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

We study the channel quantization problem for amplify- and-forward (AF) relay networks with a sum power constraint for the relay nodes. 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 a variable- length quantizer with a random infinite- cardinality codebook, and we prove that the proposed quantizer is able to achieve the full-CSI outage probability with a finite average feedback rate. Numerical simulations validate our theoretical analysis.