Advanced global navigation satellite system receiver design (797918), страница 7

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All the GPS signals arederived from the fundamental GPS frequency of 10.23MHz.BPSKmodulator× 120L2 P(Y)or C/ABPSKmodulatorL1 C/ABPSKmodulatorL1 P(Y)× 15490ºP(Y) codegenerator10.23MHz÷ 10C / A codegenerator÷ 204600DatageneratorFigure 3-3, Heritage GPS signal generation structure [Kaplan and Hegarty 2006]31Signal characteristicsGPS signals on L1 retain orthogonality because they are broadcast in phasequadrature, which can be represented as follows.S L1 (t ) = 2 PC d CA (t )aCAi (t ) cos(ω L1t ) + 2 PP d P (t )a Pi (t ) sin(ω L1t )3–2aCAi(t) is denoted the Coarse Acquisition (C/A) code, which is a 1023 chip long PRNsequence, unique to the transmitting satellite i (1 to 32), from the Gold code family()[Gold 1967].

Each bit or ‘chip’ of the C/A code, TC is 1µs long and therefore1.023is said to have a ‘chipping rate’ of 1.023 Mcps (Mega chips per second). The entireC/A code sequence repeats every 1 ms. aPi(t) is named the precision code, which is aPRN sequence, unique to the satellite i, with a chipping rate of 10.23 Mcps andrepeats once a week. This code is known as the P(Y) code because if desired, thesatellites have the ability to switch transmission to modulate the carrier with theencrypted Y code, which is only available to U.S.

government users.dCA(t), is the bi-phase navigational data signal associated with the civil C/A code andis transmitted at a rate of 50Hz. dP(t) is the navigational data associated with themilitary P code signal. The navigational data contains information necessary for thereceiver to compute position, velocity and time solutions for each satellite. ω L1 is theL1 carrier frequency, PC and PP are the C/A and P(Y) signal powers, respectively.The relative power of the currently transmitted C/A code is 3dB greater than that ofthe P(Y) code and hence, PP =PC.2One chip of the GPS C/A code propagating at the speed of light, c has a length of293 m (TC × c ) , although actual discrimination generally achieves accuracies that are avery small fraction of this.

The repeat interval of 1 ms implies a range ambiguity ofaround 300 km. However, transitions of navigational data potentially occur every20 ms, which expands the ambiguity to around 6000 km. This range ambiguity isresolvable by examination of the data stream d(t). The P(Y) code chipping rate of10.23 Mcps results in an equivalent resolution of 29 m.

Again, actual discrimination32Signal characteristicsis some small fraction of the resolution. Currently, the majority of GPS satellitestransmit only the P(Y) code signal in the GPS L2 band, which can be represented asfollows.3–3S L 2 (t ) = 2 PP d P (t )aPi (t ) cos(ω L 2t )ω L 2 is the L2 carrier frequency.The GPS C/A code is generated using two 10 bit linear feedback shift registers(LFSR), G1 and G2, as shown in Figure 3-4. Both registers are initialised with all bitsset to a logical ‘one’ state. The feedback taps of the registers are commonly describedin polynomial form as follows [Sklar 1988].G1 = 1 + X 3 + X 103–4G 2 = 1 + X 2 + X 3 + X 8 + X 9 + X 10Xi represents the ith bit of the LFSR. 37 PRN codes are generated by combining theoutput of the G1 register with a unique selection of two bits from the G2 register.12345678910Start value on epoch (all ones)1.023MHz ClockEpochcounter1ms epochC/A code,aCAi(t)12345678910Start value on epoch (all ones)Tap selectorFigure 3-4, C/A code generator33Signal characteristicsThe resulting PRN codes are maximal length sequences with N = 2 n − 1 chips, wheren is the length of the LFSR.

The periodic autocorrelation function for a PRNsequence a (t ) of length n chips, with a chip period TC can be written as follows.Λ (τ ) =1NTCNTc3–5∫ a(t )a(t + τ )dt0The autocorrelation envelope (Figure 3-5) can be approximated by a triangle function,the peak of which (amplitude A) corresponds to the perfect alignment (correlation)between the received code and the locally generated replica. Outside the correlationinterval the ideal cross-correlation function is –A/N due to the avoidance of the allzero (stable) state in the generation of Gold codes.Correlation ΛAA/NτTCTC0Figure 3-5, Ideal autocorrelation of a PRN sequenceIn practice the sequences identified by Gold exhibit a three-valued cross-correlation − 1 − t (n ) t (n ) − 2 function with values  n−1 , n−1 , n−1  , where222 2 ( n +1) / 2 + 1t (n ) =  ( n+ 2) / 2+12(odd n)(even n)3–634Signal characteristicsTherefore, Gold sequences employed for GPS C/A code have cross correlation values − 1 − 65 63 of ,, .

