MMSE transmit diversity selection for multi-relay cooperative MIMO systems using discrete stochastic gradient algorithms

This paper presents a set of transmit diversity selection algorithms based on discrete stochastic optimization for a two-phase, decode-and-forward, multi-relay cooperative MIMO system with a non-negligible direct path. Transmit diversity selection is performed jointly with channel estimation using discrete stochastic and continuous least squares optimization, respectively. Linear minimum mean square error receivers are used at the relay and destination nodes whilst no forward channel knowledge, precoding or inter-relay communication is required. Sets of candidate transmit diversity selections are generated and methods to optimize the selection whilst avoiding exhaustive searching are presented. The benefits of reducing the cardinality of these sets is shown and the performance of the proposed schemes are assessed via mean square error, bit-error rate and complexity comparisons. The performance and diversity achieved is shown to exceed that of standard multi-relay cooperative MIMO systems and random transmit diversity selection, and closely match that of the exhaustive solution.