Analysis of the use of CSK for future GNSS signals (797922), страница 3
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However, thiscomparison is not fair since the coded bit rate is differentfor both modulations. A more fair comparison could bemade between a CSK signal mapping U bits per symboland a BPSK signal having a symbol rate and a chippingrate U times faster than those of the CSK signal. In thiscase, although there still is a difference on the number ofrequired correlators (1 correlator to M correlators), thenumber of operations per second of the BPSK signal isincreased by U. Therefore, the increase of complexity of aCSK receiver with respect to a BPSK is not so high asoriginally thought.Finally, the introduction of a FFT-based demodulatorfor a CSK signal reduces the complexity (and number ofoperations) of the receiver as shown later in section VIIVII.C.
However, a FFT-based signal presents someproblems which must be further analyzed.IV. DECODING METHODSIn this section, the different pairs channel code decoding methods proposed for a CSK modulated signalare described. The pair choice plays a very important roleon the final signal structure design:Determine the demodulation performanceDetermine the receiver’s complexityDetermine the codeword durationTherefore, the final pair channel code – decodingmethod will be a trade-off between the previous 3 factorsand the signal needs.Four pairs have been proposed, three when a binarychannel code is implemented, more specifically the GPSL1C subframe 2 LDPC (1200, 600) [6], and one when Qary channel code, more specifically Reed-Solomonchannel code [4], is used.The binary channel code decoding methods are:1) Classical CSK Decoding method2) Iterative Decoding methods:a.
Horizontal dimension multistage decoding (HDMD)b. Bit-Interleaved Coded Modulation – IterativeDecoding (BICM-IT)The Q-ary channel code decoding method is:1) Reed-Solomon with Berlekamp / Forney algorithmIV.A.Classical CSK Decoding Method (CD)The classical CSK decoding method of the j th codewordis simply the traditional sequential decoding method usedin [13]: first the bits Likelihood Ratio (LR) or Log LR ofthe transmitted bits of the jth codeword are calculated andsecond, the jth codeword is decoded using the previouscalculated LR values:1) Apply equation (6) in order to calculate the LR of thebits transmitted in each CSK symbol.
The symbols apriori probabilities are assumed equiprobable.2) Gather the LR values of all the bits belonging to thejth codeword.3) Decode the jth codeword using the LR values.4) If there still are LR values belonging to other undecoded codewords, go to step 2 in order to decodethem. In Mapping A, steps 2 to 4 are repeated asmany times as bits mapped by a CSK symbol.IV.B.CSK Iterative DecodingThe fundamental idea consists in iterating/mixing thedecoding of the parallel codewords transported by a CSKmodulation with the calculation of the LR of the CSKsymbols bits. More in detail, the iterative decodingmethods consist in first using the extrinsic informationprovided by the decoding of the parallel codewordstransported by the CSK symbols as a-priori bitprobabilities on the calculation of the CSK symbols bitsLR.
Second, the new bits LR are used as new inputs to thechannel code decoder of the transported codewords.This principle can be easily understood from theoriginal expression of the CSK symbols bits LR (equation(6)): depending on the a-priori probability of the differentmatched filter outputs at instant ith, , the LR of the bitsvary. In fact, depending on this probability, more weigh isgiven to certain matched filter outputs and thus, if this apriori probability is reliable, the LR value should also bemore reliable in average.
This means, that a soft inputdecoding process using these new LR values shouldperform better than another one that does not use them.Therefore, the remaining question is how to obtainreliable a-priori probabilities.An iterative decoding method will obtain betterdemodulation performance than the classical decodingmethod but the receiver complexity will grow: the LRcalculation and the decoding of the codewords areexecuted more than once.V.B-1. Horizontal Dimension multistage decoding(HDMD)The Horizontal Dimension Multistage Decodingobtains the a-priori probabilities of equation (6) from thesuccessful verification of CRC channel codes: the a-prioriprobabilities (values) of the bits protected by the CRC aredetermined when the CRC verification is successfullyachieved. Therefore, in order to implement this decodingmethod, a CRC must be specifically introduced in eachone of the parallel transmitted codewords.
