UNIVERSITY OF NAIROBI

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1 UNIVERSITY OF NAIROBI DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING PROJECT TITLE: TRACKING LOOP OF DIRECT SEQUENCE SPREAD SPECTRUM SIGNALS. PROJECT INDEX : 012 NAME : HASSAN ALI OMAR REG NO : F17/1456/2011 SUPERVISOR : PROF. V.K. ODUOL EXAMINER : DR. AKUON Project submitted in partial fulfillment of requirements for the award of the Degree of Bachelor of Science in Electrical and Information Engineering of the University of Nairobi. Date of submission 13 th May 2016 Page

2 DECLARATION OF ORIGINALITY NAME OF STUDENT: HASSAN ALI OMAR REGISTRATION NUMBER: F17/1456/2011 COLLEGE: Architecture And Engineering FACULTY/ SCHOOL/ INSTITUTE: Engineering DEPARTMENT: Electrical and Information Engineering COURSE NAME: Bachelor o f Science in Electrical and Electronic Engineering TITLE OF WORK: TRACKING OF DIRECT SEQUENCE SPREAD SPECTRUM SIGNALS 1) 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 properly been 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 have not allowed, and shall not allow anyone to copy my work with the intention of passing it off as his/her own work. 5) 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: i page

3 CERTIFICATION This report has been submitted to the Department of Electrical and Information Engineering, University of Nairobi with my approval as supervisor:.. PROF. V.K. ODUOL Date :. ii page

4 DEDICATION To my Brother Omari Ali and my wife Judy Nduta who supported me financially and morally during my five year stay at the University. iii page

5 ACKNOWLEDGEMENT I would like to thank my supervisor Prof. Oduol who has been quite useful as my guide regarding this project. Gratitude to my lecturers who oversaw my transformation to a potential Engineer during my five years at the university. I would also like to thank my classmates who were vital in my academic and social growth, they have been of great help as friends, classmates, lab partners and roommates. They gave me hope even when it seemed impossible to push on. iv page

6 ABSTRACT Direct sequence spread spectrum (DSSS) communication systems offer significant performance advantages in view of their low probability of intercept, improved performance in multipath fading environments and their ability to avoid interference by spreading the signal over a wide bandwidth hence distributing the power. For the transmitted sequence to be correctly received and demodulated, the spreading sequence used at the receiver should be similar to that employed in the transmitter. Code acquisition in DSSS provides a coarse alignment between the sent and received signal. Code tracking fine tunes the received signal from acquisition to a tolerance of less than a chip. v page

7 TABLE OF FIGURES Figure 1: Power spectral density of signal before and after spreading... 5 Figure 2:Power spectral density of signal and interference after the dispreading process Figure 3:Spread Spectrum Communication System... 6 Figure 4: DS-SS transmitter... 7 Figure 5: DS-SS receiver... 7 Figure 6:FH-SS transmitter... 7 Figure 7:FH-SS receiver... 8 Figure 8:A block of general sequence generator Figure 9:Quadrature sub-optimal acquisition system Figure 10:Serial search loop block diagram Figure 11:Parallel search circuit Figure 12: Optimum code tracking loop: Figure 13: coherent Baseband early late tracking loop Figure 14:Non-coherent early late tracking loop Figure 15:τ-Dither non-coherent early late tracking loop Figure 16:Equivalent τ-dither noncoherent early late tracking loop Figure 17:Overal DS-SS Figure 18:Transmitter Figure 19: PN generator Figure 20:waveforms of (a)transmitted data (b) pn sequence (c) mixer output Figure 21:Output of BPSK modulator Figure 22:(a) output of modulator (b) output of channel Figure 23:Block diagram of the receiver Figure 24:Active Correlator Figure 25:Aquisition subsystem Figure 26:Tracking Subsystem Figure 27:Digital Filter Design Figure 28:SLCU subsystem Figure 29:Local PN generator Figure 30: a) user data before spreading b)user data after spreading for the same range of frequency (-500Hz to 500Hz) Figure 31: user data at 1KHz Figure 32:user Data at 2KHz Figure 33:Graph of BER against SNR for a Filter as correlator Figure 34:Graph of BER against SNR for a integrator as correlator vi page

8 TABLE OF CONTENTS DECLARATION OF ORIGINALITY i CERTIFICATION... ii DEDICATION... iii ACKNOWLEDGEMENT... iv ABSTRACT...v TABLE OF FIGURES... vi ACRONYMS AND ABBREVIATIONS... Error! Bookmark not defined. TABLE OF CONTENTS... vii 1.0 CHAPTER 1: INTRODUCTION Project Objectives Brief Background Project Scope Project Organization CHAPTER 2: LITERATURE REVIEW OVERVIEW OF SPREAD SPECTRUM COMMUNICATION PRINCIPLES OF SPREAD-SPECTRUM COMMUNICATIONS TYPES OF SPREAD SPECTRUM SYSTEMS COMPARISON BETWEEN DSSS AND FHSS...8 Systems Collocation... 8 Throughput... 9 Multipath Immunity... 9 Time and Frequency diversity DIRECT SEQUENCE SPREAD SPECTRUM vii page

