT$WINOOW,1100WI$INP_PES,1R1101WIN_SIZE,BKLOTNIN_SIZE-2,RCCALLFIR572RO,Q,p,34-fSUBI1,103BGTUMAlE_SINNO?NO?NO?PETS;********************************a**a*********a**********************a**;ThisportionofthecoderovesIMPRESdata,givenabove,;toonchip101141at$809c00101ODUALSTART,1100101P101141,1101102*M044R0PETSWIN_SIZE102*110044,100(I571’RU,*Ml.f4.NO?***************ea********cnn*****a**************cc***ana*******:CleartheDUALsesory(30000to33300)101ODUALSTART,R6101$DUAIEND,R7SUBI106,107WI0,100101106,1106PETS107STIRU,*1106+4‘**************************a**************c********c****c***************ThisportinofthecodecallsMAKE_SINtowakeatahelofallpossiblesasples;GLOBALPEGS.:R3,R4,R5,1R3theseshouldnotbeaodifiedbycalls101$NAVETRBI,E,11031016,105;acounterfortotalIofnystola1,0021102-1.0,104WISPS,R3CALLBUILD_WINNO?CALLMAKE_SINNO?ID?l.U,R4CALLBUILD_WINNO?101525,103CALLKAKE_STNNO?MDI1,105CMPISPS,R5BNZ10021Thisportionofthecodechangesthewavetableintointegertableandshiftthevaluestoupper16bits.;resultofFIRisinRU--ThisportionofthecodefindsFIRoftwovectorsoflengthCN.INPUTS:AJ(0{addrl),Afl{addr2),HK(N),RC{N-2),OUTPUTS:RU(result)FUNIIPTF3*pj(0*f(fl,*0fl144W%,R0;initializeRUIDE0.0,1(2;initialize1(2BETSRCflpy3’3*M044U)tA1(14-f(l)%,1(0IIADDF31(0,1(2,1(2ADDFR0,R2,R0;AddlastprductRETSIHerewesetupTinerlcontrolregistersandperiodregistersID?CODES101OTINECTI,1R7101ORSTCTRI,R7STIR7,*1R7101€PUNIOD,AR6IDI@COUNT,R6STIR6,*1R6ID!USETCTBIOR7STIR7,*1R7Thisportionofcodeisusedtostuffavalueatthefirstlocationofavectorandshifttheoldervaluesdownbyone.INPUTS:AR0{vectorpointer),RC)vectorsize),R0{newvalue)STUFFBETHDONEIDF*31(,pJIISTFR0,*A1k04fDONELDF1(1,1(0BETSFINISH:LOPDUALIII)REAOYFLAS,R7CNPI1(11(01,1(7BillFINISHsavetheoldvaluestuffinthenewoneOR2,IEOR2000b,STDEAD: HRDEADifreadystartotherwisewaitkeepcheckingifready:enableintruptfortiaerl;settheglobalintruptOlEinSTwaitforintruptshereHereweinitializethevariablesusedintheintruptserviceroutine.ARO,A1(l,A1(5,AR4,R4,R5areglobalTWIT:ID?CODES101@VDATAL,AR0:addressofthedataword11(0—global101€VDATA2,1R11010EDATAL,1B2IDI@EDATA2,A1(3101@WAVETADIE,AB4;setapointertotheainewavetable101INAVETADLE,A1(S101*ARO++,RO:getthefirstdatawordandlncreant101*11(1+41(1ID?ONCHI?STIRO, @CUBR_NORD1STIRl,@C0RR’ORD2LOX11(4,1(7STIR7,UTABLE:pointertothebeginningoftable10!11(2,1(7STIR7,@DATAEND110111(3,1(7STIR7,UDATAEND2Intruptserviceroutine11(0—currentaddress,currentword,—newbit,R5—32bitcountR4—sps,theseareglobalregistersforISRISR:ID?ONCUP101PSETyIAG,B7BillGETOOTLOXtAR4+4,R7:pointtobeginningofthesyitolID!