Analogy matrix completion to MIMO channel recovery

As compresed sensing (CS) theory was developed by Candes and Tao, Donoho, sparse signal or approximate sparse signal recovery can be reconstruction exactly. On the heels of CS, a remarkable new field has very recently emerged. This field addresses a broad range of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. This problem can be called as Matrix completion (MC).
In general, recovering a data matrix by a part of its entries is impossiable. However, if the unknown matrix is known to have llow rank or approximately low rank, then accurate recovery is possible. This recovery problem can be analogy to MIMO channel matrix modeling.
Channel estimation is a key problem in MIMO communication systems. In general, least square (LS) algorithm is a good candidata for channel estimation or modeling. However, this method will waste a lot of spectrum resource. If we employ the channel matrix completion, will improve greatly the spectrum resource. Recently, we will research this method on MIMO channel estiamtion. If you have some good suggestions about the MIMO channel matrix recovery, please do not hesitate to tell me. My email box is :gui@uestc.edu.cn