Network coding notions promise significant gains in wireless networks' throughput and quality of service. Future systems employing such paradigms are known to be also highly scalable and resilient to node failure and churn rates. We propose a simple framework where a single relay listens to two nodes transmitting simultaneously over the same band in the presence of Nakagami-m fading. For this multiple-access channel (MAC), we derive in closed-form the exact bit error rate of antipodal signaling with maximum-likelihood detection. As the MAC is the bottleneck in error of the overall system, this provides a good performance measure of the aggregate architecture. Using the new error expressions derived, we then propose a simple closed-loop cooperation strategy where via a ternary feedback from the relay node, significant gains in signal to noise ratio at the relay can be achieved. Our novel error analysis method is applicable to a number of other systems such as the vertical Bell labs spacetime (V-BLAST) scheme and synchronous multi-user systems.

The maximum-likelihood (ML)-detected vertical bell-labs layered space-time (V-BLAST) architecture over a Nakagami-m fading channel is considered. This fading model encompasses many fading scenarios as special cases (e.g., Rayleigh). The ML detection of BLAST systems waives the requirement of not having smaller number of receive antennas than transmit antennas: a primary limitation using other sub-optimal linear processing receivers. Using exact BER expressions, a two-by-one antipodal V-BLAST system is optimized by phase precoding requiring only a single bit of feedback from the receiver. Numerical results demonstrate that the proposed single-bit feedback scheme improves the BER performance dramatically.

Space-time codes can be decoded by the sphere decoding (SD) algorithm to reduce the complexity and retain maximum-likelihood (ML) performance. In this letter, the ML metric of quasi-orthogonal space-time block codes is written into two independent Euclidean norms, thus SD can be applied to each function independently. The new scheme reduces the complexity by at least 85% for systems with four or more transmit antennas, compared with the conventional SD algorithm.