Amplify-and-Forward Relay Networks With Variable-Length Limited Feedback

We study the channel quantization problem for amplify-and-forward (AF) relay networks and our target is to design a quantizer to minimize the outage probability. It is priorly known that any fixed-length quantizer with a finite-cardinality codebook cannot attain the same minimum outage probability as the case where all nodes in the AF relay networks have access to perfect channel state information (CSI). We propose variable-length quantizers with random infinite-cardinality codebooks for the sum and individual power constraints. We provide theoretical proofs and numerical simulations to validate that the proposed quantizers can achieve the full-CSI outage probabilities with finite average feedback rates.