Space-time codes for wireless communication: code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Here, data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals. We review the performance criteria for designing such codes under the assumption that the fading is slow and frequency non-selective established in Tarokh et al. Performance is determined by diversity gain quantified by ranks and coding gain quantified by determinants of certain matrices that are constructed from the code sequences. The performance criterion is then used to design trellis codes for high data rate wireless communication. These codes are easy to encode and decode. They provide the best trade-off between data rate, diversity gain, constellation size and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels.