Analysis and Optimization of Cooperative Amplify-and-Forward Relaying with Imperfect Channel Estimates

Abstract

Relay-based cooperation promises significant gains in a wireless network as it provides an inde-pendent path between a source and a destination. Using simple single antenna nodes, it exploits the spatial diversity provided by the geographically separated nodes in a network to improve the robustness of the communication system against fading. Among the cooperative commu¬nication schemes, the amplify-and-forward (AF) relaying scheme is considered to be easy to implement since the relay does not need to decode its received signal. Instead, it just forwards to the destination the signal it receives from the source. We analyze the performance of fixed-gain AF relaying with imperfect channel knowledge that is acquired through an AF relay-specific training protocol. The analysis is challenging because the received signal at the destination contains the product (or cascade) of source-relay (SR) and relay-destination (RD) complex baseband channel gains, and additional products terms that arise due to imperfect estimation related errors. We focus on the time-efficient cascaded channel estimation (CCE) protocol to acquire the channel estimates at the destination. Using it, the destination can only estimate the product of SR and RD complex baseband channel gains, but not the two separately. Our analysis encompasses a single AF relay system and an opportunistic system with mul¬tiple AF relays, among which one is selected to forward its received signal to the destination, based on its SR and RD complex baseband channel gains. For a single relay system, we first de¬velop a novel SEP expression and a tight SEP upper bound. We then analyze the opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect channel estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible. It results in a new analysis that is accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Further, the training protocol is an integral part of the model and analysis. Using an insightful asymptotic analysis, we then present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s). Further, the optimal energy allocation between a source and a relay is characterized when both together operate under a sum energy constraint, as has often been assumed in the literature. In summary, the sum total of the results in this work provides a rigorous and accurate performance characterization and optimization of cascaded channel estimation for AF relaying.