The autocorrelation of the GPS C/A code (PRN1) is shown1023 1023 1023 in Figure 3-6.1.21.2111023 chipslong0.8GPSΛ()0.80.60.60.40.40.20.200-0.2-5000500-0.2-10Time Delay (chips)-50510Tim e delay (chips)TimeDelay (chips)Figure 3-6, Normalised autocorrelation of GPS C/A codeA PRN code sequence can be viewed as a periodic sequence of pseudo-randomlyrepeated rectangular pulses. Therefore, the two-sided power spectral density of asequence with chip period TC and pulse amplitude A, can be written as ωT S PRN (ω ) = A 2TCsinc 2  C  2 where, sinc( x) =3–7sin( x)xThe power spectral densities (PSD) of the current GPS signals are shown in Figure3-7, assuming no filtering to the signals and 1W signal power.

The main lobe of theC/A code signal is seen to spread ±1.023 MHz around the L1 carrier. The higherchipping rate of the P(Y) code, ten times the C/A code rate, causes the spectral energyof the main lobe to be spread over ±10.23 MHz around the carrier.35Signal characteristics60Power spectral density (dBW/Hz)GPS L1 C/A codeGPS L1 P(Y) codeCarrier Frequency = 1575.42 MHz70PSK( fP)80PSK10( fP)90100201510505101520fPFrequency offset from carrier (MHz)Figure 3-7, Power spectral density of current GPS L1 signals: (unfiltered, 1W signal power)The Radio Frequency (RF) link budget for GPS signals is shown in Table 3-1.

Thefree space propagation loss, LPR is calculated as follows.LPR λ =  4π r 23–8λ is the transmitted carrier wavelength and r is the distance to the satellite(r = 25236 km at 5˚ elevation).36Signal characteristicsTable 3-1, Link budget for GPS satellitesSatellite TX power,[PT]1TX Antenna gain,[GTX](max pointing error14.3°)Required SV EIRP=[PT] + [GTX]Atmospheric losses,[LA]Propagation loss,[LPR](R = 25236km)Receiving antennagain,[GRX]Minimum receivedpower= [PT ] + [GTX ] − [L A ]L1 C/A codeL1 P(Y) codeL2 P(Y) code13.4 dBW10.4 dBW8.2 dBW13.4 dB13.4 dB11.5 dB26.8 dBW23.8 dBW19.7 dBW0.5 dB0.5 dB0.5 dB184.4 dB184.4 dB182.3 dB0 dB0 dB0 dB-158.1 dBW-161.1 dBW-163.1 dBW− [LPO ] − [LPR ] + [GRX ]Generally the received power levels of the GPS satellites are up to 5dB greater thanthe specified minimum power levels [Kaplan and Hegarty 2006].3.2GPS modernised signal characteristicsThe completion of GPS modernisation under the current plans [GPS ICD 2007] willresult in four additional navigational signals transmitted in the L-band; one militarysignal broadcast on the L1 carrier frequency, L1 M, one military and one civil signalon the L2 frequency, L2 M and L2 C respectively, and an additional civil signal onthe L5 carrier (see Figure 3-2).

The GPS block IIR satellites will transmit the new L1and L2 signals while the subsequent block IIF satellites will transmit the new L5signal. Discussions between the US and ESA are still on-going as to whether toaccept a proposal to implement a common civil signal in the L –band (L1 C). Table3-2 shows the centre frequencies, currently agreed modulation schemes, data rates andtypes of data of current and future GPS signals.1The use of square brackets [ ] denotes a dB quantity37Signal characteristicsTable 3-2, Future GPS signals [GPS ICD 2007]SignalCentreModulationMain lobeTypes ofData ratefrequencyschemebandwidthdata(sps)(MHz)(MHz)2L1 C/A1575.42BPSK-R(1)2.046Civil50L1 C1575.42BOC(1,1) or4.092 andCivilUnknownMBOC(6,1,1/11)14.332L1 P(Y)1575.42BPSK-R(10)20.46Military50L1 M1575.42BOC (10, 5)30.69MilitaryUnknownL2 C1227.6BPSK-R(1)2.046Civil50L2 P(Y)1227.6BPSK-R(10)20.46Military50L2 M1227.6BOC (10, 5)30.69MilitaryUnknownL5 I1176.45BPSK-R(10)20.46Civil100L5 Q1176.45BPSK-R(10)20.46CivilData-lessA 12 month study by the GPS Joint Program Office (JPO) [Betz 1999] resulted in thedecision to use Binary Offset Carrier (BOC) modulation for the new military signalson L1 and L2.