*BE5.ff,1(STIR7,PADCHANAoutputtothechannelSTIR6,0ADCHANBLOPCODES£0!0511(1110,11(3ID?ONCHI?ID!2LR6SN1(6,*11(3SUB!1,1(4:ifendofnyitolgetnewbitBENENHITCUll’!4,1(4HillGETOUTNOPLUSEOUTPUTID!6H,R6STI1(6,9.1(3GETOUT: HRISRRET!NENHIT:1010,1(1STIR7,@SET_FIAG101-1,1(7STIR7,0PREVHIT1SI!R7,)PREVBIT2£011,1(7STIR7,00IF_ENC10132,1(5STIR5,001TCOUNT1010,1(3511R3,@INDEX1STIR3,01N01X2101SPS,R4:typeofencodingUNitor2bit:bitcount12-global;initialize1(3forindex:setthecounterforsasplesperUN101USET_FLAG,R7HNZGETOUT101@TAHLE,1R4ID!@TAHLE,ARS101SPS,R4ID!UCUBR_NORDI,RN1.0!@CURRNHRD2,R2ID!R0,R1ID!1(2,1(3AND1,1(1AND1,1(31.SH-1,1(0STIR0,UCURR_N0R01LSH-1,1(2;checkiftheflagIasetifaet,getout:resettablepointer:resetsarplecounteroutputbitin1(1,1(3Co 0’illR2,@CURRWORD2SUBIl,R5BNZENC_BITBEREWORDID?ONCRIPTSTBl,R1t.DIZ-1,R1LOIRE1,R1ISlE1,R3IDlE-l,R3LDINZ1,R3101DDIF_ENC,R7‘ISTAl,R7LDINZRLR1LDINEBIRDBEB112_ENCNO?BRINDEXBIT2ENC:101€PREVBITl,P7NEGIR7MEltR7,RlSTIRl,€PREVBill101DPREVBfi2,R7NEGIRiMPhR7,R3$71R3,DPREVBIT1BRINDEXSETFIPkG: 101l,RiSTIR7,RDET_FLAGID?CODES101OVDATA1,ARO101DVDATA2,AR1101*A,R044RO101ID?ONCRIPSTIR0,@CURRWORD1STIR2,DCURRWORD2BRENC_BI’!;isit‘1’;ifnotifyes:isit‘1’;ifnotifyesIDIRl,Rl;converttobit‘0’or‘1’IDIN0,RJ.;‘O’ifRiwas‘—1’,unchangedotherwise101R3,R3;converttobit‘0’or‘1’IDIN0,03‘0’ifRiwas‘-1’,unchangedotherwise11)1OINDEX1,R0101INDEX2,R2LIDl,R0;mkespacefornewbitANDOfh,R0;useonly4LIDsof03OR01,03;stuffinnewbitISO1,02;jakespacefornewbitANDOfh,R2;useonly4LSBSof03OR03,02;stuffinnewbitLDI8,R7MPYI3R7,R0,IRO;storetheindexin100STIRO,DINDEX1LOP*AR4++(IRO),R7;updatethetablepointerLDI8,R7HP11307,02,100;storetheindexin100STIR2,€INDEX2LOP*AJ5++(100),R7;updatethetablepointerBRTOU’!.end*Pile:ddl.asn**Date:9Oct.1993**Use:‘1-bitconventionaldifferentialdetector****InterruptVectorsataddress0***.global.bss.globalcinit.sect“.init’RESET.wordSTARTINTO.wordSTARTINTl.wordRCVINT2.wordSTARTINT3.wordSTARTKINTO.wordSTARTRINTO.wordSTARTXINT1.wordSTARTRINT1.wordSTARTTINTO.wordSTARTTINT1.wordSTARTDINT.wordSTARTDataSectionataddress30000***StackinBIOCKOat809800hSTACK.usect“.stack”,40Db**Progra,sSectionataddressODOh“INC_BIT:decrewantthebitcountlf32ndbitreachedgetnewwordINDEX:Thitdiff.encoding;ifyes,noencoding;ifyesdotwobitenc;indexofwavetable;bk__ak*bk_l;bk__ak*bk_1;findindexofwavetabelIddl.asm10132,R5;resetbitcount101*AR0++,RO;getthenewwordIDI*ARlf4,JSTIR0,@CURRW0001STIR2,OCURRW0002CMPI@DATAEND1,ARO;checkifendisreachedBESETFLAGCMPIODATAEND2,ARIcheckifendisreachedBESETFLAGBRINC_BITCD