Random Projections for Sparse Channel Estimation and Equalization

The estimation and equalization of highly sparse wideband channels with large delay spreads is a challenging problem. The optimal maximum likelihood solution of this problem is computationally prohibitive and we must resort to sub-optimal solutions. In this paper we study the effect of the assumed number of nonzero taps, the length of the training sequence and other parameters, on the performance of one such algorithm. We also discuss an algorithm motivated by recent results in compressed sensing, where the dimension of the problem is reduced by projecting the received data on a relatively low dimensional subspace. The subspace is randomly chosen and does not assume any prior knowledge of the channel.