Design of FIR precoders and equalizers for broadband MIMO wireless channels with power constraints

This paper examines the optimum design of FIR precoders or equalizers for multiple-input multiple-output (MIMO)frequency-selective wireless channels. The matrix Bezout identity [1] can be employed to design a FIR MIMO precoder/equalizer for a left/right coprime channel. Unfortunately, Bezout precoders/equalizers usually increase the transmit/noise power in order to compensate for the deep frequency fades in channels. To overcome this problem, we describe in this paper a convex optimization technique for the optimal synthesis of MIMO FIR precoders subject to transmit power constraints, and of MIMO FIR equalizers with output SNR constraints. The synthesis problem reduces to the minimization of a quadratic objective function under convex quadratic inequality constraints, so it can be solved by employing Lagrangian duality. Instead of solving the primal problem, we solve the lower dimensional dual problem for the Lagrange multipliers. The simulation results show that optimal precoders with power constraints outperform Bezout precoders.