Asymptotic BER analysis of threshold digital relaying schemes in cooperative wireless systems

Threshold relaying is an effective technique to achieve cooperative diversity in uncoded cooperative wireless networks, which suffer from error propagation due to detection errors at the relays. This paper analyzes the asymptotic end-to-end (e2e) bit error rate (BER) of threshold digital relaying. A three node network with a source, destination and relay and with links experiencing independent Rayleigh fading is considered. It is shown that, as the average link signal-to-noise ratios (SNR) are increased simultaneously, the optimal threshold that minimizes the e2e BER increases as log(SNR). The resulting e2e BER decreases as log(SNR)/SNR2. Moreover, any threshold of the form log(cSNR), where c is a positive constant, achieves the same order of e2e BER as the one achieved by the optimal threshold and provides dual diversity. A value of c that performs very close to the optimal threshold is also proposed.