9 PSEUDO-RANDOM CODE SEQUENCES FOR SPREAD-SPECTRUM SYSTEMS GENERATION OF BINARY PSEUDO-RANDOM SEQUENCES ACQUISITION OF DS-SS SIGNAL TRACKING OF DS-SS SIGNAL Baseband early-late tracking loop i) Coherent Baseband early-late tracking loop ii) Non coherent early late tracking loop in AWGN τ-dither early late noncoherent tracking loop CHAPTER 3: DESIGN System Specification The Transmitter Data Generator PN generator Base-Band BPSK Modulator Channel Receiver Active Correlator Synchronization Unit Local PN code generator Demodulator CHAPTER 4: RESULTS CHAPTER FIVE: CONCLUSION APENDIX APENDIX 1: TABLE OF PRIMITIVE POLYNOMIALS viii page

10 1.0 CHAPTER 1: INTRODUCTION 1.1 Project Objectives The main objective of the project is to study spread spectrum communication systems with particular emphasis on Direct sequence systems. This involves studying of code tracking in DSSS systems showing its necessity. 1.2 Brief Background There was intensive use of communications warfare during World War II to intercept and interfere with hostile communications. Consequently, this stimulated a great deal of interest which led to the development of secure communications systems. This led to the development of Spread-Spectrum system, which exchanges bandwidth expansion for communications security and targets ranging for military applications. Work on spread spectrum during the 1970s prompted commercial use of the spread spectrum techniques, and theoretical work on spread-spectrum systems revealed the new system s ability to offer multiple access communications at an increased capacity compared to the time division or frequency division schemes of that time (Yue, 1983). The RAKE receiver concept (Price and Green, 1958) was developed to further accelerate the implementation of the systems. By the end of the decade, commercial applications of spread spectrum had become a reality. During the 1990s, the spread-spectrum technique was further developed into multicarrier techniques (Fazel, 1993) providing a higher diversity gain against deep fade than a single carrier spread-spectrum system could provide. The spread-spectrum multicarrier technique is based upon low rate data transmission over orthogonal frequency division multiplexing. This scheme generates multiple copies of the conventional spread spectrum; each copy is transmitted on a separate carrier. 1.3 Project Scope I am required to design and demonstrate a code tracking loop for DSSS system. Page 1

11 1.4 Project Organization This project is organized into 5 chapters: Chapter one gives introduction to the project, project objectives and project scope Chapter two gives a literature review which describes how spread spectrum communication systems are built and how they work. Chapter three gives the complete design of the code tracking system Chapter four gives the simulated results including screen shots obtained during simulation. Chapter five gives conclusion of the whole project, if the objectives and scope was achieved. It outlines future works. The project ends by outlining the appendices and references used. 2 page

12 2.0 CHAPTER 2: LITERATURE REVIEW 2.1 OVERVIEW OF SPREAD SPECTRUM COMMUNICATION Digital transmission schemes which provide satisfactory performance and an adequate bit rate can be arranged into two categories. In applications like satellite communications, these schemes provide efficient usage of the limited power available. In applications such as mobile wireless, where the schemes achieve efficient usage of the limited bandwidth available for the service in demand. However, both schemes are narrowband and vulnerable to hostile jamming and radio interference. The novelty of the spread-spectrum concept is that it provides protection against such attacks. This concept is based upon exchanging bandwidth expansion for anti-jamming capability. The bandwidth expansion in spread spectrum is acquired through a coding process that is independent of the message being sent or the modulation being used. BENEFITS OF SPREAD-SPECTRUM TECHNOLOGY i. Avoiding interception An interceptor usually measures the transmitted power in the allocated frequency band. Thus, spreading the transmitted power over a wider band undoubtedly lowers the power spectral density, and thus hides the transmitted information within the background noise. The intended receiver recovers the information with the help of system processing gain generated in the spread process. However, the unintended receiver does not get the advantage of the processing gain and consequently will not be able to recover the information. Because of its low power level, the spread spectrum transmitted signal is said to be a Low Probability of Interception (LPI) signal. Low probability of intercept (LPI) can be achieved with high processing gain and unpredictable carrier signals when power is spread thinly and uniformly in the frequency domain, making detection against noise by a surveillance receiver difficult. 3 page

