Exact Pairwise Error Probability of Space-Time Codes under MAP Decoding with Applications

We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include spacetime coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ maximal receive combining (MRC) and any kind of channel coding. We derive a closed-form single-letter expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then utilize this result to design space-time linear dispersion codes which are optimized for the source distribution. Two codes are given here which outperform V-BLAST by 9.3 dB at a frame error rate (FER) of with uniform i.i.d. input and BPSK signaling and by 8 dB for a non-uniform binary source with , MAP decoding, and Q-PSK signaling. The issue of bit-to-signal mapping is also studied. For a system with 1 transmit and 2 receive antennas which uses trellis-coded modulation with 16-QAM signaling, we observe that a better than Gray mapping outperforms Gray mapping by 1.0 dB when MAP decoding is used for transmitting binary sources with .