Second-Order Statistics of MRC Reception With a Transparent Amplify-and-Forward Relay

Abstract

Achievable spatial diversity supported by a single transparent amplify-and-forward (AF) relay relies on disintegrated channel state information (CSI) that can be acquired at the destination. This paper studies the impact of the quantization of the source-relay (SR) CSI in terms of the first- and second-order statistics of maximal-ratio combining (MRC) reception with the incomplete SR CSI at the destination. Probability density functions (PDFs) of the upper and lower bounds of the signal-to-noise ratio (SNR) achieved at the destination are derived. Corresponding level-crossing rate (LCR) and average fade-duration (AFD), which are undoubtedly required to choose parameters of forward error correcting (FEC) mechanisms across the transparent AF relay network, are evaluated via Monte Carlo simulations. The simulations show that the SNR PDF, LCR and AFD highly depends not only on the accuracy of SR CSI at the destination but also on the location of the AF relay.