13 ii. Privacy of transmission The transmitted information over the spread-spectrum system cannot be recovered without knowledge of the spreading code sequence. Thus, the privacy of individual user communications is protected in the presence of other users. Furthermore, the fact that spreading is independent of the modulation process gives the system some flexibility in choosing from a variety of modulation schemes. iii. Resistance to fading In a multipath propagation environment, the receiver acquires frequent copies of the transmitted signal. These signal components often interfere with each other causing what is commonly described as signal fading. In spread spectrum, multipath components are assumed to be independent, this means that if fading attenuates one component, the other components may not be affected, so that un faded components can be used to recover the information. iv. Improved multiple access scheme Multiple access schemes are designed to facilitate the efficient use of a given network resource by a group of users. Conventionally, there are two schemes in use: The Frequency Division Multiple Access (FDMA), and the Time Division Multiple Access (TDMA). In FDMA, the radio spectrum is shared between the users such that a fraction of the channel is allocated to each user at a time. On the other hand, in TDMA, each user is able to access the whole of the spectrum at a unique time slot. The spread spectrum offers a new network access scheme due to the use of unique code sequences. Users transmit and receive signals with access interference that can be controlled or even minimized. This technique is called Code Division Multiple Access (CDMA). 2.2 PRINCIPLES OF SPREAD-SPECTRUM COMMUNICATIONS Spread-spectrum concept has developed from the principle of Shannon theorem. If data is transmitted at a rate of R over a channel occupying a bandwidth much greater than R b, Shannon theorem indicates that reliable communications can be achieved at a 4 page

14 reduced SNR. However, if we keep the transmitted power fixed, even though the power density is substantially reduced, a surplus in the SNR is generated and can be used to combat interference and jamming. This surplus in SNR is called processing gain. The spreading of the energy is achieved by phase modulating the input data with the user code sequence. The modulation reduces the high power density of the original data to a low level. Figure 1: Power spectral density of signal before and after spreading The spreading process generates enough processing gain to protect the transmission from hypothetical jammer employing a narrow band tone. The received signal has to be converted into the original narrowband to limit the amount of input noise accompanying the wideband reception. The conversion is performed at the receiver with the aid of a locally generated code sequence causing the spread spectrum to collapse. Moreover, the de-spreading process is accompanied with spreading of the jamming power into background noise as shown below 5 page

15 Figure 2:Power spectral density of signal and interference after the dispreading process. The process is as shown below Figure 3:Spread Spectrum Communication System 2.3 TYPES OF SPREAD SPECTRUM SYSTEMS There are two main spread spectrum techniques employed in the provision of reliable communications: The Direct Sequence Spread Spectrum(DS-SS) and the Frequency Hopped Spread Spectrum systems. DS-SS system executes the spreading of the data energy in real time by phase modulating the data with a high rate code sequence directly. 6 page

16 Figure 4: DS-SS transmitter On the receiver side, the signal is multiplied by the spreading signal and then filtered to recover the narrow band transmitted signal. Figure 5: DS-SS receiver FH-SS is accomplished by forcing the narrowband carrier to jump pseudo-randomly from one frequency slot to the next according to the state of the code sequence in use. This is shown below Figure 6:FH-SS transmitter 7 page

17 At the receiver, the data is multiplied again by the frequency hoping spread signal to recover the transmitted data. Figure 7:FH-SS receiver Furthermore, a hybrid of both schemes can be developed to improve the processing gain compared to what is obtainable from a single scheme. This is the Hybrid Frequency Hopping Direct Sequence System. FHSS systems reject interference by avoiding it, whereas DSSS systems reject interference by spreading it. A hybrid system avoids interference in 2 ways: The hopping allows avoidance of interference spectrum part of the time. When the system hops into the interference it is spread and filtered as a direct sequence system. The emphasis of my project is on the tracking of DS-SS systems. 2.3 COMPARISON BETWEEN DSSS AND FHSS Systems Collocation This describes how many systems may operate on the same frequency band without interference. In DSSS systems, collocation could be based on different spreading codes (sequences) for each active system (CDMA). On condition that codes are highly distinguishable from each other. The number orthogonal pseudorandom sequences are limited and are a function of sequence length. In DSSS systems only three systems could be collocated without interference. 8 page

18 In FHSS systems, IEEE defines 79 different hops for the carrier frequency. IEEE also defines 78 hopping sequences (each with 79 hops) grouped in 3 sets of 26 sequences each. In theory 26 FHSS systems may be collocated but collisions will still occur in significant amounts. To reduce collisions, the actual number of FHSS collocated systems should be around 15 Throughput DSSS systems have the advantage of having higher capacities over FHSS. Multipath Immunity Environments with reflective surfaces such as buildings generate multiple possible propagation paths between transmitter and receiver and therefore the receiver receives multiple copies of the signal shifted in time. FHSS systems have a high multipath resistance compared to DSSS systems, hence favorable in such situations. Time and Frequency diversity The ability to retransmit a signal at later moments until the receiver acknowledges correct reception is known as time diversity. DSSS systems use time diversity, and since they retransmit on the same band so if noise is still there the transmission could be unsuccessful. FHSS use time as well as frequency diversity (packets may be retransmitted on different Hops). Even if some hops encounter noise others will not and FHSS will succeed in executing its transmission. 9 page

