Iterative equalization/decoding of LDPC code transmitted over MIMO fading ISI channels

We propose a spectrum efficient and robust space-time-frequency code system for a (N_t, N_r) MIMO, (L+1)-tap, fading channel. The LDPC (low-density parity-check) code is employed at the transmitter and iterative maximum a posteriori (MAP) equalizers are used at the receiver. We propose a novel, reduced-complexity iterative decoding and equalization scheme in which we combine the message-passing decoder, on the bipartite graph for the LDPC code, with an iterative MAP equalizer in a turbo-like manner. First, we consider a full-complexity vector MAP equalizer which runs the forward/backward algorithm on the trellis which has M^Nt×L states with M^Nt transitions from each state when an M-ary constellation is used. Second, we replace the full MAP with the bank of N_t per-antenna MAP (PAMAP) equalizers - each works on an M^L state trellis - and evaluate the performance loss due to the use of the reduced complexity scheme. The simulation results show that the performance of the PAMAP-bipartite equalization/decoding scheme is very close to the full complexity vector MAP-bipartite. In addition, in the fast fading case, the performance of the proposed space-time-frequeney system with N_t = 2, N_r = 2 and L = 2 is very close, within 0.5 dB, to the results of the LDPC code on AWGN channels.