Compressive impulse response sensing of the sparse channel in multipath environments

Channel impulse response (CIR) in noisy multipath environments can be obtained based on the least squares criterion. However, the CIR obtained is contaminated by pseudo paths. By exploiting the sparse structure of a sparse channel in multipath environments, this work presents an approach for compressed sensing that uses the Gram-Schmidt algorithm to find orthogonal bases (Gram-Schmidt matching pursuit, GSMP), which leads to a fast, orthogonal way of selecting the supports for the dictionaries. The probe signal is used to construct the dictionary matrix, whose column vectors are selected as the supports. The selected supports from dictionary matrix and the noisy received signal are used for recovering the CIR. The simulation results confirm that the proposed GSMP method, compared to LS, MP, CoSaMP, ROMP methods, provides superior performance in terms of mean square error (MSE).