Analysis of the use of CSK for future GNSS signals (797922), страница 6
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Thesegeneral constraints were derived from the principalconditions of reception and the analysis of the current andfuture GPS and GALILEO signals:Reed-Solomon (2u-1, 2u-1-1)31∙ N∙Ts63∙ N∙Ts127∙ N∙Ts255∙ N∙Ts511∙ N∙Ts1023∙ N∙TsThe number of possible configurations of CSK signalswhich increase the useful bit rate of a BPSK signal whenimplementing a RS channel code is very large asexpressed in equation (14). In Figure 14, only RS withchannel code rates equal to 1/2 or 1/4 are inspectedalthough the optimal channel codes have a code rate equalto 3/4. The reason for this choice is that optimal RSchannel codes for a large value of U (from 8 bits the RScodes begin to be really interesting) tend to have verylarge codewords in terms of bits and in terms of duration.From Figure 13 and Figure 14, it can be observed thata CSK signal implementing a LDPC(1200, 600) channelcode and using the BICM-ID and mapping A alwaysoutperforms a CSK signal implementing a RS channelcode for any number of bits mapped by a CSK symbol, U,when the useful bit rate is increased with respect to aBPSK signal.
Moreover, when BICM-ID and mapping Bare used, it appears that at least U=9 (equality) or U=10bits are required in order to have better demodulationperformance (at a BER=10-5) for the RS implementation.Table IV shows the codeword duration of a CSK signalimplementing a Reed-Solomon Channel code increasingthe useful bit rate of the reference BPSK signal by thefactor expressed in equation (14). From Table IV, it canbe seen that the codeword duration of a CSK signalimplementing the LDPC (1200,600) and mapping A islonger than the codeword duration of a CSK signalimplementing a RS channel code except for 11 or morenumber of bits mapped by a CSK symbol, U. However,the codewords for mapping B are only longer than thecodewords for a RS channel code when U=7 bits. But,remember that at least U=9 bits are necessary in order tohave a CSK signal implementing a RS channel code witha better demodulation performance (BER=10 -5) than aPROPOSED CSK-BASED SIGNALS FORGNSSThe maximum number of bits mapped by a CSKsymbol is set to 13 bits ().
This value isdetermined by the number of chips of the PRN codehaving the maximum length among all the GPS andGALILEO signals (10230 for GPS L1C and L5) [6].A received C/N0 between 15 and 45 dB-Hz [1]: Thisconstraints provides the maximum and the minimumC/N0 which a signal can expect to find.A limited time to access the codeword. Thisparameter is important in the GNSS field in order toreduce as much as possible the Time-To-First-Fix(TTFF). The TTFF will condition the choice of themaximum codeword duration. For instance:oFor Galileo, the time to is 31.63 sec at 95% forE1F and 59.4 sec for E5a [21].oFor GPS, the time is 35.5 sec at 95% for L1C/A and 17.6 sec for L1C [21].VI.A.Specific signal characteristics and constraintsThe specific signal characteristics and constraints of thetwo proposed signal objectives are presented in thissection. Table V summarizes the signal characteristics andconstraints of a CSK signal keeping the useful bit rate of areference BPSK signal.
Table VI summarizes the signalcharacteristics and constraints of a CSK signal increasingthe useful bit rate of a reference BPSK signal but keepingthe same symbol rate.Table V and Table VI define two types of codewordswhich divide the proposition of the new CSK modulatedinto two types:a) Codeword of 600 invariant bits: Analyzing the definedGPS and GALILEO signals, it is observed that around600 bits are necessary to carry the satellites ephemerisand clock error correction [22]. Since this informationis constant for a period of time, code source mappingB is proposed for this type of signals. The reason isthat the coherent accumulation of mapping B codewords (one codeword transmitted in parallel) is easierto achieve than for mapping A (U codewordstransmitted in parallel).
Moreover, only ReedSolomon codes which have a codeword with about600 information words are used.Table V: Signal characteristics and constraints for a CSK signalkeeping the useful bit rate of a reference BPSK signal.Same Useful Bit RatePRN Symb. Period1ms to 20msUseful Bit rate25bps to 500 bpsCodeword max.
Duration30sCodeword number of bits600 Invariant bits≥ 600 variant bitsMapping LDPC(1200,600)Mapping BMapping ARS code rate3/43/4Table VI: Signal characteristics and constraints for a CSK signalincreasing the useful bit rate of a reference BPSK signal but keepingthe same symbol rate.Increased Useful Bit RatePRN Symb. Period1ms to 20msUseful Bit rate250bps to 5kbpsCodeword max.
Duration10sCodeword number of bits600 Invariant bits≥ 600 variant bitsMapping LDPC(1200,600)Mapping BMapping ARS code rate1/4 or 1/21/4 or 1/2Table VII: Considered PRN Code Durations assuming that severalidentical shifted PRN codes can be repeated to create a CSK symbolReferencePRN Code DurationBPSKRef.CSK withSymbolCSK with sameBPSKIncreasedRate1 to 16ms1 to 5ms1ms1 ms(max= 16 ms)(max= 5 ms)1 to 12ms1 to 24ms1 to4 ms4ms(max= 56ms)(max= 24ms)1 to 10ms1 to 20ms1 to10 ms10ms(max= 120ms)(max= 20ms)1 to 20ms1 to 20ms1 to20 ms20ms(max= 240ms)(max= 20ms)b) Codewords of 600 or more variant bits: Information ofnew applications of services. In this case, theinformation does not have to be constant and thusmapping A can be used instead of mapping B.