19 2.5 DIRECT SEQUENCE SPREAD SPECTRUM PSEUDO-RANDOM CODE SEQUENCES FOR SPREAD-SPECTRUM SYSTEMS introduction The operations at the transmitter and the receiver generate the required processing gain without which the system could not combat jamming and interference. The spreading code sequences, used in the system, have special properties which will be introduced in this chapter. These code sequences have an important role to play in the spread-spectrum technique and have to be chosen carefully for efficient communication systems. Each code sequence used in the spread-spectrum communications must easily be distinguishable from a time shifted version of itself. Also when multiple users are accessing the system for services, each code sequence assigned to a user must be distinguishable from every other user code sequence in the set and ideally should generate little or no interference to other users sharing the channel. Two types of these sequences can be used in spread-spectrum applications: the binary code sequence and the non-binary (also known as complex) code sequence. The elements of the binary sequence are made up of real numbers ±1 while the complex sequences are generated through exhaustive computer searching such as quadratic phase and poly phase sequences which have low correlation properties. Since correlation determines the amount of interference from multiple access, Bit Error Probability performance of DS-SS communication depends on the correlation properties of the code sequence used. There are two types of spreading signals: - i) Truly random spreading signal (transmitted reference signal) ii) Pseudo-random spreading signal (Stored reference) In the transmitted reference system one would send two versions of the unpredictable carrier- one modulated by the data and the other unmodulated. The two signals were transmitted on separate channels. The receiver used the unmodulated carrier as reference signal (correlating) the data modulated carrier. 10 page

20 Advantages of transmitted reference No synchronization problems at the receiver since data modulated signal and spreading signal used for dispreading were simultaneously transmitted Disadvantages of transmitted reference The spreading code could be intercepted by a listener Twice the bandwidth and transmitted power were required to transmit a signal The stored reference system, the code is independently generated at the transmitter and the receiver. Advantages of Stored reference A well designed code signal cannot be predicted by monitoring the transmission. Disadvantages of stored reference The code sequences cannot be truly random. Pseudo random numbers appear random but they are not. These codes are the ones implemented in modern DS-SS systems. PN sequence generators are used in a number of applications especially in the area of synchronization. In simulation context the most important reason for using PN sequences is modeling data sources. By using a PN sequence generator almost all possible bit combinations having a length can be produced over the shortest possible simulation length. GENERATION OF BINARY PSEUDO-RANDOM SEQUENCES Shift registers, with linear feedback, can be used in the implementation of binary code sequence generators. Figure 8 shows a block of general sequence generator 11 page

21 Figure 8:A block of general sequence generator At each clock pulse, the content of each register is shifted to the next register on the left or right. In the diagram, the following symbols have been used These are the components that make up the generator. The generator connections can be expressed by polynomial h(x) where: h x h h x h x hx The coefficients h i are such that a connection is present if hi= 1 and no connection is present if hi = 0. The maximum period of the binary sequence generated by the r-stage shift register is limited to 2r 1 which is achievable if h(x) is primitive. A binary sequence which achieves this maximum period is called maximal-length sequence or simply msequence. The salient features of the m-sequences are their two-valued autocorrelation functions which are optimal, with the absence of any side-lobe peaks. This is the key parameter which determines the probability of detection and false alarm, during code acquisition and tracking. 12 page

22 The periodic cross-correlation function between any pair of m-sequences of the same period can be relatively large. However, the peak values depend on the sequences chosen and their respective phases. To reduce interference, it is desirable to constrain these peak values to a minimum. All m-sequences of the same length can be derived from each other by a process of proper decimation. ACQUISITION OF DS-SS SIGNAL Practical acquisition system which achieves sub-optimal performance through a compromise between acquisition time and implementation complexity are usually implemented during the Acquisition stage. There are different detectors which are used in acquisition. The detectors can be grouped into either coherent or non-coherent according to the information available concerning the carrier phase offset. A block diagram for the synchronization of a coherent detector used for QPSK system is shown in Figure 9. Figure 9:Quadrature sub-optimal acquisition system. Non-coherent detectors are most widely used in a mobile environment characterized by Doppler effects and multipath propagation since accurately estimating the carrier 13 page

