Convex constraint and semiprojected steepest descent algorithms-for single-carrier equalization in wideband MIMO systems

Two computationally efficient algorithms are proposed for equalizing wideband MIMO channels in the space-time domain. Both of proposed methods can be viewed as modifications to the steepest descent method, for implementing the zero-forcing (or unconstraint maximum-likelihood) MIMO equalizer, which allows constraints about the feasible solution set to be incorporated in the iterative estimation process. The first approach assumes that the solution belongs in a closed convex set (inside a Hilbert space) and nearest point projection on the set is performed in each iterative step. The method is guaranteed to converge in the optimum point inside the convex set and hence provides significantly better performance than the standard linear equalizers. Fast convergence to a nearly optimal estimate can be achieved by the second proposed algorithm in which the new estimate in each iteration, is semiprojected on the discrete-discontinuous solution set. The proposed algorithms are of very low complexity as the number of arithmetic operations scales only linearly with the problem´s dimensionally.