Capacity maximisation in eigen-multiple-input multiple-output using adaptive modulation and Reed-Solomon coding

Eigen-multiple-input multiple-output (MIMO) with water-filling gives the maximum information-theoretic capacity, but realising this maximisation is not straightforward because practical factors are omitted. Adaptive modulation and error coding are combined for finding the maximum practicable capacity (throughput of correctly detected bits) in eigen-MIMO. Quadrature amplitude modulation (QAM) is the logical choice of modulation and here Reed-Solomon (RS) coding is used. RS coding has the advantages of algorithmic simplicity, low-memory requirements, and decoder complexity, and its unique closed-form error probability makes it possible to obtain an optimal power allocation, signal constellation size(s), and code rate(s) on the eigenchannels, for the maximum practicable capacity. The proposed adaptive scheme is applied to two architectures for the encoders/decoders (CODECs): outer coding, where a single CODEC is deployed for the overall serial data; and inner coding, where there is a CODEC for each eigenchannel. The optimal power allocation is different to the water-filling used for the information-theoretic capacity. Also, simple and accurate approximations are found for the bit-error rate (BER) of a single Rayleigh channel and of a 2-2 system. Finally, a selection procedure between different system configurations is presented for obtaining the highest practicable capacity subject to either average or instantaneous output BER.