On error analysis and distributed phase steering for wireless network coding over fading channels

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.