Design and Implementation of a GPS receiver channel And ... - SERC

AcknowledgmentsI take this opportunity to express my deep sense of gratitude to my thesis guide Prof.S K Nandy for his constant encouragement and guidance.I thank all the faculty members & staff of SERC for their support.I am grateful to my parents and sister, whose faith, patience and love had always inspiredme to walk upright in my life.I would like to extend my heartfull thanks to my friends Adarsha,Kesavan,Mythri,Reyaz,Bharath, Chowhan, Sainath, Sankar, Sravanthi, Prasenjit, Saptarshi, Gaurav formaking my stay at IISc a memorable one.Special thanks to Reyaz who helped me all the way of my project for his valuable support.S.Babu Raoi

ContentsAcknowledgmentsList of FiguresivAbstract 1Thesis Organization 21 Introduction 32 Position determination by Satellite Navigation 62.1 Position determination using PRN code . . . . . . . . . . . . . . . . . . . 62.2 Calculation of the User Position . . . . . . . . . . . . . . . . . . . . . . . . 103 GPS signal structure and characteristics 123.1 Modulations of GPS signal . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 GPS Signal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 Frequencies,Modulation Format and PRN codes . . . . . . . . . . 153.3 Autocorrelation and PSD functions of random sequence of pulses . . . . 193.3.1 Effect of finite length PRN code on the autocorrelation functionand PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 GPS Receiver Channel 224.1 Analog front end of GPS receiver . . . . . . . . . . . . . . . . . . . . . . . 224.2 Digital receiver channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Frequency Synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29ii

CONTENTSiii5 Design of PRN code generators 315.1 C/A code generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.2 P code generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Correlation results of the implemented GPS receiver channel . . . . . . . 386 Subchip Multipath Delay Estimation using TeagerKaiser Operator 406.1 Signal and Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2 Teager-Kaiser Operator and its application for the Delay Estimation . . . 426.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Bibliography 45

List of Figures2.1 Example PRN code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Use of replica code to determine satellite code transmission time. . . . . 82.3 Range measurement timing relationships. . . . . . . . . . . . . . . . . . . 93.1 BPSK modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 DSSS modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 GPS signal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 Vector diagram of L1 GPS signal . . . . . . . . . . . . . . . . . . . . . . . 183.5 GPS code mixing with data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.6 (a)An example Random Sequence (b)Its autocorrelation function (c)PSD . . . . 203.7 (a)Autocorrelation function of a PRN sequence (b)Its PSD . . . . . . . . . . . . 214.1 Generic digital GPS receiver block diagram. . . . . . . . . . . . . . . . . . . . 234.2 Digital GPS receiver channel block diagram. . . . . . . . . . . . . . . . . . . . 254.3 (a)Autocorrelation functions of Early and Late signals generated by GPS receiverchannel.(b)Code-phase discriminator formed by difference between thecorrelation functions in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4 frequency synthesizer block diagram. . . . . . . . . . . . . . . . . . . . . . . 294.5 (a)NCO phase state. (b)cos map output. (c)sin map output. (d)phase plane.(e)phase map table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.1 General PRN code generator block diagram. . . . . . . . . . . . . . . . . . . . 315.2 C/A code generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.3 P code generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.4 clock control circut shown in figure 5.3. . . . . . . . . . . . . . . . . . . . . . 36iv

LIST OF FIGURESv5.5 Correlation results with Early,Prompt,and Late signals . . . . . . . . . . . . . 396.1 peaks shown by TK operator at multipath delays. . . . . . . . . . . . . . . . . 44

AbstractGlobal Positioning System (GPS) is a satellite-based navigation system. It is based onthe computation of range from the receiver to multiple satellites by multiplying thetime delay that a GPS signal needs to travel from the satellites to the receiver by velocityof light.This will be done by correlating the received signal with the locally generatedcarrier and individual satellite’s Pseudo Random Noise(PRN) code.The correlationis maximum when frequency and phases of the carrier and code perfectly matchesthose of the received signal.Based on these correlation values error(correcting) signalswill be generated by the baseband signal processes to correct the phase and frequencyof the locally generated carrier and code to synchronize with the received signal. Thesecorrecting(synchronizing) signals will be influenced by the multipath propagation.Soan efficient technique which is computationally least complex must be used to mitigatethe effect of multipath propagation for accurate positioning by GPS receiver.Designand implementation of a GPS receiver channel and using its simulation results to evaluatethe performance of the Teager-Kaiser operator technique for multipath delay estimationis the objective of this project.1

Thesis OrganizationThere are six chapters in this thesis presentation.The first chapter gives a brief introductionto the satellite navigation and high speed signal processing done by a GPSreceiver. The second chapter describes the position determination by satellite navigationusing PRN codes. The third chapter describes the GPS modulation and gives anoverview of the spread spectrum principles.The detailed GPS signal structure is describedin this chapter. The fourth chapter describes the components of GPS receiverchannel with a brief overview of the overall GPS receiver. The details of the PRN codegeneration given by GPS specifications is described in the fifth chapter.The characteristicsof different PRN codes are given in this chapter.Finally the sixth chapter describes the Teager-Kaiser operator and its application formultipath delay estimation.The performance of this technique is shown using the simulationresults from the implemented GPS receiver channel.2

Chapter 1IntroductionNavigation is defined as the science of getting a craft or person from one place to another.Insome cases a more accurate knowledge of our position,intended course, ortransit time to a desired destination is required.Navigation aids other than landmarksare used for such applications. These may be in the form of a simple clock to determinethe velocity over a known distance or the odometer in our car to keep track of thedistance traveled. Some other navigation aids transmit electronic signals and thereforeare more complex. These are referred to as radionavigation aids.Various types of radionavigation aids exist.Highly accurate systems generally transmitat relatively short wavelengths,and the user must remain within line of sight (LOS),whereas systems broadcasting at lower frequencies (longer wavelengths) are not limitedto LOS but are less accurate.Signals from one or more radionavigation aids enable a person (herein referred to asthe user) to compute their position. (Some radionavigation aids provide the capabilityfor velocity determination and time dissemination as well.) It is important to note thatit is the users radionavigation receiver that processes these signals and computes theposition fix. The receiver performs the necessary computations (e.g., range, bearing,and estimated time of arrival) for the user to navigate to a desired location.Global Positioning System (GPS) is a satellite-based navigation system. It is based3

Chapter 1. Introduction 5the accurate measurements.There are several techniques proposed for this purpose.Thereis a tradeoff between the performance and complexity of these algorithms.Delay estimationusing Teager-Kaiser operator is one of the highly efficient technique with subchipmultipath delay estimation capability.Also it has the additional advantage of leastcomputational complexity.The detailed description of this operator with its capabilitiesand limitations are given in the chapter6.

