THE UNIVERSITY OF NAIROBI DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

Transcription

1 THE UNIVERSITY OF NAIROBI DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING PROJECT TITLE: ACQUISITION OF DIRECT-SEQUENCE SPREAD-SPECTRUM SIGNALS PROJECT CODE: PRJ011 NAME: JOSEPH KIBUGI CHEGE REGISTRATION NUMBER: F17/1408/2011 SUPERVISOR: PROF. V.K. ODUOL EXAMINER: DR. P. AKUON This project report is submitted in partial fulfilment of the requirement for the award of the degree of Bachelor of Science in Electrical and Electronic Engineering of the University of Nairobi. Date of Submission: 13 th May, 2016

2 ii DECLARATION OF ORIGINALITY NAME OF STUDENT: REGISTRATION NUMBER: COLLEGE: FACULTY: DEPARTMENT: COURSE NAME: PROJECT TITLE: PROJECT CODE: Joseph Kibugi Chege F17/1408/2011 Architecture and Engineering Engineering Electrical and Information Engineering Bachelor of Science in Electrical and Electronic Engineering ACQUISITION OF DIRECT-SEQUENCE SPREAD- SPECTRUM SIGNALS PRJ I understand what plagiarism is and I am aware of the university policy in this regard. 2. I declare that this final year project report is my original work and has not been submitted elsewhere for examination, award of a degree or publication. Where other people s work or my own work has been used, this has been properly acknowledged and referenced in accordance with the University of Nairobi s requirements. 3. I have not sought or used the services of any professional agencies to produce this work. 4. I understand that any false claim in respect of this work shall result in disciplinary action, in accordance with University anti-plagiarism policy. Signature: Date: 13 th May, 2016.

3 iii CERTIFICATION This report was submitted to the Department of Electrical and Information Engineering, University of Nairobi, with my approval as supervisor:. PROF. VITALICE K. ODUOL Date.

4 iv ACKNOWLEDGEMENT I would like to thank my supervisor, Prof. V. K. Oduol, without whom this work would not be possible. His availability and ideas gave me the motivation I needed to complete this work. Many thanks to my parents and siblings who supported me and put up with my frequent absence as I worked on this project. Finally, immense gratitude to the Almighty God, to whom all glory and honour rightly belongs.

5 v LIST OF FIGURES Figure 1: Feedback shift register. 5 Figure 2: PN sequence waveforms. Autocorrelation function (top). 6 Power spectral density (bottom). Figure 3: DS-SS waveforms. Binary data (top). PN sequence (mid). 9 Spread binary data (bottom). Figure 4: DS baseband model. Transmitter (top left). Channel (top right). 10 Receiver (bottom). Figure 5: DS passband transmitter model. 11 Figure 6: DS passband receiver model. 12 Figure 7: Received DS signal. a) Before despreading. b) After despreading. 13 Figure 8: Block diagram of code synchronization system. 14 Figure 9: Digital matched filter. 16 Figure 10: Serial-search acquisition. 17 Figure 11: Block diagram of a non-coherent correlator 18 Figure 12: Delay-locked loop 19 Figure 13: Block diagram of DS-SS system 22 Figure 14: Block diagram of transmitter 22 Figure 15: PN generator 23 Figure 16: User data (top). PN sequence (bottom). 23 Figure 17: Spectrum of binary data (top). Spectrum of the spread signal (bottom). 24 Figure 18: Block diagram of receiver. 25 Figure 19: Transmitted (top) and received (bottom) waveforms. 25 Figure 20: Block diagram of synchronization system. 26 Figure 21: Block diagram of non-coherent correlator. 27 Figure 22: Threshold detector. 27 Figure 23: Output of threshold detector. 28

6 vi Figure 24: Block diagram of tracking system. 28 Figure 25: Output of VCO. 29 Figure 26: Block diagram of search control unit. 29 Figure 27: Normal clock (top). Synchronized clock (bottom). 30 Figure 28: Transmitter PN sequence (top). Receiver PN sequence (bottom). 31 Figure 29: Error rate calculator and display. 32 Figure 30: Jittery clock in transmitter PN generator. 32 Figure 31: Jittery clock generator. 33 Figure 32: Jittery clock output. 33 Figure 33: BER performance. 36

7 vii LIST OF TABLES Table 1: Generator polynomials 7 Table 2: Characteristics of Gold sequences 8 Table 3: BER performance for system with normal clock 35 Table 4: BER performance for system with jittery clock 35

8 viii TABLE OF CONTENTS Declaration of Originality Certification Acknowledgement List of Figures ii iii iv v List of Tables vii 1 Introduction Abstract Problem Definition Objectives Scope Justification Report Organization 2 2 Literature Review Spread-Spectrum Communication Systems Origins Definitions and Concepts Direct-Sequence Spread-Spectrum Systems Pseudo-Noise (PN) Sequences Gold Sequences Spectrum Spreading in DS-SS DS-SS with Coherent Binary Phase-Shift Keying Code Synchronization Code Acquisition Acquisition Methods Matched-Filter Acquisition Serial-Search Acquisition 17

