Title: Optimal Transceiver Design for Multi-user Communication

In this talk, we describe a formulation of the MMSE (Minimum Mean Square Error) transmitter design problem for a multi-user communication system employing either zero-forcing equalizers or MMSE equalizers. Since the natural formulations of this problem turn out to be nonconvex, we develop various alternative formulations using techniques of linear matrix inequalities (LMIs), geometric programming and second order cone programming. For the case of zero-forcing equalizers, we propose an alternating direction method to solve the optimal transmitter design problem and establish its convergence. When restricted to the diagonal designs, we further simplify the formulation to a linearly constrained entropy aximization problem which can be efficiently solved. In the case where MMSE equalizers are used at the receivers, we formulate the optimal transmitter design problem as a semidefinite program (SDP) which can be solved using the highly efficient interior point methods. When the channel matrices are diagonal (as in OFDM systems), we show that the optimal MMSE transmitters can be obtained by subcarrier allocation and optimal power loading to each subcarrier for all the users. Moreover, the optimal subcarrier allocation and power-loading can be computed fairly simply by the relative ratios of the path gains corresponding to all subcarriers.