23 frequency error and the carrier phase offset are quite difficult in such environment. The de-spreading of the received signal usually takes place prior to the carrier synchronization. Basic detectors typically comprise bandpass filters centred at the nominal carrier frequency, followed by a square law envelop detector, an integrate-dump circuit, and a decision device. When carrier frequency error and the carrier phase offset are both accurately known, then a coherent detector can be used in the search system. This typically consists of a lowpass filter implemented as integrate and dump circuit followed by a simple decision device or Bayes detector. The correlation detectors used in the acquisition systems can relatively reduce system hardware complexity and improve the decision rate. SEARCH STRATEGIES Conventionally, either serial or parallel search algorithms are employed to search the uncertainty region and to acquire the code phase. i. serial search All possible code phases are tested one by one as shown in figure 10 to verify the acquisition of the correct code phase where T i is the integration time. Figure 10:Serial search loop block diagram. The average time for the serial search to acquire the correct code phase is relatively large and a common scheme used to shorten this acquisition time is to use a two-stage detection system. The first stage is set to a low threshold and short integration time so that a relatively large incorrect code phase can be rejected abruptly. The second stage is 14 page

24 designed with an appropriate dwell time and proper decision threshold to reduce the overall acquisition time. ii. parallel search The parallel search algorithm tests all possible code phases simultaneously as shown in figure 11 resulting in a much smaller average acquisition time compared to serial search algorithm. However, the complexity of the parallel search is higher than the serial search system. Figure 11:Parallel search circuit All acquisition systems, irrespective of the type of detectors and search algorithms used, are susceptible to various types of errors the most dominant are the false alarm errors and the miss errors. The false alarm occurs when the detector output exceeds the threshold for an incorrect code phase, while the miss error occurs when the detector output falls below the threshold for a correct code phase. As a practical rule, the design of an efficient acquisition system is based on a compromise between small average acquisition time and small false alarm probability together with appropriate detection probability. 15 page

25 2.6 TRACKING OF DS-SS SIGNAL Having acquired the received code phase within less than one chip, the receiver has to track any changes in the code phase using code phase tracking loops. Code phase tracking loops are identical in operation to the conventional phase locked loops used for carrier phase tracking. The only difference in operation is that code tracking loops track the timing delay error between the received code and the locally generated code while the conventional tracking loops track the phase error between the received carrier and the reference carrier generated locally. Tracking the delay errors is based on the correlation between the received code and two different replicas of the received code: one is an early version and the other is late version of the locally generated code. There are two kinds of tracking loops:- 1. Coherent loops 2. Non-coherent loops Coherent loops make use of an available carrier phase to track while a non-coherent doesn t i.e. carrier frequency and the phase is not known. Frequently the carrier phase and frequency are unknown before tracking and hence a noncoherent loop is used. The two tracking loops can be divided further into:-loops that use two independent correlators known as full-time early late loops and loops that share a single correlator known as Tau-dither or τ-dither early late loops. Usually the aim of the tracking loops is to achieve reasonably low tracking delay jitter. Since an accurate estimate of delay can be done by match filtering the received signal and a locally generated reference signal the matched filter is used in the tracking loop because it maximizes the signal-to-noise ratio in Additive White Gaussian Noise (AGWN) channel. 16 page

26 The original tracking loop proposed by Spilker and Magill (1961) in the early 1960s for arbitrary wide band signals, such as direct sequence spread-spectrum corrupted by additive Gaussian noise, was the optimum code tracking loop. This consisted of a multiplier, to form the product of the received code, and the derivative, with respect to time, of the locally generated code. The output of the multiplier is averaged by a low pass filter to extract the dc component related to the delay error. The filter output is used to control the delay of the differentiated locally generated code waveform to maximize the cross-correlation between received and the locally generated code. However the maximum likelihood estimate requires a non-realizable loop filter. Furthermore, generating the impulse function for the derivative of the locally generated code reference is not an easy task and, therefore, the optimum tracker is not used in modern systems but forms the basis for which they are designed. Figure 12: Optimum code tracking loop: Baseband early-late tracking loop The early late tracking loop examines samples taken slightly earlier and slightly later than the instant at which the cross-correlation between the received code and the locally generated code is maximum. After comparing these instants, the code phase is adjusted accordingly. 17 page

27 i) Coherent Baseband early-late tracking loop The signal-to-noise ratio at the receiver input has to be high enough to permit the generation of a coherent carrier reference. Furthermore, we will assume the received signal contains no data modulation so that the tracking loop input is the code spreading waveform corrupted by additive Gaussian noise. If the received code signal power is P and the phase td and t d the estimate of td and that both td and t d may vary with time, then the received Signal may be given by:r t PC t td n t Where n(t) is the Gaussian White Noise with the spectral density. The loop is made up of a phase discriminator followed by an averaging loop filter and a Voltage Oscillator (VCO) that controls the phase of the locally generated code waveform. The received signal rc(t) is power divided equally between the two channels of the discriminator and correlated with the early/late code waveforms as shown in figure 13. Figure 13: coherent Baseband early late tracking loop Assume the total time difference between the two correlators is which is restricted to a range of 0 Tc then the early local code waveform can be expressed as: C t t T 2 And the late local code waveform:- 18 page