Moreover, aHDMD decoding method cannot be implemented formapping B (at least two codewords must besimultaneously transmitted).The HDMD algorithm for mapping A and a (n, k)channel code is given below. Nnd is the number ofcodewords having yet to succeed the CRC verification:1) Calculate the bits LR (using equation (6) andassuming equiprobable bits) of n CSK symbols. Nndis set to U.2) Decode the Nnd codewords having yet to succeed theCRC verification.3) Check the CRC of the Nnd decoded codewords.
Theinteractive algorithm stops if:i.All the Nnd CRCs are correct: receiver assumesthat all the codewords are correctly decoded.ii.All the Nnd CRCs are incorrect: no newinformation to be used on the LR calculation.4) Nnd is updated to the number of remaining codewordshaving yet to succeed the CRC verification.Figure 5: BICM-ID scheme5) Calculate the bits LR of the Nnd codewords havingyet to succeed the CRC verification. This calculationis made by using equation (6) and by determining thea-priori probabilities from:i.ii.The bits value if the codeword (in which the bitis) has succeeded the CRC verification.Otherwise, the a-priori probabilities areassumed equiprobable.6) Go to step 2).V.B-2. Bit-Interleaved Coded Modulation – IterativeDecoding (BICM-ID)The original BICM was discovered by [15], which giveits name, and the complete iterative method, BICM-ID,was conceived by [16].
Moreover, this method wasproposed for orthogonal M-ary modulations and noncoherent demodulation in several papers [17][18][19].For a BICM-ID method, the CSK symbol a-prioriprobabilities of equation (5) are provided by the samechannel codes implemented on the transmittedcodewords: assuming that each channel code(implemented on each one of the transmitted codewords)can provide the codeword bit probabilities after theexecution of its decoding process (partially or totally), theapplication of the BICM-ID method consists in usingthese output bit probabilities (or LR) provided by eachchannel code as inputs to the general LR bit calculationformula (equation (5)) in the form of CSK symbol a-prioriprobabilities (equation (6)).
Then, the new bits LR valuesare calculated and are fed again to the decoders of theimplemented codewords which will execute again thedecoding process (partially or totally). Finally, the processwill repeat itself until all the codewords are successfullydecoded or a certain number of iterations is reached. Ascheme of the BICM-ID method is presented in Figure 5.One of the main requirements of the BICM-ID consistsin implementing channel codes which accept Soft Input Soft Output (SISO) decoding methods. In the case of aLDPC channel code, the SISO method is called messagepassing or propagation-belief [20].
The BICM-IDalgorithm is presented next:1) Calculate the bits LR of all the bits constituting thecodewords transmitted in parallel using equation (5)and using the CSK symbol a-priori probabilities(equiprobable for the first iteration).pair channel code – decoding method and the codewordduration. Moreover, these parameters also determine thesignal BER and WER, and thus they have to bedimensioned in order to target a BER of 10-5.V.A.Figure 6: CSK symbol with respect to a BPSK symbol when keepingthe coded bit data rate2) Use the bits LR calculated in step 1) as inputs to thecodewords decoding algorithms and execute theprocess (totally or partially).3) Inspect if all the codewords are correctly decoded.i.Yes The iterative process is endedii.No Use the bit probabilities obtained in step2) from the decoding process execution inorder to calculate the CSK symbol a-prioriprobabilities.
Go to step 1)IV.C.Q-ary channel code: Reed-SolomonA Q-ary channel code is a code which uses symbols(representing a set of bits) instead of bits as basic units ofinformation. The implementation of a Q-ary channel in anorthogonal M-ary modulation consists in fully represent aQ-ary symbol with a symbol of the orthogonal M-arymodulation (Q=M).In this paper, the chosen Q-ary channel code family isthe Reed-Solomon (RS) channel codes. A RS(n, k)channel code is a systematic block channel code which isable to correct until() symbol errors [4].The RS decoding method selected in this paper is thestandard Berlekamp – Forney algorithm [4].
Finally, asopposite to the implementation of a binary channel code,a Reed-Solomon channel code uses a hard output CSKdemodulator.V. CSK SIGNAL DESIGNIn this section, the methodology used for designing aCSK modulated signal is presented. The design of a signalconsists in determining the signal parameters in order tofulfill certain objectives or requirements.
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