Advanced global navigation satellite system receiver design (797918), страница 12

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Clearly, the choice offuture GNSS signals is also driven both politically and programmatically.745Receiver theoryThis chapter describes in detail the process of acquiring and tracking various types ofGNSS signals. Detailed comparisons are drawn between different techniques andalgorithms for both PSK and BOC receivers considering both performance measuresand the relative hardware impact. The theory described here is incorporated into thereceiver designs given in Chapters 8 and 10. This chapter begins by describing thetechniques currently employed to locate and acquire PSK signals, followed by areview of the established tracking techniques for PSK signals. A summary of themore recent theory required for acquiring and tracking BOC signals is given withcomparisons of the various techniques. This chapter outlines the problems facingreceiver designers using conventional techniques for tracking BOC signals and detailsthe current progress in addressing these problems.A generic block diagram for a GNSS receiver is shown in Figure 5-1.

Although thereare a number of changes required to receive new generation GNSS signals, thegeneric functions of the receiver are still valid.Figure 5-1, GNSS receiver block diagram.GNSS signals are received through the use of a right-hand circularly polarised(RHCP) antenna and amplified using a low-noise amplifier (LNA), which essentiallydetermines the receiver’s noise figure. The radio frequency (RF) signals are down-75Receiver theoryconverted, typically in a number of stages, to an intermediate frequency (IF),sufficiently high in frequency to support the signal bandwidth.The signal is then digitised by an analogue to digital converter (ADC), with automaticgain control (AGC) and the digital IF is then passed to the receiver’s correlatorchannels.

Here, the carrier signal and code sequence are removed from the signal bycorrelating the received signal with locally generated replicas. The processor thenextracts the raw navigational data by monitoring the changes in phase angle. Thisdata can be used in combination with phase information derived from the carrier andcode tracking loops to form pseudorange and Doppler estimates, ultimately resultingin position, velocity and time information for the user.5.1Searching for PSK signalsBefore GNSS signals can be used to solve for the receiver’s position the signals mustbe found. The signals arriving at the receiver have an associated delay due to thedistance between transmitter and receiver but have also been shifted in frequency.Therefore, the receiver must search in both frequency and delay (time) domains.Assuming signal conditioning and down-conversion to a suitable IF we can model thereceived PSK signal as follows.u PSK (t ) = A × cos(ω0t + φ ) × a (t − τ ) × d5-1A is the amplitude of the signal, ω 0 is the centre frequency of the IF signal, a(t) is thePRN code sequence and d is the navigational data value having possible values of +1and -1.

τ is the time delay of the code and φ is a general phase shift implicitlyallowing for time variation in phase as follows.φ = −ω0τ + φ05-276Receiver theoryφ0 is an unrelated phase shift from the uncharacterised path from transmitter toreceiver. Allowing a time varying delay, dτ/dt accounts for the Doppler shift dφ/dt onthe incoming signal.Additive noise and interfering signals are not present in this representation to simplifythe following illustrations. The aim of a PSK receiver is to estimate the delay, τ anddemodulate the incoming navigational data.

This is accomplished using estimatingcorrelators and feedback (a digital phase locked loop). The receiver produces replica^in-phase and quadrature carrier signals with trial phase φ , which are mixed with theincoming signal. Subsequently, the signal is mixed with replica in-phase and^orthogonal PRN codes with trial time delay τ. The orthogonal code sequence isdefined as the difference between ‘early’ and ‘late’ time shifts of the code sequence,written as follows.Ta~(t − τˆ ) = a t − τˆ + DC2T   − a t − τˆ − DC 2  5-3TDC is the total separation between the early and late replica waveforms, bounded byTDC ≤ TC . Multiplication of the incoming signal by carrier and code replicas results infour correlation results denoted wII, wQI, wIQ and wQQ shown in Figure 5-2.

The firstsubscript denotes mixing with an in-phase (I) or quadrature (Q) carrier replica, thesecond subscript denotes mixing with in-phase or quadrature (orthogonal) codereplica.77Receiver theorywII∫wIQ∫wQQ∫wQIa (t − τˆ)cos(ω0t + φˆ)uPSK(t)∫sin(ω0t + φˆ)a~ (t − τˆ)a (t − τˆ)Figure 5-2, PSK correlator structureAs suggested by Dr Hodgart the resulting correlations can be written compactly usinga four element matrix as follows. wIIW =  wQITwIQ cos1 = ∫ u PSK (t )ω0t + φˆwQQ sinT0()T a (t − τˆ )  ~ dt a (t − τˆ )5-4Where T is the integration or averaging time. Combining the input signal uPSK(t) andthe receiver trial estimates the result can be converted to wIIW =  wQITTwIQ 1  vI (t )  a (t − τˆ )  = dtwQQ T ∫0  vQ (t ) a~ (t − τˆ )5-5where vI (t )  cosˆ=v(t ) =  sin φ − φ × a(t − τ ) × dv(t)Q()5-678Receiver theoryThe result of the integrals in Equation 5-5 can be written as follows.( )≈ A × cos(φ − φˆ ) × VΛ (τˆ − τ ) × d≈ A × sin (φ − φˆ ) × Λ(τˆ − τ ) × d≈ A × sin (φ − φˆ ) × VΛ (τˆ − τ ) × dwII ≈ A × cos φ − φˆ × Λ (τˆ − τ ) × dwIQwQIwQQ5-7The ‘ VΛ ’ represents the code tracking discriminator error signal, this is describedfully in the Section 5.2 of this chapter.

