llr scaling in 5g nr PUSCHThroughoutExample

Hello everyone, I am simulating the NewRadioPUSCHThroughputExample in 5g toolbox. I find that after the LLR is calculated using nrPUSCHDecode, it is scaled by csi before we do ULSCH decoding(including LDPC decoding). I am a little confused about the function of scaling which is shown below.Can anyone explain the principle of this step or recommend several papers concerning it? Thanks a lot.

csi = nrLayerDemap(csi);
Qm = length(ulschLLRs) / length(rxSymbols);
csi = reshape(repmat(csi{1}.',Qm,1),[],1);
ulschLLRs = ulschLLRs .* csi;

Answer 1

[Yash Srivastava]

In my understanding you are confused about why LLR value is scaled by CSI before ULSCH decoding.

ulschLLRs = ulschLLRs .* csi;

In 5G, due to the use of OFDM, the system model includes a large number of parallel narrowband MIMO cases, one for each OFDM subcarrier. Each of these narrowband channels can have a very different phase and gain, which are all compensated by the equalizer prior to constellation demapping which produces bit estimates. The equalization means that each received symbol has been scaled correctly for the constellation demapper, which essentially "throws away" the information about their relative gains, so scaling again by the CSI after the symbol demapping re-introduces that information. You can find more information on this topic in the following reference:

"Simplified soft-output demapper for binary interleaved COFDM with application to HIPERLAN/2", F. Tosato and P. Bisaglia, IEEE International Conference on Communications (ICC) 2002, Vol. 2, pp. 664-668.

[智超 谢]

Many thanks.

[晓晓 刘]

I don't know whether this understanding is correct: since the noise is also scaled by the MMSE equalizer, the power actually changes, but the original noise power is still used when calculating the LLR, so it is necessary to compensate the calculated LLR.

But according to this idea, we should multiply LLR by , right? Because the equalization coefficient of MMSE is . However, the csi in the example script named "NR PDSCH Throughput" is .

I would appreciate it if you could help me.

[智超 谢]

Hello, Liu xiaoxiao. I seem to have further understanding of the function of csi when I try to figure out the formula of equalizer and demodulator and I hope this will help solve your problem:

Firstly, accoding to the formula , nrChannelEstimate outputs the empirical estimation variance of n (). However, when calculating llr in demodulator, 5g nr toolbox uses Approximate LLR Algorithm like in which is the variance of x (). The relationship between and can be found in the MSE of MMSE equalizer so the multiplication of csi is used to scale to get .

Answer 2

[NIKOLAOS APOSTOLAKIS]

I am also having the same question. Furthermore, I can't quite get the meaning of CSI in nrEqualizeMMSE. Isn't this supposed to be the same as puschHest?

I would like to decompose the nrPUSCHDecode into the individual functions it performs. According to the standards and the MATLAB documentation it does demapping->demodulation->descrambling. However, I am struggling to understand the role of noise estimate in nrPUSHDecode.

I have performed the following decomposition till now:

layerDemapped = nrLayerDemap(puschEq);
demodulatedSymbols = nrSymbolDemodulate(layerDemapped{1}, pusch.Modulation, 'DecisionType', 'soft');
ulschLLRs = nrPUSCHDescramble(demodulatedSymbols, pusch.NID, pusch.RNTI);