9 ix Code Tracking Application of Spread Spectrum: CDMA 19 3 System Description Model Realization Description of DS-SS system Transmitter Architecture Channel Receiver Architecture Synchronization System Acquisition System Tracking System Search Control Unit Blocks for Performance Testing 31 4 System Performance Theoretical BER for BPSK Performance of DS-SS System 34 5 Conclusion 38 APPENDICES A MATLAB S-Function File for Jittery Clock 39 B Abbreviations and Acronyms 42 C References 43

10 1 1. Introduction 1.1. Abstract Spread-spectrum communication systems have been found to be extremely efficient at attenuating interference and have found wide usage, from their early application in the military to their current application in multiple-access systems such as code division multiple access (CDMA). However, for a spread-spectrum system to work well, synchronization of the spreading code at the transmitter and receiver must be achieved. This project investigates one of the aspects of synchronization, referred to as acquisition, with specific regard to one type of spread-spectrum system: so-called direct-sequence spread-spectrum (DS-SS) system. The goal is to design a code acquisition method and to demonstrate that it works Problem Definition Synchronization of the spreading code is of utmost importance in any spread-spectrum system. The proper operation of the system depends on how well synchronization is done. A solution to the synchronization problem consists of two parts, referred to as acquisition and tracking. Acquisition may be regarded as coarse synchronization and, being the first step in the synchronization procedure, must work very efficiently, after which tracking can be performed and synchronization ultimately achieved. This project focuses on the problem of designing an efficient code acquisition method Objectives To study code acquisition in direct-sequence spread-spectrum communication systems. To describe code acquisition and explain why it is necessary. To design and demonstrate a code acquisition method Scope It is important to note that the synchronization aspects of acquisition and tracking are not mutually exclusive, with both depending on each other for synchronization to be achieved. With this crucial point in mind, the project will describe direct-sequence spread-spectrum systems with regard to spreading sequences, transmitter and receiver design, acquisition and tracking. Applications of direct-sequence spread spectrum systems in multiple-access systems will also be described briefly. A special focus will be accorded to code acquisition with the eventual result that a code acquisition method is designed and demonstrated.

11 Justification A simulation of a direct-sequence spread-spectrum system will be performed to demonstrate code acquisition Report Organization Chapter 1 gives a general introduction to the project and describes the objectives and scope of the project. Chapter 2 presents the theoretical background of direct-sequence spread-spectrum systems and gives a detailed treatment of code synchronization. Chapter 3 describes the various parts that make up the system in detail. Chapter 4 presents the performance of the system and makes a comparison with the performance of a theoretical system. Chapter 5 concludes the project and mentions some modifications that could be made to the system.

12 3 2. Literature Review 2.1. Spread-Spectrum Communication Systems Origins Spread-spectrum communication systems owe their existence to a variety of events which took place between 1920 and The earliest applications were military in nature where such attributes of spread-spectrum systems as anti-jam capabilities and low probability of intercept (LPI) of signals was desirable. Radar engineers in the early 1920s knew about spectrum spreading for jamming avoidance and signal discrimination [2]. The earliest patent according to the U.S. Patent Office that was spread-spectrum in nature was filed by Alfred Goldsmith in Another widely held view as to who exactly invented spread-spectrum systems attributes it to actress Hedwig Eva Marie Kiesler, also known as Hedy Lamarr. She, together with pianist George Antheil, filed a patent for a secret communication system in 1941, which proposed a simple but reliable communication system based on the use of carrier waves of different frequencies that was difficult to decipher [9]. Before the 1960s, most of the work done on spread-spectrum techniques remained a secret and only in the late 1970s did it become available to the public. Spread-spectrum communication has become an increasingly popular technique and is now used in multiple-access systems such as CDMA and in systems designed to combat multipath, for instance, ground-based mobile radio environments Definitions and Concepts One of the primary design objectives in any communication system is to minimize the transmission bandwidth and to efficiently use power. This is because bandwidth and power are limited communication resources. However, in some instances, it is desirable to sacrifice the efficient use of bandwidth and power in order to meet other design objectives, such as providing a secure form of communication in a hostile environment, multiple-access capability and low probability of intercept, among others. These requirements are met by a class of signaling techniques referred to as spreadspectrum techniques. An apt definition of spread spectrum is a means of transmission in which the data sequence occupies a bandwidth in excess of the minimum bandwidth required to send it. Furthermore, the spectrum spreading is accomplished by means of a code which is independent of the data sequence. At the receiver, which