Chapter 2Position determination by SatelliteNavigationGPS utilizes the concept of TOA ranging to determine user position. This concept entailsmeasuring the time it takes for a signal transmitted by an emitter (e.g., foghorn,radiobeacon, or satellite) at a known location to reach a user receiver. This time interval,referred to as the signal propagation time, is then multiplied by the speed of thesignal (e.g., speed of sound or speed of light) to obtain the emitter to receiver distance.By measuring the propagation time of the signal broadcast from multiple emitters (i.e.,navigation aids) at known locations, the receiver can determine its position.2.1 Position determination using PRN codeGPS satellite transmissions utilize direct sequence spread spectrum (DSSS) modulation.The DSSS modulation is explained in chapter 4. DSSS provides the structurefor the transmission of ranging signals and essential navigation data, such as satelliteephemerides and satellite health. The ranging signals are PRN codes that binary phaseshift key (BPSK) modulate the satellite carrier frequencies. These codes look like andhave spectral properties similar to random binary sequences but are actually deterministic.A simple example of a short PRN code sequence is shown in Figure 2.1.6

Chapter 2. Position determination by Satellite Navigation 7Figure 2.1: Example PRN codeThese codes have a predictable pattern,which is periodic and can be replicated by asuitably equipped receiver.But they can approximate the behaviour of fully randomcodes.Hence these codes are called pseudo random codes.Each GPS satellite broadcaststwo types of PRN ranging codes: ashort coarse/acquisition (C/A)-code and a longprecision (P)-code. (The new GPS signal consists additional codes also).The C/A code has a 1-ms period and repeats constantly, whereas the P-code satellitetransmission is a 7-day sequence that repeats approximately every Saturday/Sundaymidnight.The P-code is encrypted. This encrypted code is denoted as the Y-code. TheY-code is accessible only to PPS users through cryptography. Further details regardingthese PRN codes and satellite signal structure were described in the chapter3.The distance between the satellite and the user r is computed by measuring the propagationtime required for a satellite-generated ranging code to transit from the satelliteto the user receiver antenna. The propagation time measurement process is illustratedin Figure 2.2. As an example, a specific code phase generated by the satellite at t1arrives at the receiver at t2. The propagation time is represented by ∆tWithin the receiver, an identical coded ranging signal is generated at t, with respect tothe receiver clock.This replica code is shifted in time until it achieves correlation withthe received satellite-generated ranging code. If the satellite clock and the receiverclock were perfectly synchronized, the correlation process would yield the true propagationtime. By multiplying this propagation time, ∆t, by the speed of light, the true(i.e.,geometric) satellite-to-user distance can be computed.The receiver clock will generally have a bias error from system time. Further, satellitefrequency generation and timing is based on a highly accurate free running cesium or

Chapter 2. Position determination by Satellite Navigation 9δt = Offset of the satellite clock from system time [advance is positive; retardation (delay)is negative]t u = Offset of the receiver clock from system timeT s + δt = Satellite clock reading at the time that the signal left the satelliteT u + t u = User receiver clock reading at the time the signal reached the user receiverc = speed of lightFigure 2.3: Range measurement timing relationships.Geometric range, r = c(T u - T s ) = c∆tPseudo range, ρ = c [(T u + t u ) − (T s + δt)]= c(T u − T s ) + c(t u − δt)= r + c(T u − δt)The formulae for computing the geometric and pseudo ranges are shown above. Assumingthe satellite error was compensated,the pseudo range equation becomes

Chapter 2. Position determination by Satellite Navigation 10ρ = ||s - u||+ ct uwhere vector s represents the position of the satellite relative to the coordinate originand it is located at coordinates x s ,y s ,z s within the ECEF(Earth-Centered Earth-Fixed Coordinate System) Cartesian coordinate system.. Vector s is computed usingephemeris data broadcast by the satellite.And vector u,represents a user receivers position with respect to the ECEF coordinatesystem origin. The users position coordinates x u , y u , z u are considered unknown.2.2 Calculation of the User PositionIn order to determine user position in three dimension(x u , y u , z u ) and the offset t u .pseudorangemeasurements are made to four satellites resulting in the system of equations.ρ j = ||s - u||+ ct uwhere j ranges from 1 to 4 and references the satellites. Above equation can be expandedinto the following set of equations in the unknowns x u , y u , z u and t u :ρ 1 = √ (x 1 − x u ) 2 + (y 1 − y u ) 2 + (z 1 − z u ) 2ρ 2 = √ (x 2 − x u ) 2 + (y 2 − y u ) 2 + (z 2 − z u ) 2ρ 3 = √ (x 3 − x u ) 2 + (y 3 − y u ) 2 + (z 3 − z u ) 2ρ 4 = √ (x 4 − x u ) 2 + (y 4 − y u ) 2 + (z 4 − z u ) 2where x j , y j , andz j denote the jth satellites position in three dimensions.These equations can be solved for user position u by linearisation of above equationsusing taylor series expansion about an approximate user position.After expanding the above equations about the approximate user position and consideringthe first order derivatives only the following matrix equation can be obtained.∆ρ = H∆x

Chapter 2. Position determination by Satellite Navigation 11where⎛⎛∆ρ 1∆ρ 2∆ρ = H =∆ρ 3⎜⎝⎞⎟⎠∆ρ 4 ⎜⎝a x1 a y1 a z1 1a x2 a y2 a z2 1a x3 a y3 a z3 1a x4 a y4 a z4 1⎞⎟⎠∆x =⎛⎜⎝∆x u∆y u∆z u−c∆t u⎞⎟⎠∆ρ and ∆x are the deviations of the actual user position from the approximate positionand (a x j , a y j , a z j ) are the direction cosines of the unit vector pointing from the approximateuser position to the jth satellite.So the user position can be found as follows.∆x = H −1 ∆ρu = û + ∆x

