A sphere packing bound on Rayleigh block-fading MIMO channels

We present a sphere packing bound (SPB) approach to investigate the performance limits of Rayleigh block-fading, multiple antenna systems. Specifically, we derive three sphere packing lower bounds, one tight, one loose, and one approximate, on average word error probability of space-time codes. These bounds provide us with intuition on how system parameters affect the performance limits [M. Fozunbal, S.M. Mclaughlin, and R.W. Schafer, 2002]. It is shown that the performance limits improve significantly for space-time codes that span a larger number of fading blocks. It is shown that the achievable diversity depends not only on the number of antennas and number fading blocks, K, but also on the block length, L, Moreover, it is shown that the block length, L, has a marginal effect on improving the performance limits and it is not possible to achieve arbitrarily small WEP by increasing L.