Performance bounds for MIMO bit-interleaved coded modulation with zero-forcing receivers

Tight analytical bounds on the coded bit error rate are derived for a MIMO bit-interleaved coded modulation (BICM) system with a zero forcing receiver. We show that a minimal expurgated bound exists when using Gray-labelled constellations. We also show that with N_t transmit and N_r receive antennas, the diversity order is N_r-N_t+1 multiplied by the free distance of the code. For the maximum likelihood receiver, we demonstrate that expurgation does not lead to a tight bound. The analysis provides insight into the relative performance of the MIMO-BICM ZF and ML receivers.