13 4 is operating in synchronism with the transmitter, the same code is used to despread the spectrum and the data sequence is recovered [3]. Various types of spread-spectrum signaling techniques are available. These are: Direct sequence (DS) The data sequence is used to modulate a wideband code, which is a fast pseudo-randomly generated sequence, with the result that the narrowband data sequence is transformed into a wideband noise-like signal. The resulting wideband signal then undergoes a second stage of modulation, where phase-shift keying is used. Frequency hopping (FH) The spectrum of a data-modulated carrier is widened by shifting the frequency in a pseudo-random manner. A common modulation technique used for FH is M-ary frequency shift keying (MFSK). Two characterizations of frequency hopping exist: slow FH, where several symbols are transmitted on each frequency hop; and fast FH, where the carrier frequency hops several times during the transmission of one symbol. Time hopping (TH) In this technique, bursts of signal are initiated at pseudorandom times. There are also hybrid techniques that involve both DS and FH. A more detailed discussion of DS-SS systems is now given Direct-Sequence Spread-Spectrum Systems As stated above, both DS and FH systems require the use of a noise-like spreading code referred to as a pseudo-random or pseudo-noise (PN) sequence. A brief discussion of PN sequences and another type of spreading sequence, the Gold sequence, is given below Pseudo-Noise (PN) Sequences A PN sequence is a periodic binary sequence with an autocorrelation that resembles, over a period, the autocorrelation of a random binary sequence. Its autocorrelation also roughly resembles the autocorrelation of bandlimited white noise [7]. Ideally, one would want to use a truly random binary sequence. However, for the data to be recovered, the receiver needs to know the code that was used for spreading. This knowledge is unavailable in a non-deterministic process like a random binary sequence, hence the use of PN sequences, which are deterministic. PN sequences are generated by means of a feedback shift register. These registers are made up of consecutive stages of bistable memory devices (flip-flops) and feedback logic. The flip-flops are regulated by a single clock. The block diagram below illustrates the basic features of a feedback shift register [6].

14 5 Figure 1 Feedback shift register At each tick of the clock, the state of each flip-flop is shifted to the next one down the line. At the same time, the logic circuit computes a Boolean function of the states of the flip-flops. The result of this computation is fed back as the input to the first flipflop. The sequence generated is therefore determined by the length m of the shift register. For m flip-flops, the maximum number of possible states of the shift register is 2 m. The PN sequence so generated must therefore eventually become periodic with a period of at most 2 m. In practice, PN sequences are generated by linear feedback shift registers (LFSRs). These are feedback shift registers in which the feedback logic consists of modulo-2 adders. For LFSRs, the zero state, which is the state in which all the flip-flops are in state 0, is not allowed since the output would always consist entirely of zeros. Therefore, the period of a PN sequence produced by such a feedback register consisting of m flip-flops cannot be greater than 2 m 1. When the period is exactly 2 m 1, the PN sequence is referred to as a maximal-length sequence or an m- sequence. Maximal-length sequences have a few important salient properties. These are: Balance property In each period of an m-sequence, the number of 1s is always one more than the number of zeros. Run-length property A run is a subsequence of identical binary symbols within each period of the m-sequence. In each period of an m-sequence, the run-lengths of 1s and 0s are as expected in a coin-flipping experiment, that is, half of all run-lengths are unity, a quarter are of length two, an eighth are of length three, and so on, as long as these fractions represent meaningful numbers of runs.

15 6 Delay-and-add property The modulo-2 sum of any m-sequence, when summed chip by chip with a shifted version of the same sequence, produces another shifted version of the same sequence. Correlation property The autocorrelation function of an m-sequence is periodic and binary-valued. If T c is the duration assigned to each symbol in the m-sequence and N = 2 m 1, then the following expressions represent the autocorrelation function and the power spectral density, respectively [6]: R c (τ) = { 1 N + 1 NT c τ, τ T c 1 N, else (2.1) S(f) = N δ(f) + N2 N 2 sinc 2 ( n n ) δ (f ) N NT c n= n 0 (2.2) The plots of these two waveforms are shown below [4]: Figure 2 PN sequence waveforms. Autocorrelation function (top). Power spectral density (bottom)

16 7 It can be seen that maximal length sequences exhibit many of the properties possessed by a truly random binary sequence. As a matter of fact, in the limit, the two sequences become identical as N is made infinitely large. However, a large N means an increasing storage requirement, which imposes a practical limit on the size of N. Certain conditions must be met for a maximal-length sequence to be generated. Generally, maximal-length sequences are defined by polynomials in the binary field GF(2). In this field, a primitive polynomial is a polynomial that possesses the property that the smallest integer n for which the polynomial divides 1 + x n is n = 2 m 1. It turns out that any polynomial of degree m will generate a maximallength sequence of period N = 2 m 1 if and only if it is a primitive polynomial. This is a necessary and sufficient condition. Furthermore, for a positive integer m, the number of different primitive polynomials of degree m over GF(2) is given by λ m = φ e(2 m 1) m (2.3) where φ e (n) is the number of positive integers less than and relatively prime to n (n > 0), also known as Euler s totient function. The table below shows some of the polynomials that generate maximal-length sequences for different register lengths [1]. Register length m Sequence N = 2 m -1 Number of polynomials Polynomial generators x + x x + x x 2 + x x + x x 3 + x x 2 + x x 3 + x x + x 2 + x 3 + x x + x 2 + x 4 + x x + x 3 + x 4 + x x 2 + x 3 + x 4 + x x + x x + x 3 + x 4 + x x 5 + x x + x 2 + x 5 + x x 2 + x 3 + x 5 + x x + x 4 + x 5 + x 6 Table 1 Generator polynomials

17 8 While the autocorrelation properties of PN sequences are very good, the crosscorrelation properties are quite poor. Thus, PN sequences are not suitable for use in multiple-access systems, which require that the cross-correlation between any two users to be very low (ideally zero). A special type of PN sequences, referred to as Gold sequences, meet this requirement Gold Sequences These sequences are based on Gold s theorem, stated below [11]: Let f 1 and f 2 be a preferred pair of primitive polynomials of degree n whose corresponding shift registers generate maximal linear sequences of period 2 n 1 and whose cross-correlation function θ satisfies the inequality θ { 2(n+1) 2 + 1, n odd 2 (n+2) 2 + 1, n even; n 0 mod 4 (2.4) Then the shift register corresponding to the product polynomial f 1 f 2 will generate 2 n + 1 different sequences each of period 2 n 1 and such that the crosscorrelation function of any pair of such sequences satisfies the inequality above. Gold sequences are generated by the modulo-2 addition of two maximal-length sequences of the same length. The code sequences are added chip by chip by synchronous clocking. A special set of Gold sequences is formed from preferred pairs of m-sequences. These sequences have uniform and bounded cross-correlation which is three-valued, as shown in the table below: Register length n Code length N Normalized crosscorrelation Odd 2 n 1 1 N (2 (n+1) 2 + 1) N (2 (n+1) 2 1) N Even and not 2 n 1 1 N divisible by 4 (2 (n+2) 2 + 1) N (2 (n+2) 2 1) N Frequency of occurrence ~0.50 ~0.25 ~0.25 ~0.75 ~0.125 ~0.125 Table 2 Characteristics of Gold sequences It can be seen from the table that for register lengths that are even and not divisible by 4, the cross-correlation is 1 N 75% of the time, which is quite a good performance.

18 9 Gold sequences are used widely in multiple-access systems like CDMA, frequencyhopping multiple access (FHMA) and ultra-wideband spread-spectrum communication systems due to their excellent cross-correlation properties. However, they are usually non-maximal and hence have autocorrelation functions that are worse than those of m-sequences Spectrum Spreading in DS-SS From Fourier theory, it is known that multiplying two signals in the time domain is equivalent to convolving the spectra of the two signals in the frequency domain. Accordingly, given a narrowband message signal b(t) and a wideband PN signal c(t), the product signal m(t) will have a spectrum that is nearly the same as the wideband PN signal. Thus, the PN signal performs the role of a spreading code. The process of multiplying the message signal and the PN signal causes each message bit to be chopped up into small time increments referred to as chips. This is illustrated in the waveforms below: Figure 3 DS-SS waveforms. Binary data (top). PN sequence (mid). Spread binary data (bottom)

19 10 Consider the following baseband model of a DS system consisting of the transmitter, channel and receiver [6]. Figure 4 DS baseband model. Transmitter (top left). Channel (top right). Receiver (bottom) The transmitted signal may be expressed as m(t) = b(t)c(t) (2.5) The received signal r(t) consists of the transmitted signal m(t) plus additive interference j(t) introduced in the channel. Thus, r(t) = m(t) + j(t) = c(t)b(t) + j(t) (2.6) At the receiver, the signal r(t) is demodulated. The demodulation involves multiplication with a local PN sequence which is an exact replica of the sequence used in the transmitter. Assuming that the two PN sequences operate in perfect synchronism, the output z(t) of the multiplier at the receiver is z(t) = c 2 (t)b(t) + c(t)j(t) (2.7) Assuming the PN sequence alternates between -1 and +1, squaring destroys the alternation and thus z(t) = b(t) + c(t)j(t) (2.8) Thus, the message signal is recovered at the receiver. However, multiplication of the interference j(t) with the local PN sequence will spread its spectrum as it did the data at the transmitter. Hence, at the receiver, the message is narrowband while the interference is wideband. All that remains is to apply the multiplier output to a low-

20 11 pass filter with a bandwidth just large enough to accommodate the message signal, filtering out almost all the power in the interference and significantly reducing its effect at the receiver. Hence, a DS spread-spectrum system is seen to be able to reject interference effectively, as well as ensure low probability of intercept for the message signal. The use of the spreading code produces a wideband transmitted signal that appears noiselike to a receiver that has no knowledge of the spreading code DS-SS with Coherent Binary Phase-Shift Keying Coherent BPSK is incorporated into the transmitter and the receiver to enable this technique to be used in passband transmission. The figure below shows a block diagram of the transmitter [4]. Figure 5 DS passband transmitter model A message sequence {b k } is a stream of 1s and 0s. This sequence is first fed to a polar NRZ level encoder (not shown) which does the mapping 0 1, 1 +1, converting the unipolar sequence to a bipolar one. The bipolar sequence b(t) is then multiplied with the PN sequence c(t). This is the first stage of modulation. The second stage of modulation consists of a BPSK modulator which performs phase modulation on the message signal m(t) to yield a phase-modulated signal x(t) which is transmitted. The figure below shows a block diagram of the receiver [4].

21 12 Figure 6 DS passband receiver model At the receiver, two stages of demodulation are performed. The received signal y(t) can be represented as y(t) = 2E s T S b(t)c(t) cos(2πf c t + θ) (2.9) Here, E s is the energy of the received signal, T s is the duration of one symbol of the data sequence and θ(t) is the phase modulation, takes on values of 0 or π depending on the polarities of the data sequence and the PN sequence at any one time. The transitions of the data symbols and the PN chips coincide such that the ratio of T s to T c (the chip time) is an integer. If the bandwidth of the received signal y(t) is B ss and that of a conventionally modulated signal b(t)cos (2πf c t) is B, then the spreading due to c(t) is found to yield B ss B, that is, the signal occupies a bandwidth in excess of the minimum bandwidth necessary to send it. The first stage of demodulation involves coherent detection wherein the received signal y(t) and a locally generated carrier are applied to a product modulator, followed by low-pass filtering. This reverses the phase-shift keying applied to the transmitter signal. The second stage of demodulation involves despreading wherein the low-pass filter output is multiplied by a locally generated replica of the PN sequence and then integration is performed over a bit interval. Finally, a decisionmaking device gives the final output sequence. The figure below shows how the received signal together with interference (assumed narrowband) appear before and after despreading occurs [4].

22 13 Figure 7 Received DS signal. a) Before despreading. b) After despreading It can be seen that the received signal before despreading contains the desired signal whose spectrum has been spread at the transmitter and narrowband interference. However, after despreading, the spectrum of the interference is spread over a large bandwidth while the desired signal now occupies a narrow bandwidth. Low-pass filtering then extracts the desired signal and eliminates most of the original interference energy. An important figure of merit for a DS spread-spectrum system is referred to as the processing gain, denoted as PG. The processing gain is a measure of the interference rejection capability and is given as PG = T s T c = B ss B = B ss 2R s (2.10) Here, R s is the data rate. Hence, the greater the processing gain of the system, the greater will be its ability to suppress interference Code Synchronization At the spread-spectrum receiver, the corresponding chips in the spreading sequence must precisely or nearly coincide. Any misalignment causes the signal amplitude at the demodulator to fall in accordance with the autocorrelation function, leading to signal degradation. Use of precision clocks in the transmitter and the receiver may help to limit the uncertainty but there is still the potential of synchronization problems due to clock drift, range uncertainty and the Doppler shift. There are various ways in which code synchronization in a spread-spectrum system may be achieved. Separately transmitted pilot or timing signals or using feedback signals from the receiver to the transmitter are some of the ways. However, both of these ways accrue significant costs in power and overhead. A method which is more modest in power and overhead is to use the received signal to acquire synchronization.

23 14 A commonly used method for synchronization is maximum likelihood estimation where candidate values for phase offset and frequency offset are tested and those that maximize a likelihood function are picked as the correct values. Synchronization consists of two parts: acquisition and tracking. Code acquisition is the operation by which the phase of the receiver-generated sequence is brought to within a fraction of a chip of the phase of the received sequence. Code tracking is the operation by which synchronization errors are further reduced or at least maintained within certain bounds. Acquisition and tracking devices regulate the clock rate, adjusting the timing offset of the local sequence to the timing offset of the received sequence. The figure below shows a code synchronization system [1]. Figure 8 Block diagram of code synchronization system Code Acquisition Consider a received signal r(t) given by r(t) = s(t) + n(t) (2.11) where s(t) is the desired signal and n(t) is white Gaussian noise. The desired signal s(t) can be represented as s(t) = 2Sc(t τ) cos(2πf c t + 2πf d t + θ) (2.12) where S is the average power, c(t) is the PN waveform, θ is the random carrier phase and τ and f d are the code phase offset and frequency offset, respectively, which must be estimated. If the received waveform r(t) is expanded in terms of N orthonormal basis functions, an observation vector given by r = [r 1 r 2 r N ] will result. The likelihood function for the unknown code phase offset τ and frequency offset f d will be given by the

24 15 conditional density function of r given τ and f d. Since the carrier phase θ is a random variable, the likelihood function Λ(r) will be given by the expectation of the conditional density function with respect to θ: Λ(r) = E θ [f(r τ, f d, θ)] (2.13) Thus, the maximum-likelihood estimates will be those values of τ and f d that maximize the likelihood function. It can be shown that when an expansion in the orthonormal functions is done, the likelihood function can be expressed as Λ[r(t)] = J 0 ( 2 2SR(τ, f d) N 0 ) (2.14) where J 0 () is the modified Bessel function of the first kind of order zero, N 0 2 is the variance of each coefficient in the expansion of r(t) and T R(τ, f d ) = [ r(t)c(t τ) cos(2πf c t + 2πf d t) 0 2 dt] T 2 + [ r(t)c(t τ) sin(2πf c t + 2πf d t)dt] 0 (2.15) Since J 0 (x) is a monotonically increasing function of x, R(τ, f d ) is a sufficient statistic for maximum likelihood estimation. A device that implements this statistic is termed a non-coherent correlator. Thus, acquisition provides coarse synchronization by limiting the choices of the estimated values to a finite number of quantized candidates. The frequency offset is usually negligible (so long as Nf d T c is relatively small [5]) hence the focus is on the timing offset τ. One acquisition method is to use a parallel array of processors, each of which is matched to quantized values of the timing offset. The largest processor output then indicates which candidates are selected as estimates. Although quite fast, it is very complex and costly. A much simpler method is to use serial searching where each of the candidate offsets are searched serially. This method takes time for a decision to be made. However, this method will be utilised in this project.

