llr scaling in "NR PDSCH Throughput" Example

Hello everyone, I am simulating the NR PDSCH Throughput Example in 5g toolbox. I find that after the LLR is calculated using nrPDSCHDecode, it is scaled by csi before we do LDPC decoding. I am confused about the function of scaling which is shown below. Another answer (llr scaling in 5g nr PUSCHThroughoutExample) explained that "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." I'm still confused about the term "relative gains".

I don't know whether this understanding is correct: since the noise is also scaled by the MMSE equalizer, the noise variance 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.

Qm = length(dlschLLRs{cwIdx})/length(rxSymbols{cwIdx}); % bits per symbol

csi{cwIdx} = repmat(csi{cwIdx}.',Qm,1); % expand by each bit per symbol

dlschLLRs{cwIdx} = dlschLLRs{cwIdx} .* csi{cwIdx}(:); % scale by CSI