28 C t t T 2 Where T is the chip duration Baseband early late tracking loop in noisy channels If we denote the delay error normalized with respect to the chip duration as δ= t t T Since the received power is divided equally between the two arms of the tracking loop, we divided the received signal by 2. The early correlator output, y1 (t) is: y t = P C t t 2 C t t + T 2 + n t C t t T 2 + n t The late correlator output, y2(t) is: y t = P C t t 2 The discriminator output ε t = y t y t Thus ε t = C t t C t t T C t t C t t + T 2 C t t + T + n t Where n t = n t C t t T 2 The error signal, ε (t), is composed of two terms: - The first term is a dc component that drives the Voltage Controlled Oscillator (VCO) and the second term is a random 19 page

29 signal produced by the noise process n t causing tracking jitter defined by the loop s tracking error variance. ε t = P D t, t P n t The dc component of the error signal εdc(t) is given by the time average of ε(t). ε P D t, t 2 = Normally, n t is not a Gaussian distributed process but acquires white power spectral density. However, for small tracking error, δ, the noise n t can be approximated as a Gaussian process and the tracking loop can be represented by a linear Phase-Locked Loop (PLL) so that much of the PLL analysis also applies to the code tracking loop. On solving for D t, t D t, t it is found that; = R t t T 2 R t t + T 2 Substituting for δ D δ = R δ T R 2 δ+ T 2 D δ is known as the S-curve characteristics of the tracking loop. From the S-curve, it can be seen that D δ is linearly related to δ at δ = 0. This is the normal operating region of the tacking loop. The variance of the tracking error (σ ) is expressed in terms of the received signal-tonoise power ratio within the loop bandwidth as: 20 page

30 σ = σ = 2 SNR 1 1+ N 1 2 SNR 1+ 1 N for 0 < < 1 for 1 < < N 1 Where SNR is the loop signal-to-noise ratio for signal power P and loop bandwidth B : SNR = ii) P N B 2 Non coherent early late tracking loop in AWGN Since practical spread spectrum systems have low SNR, the coherent recovery is usually difficult since it requires a high SNR to operate. Consequently, the reference carrier is locally generated. And since there will most likely be a phase difference between the received and the local reference carrier, we expect the received signal input to the tracking loop to contain some data modulation. A simple phase discriminator that avoids these difficulties applies energy detection which is insensitive to carrier phase or data modulation. The received signal from AWGN channel is data and spreading code modulated carrier: r t = PC t t cos ω t + θ t t + + n t where P, t, ω, θ t, and n t are the received power, transmission delay, carrier radian frequency, carrier phase representing transmitted data, carrier random phase φ uniformly distributed over (0,2π), and zero mean white Gaussian noise process respectively. The band-limited received noise n(t) has the two-sided power spectral density of W Hz. n t = 2 n t cos ω t n t sin ω t where n t and n t are the inphase and quadrature zero mean white Gaussian noise process. 21 page

31 The code waveforms from the early and late branches are given by C C t t T 2 C C t t T 2 The reference local oscillator output is: The schematic of the non-coherent early late tracking loop is as shown in figure 11. Figure 14:Non-coherent early late tracking loop Assuming unity gain phase detectors, their outputs are: And 22 page

32 ρ If we define the SNR in the loop bandwidth bandwidth ρ and the SNR in the IF filter and the tracking jitter will be given by; σ 1 1 2ρ 2 ρ τ-dither early late non coherent tracking loop The early late tracking loop described above may suffer from unequal gains in the tracking loop branches leading to discriminator output offset, such that the output is not zero when the loop generates zero code phases tracking error. The tau Dither tracking loop time shares a single channel instead of using two channels. The single correlator channel in Figure 15 is used alternately as the early correlator and late correlator using signal s(t) at a dithering (switching) frequency. The dithering frequency fdith is too low, relative to the IF filter bandwidth, to cause no filter transience, but is significantly high, compared with the bandwidth of the loop filter, to ignore fdith harmonics. The equivalent circuit of the tau Dither tracking loop is shown in figure 16. The output of the correlators 1 and 2 can be given by the equations below If the filters introduce no distortion, the discriminator output is given by:- 23 page

33 Figure 15:τ-Dither non-coherent early late tracking loop Figure 16:Equivalent τ-dither noncoherent early late tracking loop 24 page

34 This can be simplified by substituting the values of 1and 2to give:- This error signal is used to drive the VCO which inturn regulates the clock of the local PN generator. 25 page

35 3.0 CHAPTER 3: DESIGN The DS/SS is designed by using MATLAB -Simulink version 8.5(R2015a) because it is a reliable design software with accurate results and widespread tools library. Also the waveforms and spectra at any point of design can be obtained by using scope or frequency spectrum, this is important in checking the design. I used the communication block set, DSP block set, Simulink-Extras and other block set of MATLAB-Simulink. Figure 17 shows the overall system implemented. 26 page