25 Acquisition Methods A common feature of all acquisition methods is that the received signal and the locally generated PN sequence are first correlated to establish a measure of similarity between them. This measure is then compared to a threshold to determine if the two signals are in synchronism. If they are, a verification algorithm is started. Some dwell time is usually necessary while testing synchronism to avoid false locking. After this, tracking can begin. The two main acquisition methods are matched filter acquisition and serial-search acquisition, also known as the sliding correlator. These are briefly described below Matched-Filter Acquisition The figure below illustrates a digital matched filter that can be used for noncoherent acquisition [4]. Figure 9 Digital matched filter The received waveform is decomposed into in-phase and quadrature components, each of which is applied to a separate branch. Each component is passed through a filter, a sampler and a one-bit digitizer. The digitizer makes hard decisions on the sample values by observing their polarities. The output of the digitizer is then fed into a transversal filter, which consists of a shift register and a correlator. The shift register stores the sequence chips and compares them to the stored reference chips. The correlator outputs are then squared and summed. Thus, this filter generates the statistic R(τ, 0). Matched-filter acquisition gives the shortest acquisition time but is hardwareintensive for parallel implementation. The hardware increases with the PN codelength and hence this method is mostly used for short codes.

26 Serial-Search Acquisition This method consists of a search among candidate code phases of a local sequence till it is determined that the local sequence is nearly synchronized with the received spreading sequence. The search positions are referred to as cells, which are regions of timing uncertainty. The figure below illustrates the implementation of serial-search acquisition [4]. Figure 10 Serial-search acquisition The received signal together with the local PN sequence are applied to a noncoherent correlator which generates the statistic R(τ, 0). If the received and local spreading sequences are not aligned, the autocorrelation value is low and hence the threshold value is not exceeded. The cell under test is thus rejected and the phase of the local sequence is advanced or retarded by generating and extra clock pulse or by blocking one. If the received and local spreading sequences are aligned to within a certain arbitrary value (say, half a chip), then the autocorrelation value will be high and the threshold value will be exceeded. The search is then stopped and the cell is selected as the correct one. Demodulation and tracking can then commence. The amount of time required to test a cell is referred to as the dwell time and is approximately equal to the integration period in the non-coherent correlator. An acquisition system in which a single test determines whether a cell is accepted as the correct one or not is termed a single-dwell system; one in which subsequent verification tests are required before a decision is made is termed a multiple-dwell system. The figure below illustrates how a serial-search acquisition system may be implemented using a non-coherent correlator [1].

27 18 Figure 11 Block diagram of a non-coherent correlator Code Tracking Code tracking will be very briefly discussed as it is not the subject of this project; however, mention of it is important since acquisition and tracking are not mutually exclusive but rather depend of each other for synchronization to be achieved. Once receiver timing has been synchronized to within a fraction of a chip time, the estimate should further be refined to approach zero. Corrections must be made continuously because of the relative motion of transmitter and receiver and the instability of clocks. A popular method used for tracking is the delay-locked loop (DLL). This is shown in the figure below [4].

28 19 Figure 12 Delay-locked loop The locally generated PN sequence p r (t) of the tracking loop is offset from the incoming PN sequence p(t) by a time τ < T c 2. Within the DLL, two PN sequences are delayed from each other by one chip time (T c ), that is, p r (t + T c 2 + τ) (advanced sequence) and p r (t T c 2 + τ) (delayed sequence). When τ is positive, the error signal causes the voltage-controlled clock to increase its frequency, thereby forcing τ to decrease. Conversely, when τ is negative, the error signal causes the voltage-controlled clock to decrease its frequency, thereby forcing τ to increase. In this way, tracking of the PN sequence is achieved Application of Spread-Spectrum: Code Division Multiple Access (CDMA) CDMA is a multiple access technique for wireless communications that is implemented by spread-spectrum techniques. Unlike time division multiple access (TDMA) which requires time synchronization of individual users, or frequency division multiple access (FDMA) which requires bandwidth allocation, all the users in a CDMA system have full time and full bandwidth and can transmit simultaneously. In a CDMA system, each user is assigned its own PN sequence which is approximately orthogonal to all other sequences. The receiver performs a time correlation operation in order to detect only the specific desired sequence. All other sequences appear as noise to this particular receiver due to decorrelation. Of course, this receiver needs to have a knowledge of the PN sequence used by the transmitter. Thus, with the use of SS techniques, it is possible for multiple users to transmit simultaneously in the same frequency band, and yet the data can be decoded by a receiver, provided that the receiver uses a PN code that is identical to, and synchronized with, the particular SS signal that is to be decoded. However, the quality of communication

29 decreases as the number of users increases. CDMA (unlike TDMA or FDMA) is said to have a soft capacity limit since there is no absolute limit on the number of users; the system performance degrades for all users as the number of users is increased, and improves as the number of users is decreased. 20

30 21 3. System Description This section describes in detail the complete direct-sequence spread-spectrum system. The various parts of the system, namely, transmitter, receiver, channel, acquisition and tracking together with the subsystems contained therein are presented in depth Model Realization The system was modeled using Simulink, which is a companion software to MATLAB. Simulink is extremely well-suited to modeling many kinds of systems due to its vast array of packages tailor-made for various applications including, but not limited to, communication systems, computer vision, robotics and control systems. Simulink models systems using blocks which represent real-life systems. The software is user-friendly since each block has a description and a way to vary various parameters, making it quite versatile. It also contains visual tools such as displays, scopes, spectrum analyzers, among others which further lend to its facility in use. The Communications Blockset was mainly used in modeling the system, as well as other commonly-used blocks and mathematical operations. This blockset contains blocks pertaining to communication systems such as filters, modulators, demodulators, sequence generators and channels as well as utility blocks such as bipolar-to-unipolar converters and bit error rate calculators Description of DS-SS system The following system specifications were used: Bit rate 10 bits/second Chip rate 1000 chips/second Length of PN sequence 127 chips Modulation/Demodulation Binary phase-shift keying (BPSK) The system was broken down into four main sections: Transmitter Channel Receiver Synchronization (acquisition and tracking) The complete system is shown below.

