Analysis of the use of CSK for future GNSS signals (797922), страница 4
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Two differentsignal objectives are proposed in this work:1) Signal keeping a predefined useful bit rate withrespect to a reference BPSK signal2) Signal increasing a predefined useful bit rate withrespect to a reference BPSK signal but keeping thesame symbol duration (or rate).The CSK signal parameters to be determined are thenumber of bits mapped by a CSK symbol, the number ofconsecutive PRN codes constituting a CSK symbol, theReference BPSK signalThe chosen reference signal is based on the GPS L1Csignal since this signal implements the most powerfulchannel code among all the defined GNSS signals at theepoch of this study.Therefore, the selected channel code is the LDPC(1200,600) of subframe 2.
The application of this channelcode generates codewords with a duration of 1200symbols (1200∙Ts).V.B.CSK signal with the same useful bit rateIn this section, the methodology used to design a CSKsignal keeping the same useful bit rate as a referenceBPSK signal is presented and its application to theproposed pair channel codes –decoding methods is given.V.B-1. MethodologyA CSK signal keeping the same useful bit rate as areference BPSK signal is created by mapping U bits perCSK symbol and by increasing U times the length of theCSK symbol period with respect to the BPSK signalsymbol duration (see Figure 6). In doing so, the finaluseful bit rate of the CSK modulated signal is the same asthe BPSK signal: although the rate is increased by U dueto the introduction of a CSK modulation, the rate is alsodivided by U due to the increase of the CSK symbolduration.In order to generate the extended CSK symbol, thereare 2 possible options.
On one hand, the CSK symbol canbe generated from a long PRN code spanning the entireCSK symbol. On the other hand, the CSK symbol can begenerated by consecutive PRN codes with the same lengthas the BPSK signal original PRN code and having all ofthem the same circular cyclic shift (the demodulator mustcoherently accumulate consecutive PRN codes in order torecover the power of the entire CSK symbol).Moreover, if the CSK modulated signal introduces anew channel code different from the reference BPSKsignal (only in the RS case), the useful bit rate of the CSKmodulated signal will vary: the number of coded bitsrepresenting a useful bit is different for both modulatedsignals.
Therefore, taking into account the CSKmodulation and the change of channel code, in order tokeep the same useful bit rate of a reference BPSK signal,a CSK signal must have a symbol duration equal to:(8)Whererepresents the channel code rate of thechannel code andrepresents the symbol duration ofmodulation .The new codeword duration,, will depend onthe number of bits constituting the codeword, n, thenumber of bits mapped by a CSK symbol which belong tothe same codeword, S (S=1 for mapping A and S=U formapping B) and the CSK symbol duration:(9)For a Reed-Solomon channel code, since the number ofbits of a codeword is defined by construction, equation (9)can be expressed as:()(10)The analysis of the demodulation performance of aGNSS signal is usually done by expressing the BER (orWER) as a function of the signal C/N0.
However, in thedigital communication field, the comparison betweenmodulations (or modulations plus channel codes) is madeusing the Eb/N0 since this figure of merit subtracts thedemodulation performance dependence on the useful bitrate (or symbol rate). In this paper, the comparison is alsomade through the Eb/N0 since this will allow presentingthe CSK signal design parameters regardless of the finalselected useful bit rate. Equation (11) shows that if theBPSK and CSK signals have the same useful bit rate, ,having the same C/N0 value at the RF block output isequivalent to have the same Eb/N0:()Figure 7: BER vs Eb/N0 for a reference BPSK signal and for a CSKsignal using Classical Decoding method (CD) and HorizontalDimension Multistage Decoding (HDMD) with mapping A.(11)V.B-2.
ApplicationThe demodulation performance (BER vs Eb/N0) of thereference BPSK signal and the demodulation performanceof a CSK signal implementing a LDPC (1200, 600)channel code and using the classical decoding method, theHDMD method and the BICM-IT method for mappings Aand B are presented in Figure 7, Figure 8 and Figure 9.
