Calculating and Achieving Capacity on the Unknown Fading MIMO Channel

This paper calculates both an upper bound and a constructive lower bound on the capacity of an N transmitter, K receiver MIMO fading network. The channel between the transmitters and the receivers is Rayleigh flat fading with fading coefficients unknown to both transmitters and receivers. The lower bound is derived from a practicable successive decoding scheme, and when N is significantly larger than K, it approaches the upper bound with increasing coherence length of the fading process. Obviously, in the limit of large coherence lengths, the system becomes coherent and so is trivial. However, the lower and upper bounds of this paper are close to the MIMO capacity even when the system is highly non-coherent. For example, with N = 50, K = 15 and a coherence length of 200, the achievable rate of the successive decoding scheme diverges from the upper bound by just 6%, even when it is only 40% of coherent capacity. At this design point, the scheme achieves a rate of 13 bits/sec/Hz, significantly greater than any current cellular standards