31 22 Figure 13 Block diagram of DS-SS system Transmitter Architecture The transmitter model is shown below. Figure 14 Block diagram of transmitter The user data was generated by a Bernoulli binary generator at the rate of 10 bits/second. The probability of 1s and 0s was equal hence this was a good representation of real-life data which is usually random e.g. speech. The user data was then multiplied by the PN sequence to spread its spectrum. BPSK modulation was then carried out for passband transmission. The PN generator was built out of seven D flip-flops to give a code length of N = = 127. The generator polynomial used was 1 + x + x 7 which was gotten by

32 23 using the outputs of the first and seventh flip-flops in the feedback logic. The PN generator is shown below. Figure 15 PN generator The clock was set to run at 1000 Hz so as to generate a PN sequence at a rate of 1000 chips/second. There was also an option of using a variable clock so as to observe the performance of the system with regard to synchronization. The waveforms below show the user data and the PN sequence. Figure 16 User data (top). PN sequence (bottom)

33 24 Below, the spectra of the user data and of the spread sequence are shown. It can be seen that the spectrum has been made wider. While the spectrum of the user data has most of its energy from 0 5 Hz, the spread signal occupies a bandwidth of 1 khz. This is the spreading mechanism. It can also be noted that the magnitude of the spread signal is larger. Figure 17 Spectrum of binary data (top). Spectrum of the spread signal (bottom).

34 Channel An additive white Gaussian noise (AWGN) channel was used in the DS-SS model Receiver Architecture The figure below shows the receiver model. Figure 18 Block diagram of receiver. At the receiver, the phase-shift keying was undone using a BPSK demodulator. This was followed by despreading using a synchronized PN sequence generated by a local PN generator. Filtering and signal shaping was then done to receive an estimate of the transmitted user data. The figure below shows the transmitted and received user data for a signal-to-noise ratio (SNR) of 10 db. Figure 19 Transmitted (top) and received (bottom) waveforms

35 26 It can be seen that the data can be recovered at the receiver after despreading using a local PN generator Synchronization System The figure below shows the synchronization system. Figure 20 Block diagram of the synchronization system It can be seen that there are three main sections in the synchronization system, namely, the acquisition system (made up of the non-coherent correlator and the threshold detector), the tracking system and the search control unit. Each of these is now described separately Acquisition System Serial-search acquisition with non-coherent correlation was used in the acquisition system. A non-coherent correlator was used since in a DS-SS system, the carrier frequency is not normally known during time synchronization, disqualifying the use of a coherent correlator. The internal components making up the noncoherent correlator are shown in the figure below.

36 27 Figure 21 Block diagram of non-coherent correlator The data from the channel is multiplied by an in-phase and quadrature sinusoidal waveform at the carrier frequency to generate in-phase and quadrature components of the received data. Each component is passed through a chipmatched filter and sampled at the rate of the synchronized clock (more on this later). The sampled components are then multiplied by the local PN sequence and passed through a square-law detector and finally summed to generate correlated data. The correlated data is then taken to a threshold detector, shown in the figure below. Figure 22 Threshold detector. The threshold detector consists of a filter and a comparator. The correlated data is filtered and then compared to a threshold. The output of the comparator is HIGH if the data is greater than or equal to the threshold and LOW if it is less

37 28 than the threshold. Thus, a 1 or a 0 is output from the threshold detector, as shown in the figure below. Figure 23 Output of threshold detector Tracking System The tracking system was implemented as a DLL, as shown in the figure below. Figure 24 Block diagram of tracking system The three inputs to the DLL are gotten from the non-coherent correlator. The early PN sequence is the synchronized sequence while the late PN sequence is gotten from the output of the sixth flip-flop in the local PN generator. These sequences are correlated with the data from the channel using the filter and the envelope detector. The two components are then summed and taken to a voltage-

38 29 controlled oscillator (VCO). The VCO produces a sinusoidal signal whose frequency varies with the amplitude of the input signal. After signal shaping using the limiter and the bipolar-to-unipolar converter, a square wave with varying frequency results, as shown in the figure below. Figure 25 Output of VCO. Thus, the DLL uses the delayed and advanced PN sequences to produce a signal which tracks the received sequence Search Control Unit The figure below shows the search control unit. Figure 26 Block diagram of search control unit

39 30 The clock in this unit had a period of a fifth of the chip time, i.e. T = 1 s = This ensured that the serial search was performed over decision regions (or T c 5 cells) much less than a chip size, improving accuracy. The clock output is first inverted to enable it to drive a negative-edge triggered flip-flop. The inverted clock and the signal from the threshold detector serve as inputs to a NAND logic gate. The logic gate gives a HIGH output whenever the clock and the detected signal are 90 out of phase or are both LOW. Whenever the clock and the detected signal are both HIGH, the output of the NAND gate is LOW. The J-K flip-flop has shorted inputs hence it acts as a T flip-flop. Whenever the input to a T flip-flop is HIGH, the output of the flip-flop is LOW and vice versa; the flip-flop performs toggling. Thus, if the clock and the detected signal are not synchronized, the search control unit generates an extra clock pulse, effectively slowing down the clock. The output of the flip-flop is then modulo-2 added with the signal from the tracking system, giving rise to a synchronized clock signal. The figure below compares the normal clock and the synchronized clock. Figure 27 Normal clock (top). Synchronized clock (bottom). It is this synchronized clock that drives the local PN generator to give rise to a synchronized PN sequence which can be used at the receiver to recover the data. The figure below compares the transmitter and receiver PN sequences.

