Distortion Exponents for Multi-Relay Cooperative Networks with Limited Feedback

In this paper, we study the transmission of a Gaussian signal in a multi-relay cooperative system, where each relay is half-duplex and employs the amplify-and-forward (AF) relaying protocol. We focus on the analysis of the distortion exponent that characterizes the high signal-to-noise ratio (SNR) behavior of the end-to-end distortion of the received signal. Specifically, we investigate the feedback scheme where the limited channel state feedback is combined with separate source and channel coding to help the transmission. The feedback scheme is followed by three AF-based multi-relay cooperation protocols, respectively, namely the orthogonal AF protocol, the nonorthogonal AF protocol, and the slotted AF protocol. We derive the optimal distortion exponents of all three cases, and illustrate the effect of the feedback resolution, bandwidth ratio, and number of relays on the optimal distortion exponent. It is shown that the feedback scheme outperforms the best known non-feedback strategies for multi-relay cooperative systems with only a few bits of feedback information.