The symbol ‘Λ’represents the ideal PSKcorrelation function, which can be written τˆ − τ1 −Λ(τˆ − τ ) = TC05-8for − TC ≤ (τˆ − τ ) ≤ TCotherwiseT≈1a(t − τ )a(t − τˆ )dtT ∫0The Λ( ) function approximates the (almost) triangular correlation function of PSK^PRN codes, ignoring cross correlation errors. This function peaks on τ → τ , withtotal width we define as 2×TC. This can be seen by inspecting the result wII derivedfrom Mathcad simulation and shown in Figure 5-3.1.25110.750.50.500.2511.510.500.51-11.500Phase error (rads)0.25-0.510.5Code error (chips)-1Code error (chips)ΛFigure 5-3, Correlation profile of wII against code error (chips) and phase error (radians)79Receiver theoryFor PSK signals the result of wII is a single correlation peak, however the correlationstill has a phase dependency and may be inverted with the sign of the navigationaldata.

At start-up the GNSS receiver must search for each signal with no knowledge ofthe phase of the received carrier. Phase independency for the PSK search correlationis achieved by adding the square of the wII correlation combined with the square ofthe quadrature wQI correlation. This forms an unambiguous peak for the searchprocess, which is independent of phase error and the sign of the navigational data(d2)=1 .wSPSK = wII + wQI = 2 A2 Λ2 (τˆ − τ )225-9The correlation profile of wSPSK is shown against code error and carrier phase error inFigure 5-4. It can be seen that the search correlation is independent of carrier phaseerror.10.5010.5-100Phase error (rads)-0.51Code error (chips)-1ΛFigure 5-4, PSK search correlation wSPSKThe search is a 2 dimensional process, locating the signal in time (code delay) andfrequency.

Traditionally, a serial search technique is used, holding a steady frequencywhile shifting through all possible code offsets, before moving to the next possiblefrequency (Figure 5-5). The frequency range the receiver is required to search acrossis strongly dependant on the dynamic environment the receiver is to operate in and thequality of the receiver clock. For a typical terrestrial receiver the frequency search80Receiver theoryrange can be up to ±10 kHz, however for space receivers the range can expand up to±50 kHz [Unwin 1995].f0 + 3∆ff0 + 2∆ff0 + ∆fFrequency bins∆f ≈ 500 HzfCSignalf0 – ∆ff0 – 2∆ff0 – 3∆f≈ 0.5 chipsCode delay binsFigure 5-5, Serial GNSS signal searchFrequency is typically searched in bins of 500 Hz (for T = 1ms).

The normalisedcorrelation gain GF, with frequency error ∆f is given by [Mitel 1996]GF =sin (π × ∆f × T )(π × ∆f × T )5-10where T is the integration period. The correlation gain is shown in Figure 5-6 for anintegration time of 1msec. The minimum correlation gain for frequency bins of500Hz is -4dB. Extending the integration period allows detection of weaker signals.However, the frequency bins are narrowed resulting in longer search times andpotentially reductions in correlation gain due to changes in the Doppler during thecorrelation time.81Receiver theory0-5Correlation gain (dB)-10-15-20-25-30-35-40-2500 -2000 -1500 -1000 -5000500 1000 1500 2000 2500Frequency offset (Hz)Figure 5-6, Correlation power loss with frequency offsetThe code is typically searched in ½ chip bins.

Within the correlation interval(τˆ − τ ≤ ± TC ) the normalised correlation power Gτ, with code delay error, τˆ − τisgiven byGτ = Λ2 (τˆ − τ )5-11For ½ chip code bins the minimum correlation gain is -6dB. Narrower code andcarrier bin width will result in more reliable signal detection. However, the searchtime will increase because there are now more bins to search through.The serial search technique is inherently slow and may take a number of minutes todetect signal presence reliably.

Modern receivers use search techniques based on FastFourier Transforms (FFT), which can detect the signal presence within a matter ofmilliseconds [Van Nee and Coenen 1991]. The basic principle of FFT signaldetection is shown in Figure 5-7, first presented in [Kilvington 1986]. The receivedsignal is mixed into real (in-phase) and imaginary (quadrature) components and itsFourier transform computed. The result is then conjugate multiplied by the Fouriertransform of the code sequence. Multiplication of signals in the frequency domain isequivalent to correlating signals in the time domain.

Therefore, the correlation acrossall code offsets can be computed by taking the inverse Fourier transform.82Receiver theoryaI (t − τ )ADCA(ω )e − jωtu(t)2A(ω ) e − jωtsin(ω 0 t )IFFTFFTcos(ω 0 t )Λ (t − τ )2A* (ω )FFTADCaQ (t − τ )a(t)Figure 5-7, FFT signal detection principleFigure 5-8 shows the FFT detection of a GPS C/A code signal. The result of a singleFFT detection can deliver the equivalent to an entire serial search in a matter ofmilliseconds.

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