40 31 Figure 28 Transmitter PN sequence (top). Receiver PN sequence (bottom). It can be seen that the receiver PN sequence does not vary in the same manner as the transmitter PN sequence due to the latter s adjustment by the search control unit Blocks for Performance Testing. The Error Rate Calculator block form the Communications Blockset was used to test the performance. This block computes the bit error rate using the transmitted and received signals and outputs three sets of data: the bit error rate, the number of errors detected and the number of symbols compared. These were displayed using the Display block. The figure below illustrates this.

41 32 Figure 29 Error rate calculator and display Thus, the simulation above yielded a bit error rate of or 0.8%. Out of 1000 symbols compared, 8 errors were detected. A jittery clock generator was also included in the transmitter PN generator as shown below. Figure 30 Jittery clock in transmitter PN generator Selection between a normal clock and the jittery clock generator was possible using a manual switch. The purpose of the jittery clock generator was to simulate a realworld system where clock drift and instability would be unavoidable. The internal structure of the jittery clock generator was as shown in the figure below.

42 33 Figure 31 Jittery clock generator A MATLAB function was used [12] to create a clock with jitter to simulate a real clock which would inevitably suffer from drift and instability. The Rate Transition block was used to ensure that only discrete samples were used in the system. Most of the blocks in the system required discrete samples hence the need for this block. The figure below shows the output of the jittery clock generator. Figure 32 Clock with jitter

43 34 4. System Performance This section describes the performance of the direct-sequence spread-spectrum system. For a spread-spectrum system, the parameters of interest are usually the acquisition time and the bit error rate (BER). In this system, acquisition is instantaneous since no delay is introduced in the channel. However, the BER performance of the system is investigated with regard to two conditions: system driven by a normal clock and system driven by a jittery clock Theoretical BER for BPSK The BER, also known as the probability of bit error, denoted by P e, is a measure of the level of deterioration in a digital communication system. The BER for modulation schemes in an AWGN channel is found using the Q-function of the distance between the signal points. The Q-function is defined as [8] Q(z) = 1 2π x2 exp ( 2 ) dx z (4.1) For a BPSK system, the theoretical BER is given by [2] [8] BER BPSK = Q ( 2E b N 0 ) (4.2) Here, E b is the energy per bit and N 0 is the power spectral density of the noise in the channel (in this case, white noise) Performance of DS-SS system Simulations were run on the DS-SS system using Simulink. Two conditions were investigated, namely, system with normal clock and system with jittery clock. The number of symbols compared was The tables below show the BER performance of the system under both conditions.

44 35 E b Normal clock N 0 (db) BER Table 3 BER performance for system with normal clock E b Jittery clock N 0 (db) BER Table 4 BER performance for system with jittery clock

45 36 The following MATLAB code snippet was written to plot the data above, as well as the theoretical BER to provide a visual comparison between the systems. % DS-SS system performance % Theoretical BER for BPSK is given by Q(sqrt(2*Eb/No)) x = 0:10; % Eb/No snr = 10.^(x/10); y = qfunc(sqrt(2*snr)); semilogy(x,y); hold on; % BER against Eb/No for system with normal clock y1 = [ ]; semilogy(x,y1,'r-*'); hold on; % BER against Eb/No for system with jittery clock y2 = [ ]; semilogy(x,y2,'g-o'); title('bit error rate performance'); grid on; xlabel('eb/no (db)'); ylabel('ber') legend('theoretical','normal clock','jittery clock'); The plots of the three systems are shown below. Figure 33 BER performance From the graphs above, it can be seen that for both systems, the performance is as expected: the BER improves as the SNR is increased. For the system driven by a normal clock, it can

46 37 be seen that at an SNR of 10 db, a BER of is achieved, which is quite close to the figure usually used in industry which is around When the system is driven by a jittery clock, it is found to have exactly the same performance as the system with the normal clock. This demonstrates that the acquisition system works as expected and acceptable reception is gotten at the receiver.

47 38 5. Conclusion This project was established to investigate code acquisition in direct-sequence spread-spectrum communication systems. The serial-search acquisition method was implemented using a noncoherent correlator. A working model was built using Simulink and was tested. It was demonstrated in the previous chapter that the acquisition method works and the overall system had a bit error rate performance comparable to that required in practice. A fuller treatment of direct-sequence spread-spectrum communication systems would investigate the performance of the system in fading channels, in addition to AWGN channels. Delays could be introduced in the channel and the time the system took to acquire acquisition would be a performance parameter. Further, the system could be modified to compute probabilities of false alarm and false detection and these two parameters could be used to plot the receiver operating characteristics of the system.