Practicable MIMO Capacity in Ideal Channels

The impact of communications signal processing such as QAM modulations (instead of gaussian signals), finite block lengths (instead of infinitely long codes), and using simpler algorithms (instead of expensive-to-implement ones), etc., is a lower practicable capacity efficiency than that of the Shannon limit. In this paper, the theoretical and practicable capacity efficiencies for known-channel MIMO are compared for two idealized channels. The motivation is to identify worthwhile trade-offs between capacity reduction and complexity reduction. The channels are the usual complex gaussian random i.i.d., and also the complex gaussian circulant. The comparison reveals new and interesting capacity behaviour, with the circulant channel having a higher capacity efficiency than that of the random i.i.d. channel, for practical SNR values. A circulant channel would also suggest implementation advantages owing to its fixed eigenvectors. Because of the implementation complexity of water filling, the simpler but sub-optimum solution of equal power allocation is investigated and shown to be worthwhile.