I have a technical question about Massive MIMO to discuss with you . If each user feedback their compressed low dimensional channel \hat h. The compress method can employ compress sensing (PCA,2D-DCT) like the paper attached. When all the users feedback their individual \hat h, The BS perform multi-user precoding like ZF\RZF,etc. In general, the BS should recovery the channel h and employ precoding. I am wondering that may I use the low dimensional \hat h to do precoding. I have read your paper about beamforing, if all user's orthogonal space are obatined, the performance will be the same as use ture h to perform precoding. If I use the feedback \hat h with a pre-known matrix and prove ZF precoding just depend on \hat h, it may be right. Howerver, I have no idea to prove that . What do you think about this question? Thanks !
I am not sure who this message is directed to. Anyway, I think the approach that you describe make sense for MU-MIMO in FDD mode. Each user feeds back an estimate of its channel, which might be compressed if there is sparsity in the channel (but that is not always the case in reality). Then these estimates are utilized to compute a precoding matrix, using any of the conventional techniques. The precoder needs to computed in the uncompressed domain, I think, because if the user channel are compressible then they will probable use different subspaces.
I don't think there is anything that you need to "prove", since what you describe is a heuristic algorithm. There is no optimality or anything like that, but you can hopefully get a reasonably good communication performance.
Thank you Emil, you mean I must recovery the compressed channel and then compute a precoding matrix. I do not use compress sensing like other researches. I use convex optimization and obtain a closed form solution and this result is shown to be equivalent to PCA, and this method have robustness to the h with additive noise. What do you think this idea? Is it have novelty?
Yes, I think you need to recover the complete channel. The reason is that if the user channels are sparse, then they are likely not sparse in the same way (i.e., they exist in different subspaces, due to different angular properties of the channels).
I don't know the literature on compressed sensing for precoding very well, so I cannot tell what is novel and what is not. What you describe sounds like the standard way to apply compressed sensing techniques, but there can still be novelty in the implementation details. If you plan to perform research this area you should definitely read up on the literature so that you can judge what is novel and so that you know what to compare your approach with.
Dear Emil, Thank your great comments, you are right. The users channel may be correlated if I assume that they are share some common scatters. Regarding precoder, it should be recovery the estimate channel. I think i should make some adjustment , such as perform multiuser scheduling
I have read some related papers. My work have same results to the existed papers. I use affine set representation to formulate a problem. Then, I got the optimal solution, this solution is also the existed conclusion.
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