Transceiver optimization for block-based multiple access through ISI channels

In this paper, we describe a formulation of the minimum mean square error (MMSE) joint transmitter-receiver design problem for block-based multiple access communication over intersymbol interference (ISI) channels. Since the direct formulation of this problem turns out to be nonconvex, we develop various alternative convex formulations using techniques of linear matrix inequalities (LMIs) and second-order cone programming (SOCP). In particular, we show that the optimal MMSE transceiver design problem can be reformulated as a semidefinite program (SDP), which can be solved using highly efficient interior point methods. When the channel matrices are diagonal (as in cyclic prefixed multicarrier systems), we show that the optimal MMSE transceivers 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 (in polynomial time) by the relative ratios of the magnitudes of the subchannel gains corresponding to all subcarriers. We also prove that any two users can share no more than one subcarrier in the optimal MMSE transceivers. By exploiting this property, we design an efficient strongly polynomial time algorithm for the determination of optimal powerloading and subcarrier allocation in the two-user case.