Low-complexity iterative per-antenna MAP equalizer for MIMO frequency selective fading channels

We consider the equalization of a (N-t, N-r) MIMO, L + 1-tap fading channel. We first evaluate the performance of a full complexity, vector MAP equalizer which runs the forward/backward algorithm on a trellis which has M-Nt X L states with MNt transitions from each state when an M-ary constellation is used. This MAP equalizer achieves the N-r x (L+1) diversity benefit while realizing N-t x log(2) (M) bits/sec/Hz. We then propose a novel iterative per-antenna MAP(PAMAP) approach which can be used (1) to reduce the complexity and (2) to achieve the full diversity order Nt x Nr x (L + 1) at the rate of log 2 (M) bits/sec/Hz. The proposed equalizer consists of a probabilistic "signal separator" and a bank of Nt PAMAPs each having M-L states with M transitions from each state. The signal separator and the PAMAPS exchange extrinsic information during iterations. Simulation results indicate that the proposed receiver closely achieves the performance of the full complexity MAP within 2 to 3 iterations. The proposed scheme saves a significant amount of complexity in uncoded systems with a large number of transmit antennas and a high modulation order. In coded systems, the PAMAP scheme becomes more beneficial when iterative equalization and decoding is used.