Chapter 3GPS signal structure and characteristicsThe GPS signal format is known as direct sequence spread spectrum.The term direct sequenceis used when the spreading of the spectrum is accomplished by phase modulationof the carrier.This chapter will describe the modulations of GPS signal,Componentsof GPS signal,and autocorrelation function of the Rectangular PRN codes and its exploitationfor acquisition and tracking of GPS signal.3.1 Modulations of GPS signalBPSKBinary phase shift keying (BPSK) is a simple digital signaling scheme in which an RFcarrier is either transmitted as it is or with a 180 o phase shift over successive intervalsin time depending on whether a digital 0 or 1 is being conveyed an example is shownin the figure 3.1.BPSK signal, as illustrated in Figure 3.1, can be thought of as the product of two timewaveforms: the unmodulated RF carrier and a data waveform that takes on a valueof either +1 or -1 for each successive interval of T b= 1/R b seconds, where R b is thedata rate in bits per second. The data waveform amplitude for the kth interval ofT b seconds can be generated from the kth data bit to be transmitted using either the12

Chapter 3. GPS signal structure and characteristics 14Figure 3.2: DSSS modulationsymbol; and the reciprocal of the chip period is known as the chipping rate, R c . Theindependent time parameter for the PRN waveform is often expressed in units of chipsand referred to as codephase. The signal just described is called spread spectrum, becauseof the wider bandwidth occupied by the signal after modulation by the high-ratePRN waveform. In general, the bandwidth is proportional to the chipping rate. Thereare three primary reasons why DSSS waveforms are employed for satellite navigation.First and most importantly, the frequent phase inversions in the signal introduced bythe PRN waveform enable precise ranging by the receiver.Second, the use of differentPRN sequences from a well-designed set enables multiple satellites to transmit signalssimultaneously and at the same frequency. A receiver can distinguish among thesesignals, based on their different codes. For this reason, the transmission of multipleDSSS signals having different spreading sequences on a common carrier frequency isreferred to as code division multiple access (CDMA). Finally DSSS provides significantrejection of narrowband interference. The chip waveform in a DSSS signal does

Chapter 3. GPS signal structure and characteristics 15not need to be rectangular (i.e., a constant amplitude over the chip period).In principle,any shape could be used and different shapes can be used for different chips.DSSSsignals generated using BPSK signaling with rectangular chips as BPSK-R signals. Severalvariations of the basic DSSS signal that employ nonrectangular symbols have beeninvestigated for satellite navigation applications in recent years. Binary offset carrier(BOC) signals are generated using DSSS techniques but employ portions of a squarewave for the spreading symbols [2].3.2 GPS Signal StructureThe GPS Satellites(refer to as SV’s) transmit navigation signals on two carrier frequenciescalled L1, the primary frequency, and L2, the seconda ry frequency. The carrierfrequencies are DSSS modulated by spread spectrum codes with unique PRN(PseudoRandom Noise) sequences associated with each SV and by a common navigation datamessage. All SVs transmit at the same carrier frequencies in a CDMA fashion. In orderto track one SV in common view with several other SVs by the CDMA technique, aGPS receiver must replicate the PRN sequence for the desired SV along with the replicacarrier signal,including Doppler effects. Two carrier frequencies are required to measurethe ionospheric delay, since this delay is related by a scale factor to the differencein signal TOA(time of arrival) for the two carrier frequencies. Single frequency usersmust estimate the ionospheric delay using modeling parameters that are broadcast tothe user in the navigation message.3.2.1 Frequencies,Modulation Format and PRN codesA block diagram that is representative of the SV signal structure for L1 (154 f 0 ) and L2(120 f 0 ) is shown in Figure 3.3 (where f 0 is the fundamental frequency: 10.23MHz).As shown in Figure 3.3, the L1 frequency (154 f 0 ) is modulated by two PRN codes(plus the navigation message data), the C/A code, and the P code. The L2 frequency

Chapter 3. GPS signal structure and characteristics 16(120 f 0 ) is modulated by only one PRN code at a time. One of the P code modes hasno data modulation. The nominal reference frequency, f 0 , as it appears to an observeron the ground, is 10.23 MHz. To compensate for relativistic effects, the output of theSV’s frequency standard (as it appears from the SV) is 10.23 MHz offset by a ∆ f /f of4.467×10 −10 . This results in a ∆ f of 4.57 ×10 −3 Hz and f 0 = 10.22999999543 MHz. To theGPS receiver on the ground, the C/A code has a chipping rate of 1.023 ×10 6 chips/s( f 0 /10 = 1.023 MHz) and the P code has a chipping rate of 10.23 ×10 6 chips/s ( f 0 = 10.23MHz).The C/A code signal uses a BPSK-R(1) (means BPSK modulation using 1MHzchipping rate) modulation and the P code uses a BPSK-R(10) modulation.Where The Pcode is available only to specific users such as military.Figure 3.3: GPS signal structureAs figure 3.3 shows the same 50-bps navigation message data is combined with both

Chapter 3. GPS signal structure and characteristics 17the C/A code and the P(Y) code prior to modulation with the L1 carrier. An exclusiveorlogic gate is used for this modulation process, denoted by . Since the C/A code data and P(Y) code data are both synchronous operations, the bit transition ratecannot exceed the chipping rate of the PRN codes. Also note that BPSK modulation isused with the carrier signals. The P(Y) code data is modulated in phase quadraturewith the C/A code data on L1. As shown in Figure 3.3, the L1 carrier is phase shifted90 o before being BPSK modulated by the C/A code data.Then this result is combinedwith the attenuated output of the BPSK modulation of L1 by the P(Y) code data. The3-dB amplitude difference and phase relationship between P code and C/A code on L1are illustrated by the vector phase diagram in Figure 3.4. Figure 3.5 illustrates the resultof P code data and C/A data. As observed in Figure 3.4, the exclusive-or processis equivalent to binary multiplication of two 1-bit values yielding a 1-bit product usingthe convention that logical 0 is plus and logical 1 is minus.There are 204,600 P(Y) code epochs between data epochs and 20,460 C/A code epochsbetween data epochs, so the number of times that the phase could change in the PRNcode sequences due to data modulation is relatively infrequent, but the spectrum changesdue to this modulation are very significant.There are 154 carrier cycles per P(Y) code chip and 1,540 carrier cycles per C/A codechip on L1, so the phase shifts on the L1 carrier are relatively infrequent.The L2 frequency(1,227.60 MHz) can be modulated by either the P(Y) code data or the C/Acode data or by the P(Y) code alone as selected by the CS(Ground based Controlsigment which monitors and controls the satellite navigation). The P(Y) code and C/Acodes are never present simultaneously on L2 prior to GPS modernization unlike thecase with L1. In general, the P(Y) code data is the one selected by the CS. There are120 carrier cycles per P(Y) code chip on L2, so the phase transitions on the L2 carrierare relatively infrequent. Table 3.1 summarizes the GPS signal structure on L1 and L2.

