Analysis of the use of CSK for future GNSS signals (797922), страница 5
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In fact, a channel code increases isdemodulation performance when the code rate isdecreased, which implies a lower Es/N0 when Eb/N0 isfixed (as in this case) [3]. However, an orthogonal M-arymodulation increases its demodulation performance whenEs/N0 increases as well [13]. Therefore, the RS channelcodes which better fulfill the trade-off between these twoaspects, CSK modulation and channel code, have beensearched and are presented in Figure 10. These RSchannel codes have a code rate equal to about 3/4.From Figure 10, it can be observed that when U=8, aCSK signal implementing a RS channel codes has aboutthe same demodulation as a reference BPSK signal, and itis even better when U is larger.
However, a CSK signalwith LDPC(1200,600) using BICM-ID with mapping Aoutperforms a CSK signal with a RS channel for theinspected U values.Table II shows the symbol duration and the codewordduration of a CSK signal implementing an optimal ReedSolomon Channel code (depending on U) and keeping theuseful bit rate of the reference BPSK signal. From TableII, it can be seen that when U is equal to 7 the codewordduration of the optimal Reed-Solomon and the referenceBPSK signal codeword are about the same. However, Uhas to be at least equal to 8 to obtain the samedemodulation performance for both types of signals.
Butwhen U=8, the codeword duration of the CSK signalimplementing an optimal RS channel code is about 3times longer than the BPSK signal codeword duration.identically shifted PRN codes which represent a 64-aryCSK symbol (U=6 bits, N=2, for 3 bits/symbol).Finally, equation (13) is only valid when the BPSKsignal and the CSK signal implement a channel code withthe same code rate. However, this does not have to be thecase for the inspected Reed-Solomon channel code andthus equation (13) is generalized to:Figure 11: Different possible combinations of CSK symbolsproducing a bit rate increased by a factor of 3 with respect to theoriginal BPSK signalV.C.CSK signal with increased useful bit rateIn this section, the methodology used to design a CSKsignal increasing the useful bit rate of a reference BPSKsignal but keeping the same symbol rate (or duration) ispresented and its application to the proposed pair channelcodes –decoding methods is given.V.C-1. MethodologyThe increase of the useful bit rate is obtained by simplyapplying the CSK modulation instead of the BPSKmodulation and thus, the useful bit rate is increased by aU factor.Moreover, although one of the signal hypotheses is tokeep the original signal symbol duration, a CSK symbolcan be artificially extended by coherently accumulating Nconsecutive identical circular shifted PRN codes.
In fact,the original signal parameters which should remainconstant in order to maintain the original signal spectrumand original inter and intra interference characteristics arethe chipping rate and the PRN code length. Therefore,there is no impediment to coherently accumulate N PRNcodes to construct a new symbol with a larger duration,(see equation (12)).(14)The comparison among the demodulation performanceof different pair channel – decoding methods is made by| ).
In thiscomparing the BER vs normalized C/N0 (case, the C/N0 is still not used since it is preferred toexpressthefinaldemodulationperformanceindependently from the symbol rate (easier to generalizethe results to any PRN code period). Moreover, the Eb/N0cannot be used since the comparison is also madebetween different useful bit rates and the term which isoriginally fixed is the Es/N0.
However, due to thepossibility of artificially extending the CSK symbol, theEs/N0 varies among different CSK configurations.Therefore, this paper has decided to express thedemodulation from an artificial figure of merit which issimply the C/N0 normalized by the rate of the originalBPSK symbol (or PRN code).(|)((|))(15)(16)Finally, the normalized C/N0 required for an artificiallyextended CSK symbol can be calculated from thenormalized C/N0 of the original CSK symbol:| ()| ( )( )(17)(12)| ( ) is the normalized C/N0 associated toWherea signal with a factor of increased data rate of x.The new signal bit rate is thus equal to:(13)And this means that whereas for a BPSK signal theaccumulation process results into a decrease of the bitrate, for a CSK modulation the final bit rate is stillincreased if N < U.
From now on, in this paper, the choiceof the U and N parameters is called the CSK configurationof a CSK signal. Moreover, this paper calls equivalent theCSK configurations which provide the same bit rate butusing different U and N values (U/N = U’/N’).Figure 11 presents an example of two equivalent CSKconfigurations which increase the original BPSK signalbit rate by a factor of 3. The first configuration consist insimply changing the original BPSK symbol by a 8-aryCSK symbol (U=3 bits, N=1, for 3 bits/symbol), whereasthe second one consist in accumulating 2 consecutiveThe duration of the new codewords of the CSKmodulated signal with increased useful bit rate are easilydetermined from the codeword duration of the CSK signalwith the same useful bit rate (see equation (8)). The onlydifference is that the CSK symbol is not expanded by thenumber of bits mapped by a CSK but by the number ofcoherent accumulated PRN codes:(18)As well as in the previous case, this expression can becustomized by a Reed-Solomon signal:()(19)V.C-2.
ApplicationThe demodulation performance (BER vs norm C/N0) ofa CSK signal implementing a LDPC (1200, 600) channelcode and using the classical decoding method formapping A is presented in Figure 12. In this figure,different CSK configurations (U and N pair of values) areused in order to attain an increase of twice the original bitrate.
From Figure 12, it can be seen that configurationswith larger U and N values outperform configurationswith smaller values. However, the former configurationsincrease the receiver complexity (U is larger).The demodulation performance (BER vs norm C/N0) ofdifferent CSK signals with increased bit rate with respectto a reference BPSK signal is presented in Figure 13.These CSK signals implement a LDPC (1200, 600)channel code and use the classical decoding method andthe BICM-IT method for mappings A and B. The CSKconfigurations (U, N) implemented for these CSK signalsalways have a coherent accumulation number of PRNcodes equal to 1 (U, N=1). From Figure 13, the sameconclusions from Figure 7 and Figure 8 can be extracted:BICM-IT outperforms Classical Decoding and mapping Aoutperforms mapping B.Table III shows the codeword duration of a CSK signalimplementing the LDPC(1200,600) channel code andincreasing the useful bit rate of the reference BPSK signalby a factor of U/N.
The codeword duration is given as afunction of the number of bits mapped by a CSK symbol,U, the number of PRN codes coherently accumulated, N,and the implemented mapping. From Table III, the sameconclusions from Table I can be extracted: mapping A haslonger codewords than mapping B. Moreover, it can beobserved that although using CSK configurations withhigh U and N values provide better demodulationperformance (regardless of the implemented mapping),when using mapping A these configurations have longercodewords than equivalent CSK configurations withlower U and N values.
Therefore, a trade-off betweendemodulation performance and codeword duration /receiver complexity is found when using mapping A.However, when using mapping B, the codewords haveexactly the same duration when using equivalent CSKconfigurations. Therefore, the previous trade-off is limitedbetween the demodulation performance and the receivercomplexity.Figure 12: BER vs norm C/N0 for a different (U,N) configuration ofa CSK signal using Classical Decoding method (CD) with mappingA when increasing the bit rate by a factor of 2 w/r to a BPSK signal.Figure 13: BER vs normalized C/N0 for CSK signals with increasedbit rate with respect to a BPSK signal. CSK signal use ClassicalDecoding method (CD) and Bit-Interleaved Coded Modulation Iterative Decoding (BICM-IT) with mapping A and mapping B.
Allthe CSK configurations are defined (U, N=1).The demodulation performance (BER vs normalizedC/N0) of different CSK signals with increased bit ratewith respect to a reference BPSK and implementing aReed-Solomon (RS) channel code is presented in Figure14. The CSK configurations (U, N) implemented for theseCSK signals always have a coherent accumulationnumber of PRN codes equal to 1 (U, N=1).Figure 14: BER vs normalized C/N0 for CSK signals with increasedbit rate with respect to a BPSK signal.
CSK signal implement ReedSolomon (RS) channel codes with code rate equal to 1/2 or 1/4. Allthe CSK configurations are defined (U, N=1).Table III: Codeword duration of a CSK signal implementing aLDPC(1200, 600) channel code when increasing the useful bit rate ofa reference BPSK signal by a factor of U/N.Bits per CSKsymbol, U45681112Mapping B300∙N∙Ts240∙N∙Ts200∙N∙Ts150∙N∙Ts≈110∙N∙Ts100∙N∙TsMapping A1200∙N∙TsTable IV: Codeword duration of a CSK signal implementing aReed-Solomon channel code when increasing the useful bit rate of areference BPSK signal by a factor of (U/N).Bits per CSKsymbol, U5678910CSK signal implementing the LDPC(1200,600) and usingBICM-ID with mapping B.VI.In order to design a signal that is realistically usable forGNSS users, it was decided to take into account a certainnumber of constraints specific to the GNSS field.
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