TheReed-Solomon channel codes are no longer restrictedby the size of codeword information bits.VI.B.Specific signal characteristics and constraintsTable XI and Table XII show the CSK signal designparameters when the codewords carry 600 invariant bits.Table XI presents the design of a CSK signal keeping thesame useful bit rate as a BPSK signal and Table XIIpresents the design of a CSK signal increasing the usefulbit rate as a BPSK signal.Table XIII and Table XIV show the CSK signal designparameters when the codewords carry 600 or more variantbits.
Table XIII presents the design of a CSK signalkeeping the same useful bit rate as a BPSK signal andTable XIV presents the design of a CSK signal increasingthe useful bit rate as a BPSK signal.Table XI, Table XII, Table XIII and Table XIV must beinterpreted as the choice made by the authors’ paper asthe most suitable CSK signal design parameters for eachone of the analyzed cases. Nevertheless, the reader coulddesign a CSK signal with other parameters which bettersuits its signal needs. Moreover, these tables do not try toselect one pair channel code – decoding method withrespect to the other ones.
In fact, these tables show thatthe final choice will be made depending on the signalcharacteristic or constraint the designer wants to givepriority. For example, looking at Table XIV and the caseof analysis {reference BPSK symbol equal to 4ms(125bps) and final useful bit rate equal to 500 bps}, thesignal choice will be: BICM-ID for demodulationperformance priority, RS for codeword duration priorityand Classical decoding (CD) for receiver complexitypriority.Finally, the reader must remark that the HDMD methodwas not included on the tables. The reason is that HDMDprovides a worse demodulation performance than BICMID but has a higher receiver complexity than CD.VII.IMPACT OF A CSK MODULATION ON AGNSS RECEIVERIn this section, the constraints that lie in the receptionof a CSK signal on a GNSS receiver, compared to thereception of a classical BPSK signal are analyzed.VII.A.
CSK signal modelThe proposed CSK signal is assumed to have 2components: a data component only carrying CSKsymbols and a pilot component necessary to synchronizethe signal. The option of having a hybrid data component(a part with BPSK symbols and a part with CSK symbols)was shown not to improve the signal acquisitionsensitivity in [14] and thus is discarded for this purpose.The pilot component has a primary PRN code of thesame length as the CSK symbols PRN code. Moreover,both PRN codes are synchronized in order to facilitate thesynchronization and demodulation of the data componentfrom the pilot component.
Additionally, the pilotcomponent should incorporate a secondary codesynchronized with the codewords of the data component(as GPS L1C [6]).Table VII shows the different PRN codes periodsdepending on the proposed CSK signal option. It wasassumed that the duration of a PRN code would not begreater than 24ms, which is close to the maximum usualvalues for a GNSS signal (between 1 and 10 ms).Different allocations of power between the data and pilotcomponent are analyzed:VII.B.Data: 25%, Pilot: 75%Data: 50%, Pilot: 50%Data: 75%, Pilot: 25%Reference BPSK signal modelThe reference BPSK signal model used to compare theimpact of a CSK modulated signal on a GNSS receiverwith a BPSK modulated signal have two components, aBPSK modulated data component and pilot component.For both components of the BPSK signal, theimplemented PRN code has the same length and chippingrate as the components of the CSK modulated signal.
Forthe data component, the only difference is obviously theimplemented modulation.VII.C. Impact of CSK on the Receiver ArchitectureThe increase of the receiver’s complexity when using aCSK modulated signal is found on the demodulator blockwhich is more complex than the demodulator of a BPSKsignal as seen in section II-II.C. In this section, theincrease of complexity is shown by means of presentingthe number of multiplications which should be conductedin a CSK modulator in comparison to a BPSKdemodulator.Two types of demodulators are proposed for a CSKmodulated signal, the bank of matched filters (orcorrelators) and the FFT-based correlator.
Moreover,there are two algorithms which can be implemented toapply the FFT-based correlator: the traditional IFT and FTcalculation method or the radix-2 Cooley-Tukey FFTalgorithm [23].Table VIII shows the number of multiplicationsrequired for the different types of CSK demodulatorswhen a CSK mapping U bits and spanning N=1 identicalPRN codes is transmitted. Moreover, in order to allow fora fair comparison with a BPSK signal, the number ofmultiplications required for the traditional BPSKdemodulator is shown when U bits are sequentiallydemodulated. From Table VIII, two conclusions can beextracted. First, for the two values of PRN codes lengthbeing analyzed (1023 and 10230), the radix-2 CooleyTukey FFT algorithm demodulator always requires thesmaller number of multiplications to demodulate a CSKsymbol among the 3 proposed CSK demodulators.However, even this modulator requires a larger number ofmultiplications than the typical BPSK demodulator.Besides, the difference in number of multiplicationsbetween the Radix-2 CSK demodulator and the BPSKdemodulator is increased when identical PRN codes arecoherently accumulated (N > 1).Table VIII: Number of Multiplications for CSK Demodulation forthe transmission of U bits per CSK symbol when N=1 PRN codesare coherently accumulated.
Number of multiplications for BPSKmodulation when U bits are sequentially demodulated.Number of MultiplicationsCSKBPSKPRNBank ofRadix- TraditionalCodeUTraditionalCorrelator2IFFTLengthCorrelation112647168065472613861023112642682882618888184824576011796486547206138062457604325376261888081840810230169082881047552010230010 2457606723993641902080200460012 245760Finally, when considering using the FFT-basedcorrelator, one has to keep in mind that it createsconstraints on the sampling frequency.
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