Finite-SNR Diversity-Multiplexing Tradeoff in Bidirectional Cooperative Networks

Analog network coding (ANC) and time division broadcasting (TDBC)are two major protocols used in bidirectional cooperative networks with half-duplex terminals. Most previous work on those two protocols was based on the assumption that there was no direct channel between the two sources. In this paper, we remove this limitation and investigate both protocols in a general bidirectional cooperative network with a direct channel between the two sources. Lower bounds on the outage probabilities of the two protocols are derived first. These lower bounds are very close to the exact outage probabilities in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on the lower bounds, the finite-SNR diversity-multiplexing tradeoffs (DMTs) of the ANC and TDBC protocols are obtained. These tradeoffs establish a framework which enables us to make a comprehensive comparison between both protocols.