Chapter 3. GPS signal structure and characteristics 18Figure 3.4: Vector diagram of L1 GPS signalFigure 3.5: GPS code mixing with data

U N I V E R S I D A D E D O E S T A D O D E S A N T A C A T A R I N ACENTRO DE EDUCAÇÃO FÍSICA, FISIOTERAPIA E DESPORTOS§ 3º A critério da Instituição de Ensino Superior, o projeto pedagógico do cursode graduação em Educação Física poderá propor um ou mais núcleostemáticos de aprofundamento, utilizando até 20% da carga horária total,articulando as unidades de conhecimento e de experiências que ocaracterizarão.§ 4º As questões pertinentes às peculiaridades regionais, às identidadesculturais, à educação ambiental, ao trabalho, às necessidades das pessoasportadoras de deficiência e de grupos e comunidades especiais deverão serabordadas no trato dos conhecimentos da formação do graduado emEducação Física.Art. 8º Para o Curso de Formação de Professores da Educação Básica, licenciaturaplena em Educação Física, as unidades de conhecimento específico que constituemo objeto de ensino do componente curricular Educação Física serão aquelas quetratam das dimensões biológicas, sociais, culturais, didático-pedagógicas, técnicoinstrumentaisdo movimento humano.Art. 9º O tempo mínimo para integralização do curso de graduação em EducaçãoFísica será definido em Resolução específica do Conselho Nacional de Educação.Art. 10. A formação do graduado em Educação Física deve assegurar aindissociabilidade teoria-prática por meio da prática como componente curricular,estágio profissional curricular supervisionado e atividades complementares.§ 1º A prática como componente curricular deverá ser contemplada no projetopedagógico, sendo vivenciada em diferentes contextos de aplicaçãoacadêmico-profissional, desde o início do curso.§ 2º O estágio profissional curricular representa um momento da formação emque o graduando deverá vivenciar e consolidar as competências exigidas parao exercício acadêmico-profissional em diferentes campos de intervenção, soba supervisão de profissional habilitado e qualificado, a partir da segundametade do curso.Rua Pascoal Simone, 358, Coqueiros, Florianópolis, Santa Catarina, BrasilFone/Fax (0**48) 3321-8600 – Sítio Eletrônico: www.cefid.udesc.br24

Chapter 3. GPS signal structure and characteristics 20power spectral densities are shown in the figures 3.6.Figure 3.6: (a)An example Random Sequence (b)Its autocorrelation function (c)PSDThe important property of a DSSS signal using a random binary code is that it correlateswith itself in one and only one place(within one chip offset), and it is uncorrelatedwith any other random binary code or with itself if the offset(τ) is more than one chipperiod.Because of this property satellite can recognize a particular satellite and canknow whether the received signal is within one chip offset or not. But satellite navigationsystems employing rectangular chips have similar autocorrelation and power

Chapter 3. GPS signal structure and characteristics 21spectrum properties to those described for the random binary code case, but they employPRN codes that are perfectly predictable and reproducible. This is why they arecalled pseudo random codes.3.3.1 Effect of finite length PRN code on the autocorrelation functionand PSDBecause of the finite length of the PRN codes used by satellites the code repeats afterevery finite interval N (but approximate random nature within this interval).Hence thethe autocorrelation function described above will become periodic with period N andfunction out side the chip period won’t completely vanish.So the actual autocorrelation function for PRN sequence is given by⎧⎪⎨ A ( ( ))2 1 − |τ|TR PN (τ) =c1 +1N⎪⎩− 1 Nfor|τ − nT c | ≤ T celsewhere(3.5)where n = 0,±1,±2,±3,.......This function and its PSD are shown in the figure 3.7.Figure 3.7: (a)Autocorrelation function of a PRN sequence (b)Its PSD

Chapter 4GPS Receiver ChannelThe ultimate goal of GPS is to provide position,velocity,and time.To achieve these theprimary tasks it has to perform are measurement of range and range-rate and demodulationof the navigation data. The navigation data are the 50-bits/s data stream modulatedonto the GPS signal. The navigation data contain the satellite clock and orbitalparameters which are used in the computation of user position.4.1 Analog front end of GPS receiverMost modern GPS receiver designs are digital receivers. Block diagram of a digitalGPS receiver is shown in figure 4.1. The GPS RF signals of all SVs in view are receivedby a RHCP(right hand circularly polarized) antenna with nearly hemispherical (i.e.,above the local horizon) gain coverage. These RF signals are amplified by a low noisepreamplifier (preamp), which effectively sets the noise figure of the receiver. Theremay be a passive bandpass prefilter between the antenna and preamp to minimizeout-of-band RF interference. These amplified and signal conditioned RF signals arethen down-converted to an IF using signal mixing frequencies from local oscillators(LOs).The LOs are derived from the reference oscillator by the frequency synthesizer, based22

Chapter 4. GPS Receiver Channel 23Figure 4.1: Generic digital GPS receiver block diagram.on the frequency plan of the receiver design. One LO per downconverter stage is required.The LO signal mixing process generates both upper and lower sidebands ofthe SV signals, so the lower sidebands are selected and the upper sidebands and leakthroughsignals are rejected by a postmixer bandpass filter. The signal Dopplers andthe PRN codes are preserved after the mixing process. Only the carrier frequency islowered, but the Doppler remains referenced to the original L-band signal. The A/Dconversion process and automatic gain control (AGC) functions take place at IF. Notshown in the block diagram are the baseband timing signals that are provided to thedigital receiver channels by the frequency synthesizer phase locked to the referenceoscillators stable frequency. The IF must be high enough to provide a single-sidedbandwidth that will support the PRN code chipping frequency. An antialiasing IF filtermust suppress the stopband noise (unwanted out-of-band signals) to levels that areacceptably low when this noise is aliased into the GPS signal passband by the A/Dconversion process. The signals from all GPS satellites in view are buried in thermal

