Impact of Outdated Channel Estimates on Opportunistic Two-Way ANC-Based Relaying With Three-Phase Transmissions

In this paper, we investigate the impact of outdated channel estimates on the overall performance of a two-way multirelay system that employs a three-phase (3P) analog network coding (ANC)-based opportunistic relay selection (ORS) scheme under Rayleigh fading. Specifically, considering the imperfect estimation and the time variation of the fading channels, we formulate the 3P ANC-based ORS strategy for the best relay among multiple relays in terms of both outdated and imperfect channel state information (CSI). With such a practical CSI modeling, we derive a tight lower bound expression for the overall outage probability (OOP) and an upper bound expression for the ergodic sum-rate (ESR) of the considered scheme. In addition, by deriving an asymptotic outage behavior in the high signal-to-noise ratio (SNR) regime, we highlight the impact of outdated and imperfect CSI on the achievable diversity order. Moreover, based on the asymptotic analysis, we investigate three optimization problems, namely, optimal relay power allocation for fixed relay location, optimal relay location for fixed power allocation, and jointly optimal relay power allocation and location to minimize the OOP and to maximize the ESR of the considered system. Our results reveal that the optimal relay power allocation has a more significant impact on the performance when the CSI is imperfect, whereas the optimal relay location has a more noticeable impact when the CSI is outdated and unbalanced over the two hops. Furthermore, we show that the imperfect CSI can degrade system performance more severely than the outdated CSI, and it can even reduce the system diversity order to zero. The numerical and simulation results corroborate our theoretical analysis and findings and demonstrate that the 3P ANC-based ORS scheme can achieve better performance than its two-phase counterpart, depending upon the quality of the direct link, particularly in the medium-to-high-SNR regime.

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