C)PrmnnrybuscontrolExpansionbuscontrolsauplespersynbolNunersofsasplesinFIRwindow;startaddressofDUALsm;endaddressofDUAL(—BANK3}:startaddressofonchipRAI41WIR6,AR6OPTSR7STI00,*+4HereweinitializetheintruptroutinevariablesLDPCODESWIORCVDATh,A02WI@SERIALO,AR3LOPONCAIPWIAR3,R7511R7,OSERIALOLDF0,07STYR7,I_SMP_TSTYR7,HQ_S)jWAITHER!:;waithereforintruptsBRWAIT_BEBERCV:intruptserviceroutineLOPCODESLDIOADCHANAL,A0O;readchannelAWIHADCUANB1,AR1:readchannelBLOT*J0R0WI•AR1,RlASH-16,00ASH-16,RlFLOATRO,R4FLOATRl,R5;atthispointR4andR5containthecurrentI,QsasplesLDPONCEIPWYt_S?€’_T,R2LDFQ_SNP_T,R3STY04,HI_SMP_TSTYR5,00_SHP_THPYF04,03HP!F05,02SERFR3,R2LDThE2h,06WIGT6h,R6WISERThLO.AR3STIR6,*AR3.textSTACK_ADDR.wordSTACKPRIMCTL.word00808064hEERCTL.word00808060hPRINWD.word00000800hEWD.word00000000hADCHANA1.word604000hADCHEABL.word804001hSERIALO.wørd808042hconstantsintheprogramSF5.set8WINSIZE.set24READY.set11READYFLAG.set030001hDUALSIART.word030000hDUALEND.word033300hRAM1.word0809c00h;outputdataRCVVATAword030010h;programvariablesREADIFLAG.set809d00hSERIALQ.set809d01hI_SMP_T.set809d02hQ_SMP_T.set809d03hCODES.setDUAL.set3000DbONCE.set809c00hOR2,1KOR2000h,ST:1saspleofprevioussyirbol;enableintruptfortiserl:settheglobalintruptGIEinSTthefollowingcodesetsupthestackpointerandinitializesDSPhardwareasoutlinedintheuser’ssanualSTART:LOPCODES:getthepageofstoredadressLDI@S’!ACK_ADDR,SP;setupstackpointerLDINPRINCTL,AROSetupprimrybuswaitstatesWI€PRINWD,RHSTIR0,AR0WINECT1,AROSetupexpansionbuswait-states.LDI8EWD,R0STIR0,*AROWIOSERIALO,AROLDI2h,R0STIRH,*ARO:setCLXOserialportasoutoutCleartheDUALsanory(30000to33300)LOTDUALST3RT,R6LDIUDURLEND,R7SUBIR6,R7WIO,RO:getthepreviousaaiples;keepthecurrentsaiples:fornexttue;t_SMP(0)*Q5(7);Q_SMP(0)tI_SW(7)GETOUT:;outputthereceivedbittotheandemtesterRETI.endNurhersofsasplesinFIRwindowInterruptVectorsataddress0.sect“.initOESET.wordSTAR’!INTO.wordSTARTINTl.wordRCVINT2.wordSTARTINT3.vordSTARTXIN’!O.wordSTARTRINTO.vordSTARTXINT1.wordSTARTRINT1.wordSTARTTINTO.wordSTARTTINT1.wordSTARTDINT.wordSTART***DataSectionataddress30000***.data:cosineandsinevaluedofthephasedelayalpha.float0.277314653296.float0.270600445468.float-0.27060045987.float-0.277314653306.float0.960779154159.float0.962691746429.float0.962691746423.float0.960779154156CCCStackinBIOCKOat809800h***STACK.usect“.stack”,400hProgramSectionataddressODOh.textSTACK_ADDR.wordSTACKPRI!4CTI..word00808064hEIPCTI,.word00808060hPRINWD.word00000800hEXPWD.word00000000hIIDCBANA1.word804000hADcBANB1.word804001hSERIALO.word808042hconstantsintheprogramSPS.set8WIN_SIZE.set24LEADY.set11JUAISTART.word030000hDUALEND.word033300hRAII1.word0809c00h;outputdataRCVDATA.word030010h;programvariablesAUX1.wordAUX2.wordRZADYFIAG.setSERIALO.setI_SMP_T.setQ_SMP_T-setBK1.setBK2-setCODESDUAL08CM!?thefollowingcodesetsupthestackpointerandinitializesDSPhardwareasoutlinedintheuser’swanualSTART:IDPCODES101€SThCK_ADDR,SP101@PRIMCTL,AROIDIOPRINWD,R0STIR0,*ARO101NEXPC’!L,AROIDEOEXPWD,R0STIR0,*AROIDI€SERIALO,AROIDE2h,R0STIR0,*ARO;setCLXOserialportasoutput.CC*****************C********C*CCC******C**CC*;mvethedatafromDUAL(30000)toONCRIP(809c00)IDEODUIiLSTART,AROIDIORN41,AR1IDF*ARO++, ROOPTS81DF*AR014, ROIISIPRO,CAR1H.CleartheDUALamsory(30000to33300)ID!NDUIiLSTART,R6ID1@DUIiLEND,R7SUB!R6,R7ID!0,R0IDER6,0R6RPTSR7SI!RO,*AR6++Idfl.asmI****************C*******************************************CFile:dfl.asmCDate:21Feb1993*Use:‘1—bitdecisionfeedbackdetection’**CC****CC***************C***CC*C****C*********CC***C*C****C;startaddressofDUAL1mm;endaddressofDUAL{—BANK3):startaddressofonchipRADIi;cosvaluesofthetastoredheresin””;currentQsaiplestoredhere;Isaipleofprevioussyshol:0previousnrzbitonebeforeprevious809c00h809c04h809d00h809d01h809d02h809d03h809d04h809d05h.set0.set30000h.set809c00h;getthepageofstoredadress;setupstackpointerSetupprinarybuswaitstates;costheta:sinthetaPrianrybuscontrolExpansionbuscontrolsanplespersyitholSetupexpansionbuswait-states.HereweinitializetheintruptroutinevariablesLDPCODESLDI8RCVDATA,.AR2WIOSERIALO,AR3LDPONCHIFLDIAR3,R7STIR7,@SERIALORCV:LDF0,R7SITR7,NISMPTSITR7,80SMPT!DI0,R7511R7,OBK1$11R7,80K2LDPCODESLDI81,DCHANA1, ARCWI€ADCHANB1,AR1LDI*1.J0R0LDI*ARl,RlASH-16,R0ASH-16,RlFLOATROFLOATRlatthispointRDandRicontainthecurrent1,0sasplesWICAUX1,ARC;pointertocosthetaWICAUK2,ARipointertosinthetaLDP014CH1PWI@BKL,R2LDIDBK2,R3STIR2,CBK2;bk(2j—bk)l]LSHl,R2ORR3,R2LDI02,IROLDF*+ARO(IN0)p,;auxlLDF*+1J1(fl0)R3aux2LDF8I_SMF_1,R4LDFQOSMPI,R5SITR0,CISMPTSITRl, CQSMPTMPIT3R4,R2,R6MPYF3R5,R3,R7SURFR7,R6MPYFR5,R2MPYFR4,R3ADDF3R2,R3,R7:R7-isagMF’IFR6,R0:ISMP(0)*reel.includetable.asn.glohal.bss.globalcinitInterruptVectorsataddress0***.sect‘.init’RESET.vordSTARTINTO.wordSTARTINTl.wordISR1572.wordSTART1573.wordSTARTXINTO.wordSTARTRINTO.wordSTARTXINT1.wordSTARTDISh.wordSTARTTINTO.wordSTARTTINT1.wordSTARTDINT.wordSTARTDataSectionataddress30000***.dataispluseresponseoftheGLPF.float0.0013.float0.0038.float0.0104.float0.0255.float0.0565.float0.1133.float0.2055.float0.3372.float0.5004.float0.6716.fjoat0.8152WRITR7,R1ZsDDFR0,R1LDThE2h,R6IDIGT6h,R6WI@SERIELO,AR3STER6,*AR31582,R6571R6,CBK1RETI.end:0_SOP(0)*jq;thisisdd;outputthereceivedbittondemtesterbk(11—bk(0)OR2,IEOR2000h,STWAIT_HERE:BRWAIT_HERE:enableintruptfortlixmrl:settheglobalintruptOlEinST;waitforintruptsGETOUT:Igznsktx.asm:readchannelA;readchannelB*************************************************File:gmsktx.asia*Date:iiMarch1994*Use:‘Gmsktransmitter’**************************************************:keepthecurrentsanples;fornexttine;reei;R6—reel:iangCD CD-textSTACKADUR-wordSTACKPRIWDTI-word00800064hEXPCTL-word0080806GbPRD4WD-word0000000DbETYWD-word00000000hADCEANA-set804000hADCED21B-set80400lhSERIALO-word808042hTIMECTL-word0080803GbPERIOD-word00008038hRSTCTRL-word00000603hSETCTRL-word000006CThPrirerybuscontrolExpansionbuscontrol;FSX/DXICLYJCPORTCONTROLTiserlcontrolregisterTismrlperiodregister-float0-0950-float0-8886-float0-7979-float0-6480-float0-4759-float0-3161-float0-1099-float0-1032-float0-0507-float0-0225-float0-0091-float0-0033-float0-0011***StackinBLOCKOat809880b**STACK-usect-stack”,400hProgramSectionataddressODObVDATA-word30010hstartofthedataDUALSTIRT-word030000b:startaddressofDUALsamDUALEND.word03330Db;endaddressofDUAL(—BANK3)KOHl-word0809c00h;startaddressofonchipRAM1RAMEND-wordBo9cffhonlypartofrasilCODES-set0DUAL-set30000hONCRIP-aet809c00bthefollowingcodesetsupthestackpointerandinitializesDSPhardwareasoutlinedintheuser’sannualSTART:LOPCODES;getthepageofstoredadressLDIGSTACKADDR,SP;setupstackpointerWIOPRIOKTL,AR0SetupprinnrybuswaitstatesWI0PRIMWD,R0STIR0,*AROWI0EBPCTL,ARO:Setupexpansionbuswait-statesLDI0EKPND,RUSTIRO,*7ffi0WIPSERIAL0,ARO;setdigitaloutputto0LDI22h,R0STIR0,*AROconstantsintheprogramCOUNT-word200Tirerperiod—24riicrosecSI’S-set8saaplespersystolWIN_SIZE-set24WurhersofsaxplesinFIRwindowNt-set10000sizeofsinandcostablesMOD1-float2-0HOD2-float-2-000104-float0.7SlOSlO6e-3DA’IPES-float32751-01volt—l09l7,3volt—32751-0ARAB!