36 Figure 17:Overal DS-SS Page 27

37 3.1 System Specification. HASSAN ALI OMAR F17/1456/20 11 The following were the specifications of the system designed. Data rate: 1 Kb/s. PN code rate: 32KHz. PN code length: 7 bits (maximal linear code). Modulation type: equivalent baseband BPSK. Acquisition method: serial search (dwell time scheme). Tracking method: delay locked loop (DLL). Processing gain is equal to :- G bandwidth of pn generator Data bandwidth clock rate Data Rate 32KHz dB 1KHz 3.2 The Transmitter. The transmitter consisted of a PN generator, a mixer and a baseband BPSK modulator. Since modulation is performed in baseband, no radio frequency RF carrier is present therefore the detection of the signal in the receiver uses low pass filter. Figure 18:Transmitter Page 28

38 3.2.1 Data Generator The data generator used was a Bernoulli Data Generator from the communication blockset with a 50% probability of a zero and 50% probability of a one. As shown in figure PN generator The PN generator implemented had a minimal polynomial given by fx 1 x x. The PN is generated by using three stages D Flip-Flop from Simulink-Extras with a two feedback taped at x and x., Ex-ORed to the input of the first stage D Flip-Flop, in order to get 7 bit length maximal(2 1) as shown in figure 19 below. Figure 19: PN generator The transmitted data is modulo-2 added (with mixer) with the PN generator output to get the spread data as shown in figure Base-Band BPSK Modulator Here the signal was modulated using binary phase shift keying from the mixer. This converted the signal to bipolar with a reverse phase of either 0 or 180 degrees. As shown in figure Channel The channel used was the Additive White Gaussian Noise(AGWN) Channel. The waveform after transmission at -10 db is shown in figure 20 (b). 29 page

39 Figure 20:waveforms of (a)transmitted data (b) pn sequence (c) mixer output Figure 21:Output of BPSK modulator 30 page

40 Figure 22:(a) output of modulator (b) output of channel 3.4 Receiver The receiver was made up of: - 1. Active correlator 2. Synchronization Unit 3. Baseband BPSK demodulator 4. Local Pn code generator with a variable clock The overall block diagram of the receiver is shown in figure 23. Figure 23:Block diagram of the receiver 31 page

41 3.4.1 Active Correlator It is made up of a mixer and a fourth order Butterworth filter to de-spread the signal. The received signal is only de spread when the locally generated pn sequence and the received pn code have the same phase. The cutoff frequency of the filter is set to the data rate of 1KHz. The implemented active correlator is as shown in figure 24. Figure 24:Active Correlator The manual switch was used to measure the performance when using a digital filter and an integrator in the circuitry Synchronization Unit The synchronization unit consisted of: - i) Acquisition ii) Tracking iii) Voltage Controlled Oscillator(VCO) iv) Search and Lock Control Unit(SLCU) The output of the Active correlator is compared with a threshold level in acquisition if the threshold is exceeded, no delay will be introduced to the Local PN generator clock. This will mean that initial course synchronization has been achieved and tracking(fine synchronization) will be commenced. If the threshold is not reached, 32 page

42 Local PN clock is delayed by half a chip, and the acquisition process is repeated. After acquisition has been made, SLCU initiates tracking Acquisition The block diagram used to implement Acquisition (Serial search) was as shown in figure 25. Figure 25:Aquisition subsystem It consisted of a square law envelope detector and an integrate and dump to detect the correlated signal energy at constant test time intervals (dwell time). The output of the integrator is then compared with a threshold voltage and if the threshold is exceeded the phase of the local PN is corrected and tracking will be initiated, else a phase update signal is sent by the SLCU to try and correct the phase offset Tracking The tracking method implemented was the delay locked loop(dll) method due to ease of implementation and also its quite accurate. The tracking loop consists of two branches as shown in figure 26. Figure 26:Tracking Subsystem 33 page

43 The common input to the lower and upper branch is the input from the AWGN channel. The second input to the upper mixer is the output on the last flip flop of the local PN generator(early) while the second input to the lower mixer is the output of the second flip flop of the Local PN generator(late). Both branches are comprised of a mixer, a digital IIR low pass Butterworth filter and a Square law envelope detector. These detects the energy of the late and the early signals coming into the branches at constant dwell times. The filter used had a sampling frequency of 64KHz (Nyquist rate) and a cutoff frequency same as the data rate i.e. 1 KHz. As shown in figure 27. Figure 27:Digital Filter Design The summer at the output of the tracking loop subtracts the two signals to generate and error signal Voltage Control Oscillator The Error signal from the tracking loop drives the Digital VCO so as it can correct the clock frequency of 32KHz. The VCO runs at the frequency of the PN generator of the transmitter. The limiter was used to convert the sinusoid from the VCO to a square wave signal. 34 page

