Turbo Equalizers for MIMO Systems: Optimality Consideration

In this paper, we show how many of the well-known low complexity linear turbo equalizers, including the zero-forcing (ZF) and minimum mean square error (MMSE) soft-input soft-output (SISO) equalizers, can be obtained as solutions to the variational optimization problem, originating from statistical physics. The imposed variational optimization framework provides an interesting link between the a posteriori probability (APP) based demodulators and the linear SISO equalizers, enabling us to gain new insight into the optimality of these equalizers in the context of turbo processing. Moreover, it suggests improved designs which either tune the known ones or combine the linear filtering and the nonlinear message-passing algorithms. Finally, simulation results are provided to confirm the advantages of the proposed new designs for the MIMO systems