Optimizing quantize-map-and-forward in slow fading relay networks

Quantize-Map-and-Forward (QMF) relaying has been shown to achieve the optimal diversity-multiplexing tradeoff (DMT) for the slow fading single-antenna relay channel, regardless of whether the relay is full-duplex or half-duplex. A key reason for the DMT optimality is that quantizing at the noise level suffices to achieve the cut-set bound approximately and hence the relay does not need any instantaneous channel state information (CSI). However, DMT only captures the high SNR performance and potentially, limited CSI at the relay can help improve the performance in moderate SNR regimes. In this work we propose an optimization framework for QMF relaying in slow fading relay channels. Focusing on vector Gaussian quantizers, for the full-duplex relay we optimize the outage probability by finding the best quantization level according to the available CSI at the relay and the channel statistics. For the half-duplex relay we find good relay schedules using the same framework. Numerical evaluations show the improvement of taking the CSI into account over noise-level quantization and static schedules in moderate SNR regimes.