High SNR approximation for performance analysis of two-way multiple relay networks

Signal-to-Noise Ratio (SNR) is the key parameter in the performance evaluation of Two-Way, Amplify-and-Forward, Multiple-Relaying (TAF-MR) networks. This paper introduces new methods that use high SNR (HSNR) level approximations to analyze accurately the Bit Error Rate (BER), optimize the Relay Location (RL), and balance the energy efficiency (EE) and spectral efficiency (SE) of such networks. We consider a flat-fading channel and a strategy for selecting a relay with the highest SNR. Standardized BER expressions are obtained for a wide range of SNRs (low, high, and optimal) to yield more accurate predictions of the BER performance. Thus, by using HSNR, a unified analysis for calculating the Asymptotic BER (ABER) and the exact BER (EBER) performance is developed. The optimal SNR level is obtained by optimizing the power of network sources, which include the relay and user powers. Further, we propose a method for integrating the RL with the balancing of the EE and SE optimally to achieve the best EE improvement. The derived expressions for the methods are validated by simulation.