44 Search and Lock Control Unit(SLCU) The block diagram of the SLCU implementation is as shown in figure 28. The clock produces a pulse at half the chip period i.e. 64KHz which is inverted and fed into the NAND gate in order to check the status of Acquisition system. The NAND outputs either a HIT (Acquisition has occurred) so as to proceed with tracking or not. If there is no HIT, a phase replica is tested again until a HIT is gotten. The T Flip-flop is used to generated a half chip clock at each half chip period in case there is no HIT i.e. Speed up the clock. The clock is gotten after modulo two additions of the VCO clock with the T-flip-flop output. Figure 28:SLCU subsystem The final clock update will either be at the chip rate(normal speed) if acquisition occurred or at half chip rate(local PN code faster than the received PN code) if acquisition process does not reach it is final decision Local PN code generator The local PN generator was designed similar to the PN generator in the transmitter except that the clock that runs it came from the output of the SLCU. The early and late sequences were tapped as shown in figure page

45 Figure 29:Local PN generator Demodulator I used the baseband BPSK demodulator from the communications block set with a log-likelihood-ratio decision mode. After demodulation, I passed the signal through an integrate and dump to stabilize it, passed it through a limiter to get a waveform that is bipolar with 2-ary (from -1 to 1) and then converted the signal to unipolar to get the output of the whole system. 36 page

46 4. CHAPTER 4: RESULTS In the results, I focus on showing the spreading has been achieved and also dispreading, I also show the tracking for different values of user frequency. The spreading process is shown using spectrum analyzer as shown in figure 24. The power density at 0 Hz is at 25dBm before spreading but reduces to approximately 11dBm after spreading. This will improve if a spreading signal of longer minimal length(2 L -1) is used. I also took the user input data and the output data for various user frequency to compare them. Scenario 1: user data at 1 KHz The results for the system with user data at 1KHz and the spreading signal maintained at 32KHz is as shown in figure 31. It is seen that the received signal has errors during the early stages of tracking between seconds but after that the signals are the same. Figure 30: a) user data before spreading b)user data after spreading for the same range of frequency (-500Hz to 500Hz) 37 page

47 Figure 31: user data at 1KHz Scenario 2: user data at 2 KHz The results when the user frequency is adjusted to 2 KHz is as shown in figure 32. The system tracks the signal even if the user frequency changes, this only happens if the VCO quiescent frequency is adjusted to match the user frequency. Figure 32:user Data at 2KHz For 4KHz the tracking system failed. This is because the tracking system was designed to work for a user data of 1KHz and hence can only work for frequencies above and under 1KHz to some limit set by the S-curve of the system. 38 page

48 I also investigated the performance of the system under different signal to noise ratios with a digital filter as the correlator and with an integrator as the correlator. The graphs obtained were as shown in figures 33using a digital filter correlator and 34 using an integrator. From the graphs, it is evident that the integrator performs better than the digital filter. As the SNR was raised, the number of errors recorded reduced for the same amount of sample time. BER to SNR BER SNR Figure 33:Graph of BER against SNR for a Filter as correlator 39 page

49 BER to SNR BER SNR Figure 34:Graph of BER against SNR for a integrator as correlator 40 page

50 5. CHAPTER FIVE: CONCLUSION Spread Spectrum techniques have some powerful properties which make them an excellent candidate for networking applications. Today this technology forms the basis for the NavStar Global Positioning System(GPS), Joint Tactical Information Distribution System/Link-16(JTIDS) Used in aircraft, ships and Land vehicles. In the project, a code tracking system has been designed and simulated using Math works, Simulink software. The project required the design of a direct sequence tracker and demonstration that it works which was done in chapter 3 of design and chapter 4 of results. FUTURE WORK My project only focused on a single signal being received by the receiver which might not always be the case especially in hilly or urban areas where diffraction and reflections occur thus at the receiver, several signals are received and the receiver has to work out which is the correct signal. A Rake receiver may be implemented which averages the signal power for all the signals and approximates the received signal. This is done by assigning different correlators to the incoming signals called Rake Fingers. The finger outputs are then weighted and combined constructively to yield estimates of transmitted signal. 41 page

51 REFERENCES [2] M. A. Abu-Rgheff, INTRODUCTION TO CDMA WIRELESS COMMUNICATIONS, Chennai India: Macmillan, [3] Wem-Ho Sheen, "A New Tracking Loop for Direct Sequence Spread Spectrum Systems on Frequency-Selective Fading Channels," IEEE, [4] T. F. Wong, "Spread Spectrum & CDMA," National Technological university, [5] Viterbi, CDMA Principles of Spread Spectrum Communication, Addision- Wesley, [6] R. Dixon, Spread Spectrum Systems with Commercial Applications, Wiley, page

52 APENDIX APENDIX 1: TABLE OF MINIMAL POLYNOMIALS APENDIX 2: ELEMENTS GF page