Blind deconvolution using compressed sensing in time dispersive MIMO OFDM systems

In this paper, we propose a blind algorithm for channel identification and signal separation in MIMO OFDM systems with Nyquist sampling at the baseband. To estimate in time the channel and the input signals using compressed sensing, we exploit the sparsity structure of the matrix type channel impulse responses and the Gaussian characteristics of the transmitted OFDM signals. The matching pursuit sparse algorithm is applied in the channel recovery. First, we develop the method for blind deconvolution in SISO systems where after estimating the channel, a zero-forcing (Z-F) equalizer in the frequency domain recovers the transmitted QAM symbols. Then, we apply the method in the MIMO setting. This is accomplished by decomposing the matrix type convolution representing the mixing process in the MIMO time dispersive channel into systems of equations similar to the SISO case. Specifically, in the MIMO system, the SISO type sparse channel estimation is performed independently and in parallel for every receive antenna. The QAM symbol recovery on spatial streams is performed at every subcarrier using a matrix equivalent to the Z-F equalizer. The good estimation convergence of the method and its resilience in different SNR scenarios is verified through extensive simulations.