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

An Introduction to Compressed Sensing

Conventional signal sampling is that the sampling rate must be at least twice the maximum frequency presented in the signal. In the field of signal sampling or compressed, Shannon theorem plays an implicit role. However, the signal is uniformly sampled at or above the Nyquist rate. Thus, this sampling is not a effective approach. Fortunately, Candes and Tao, Donoho have introduced a new sampling theory: Compressed sensing, which was beyond Nyquist sampling theory. CS theory asserts that one can recover certain signals and images from far fewer samples or measurments than traditional methods use. To make this possible, CS relies on two priciples: signal sparsity and incoherence of measurment matrix.

On channel estimation problem, we can introduce CS theory. In general, there always exist a large delay spread and only has a few dominant taps in high data rate wireless communication. that is to say, this multipath channel has sparsity. In the process of channel estimation, training matrix can be designed Toeplitz structre which satisfies Restrict Isometry property (RIP).