-set11IMPPES-word0809cOOh;pointertoispluseresponseWINDOW-word809c32h;pointertoNRZsequenceWAVETABLEword809c64hpointerto6111outputtableDIPEWCset80940Dblbitor2bitP0EVBIT-set809d02ftusedfor2bitencodingSET_FLAG-set009d04hTABLE-set809d05hPEASE-set809d07hstorageforpbadephiCOS_POINTER-set809d00hSIN_POINTER-set809d09hSERIALO-setGO9dOahSINPOINTER-setBO9dObhNODVALUE1-setOO9dOchMODVALUE2-setBO9dOdhThefollowingcodeinitializesOWCEIPaeroryOO9cOO-OO9cffWI€RAM1,R6WIIRAHEND,R7SUEZR6,R7WI0,RQLU!R6,AR6OPTSR7STYR0,*AR6If;*******************C*******************************C*******************:ThisportionofthecodeauvesIMP_PBSdata,givenabove,;toonchipRAND. at$809c00WIPDUALSTART, AROWI€RANLAR1WYARO+-f,R0OPTSWIN_SIZEWYtAR0H-,R0I)STYRO,tATtll-fWUP;CleartheDUALaesory(30000to33300)tEl@DUALSTART, R6WI@DUALEWD,R7CALLCLEARThisportionofthecodeadjuststhesineandcosinetablesintable-asm-Sothatthevaloascanbeoutputto0/AsI-a 0 0LDPCODESLOl@COS_TABLE,0R7LOIOSINTABLE,0R6LOINL-l,RCRPTBFINSR1LOP*Rp77j7LOF*00606MPIP000CRES,R7HPYF600COZS,R6FIXRiFIXR6LSU16,R71,511l6,R6511R7,*AR74fFTNSB1:$71R6,*RR64f;adjusttheoutputvoltageLOP1.0,04CALLBUILD_WINHOPLOISPS,R3CALLMORESINNOPROOT1,05incresentthecounterGiPISPS,R50HZLOOP1HOPBRMAIN_ROUTINE****************************************IThisportionofthecodebuildsNRZsequencesINPUTS: R5{systolI0-7)BUILD_WIN: LOlONINOOW, 000LOP—1.0,00initializeregistersLOP-1.0,01LOP-1.0,0275101,05LOIREl.O,R075102,05LOFNE1.0,0175104,05LOIRE1.0,02OPTSSPS-lSIPR0,1ARO++OPTSSPS-lSIP01,*00014OPTSSPS-lSIPP2,*000+4PETS******************************************************ThisportionofthecodecreatestheGLUT’outputsyrbol.INPUTS:0R3{locationinanwhersystoltobelocated),R3{sps),R4{newbit)OUTPUTS :003 1locationofnextsysi)MAKESIN: LOTININOON,000LOTWTN_STZE-l,RCLOP04,00loadinnewvalueCALLSTUFFLOTONINOOW, 000LOT0INP_RES,AR1LOTNIN_STZE,BKLOTWIN_SIZE-2,RCCALLFIRMPh@NOBN,R0RHORUSIPR0,ThR3+fSOOT1,03BOlDMAZE_SINNOPWOONOPPETSthisportionofthecodeisinitializesthevariablesofTSRLOPCODESLOT0WAVETABLE,AR1:setapointertothewavetableLOTOCOSTABLE,002LOT@SINTABLE,AR3LOTOSERIALO,004LOPOMOO1,R7LOP0NO02,R6LOPONCHIPSIPR7,0MOOVA1UEI.SIPR6,IMOOVALUE2LOT001,07SIT07,ITABLE;pointertothebeginningoftableLOTAR2,R7SITR7,ICOSPOINTERLOTAR3,R7SITR7,0STNPOINTERLOT004,07SITR7,ISERTALOLOT0,R7SITR7,05E1_PLAGSITR7,0SINPOINIERLOP0.0,07initialpbaseSIPR7,@PBASELOT-1,07SITR7,0PREVOTTLOT1,07SITR7,00IP_ENC:typeofencodinglbitor2bitThisportinofthecodecallsMAKE_SINtoanteatabelofallpossiblesasples:GLOBALPEGS.:03,04,05,003thesesbouldnotbeandifiedbycallsLOPCODESLOTIWAVETABLE,AR3LOT0,05acounterfortotalIofsysbolsLOOPLLOP—l.0,R4LOTSPS,R3CALLBUILD_WINHOPCALLMAKE_SINHOP;resultofFIRisin00norsnlizethefilteroutputI-a 0 