Compressive sampling and adaptive multipath estimation

In many signal processing problems such as channel estimation and equalization, the problem reduces to a linear system of equations. In this proceeding we formulate and investigate linear equations systems with sparse perturbations on the coefficient matrix. In a large class of matrices, it is possible to recover the unknowns exactly even if all the data, including the coefficient matrix and observation vector is corrupted. For this aim, we propose an optimization problem and derive its convex relaxation. The numerical results agree with the previous theoretical findings of the authors. The technique is applied to adaptive multipath estimation in cognitive radios and a significant performance improvement is obtained. The fact that rapidly varying channels are sparse in delay and doppler domain enables our technique to maintain reliable communication even far from the channel training intervals.