Inthese figures, the demodulation performance is presentedfor different number of bits mapped by a CSK symbol, U.From Figure 7 and Figure 8, it can be observed that aCSK signal using CD and mapping A has worsedemodulation performance (BER=10-5) than a referenceBPSK signal for. Besides, Figure 9 shows thatusing mapping B, the BPSK signal always outperformsthe CSK modulated signal with CD by at least 0.7dB.From Figure 7 and Figure 8, it can also be observed that aCSK signal using HDMD or BICM-ID outperforms aCSK signal using CD when mapping A is implemented.In fact, improvements of about 0.7-0.9 dBs are foundbetween BICM-ID and CD.
The recommendation fromFigure 8 is to use U = 6 or 8 bits at most if possible.Moreover, BICM-ID always outperforms HDMD.Figure 8: BER vs Eb/N0 for a reference BPSK signal and for a CSKsignal using Classical Decoding method (CD) and Bit-InterleavedCoded Modulation - Iterative Decoding (BICM-IT) with mapping A.Figure 9: BER vs Eb/N0 for a reference BPSK signal and for a CSKsignal using Classical Decoding method (CD) and Bit-InterleavedCoded Modulation - Iterative Decoding (BICM-IT) with mapping B.Table I: Codeword duration of a CSK signal implementing aLDPC(1200, 600) channel code when keeping the same useful bitrate of a reference BPSK signalBits per CSKsymbol, UMapping A6000∙Ts7200∙Ts9600∙Ts13200∙Ts14400∙Ts5681112Mapping B1200∙TsTable II: Symbol and codeword duration of a CSK signalimplementing an optimal Reed-Solomon channel codeChannel CodeUTs,CSKTcw,CSKRS (63,45)68.3∙Ts522.9∙TsRS (127,91)710.04∙Ts1275.08∙TsRS (255,191)811.98∙Ts3054.9∙TsRS (511,391)913.78∙Ts7041.6∙TsRS (1023,799)1015.62∙Ts15979.26∙TsFinally, from these two figures it can be observed thata CSK signal using HDMD outperforms the referenceBPSK signal when at least 6 bits are mapped by a CSKsymbol (4 or 5 bits should be tested), and that a CSKsignal using BICM-ID always outperforms the referenceBPSK signal with mapping A.
More specifically, a BPSKreference signal needs at least 0.6dB more than a CSKsignal with BICM-ID to obtain a BER of 10-5. In any case,this comparison is not entirely fair since the use ofiterative decoding methods makes that the equivalentchannel code implemented in a CSK signal has a sizeequal to U∙n coded bits whereas the BPSK signal channelcode only has a length of n coded bits (the receiver shouldwait the same exact amount of time, or in other words, thesame number of bits, before being able to decode thecodeword). Therefore, an entirely fair comparison shouldbe done with a reference BPSK signal having a channelcode of U∙n coded bits.From Figure 9, it can be seen that the reference BPSKsignal still outperforms a CSK signal with BICM-ID withmapping B by about 0.4-0.5dB when a BER equal to 10-5is targeted. Besides, BICM-ID improves CD by about 0.20.4dB for a BER equal to 10-5.
In fact, since the BICM-IDmethods reaches a saturation when U=6 bits, therecommendation is to use U equal to 5 or 6 bits ifpossible.Table I shows the codeword duration of a CSK signalimplementing the LDPC (1200,600) channel code andkeeping the useful bit rate of the reference BPSK signal.The codeword duration only depends on the implementedmapping.
From Table I, it can be seen that althoughmapping A provided better demodulation performancethan mapping B, its codeword duration is longer.Mapping B has the same codeword duration as thereference BPSK signal.Figure 10: BER vs Eb/N0 for a reference BPSK signal and forCSK signal with Reed-Solomon channel codes.The demodulation performance (BER vs Eb/N0) of thereference BPSK signal and the demodulation performanceof a CSK signal implementing a Reed-Solomon (RS)channel code is presented in Figure 10. In these figures,the demodulation performance is presented for differentnumber of bits mapped by a CSK symbol, U.The RS codes presented in Figure 10 are the RSchannel codes which present the better demodulationperformance for each different number of bits mapped bya CSK symbol, U.
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