Distributed GABBA space-time codes in amplify-and-forward relay networks

Cooperative communications via distributed space-time codes has been recently proposed as a way to form virtual multiple-antennas that provide dramatic gains in slow fading wireless environments. In this paper, we consider the design of practical distributed space-time codes for wireless relay networks using the amplify-and-forward (AF) scheme, where each relay transmits a scaled version of the linear combinations of the received symbols and their complex conjugate. We employ GABBA codes, which are systematically constructed, orthogonally decodable, full-rate, full-diversity space-time block codes, in a distributed fashion. Our scheme is valid for any number of relays with linear orthogonal decoding in the destination, which make it feasible to employ large numbers of potential relays to improve the diversity order. We generalize the distributed space-time codes in AF mode when the source-destination link contributes in both phases of the transmission. Assuming MPSK or M-QAM constellations and maximum likelihood (ML) detection, we derive an approximate formula for the symbol error probability of the investigated scheme in Rayleigh fading channels. The analytical results are confirmed by simulations, indicating both the accuracy of the analysis, and the fact that low-complexity, flexible, and high-performing distributed space-time block codes can be designed based on GABBA codes.