Chapter 4. GPS Receiver Channel 24noise at IF. At this point the digitized IF signals are ready to be processed by each ofthe N digital receiver channels. No demodulation has taken place, only signal gain andconditioning plus A/D conversion into the digital IF.This digitized IF signal will be processed by a set of channels which will normallyimplemented on ASIC or FPGA.A channel may be assigned to a single satellite ormultiple channels using multiplexing depending upon the availability of hardwareresources.The next section describes the detailed GPS receiver channel architecture.4.2 Digital receiver channelFigure 4.2 illustrates a high-level block diagram typical of one of the digital receiverchannels where the digitized received IF signal is applied to the input. For simplification,only the functions associated with the code and carrier tracking loops are illustrated,and the receiver channel is assumed to be tracking the SV signal in steadystate. Referring to Figure 4.2, first the digital IF is stripped of the carrier (plus carrierDoppler) by the replica carrier (plus carrier Doppler) signals to produce in-phase (I)and quadraphase (Q) sampled data. Note that the replica carrier signal is being mixedwith all of the in-view GPS SV signals (plus noise) at the digital IF.The I and Q signalsat the outputs of the mixers have the desired phase relationships with respect to thedetected carrier of the desired SV.The NCO shown in the figure is described in the next section.This produces a staircasefunction whose period is the desired replica carrier plus Doppler period. The sineand cosine map functions convert each discrete amplitude of the staircase function tothe corresponding discrete amplitude of the respective sine and cosine functions. Byproducing I and Q component phases 90 apart, the resultant signal amplitude can becomputed from the vector sum of the I and Q components, and the phase angle with

Chapter 4. GPS Receiver Channel 25Figure 4.2: Digital GPS receiver channel block diagram.respect to the I-axis can be determined from the arctangent of Q/I. In closed loop operation,the carrier NCO is controlled by the carrier tracking loop in the receiver processor.In phase lock loop (PLL) operation, the objective of the carrier tracking loop isto keep the phase error between the replica carrier and the incoming SV carrier signalsat zero. Any misalignment in the replica carrier phase with respect to the incomingSV signal carrier phase produces a nonzero phase angle of the prompt I and Q vectormagnitude, so that the amount and direction of the phase change can be detected andcorrected by the carrier tracking loop.The autocorrelation function of the PRN sequence described in the previous chapterwill be used for this purpose.The GPS receiver generates a set of 3 codes calledEarly(E),Prompt(P) and Late(L) signals.E and L are typically separated in phase by 1

Chapter 4. GPS Receiver Channel 26chip and P is in the middle. Correspondingly the autocorrelation functions for the Eand L signals will be shifted left and right respectively by half chip period as shownthe figure 4.3.In Figure 4.2, the I and Q signals are correlated with early, prompt, and late replicacodes (plus code Doppler) synthesized by the code generator, a 2-bit shift register, andthe code NCO. In closed loop operation, the code NCO is controlled by the code trackingloop in the receiver processor.The code NCO produces twice the code generatorclocking rate, 2 f co , and this is fed to the clock input of the 2-bit shift register. Thecode generator clocking rate, f co , that contains the nominal spreading code chip rate(plus code Doppler) is fed to the code generator. The NCO clock, f c , should be a muchhigher frequency than the shift register clock, 2 f co .With this combination, the shift registerproduces two phase-delayed versions of the code generator output. As a result,there are three replica code phases designated as early (E), prompt (P), and late (L).Not shown are the controls to the code generator that permit the receiver processor topreset the initial code tracking phase states that are required during the code searchand acquisition (or reacquisition) process.The prompt replica code phase is alignedwith the incoming SV code phase producing maximum correlation if it is tracking theincoming SV code phase. Under this circumstance, the early phase is aligned a fractionof a chip period early, and the late phase is aligned the same fraction of the chipperiod late with respect to the incoming SV code phase, and these correlators produceabout half the maximum correlation. Any misalignment in the replica code phase withrespect to the incoming SV code phase produces a difference in the vector magnitudesof the early and late correlated outputs so that the amount and direction of the phasechange can be detected and corrected by the code tracking loop as shown figure 4.3.When the PLL is phase locked, the I signals are maximum (signal plus noise) and theQ signals are minimum (containing only noise).

Chapter 4. GPS Receiver Channel 27Figure 4.3: (a)Autocorrelation functions of Early and Late signals generated by GPS receiverchannel.(b)Code-phase discriminator formed by difference between the correlation functionsin (a).

Chapter 4. GPS Receiver Channel 28Predetection IntegrationPredetection is the signal processing after the IF signal has been converted to basebandby the carrier and code stripping processes, but prior to being passed througha signal discriminator. Extensive digital predetection integration and dump processesoccur after the carrier and code stripping processes. This causes very large numbersto accumulate, even when 1 to 3 bits of quantization resolutions are used for IF A/Dconversion.The code wipeoff process that follows usually involving only 1-bit multiplication.Figure4.2 shows three complex correlators required to produce three inphasecomponents, which are integrated and dumped to produce I E , I P , I L and threequadraphase components integrated and dumped to produce Q E , Q P , Q L . The carrierwipeoff and code wipeoff processes must be performed at the digital IF sample rate,which is of the order of 50 MHz for a military P(Y) code receiver (that also operateswith C/A code), 5 MHz for civil C/A code receivers that use 1-chip E-L correlatorspacing, and up to 50 MHz for civil C/A code receivers that use narrow correlatorspacing for improved multipath error performance. The integrate and dump accumulatorsprovide filtering and resampling at the processor baseband input rate, which canbe at 1,000 Hz during search modes or as low as 50 Hz during track modes, dependingon the desired dwell time during search or the desired predetection integrationtime during track.The hardware integrate and dump process in combination with thebaseband signal processing integrate and dump process defines the predetection integrationtime.Predetection integration time is a compromise design. It must be as longas possible to operate under weak or RF interference signal conditions, and it must beas short as possible to operate under high dynamic stress signal conditions.

Chapter 4. GPS Receiver Channel 294.3 Frequency SynthesizerThe local carrier and code frequencies are synthesized from a high frequency sourcein the receiver using a numerically controlled oscillator(NCO).Figure 4.4. shows theblock diagram of a frequency synthesizer.Figure 4.4: frequency synthesizer block diagram.The NCO consists a hold register of fixed number of bits.In each clock cycle the valuehold by this register will be incremented by fixed value M which will be determinedby the frequency selection as follows.If the desired output frequency is f op and holdregister is of size N bits.After every 2 N /M clock cycles the hold register overflows andreset to 0.Hence the frequency will be divided by 2 N /M.Hence M value can be obtained2using the following formula M = f Nop f s.Where f s is the receivers clock frequency.Onereplica carrier cycle and one replica code cycle are completed each time the NCO overflows.TheNCO phase diagram,cos and sin map diagrams are shown in figure 4.5.The number of bits, j, is determined for the sin and cos outputs. The phase plane of

Chapter 4. GPS Receiver Channel 30Figure 4.5: (a)NCO phase state. (b)cos map output. (c)sin map output. (d)phase plane.(e)phase map table.360 degrees is subdivided into 2 j = K phase points.K values are computed for eachwaveform, one value per phase point. Each value represents the amplitude of thewaveform to be generated at that phase point. The upper j bits of the holding registerare used to determine the address of the waveform amplitude.Rate at which phaseplane is traversed determines the frequency of the output waveform.