I-AORZ000b,ST:aettheglobalintruptGINinSTSTUFFRPTBDONEWF*MUR1IISTYRU,9R01-fDONEWFRl,RUNETSSUB!R6,R7WIN1,RiRNDEADWIO,ROLDIR6,ARURPTSR7STIRU,‘ARD++NETSsavetheoldvaluestuffinthenewoneWPONUBIPWI€SETLAG,RiBNZGETOUTDIP!O,R4HZNENBITFIRThisportionofthecodefindsFIRoftwovectorsoflengthN.INPUTS:ARU{addrl),AR1{addr2),BK{N),RCIN-2),OUTPUTS:RO{result)MPYF3*ARU++(l),*ARl4f(l)%,RU;initializeRHWYO.U,R2;initializeR2NETSRCppy*ARU44(l),*APd4f(l)%,RQIIADDFSRO,E2,R2ADDFRO,R2,RO;AddlastprductBETSDEAD:BRDEADThisportionofcodeisusedtostuffavalueatthefirstlocationofavectorandshifttheoldervaluesdownbyone.INPUTS:ARO{vectorpointer),RC{vectorsize),RU{newvalue)ThissectionclearssesorychunksspecifiedbyARO-->AR1CLEAR:IntruptserviceroutineRi-newbit,Ri—wavetableindexAR1—pointertowavetableR4—aps,theseareglobalregistersforISRISR:iffirstsanplegetnewbitTRANSMIT: LUFtARl++,Ri;pointtoGLPFoutputsysbolENDRiRNDRI•**C***PHASEACCUMULATOR**C********LUFU,RSLUF@PHASE,R6:getpreiviousphaseENDR6ADDFR7,R6;integrateENDR6ENDR6LDFN@MO7LUE1,R5(phase)ind2pioperation01FF€MUD_VALUE1,R6WFG’F€MODVALUE2,R5ADDFR5,R6ENDR6STYR6,€PBASE;storethephasefornextUseMUTTO.5,R6FLOATNL,R5WITR5,R6FIXR6WIR6,IR1STER6,€SYM_POINZRWI€COS_POINIER,AR6WI)SINPOINTER,AR1LU!t+AR6(IR1),R6ED!*+M7(Bl)R7SI!RH,NAUCHANA;outputIsaspleSI!R7,@ADCHANB:output0saspleED!PSERIALO,AR3;aendaplusetothereceiveronceeverysaspleED!22H,R6DPI8,E4LDIEQ62h,R6SI!R6,CAR3SUB!l,R4;ifendofsystolgetnewbitGETOHI:BET!NENBIT:LDPUNCUIPED!SPS,R4:resetthesysbolcounterED!@TABLE,AR1;resetthetablepointerWI@SERIALO,AR3HerewesetupTiserlcontrolregistersandperiodregistersBEGIN_IRENS:WPCODESWINTDIECTE,AR7LDI@RSTCTRLRISTIE7,*AR7LDI@PETUOD,AR6WI@COUNI,R6SI!R6,*AR6LDIUSETC’rEi,RiSI!RT,*AR7LDIHNAVETABLE, Ml:setapointertothewavetableLU!UVDATA,AROLDIU,R3;initializeRIforindexLDIU,R4;setthecounterforsasplesperayeLU!OOffh,BK0 t’3OR2,IN;enableintruptfortinerlWI26b,R6STIR6,tJJ3;output aplusetothemdentestertogetabitWI*AN3R1AND0800h,Rl;mskthebittobetransriittedWE-ll,RlbitisinRiINC_BIT:differentailyencodethebit75Thl,Rlisit‘1’WIZ-i,Ri:1.1notJIDINDi,Ri.ifyesiWI@DIFENC,R775ThLR7Witdiff.encodingWINDRi,R1;ifyesnoencodingBZBIT2_ENC;ifyesdotwobitencBRINDEX;indexofthesystolin61ffoutputtableBIT2_ENC:WIØPREVBIT,R7:bk__ak*bk_iNEGIRiMPYIRi,Rl571R1,@PREVBITINDEX:WIRi,Ri;converttobit‘0’or‘1’WIN0001:‘O’ifRiwas‘-1’,unchangedotherwiseISOi,R3;snkespacefornewbitANDOfh,R3;useonly4ISB5of003ORRi.R3;stuffinnewbitIDI8,R7HEllSR7,R3,IRO;storetheindexinThOLDF*Mi++(IN0) ,Ri;updatethetablepointerBRTRANSMIT.endIa C ca

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