Optimal Transceiver Design via Convex Programming

This paper addresses the problem of designing a multi-user Single-Input-Single-Output (SISO) communication system in the MMSE sense via modern optimization theory. In particular, the joint design of optimal transmitter/receiver (transceiver) pair under the constraints of fixed finite transmission power and the receivers employing zero-forcing equalizers is considered. We devise an Alternating Direction Method and also establish its convergence. Our optimal MMSE transceiver design problem, the natural formulation of which turns out to be nonconvex, is eventually reformulated as (Semi-definite Programming) SDP subproblems whose computational complexity has been substantially decreased. Computer simulations through SeDuMi software show that the devised transceivers have much more superior mean square error performance than the existing transceivers.