This modulation type will also be implemented for Galileo signals invarious forms. BOC modulation is a rectangular sub-carrier modulation (sine orcosine) of the PRN spreading code and is denoted BOC( f S , f C ), where, f S is the subcarrier frequency, f C is the PRN code chipping rate and both are multiples of1.023×106. The subcarrier frequency is chosen such that it has an integer number ofhalf periods, TS (sub-chips) within a chip of the spreading sequence.

A number ofdifferent BOC modulations are depicted in Figure 3-8. The normalised PSD of a sinephased BOC signal can be written as [Betz 2001]2  πf   πf   sin  sin     2 f S   fC  fc  πf cos πf  2f   S S BOC S ( f ) = 2  πf   πf   sin  cos    2 f S   f C  fc  πf cos πf  2f   S 3–9for 2 f S f C evenfor 2 f S f C odd2For BOC modulations the main lobe bandwidth is defined as the bandwidth encapsulating the largesttwo spectral lobes.38Signal characteristicsIf the BOC subcarrier is cosine phased with respect to the code sequence thenormalised PSD can be written asS BOCC ( f ) =   2 sin 2  πf  sin  πf  4 f S   f C  fC  πf fcosπ2f S2   2 sin 2  πf  cos πf  4f   f  S  CfC  πf πf cos2f S3–10for 2 f S fC even2for 2 f S f C oddThe most desirable effect of BOC modulation is that it produces replicas of the spreadsignal pushed away from the centre frequency at ± f S .

Hence, the spectral energy isshifted away from the carrier frequency, potentially allowing localised jamming of thecivil signal without significantly affecting the integrity of the military signal.Frequency reuse is the primary justification for using BOC modulation for GNSSsystems, reducing or eliminating the spectral overlap of the signals within a givenbandwidth. However, BOC modulation also claims potential advantages in multipathmitigation and code tracking accuracy. These issues are addressed in detail inChapter 4.The GPS M code signals are to be transmitted using a BOC(10, 5) modulation.Therefore, the main lobes of the signal will be spread over 10.23MHz and the lobeswill be shifted ±10.23MHz away from the carrier.

The modernised signals for L1 areshown in Figure 3-9 with the M code signal.Recently a joint GPS-Galileo working group [Hein et al 2006] have proposed acommon multiplexed BOC (MBOC) structure for future L1 civil signals. Studies onthis signal were beyond the scope of this project due to its late introduction.Therefore, MBOC is considered in the Chapter 11 of this report, describing extensionsof this work.39Signal characteristics60PSK-R(1)“a chip”Power spectral density (dBW/Hz)− 6070PSK( fP ) 8090− 100100TC420−524fP5Frequency offset from carrirer (MHz)60BOC(1,1)-sineTS“a sub-chip”Power spectral density (dBW/Hz)− 6070BOCs ( fP ) 8090− 10010042−5024fPTC5Frequency offset from carrier (MHz)60Power spectral density (dBW/Hz)− 60BOC(2,1)-sine70BOCs ( fP )8090− 100100420−524fP5Frequency offset from carrier (MHz)TC60BOC(2,1)-cosinePower spectral density (dBW/Hz)− 6070BOCc( fP ) 8090− 1001004−5202fP45Frequency offset from carrier (MHz)Figure 3-8, Spreading waveforms and PSD of BPSK(1), BOC(1,1)-sine, BOC(2,1)-sine andBOC(2,1)-cosine modulations40Signal characteristics60Power spectral density (dBW/Hz)GPS L1 C/A codeGPS L1 P(Y) codeGPS L1 M codeCarrier Frequency = 1575.42 MHz70PSK( fP)PSK10( fP) 80BOCs ( fP)90100201510505101520fPFrequency offset from carrier (MHz)Figure 3-9, Power spectral density of future L1 GPS signals (unfiltered, 1W signal power)The spectral shape of the current baseline for the modernised GPS L2 band isequivalent to that shown in Figure 3-9, with a centre frequency of 1227.6 MHz.

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