The rate-diversity trade-off for linear space-time codes

We study the relative impact of rate and raw diversity order on the capacity and performance of linear space-time codes. Outage capacity is not directly affected by raw diversity order, but it is strongly impacted by the rate of a space-time code. Specifically, if a linear space-time code operating over a t-input, r-output Rayleigh-fading channel has rate R < min(t, r), we show that it achieves at most a fraction R/min(t, r) of the channel's outage capacity at high SNR. In the absence of outer codes, the performance of the space-time code depends strongly on both the rate and the raw diversity order. Since low complexity space-time codes with both high rate and high raw diversity order are hard to find, there is a trade-off between rate and raw diversity order. We propose a heuristic rule of thumb: start with a rate equal to min(t, r) and lower it until a space-time code with raw diversity order of min(tr, 4) can be found. In particular, when there are 4 or more receive antennas, the rate should be min(t, r). Simulation results for an 8 x 8 Rayleigh channel show that the rate-8, diversity-8 V-BLAST encoder outperforms a rate-4, diversity-16 Alamouti-based GLST ill encoder by 7 dB with ML decoding.