Chapter 5Design of PRN code generatorsFigure 5.1 depicts a high-level block diagram of the direct sequence PRN code generationused for GPS C/A code and P code generation to implement the CDMA technique.Each synthesized PRN code is derived from two other code generators. In each case,Figure 5.1: General PRN code generator block diagram.31

Chapter 5. Design of PRN code generators 32the second code generator output is delayed with respect to the first before their outputsare combined by an exclusive-or circuit. The amount of delay is different for eachSV. In the case of P code, the integer delay in P-chips is identical to the PRN number.For C/A code, the delay is unique to each SV, so there is only a table lookup relationshipto the PRN number. These delays are summarized in Table 5.1. The C/A codedelay can be implemented by a simple but equivalent technique that eliminates theneed for a delay register. This technique is explained in the following paragraphs.5.1 C/A code generationThe GPS C/A code is a Gold code [3] with a sequence length of 1,023 bits (chips). SinceFigure 5.2: C/A code generator.

Chapter 5. Design of PRN code generators 33the chipping rate of the C/A code is 1.023 MHz, the repetition period of the pseudorandomsequence is 1,023/(1.023×10 6 Hz) or 1 ms. Figure 5.2 illustrates the designarchitecture of the GPS C/A code generator.Not included in this diagram are the controls necessary to set or read the phase statesof the registers or the counters. There are two 10-bit shift registers, G1 and G2, whichgenerate maximum length PRN codes with a length of 2 1 0 − 1 = 1,023 bits. (The onlystate not used is the all-zero state). It is common to describe the design of linear code∑generators by means of polynomials of the form 1 + X i , where X i means that theoutput of the ith cell of the shift register is used as the input to the modulo-2 adder(exclusive-or), and the 1 means that the output of the adder is fed to the first cell. Thedesign specification for C/A code calls for the feedback taps of the G1 shift register tobe connected to stages 3 and 10. These register states are combined with each other byan exclusive-or circuit and fed back to stage 1. The polynomial that describes this shiftregister architecture is: G1 = 1 + X 3 + X 10 . The polynomials and initial states for boththe C/A-code and P-code generator shift registers are summarized in Table 5.2.The unique C/A code for each SV is the result of the exclusive-or of the G1 direct outputsequence and a delayed version of the G2 direct output sequence. The equivalentdelay effect in the G2 PRN code is obtained by the exclusive-or of the selected positionsof the two taps whose output is called G21. This is because a maximum-length PRNcode sequence has the property that adding a phase-shifted version of itself producesthe same sequence but at a different phase. The function of the two taps on the G2 shiftregister in Figure 5.2 is to shift the code phase in G2 with respect to the code phase inG1 without the need for an additional shift register to perform this delay. Each C/Acode PRN number is associated with the two tap positions on G2. Table 5.1 describesthese tap combinations for all defined GPS PRN numbers and specifies the equivalentdirect sequence delay in C/A code chips. The first 32 of these PRN numbers are reservedfor the space segment. Five additional PRN numbers, PRN 33 to PRN 37, are

Chapter 5. Design of PRN code generators 34reserved for other uses, such as ground transmitters (also referred to as pseudosatellitesor pseudolites). C/A codes 34 and 37 are identical.5.2 P code generationThe GPS P code is a PRN sequence generated using four 12-bit shift registers designatedX1A, X1B, X2A, and X2B. A detailed block diagram of this shift register architectureis shown in figure 5.3 [4]. Not included in this diagram are the controls necessaryto set or read the phase states of the registers and counters. This reset and clock controllogic were shown in figure 5.4. The X1A register output is combined by an exclusiveorcircuit with the X1B register output to form the X1 code generator and that the X2Aregister output is combined by an exclusive-or circuit with the X2B register output toform the X2 code generator.The composite X2 result is fed to a shift register delay ofthe SV PRN number in chips and then combined by an exclusive-or circuit with the X1composite result to generate the P code. The design specification for the P code calls foreach of the four shift registers to have a set of feedback taps that are combined by anexclusive-or circuit with each other and fed back to their respective input stages. Thepolynomials that describe the architecture of these feedback shift registers are shownin Table 5.2, and the logic diagram is shown in detail in Figure 5.3. As shown in Figure5.3,the natural cycles of all four feedback shift registers are truncated. For example,X1A and X2A are both reset after 4,092 chips,eliminating the last three chips of theirnatural 4,095 chip sequences. The registers X1B and X2B are both reset after 4,093 chips,eliminating the last two chips of their natural 4,095 chip sequences. This results in thephase of the X1B sequence lagging by one chip with respect to the X1A sequence foreach X1A register cycle. As a result, there is a relative phase precession between theX1A and X1B registers. A similar phase precession takes place between X2A and X2B.At the beginning of the GPS week, all of the shift registers are set to their initial statessimultaneously, as shown in Table 5.2.

Chapter 5. Design of PRN code generators 35Figure 5.3: P code generator.

Chapter 5. Design of PRN code generators 36DQClk_cntrlResumeHaltEnResetRstClkFigure 5.4: clock control circut shown in figure 5.3.Also, at the end of each X1A epoch, the X1A shift register is reset to its initial state. Atthe end of each X1B epoch, the X1B shift register is reset to its initial state. At the end ofeach X2A epoch, the X2A shift register is reset to its initial state. At the end of each X2Bepoch, the X2B shift register is reset to its initial state. The outputs (stage 12) of the Aand B registers are combined by an exclusive-or circuit to form an X1 sequence derivedfrom X1A X1B, and an X2 sequence derived from X2A X2B. The X2 sequence isdelayed by i chips (corresponding to SVi) to form X2i. The P code for SVi is Pi = X1 X2i.There is also a phase precession between the X2A/X2B shift registers with respect tothe X1A/X1B shift registers. This is manifested as a phase precession of 37 chips perX1 period between the X2 epochs (shown in Figure 5.3 as the output of the divide by37 counter) and the X1 epochs. This is caused by adjusting the X2 period to be 37chips longer than the X1 period. The details of this phase precession are as follows.The X1 epoch is defined as 3,750 X1A cycles. When X1A has cycled through 3,750 ofthese cycles, or 3,750×4,092 = 15,345,000 chips, a 1.5-second X1 epoch occurs. WhenX1B has cycled through 3,749 cycles of 4,093 chips per cycle, or 15,344,657 chips, it iskept stationary for an additional 343 chips to align it to X1A by halting its clock controluntil the 1.5-second X1 epoch resumes it. Therefore, the X1 registers have a combinedperiod of 15,345,000 chips. X2A and X2B are controlled in the same way as X1A and

Chapter 5. Design of PRN code generators 37Table 5.1: Code Phase AssignmentsSV PRN C/A-code Tap C/A-code P codeNumber Selection delay(chips) delay(chips)1 26 5 12 37 6 23 48 7 34 59 8 45 19 17 56 26 18 67 18 139 78 29 140 89 310 141 910 23 251 1011 34 252 1112 56 254 1213 67 255 1314 78 256 14. . . .. . . .. . . .. . . .33 510 863 3334 410 9503 3435 17 947 3536 28 948 3637 410 9503 37X1B, respectively, but with one difference: when 15,345,000 chips have completed inexactly 1.5 seconds, bothX2A andX2B are kept stationary for an additional 37 chipsby halting their clock controls until the X2 epoch or the start of the week resumesit. Therefore, theX2 registers have a combined period of 15,345,037 chips, which is 37chips longer than the X1 registers.Note that if the P code were generated by X1 .X2, andif it were not reset at the end of the week, it would have the potential sequence lengthof 15,345,000× 15,345,037 = 2.3547×10 14 chips. With a chipping rate of 10.23×10 6 , thissequence has a period of 266.41 days or 38.058 weeks. However, since the sequence istruncated at the end of the week, each SV uses only one week of the sequence, and 38unique one-week PRN sequences are available. The sequence length of each P code,

Chapter 5. Design of PRN code generators 38Table 5.2: GPS Code Generator Polynomials and Initial StatesRegister Polynomial Initial StateC/A code G1 1 + X 3 + X 10 1111111111C/A code G2 1 + X 2 + X 3 + X 6 + X 8 + X 9 + X 10 1111111111P code X1A 1 + X 6 + X 8 + X11 + X 12 001001001000P code X1B 1 + X 1 + X 2 + X 5 + X 8 + X 9 + X 10 + X 11 + X 12 010101010100P code X2A 1 + X 1 + X 3 + X 4 + X 5 + X 7 + X 8 + X 9 + X 10 + X 11 + X 12 100100100101P code X2B 1 + X 2 + X 3 + X 4 + X 8 + X 9 + X 1 2 010101010100with the truncation to a 7-day period, is 6.1871×10 12 chips. As in the case of C/A code,the first 32 PRN sequences are reserved for the space segment and PRN 33 through 37are reserved for other uses (e.g., pseudolites). The PRN 38 P code is sometimes usedas a test code in P(Y) code GPS receivers, as well as to generate a reference noise level(since, by definition, it cannot correlate with any used SV PRN signals). The unique Pcode for each SV is the result of the different delay in the X2 output sequence. Table5.1 shows this delay in P code chips for each SV PRN number.The P code delays (inP code chips) are identical to their respective PRN numbers for the SVs, but the C/Acode delays (in C/A code chips) are different from their PRN numbers. The C/A codedelays are typically much longer than their PRN numbers. The replica C/A codes fora conventional GPS receiver can be synthesized by programming the tap selections onthe G2 shift register.5.3 Correlation results of the implemented GPS receiverchannelAccording to the specifications of PRN code generation described in this chapter andreceiver channel architecture described in chapter 4 a receiver channel is implementedusing xilinx system generator.Using this channel the correlation values of incomingsignal for various phase delays are obtained.The incoming signal is modeled by givingvariable delay before being fed to the receiver channel input.The results are shown in

Chapter 5. Design of PRN code generators 39the figure 5.5.Correlation of the received signal with Early,Prompt,and Late C/A code Vs Code phase offset0.5 x 104 Code phase offset0IeIpIlQeQpQl−0.5−1−1.5−2−2.50 10 20 30 40 50 60 70Figure 5.5: Correlation results with Early,Prompt,and Late signals

Chapter 6Subchip Multipath Delay Estimationusing TeagerKaiser OperatorTraditional approaches used for channel estimation generally fail in estimating closelyspacedmultipath components in code-division multiple access (CDMA) systems. Applicationof Teager-Kaiser operator[8] for downlink WCDMA multipath delay estimationis a highly efficient technique with subchip resolution capability.[5].This techniquehas the advantage of simplicity and efficiency compared to the other available techniques.Butthe performance of this technique is influenced by the shape of the pulsewaveform used.It performs well for rectangular pulse than other pulse shapes.Thiswill be described in the following sections.6.1 Signal and Channel ModelIn a downlink DS-CDMA scenario with K users in the system, the received signal canbe written as [9].r(t) =K∑k=1√Pk∞∑n=−∞b n,kL∑α n,l s n k (t − τ n,l) + η(t) (6.1)l=1where40

Chapter 6. Subchip Multipath Delay Estimation using TeagerKaiser Operator 41P k is the power of user k.b n,k is the transmitted data symbol n of user k. α n,l and τ n,l arethe complex attenuation coefficient and delay,repectively, of the l th path during thesymbol n. L is the number of channel paths.s n k(.) is the signature of user k during thesymbol n. η(.) is the complex additive white Gaussian noise.The user signatures are expressed as follows.S Fk −1∑s n k (t) =m=0c n m,k p(t − mT c − nS Fk T c ) (6.2)where c n m,k is the code value of m th chip of user k during the symbol n, T c is the chipinterval, p(.) is the chip pulse shape, S Fk is the spreading factor of user k.Delay estimation is based on the cross-correlation between the received signal r(t) andthe replica of the desired user signature. The output of the correlator is given by [11].y n (τ) = √ P k b n,kL∑α n,l R(τ − τ n,l ) + ˜η(τ) (6.3)l=1where ˜η(.) is an additive Gaussian noise process incorporating the effects of noise, multiuserinterference, interpath and intersymbol interference, and R(τ) is the pulse shapeautocorrelation function, which is given for a rectangular pulse shape by equation 3.2.Equation 6.3 implies that for rectangular pulse shape, the output of the correlator isa superposition of shifted triangular pulses weighted by the complex channel tap coefficientsand the data modulation within some additive noise. To avoid the effect ofmultipaths the contribution of interfering paths must be subtracted from the outputof the finger tracking the path of interest.For that we need to know these multipathdelays.

Chapter 6. Subchip Multipath Delay Estimation using TeagerKaiser Operator 42There are several delay estimation algorithms available for estimating these delays[5].The performance of the delay estimators is defined by the error statistics such as theacquisition probability(probability of estimating all multipath delays within a certainfixed error limit), the mean or the variance of the error,root mean square error (RMSE)of the multipath delays etc.TK based algorithm is one of the highly efficient techniques[6] with additional advantageof lowest complexity.It will give best performance for rectangular pulse shape.Thedescription of this Operator and the results obtained using this operator are shown inthe following section.6.2 Teager-Kaiser Operator and its application for the DelayEstimationThe nonlinear quadratic TK operator was first introduced for measuring the real physicalenergy of a system[7].Since its introduction, several other applications have beenfound for TK operator.The Structure of the correlation function 6.3 can be exploited with the aid of the nonlinearTK operator[8] ψ[.] defined below for continuous time function.ψ C [x(t)] = ẋ(t)ẋ ∗ (t) − 1 2 [ẍ(t)x∗ (t) + x(t)ẍ ∗ (t)]. (6.4)Similarly, the discrete-time Teager operator of a complex valued signal is given by[10]ψ D [x(n)] = x(n − 1)x ∗ (n − 1) − 1 2 [x(n − 2)x∗ (n) + x(n)x ∗ (n − 2)]. (6.5)For a real signal equation 6.5 comes into very simple form asψ D [x(n)] = x 2 (n − 1) − x(n)x(n − 2). (6.6)

Chapter 6. Subchip Multipath Delay Estimation using TeagerKaiser Operator 43By applying the continuous TK operator to 6.3, the following equation can be obtained.ψ C [y n (τ)] = 1 T cL∑l=1+ 1 L∑TC2 l=1+ ˜η T K (τ).L∑Re[α n,l α ∗ n, j]R(τ − τ n,l ) × δ(τ − τ n,l )j=1L∑α n,l α ∗ n, j × sign((τ − τ n,l )(τ − τ n,j )) × Π(τ − τ n,l , T c ) × Π(τ − τ n,j , T c )j=1⎧⎪⎨ 1 |t| ≤ T cΠ(t, T c ) =⎪⎩ 0 otherwise(6.7)where Π(t, T c ) stands for a rectangular function with unit amplitude and duration 2T ccentered at τ = 0. δ(τ) stands for the Dirac function,and ˜η T K (τ)is the additive whiteGaussian noise at the output of the TK operator.This δ(.) function is the result of the sharp edges of the rectangular pulse shape. i.e Theperformance of this tecqnique is influenced by the pulse shape.From equation 6.7 it is very clear that the TK operator applied to the output of thecorrelator provides clear time-aligned peak locations of the closely spaced paths in thepresence of a certain ”noise” floor [second and third terms of 6.7].

Chapter 6. Subchip Multipath Delay Estimation using TeagerKaiser Operator 446.3 Simulation ResultsThe correlation data for different multipath delays is obtained using the implementedGPS receiver channel.The attenuation factor α n,l is taken into account by giving differentweights to these time shifted triangular pulses.The results are shown in figure 6.1.Multipath Delay Estimation Using Teager−Kaiser Operator.2.5 x 104 Delay2LOS(desired signal)1/4 chip delay1/2 chip delay0.9 chip delayTK response1.510.500 50 100 150 200 250Figure 6.1: peaks shown by TK operator at multipath delays.6.4 ConclusionA GPS receiver channel was implemented and it is used to evaluate the performanceof the Teager-Kaiser operator for subchip multipath DS-CDMA delay estimation.Fromthe equation 6.6 and results obtained it can be concluded that Teager-Kaiser techniqueshowing very good performance for rectangular pulse with least computational complexity.

Chapter 6. Subchip Multipath Delay Estimation using TeagerKaiser Operator 456.5 Future WorkTeager-Kaiser method is showing excellent performance for rectangular pulse withleast computational complexity.Efficient algorithms must be designed to make it independentof the pulse shape for showing high performance.This can be done by combiningthis technique with other efficient but complex techniques and optimizing theperformance.

Bibliography[1] Simon, M., et al., Spread Spectrum Communications Handbook, New York:McGraw-Hill,1994.[2] Betz, J., ”Binary Offset Carrier Modulations for Radionavigation,” NAVIGATION:Journal of The Institute of Navigation, Vol. 48, No. 4, Winter 20012002.[3] Gold, R., ”Optimal Binary Sequences for Spread Spectrum Multiplexing,” IEEETrans. on Information Theory, Vol. 33, No. 3, 1967.[4] ARINC, NAVSTAR GPS Space Segment/Navigation User Interfaces, IS-GPS-200D, ARINC Research Corporation, Fountain Valley, CA, December 7, 2004.[5] E. S. Lohan, R.Hamila, A. Lakhzouri, and M. Renfors, ”Highly efficient techniquesfor mitigating the effects of multipath propagation in DS-CDMA delay estimation,”IEEE Transactions on Wireless Communications, vol. 4, no. 1, pp. 149162,2005.[6] R. Hamila, E. S. Lohan, and M. Renfors, ”Subchip multipath delay estimationfor downlink WCDMA system based on Teager-Kaiser operator” IEEE Commun.Lett., vol. 7, pp. 13, Jan. 2003.[7] J. F. Kaiser, ”On a simple algorithm to calculate the ’energy’ of a signal,” in Proc.IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), 1990, pp.381384.46

BIBLIOGRAPHY 47[8] R. Hamila, J. Astola, F. A. Cheikh, M. Gabbouj, and M. Renfors, ”Teager energyand the ambiguity function,” IEEE Trans. Signal Processing, vol. 47, pp. 260262,Jan. 1999.[9] ”Physical layer-general description,” 3GPP, 3GPP Tech. Rep. TS 25.201 V3.0.0,1999.[10] E. S. Lohan, R. Hamila, and M. Renfors, ”Performance analysis of an efficientmultipath delay estimation approach in CDMA multiuser environment,” Proc.12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, pp.610, 2001.[11] R. Van Nee, Multipath and Multi-Transmitter Interference in Spread-SpectrumCommunication and Navigation System. Delft, The Netherlands:Delft Univ.Press, 1995.