Beamforming with limited feedback in amplify-and-forward cooperative networks

A relay selection approach has previously been shown to outperform repetition-based scheduling for both amplify-and-forward (AF) and decode-and-forward (DF) cooperative networks. The selection method generally requires some feedback from the destination to the relays and the source, raising the issue of the interplay between performance and feedback rate. In this paper, we treat selection as an instance of limited-feedback distributed beamforming in cooperative AF networks, and highlight the differences between transmit beamforming in a traditional multi-input single-output (MISO) system and the distributed case. Specifically, Grassmanian line packing (GLP) is no longer the optimal codebook design, and orthogonal codebooks are no longer equivalent to each other. We derive the high signal-to-noise ratio expressions for outage probability and probability of symbol error for unlimited-feedback and selection schemes. The gap in performance between unlimited-feed back and selection beamforming is found analytically to grow rapidly with the number of relays. We compare the selection protocol to a limited-feedback distributed beamformer that assigns codebooks based on the Generalized Lloyd Algorithm (GLA), and one that uses random beam-vectors. The main conclusion is that the performance improvement to be seen using the very complex GLA is small, and that many more feedback bits are required with random beamforming than selection for the same performance. These results indicate that the selection protocol is a very attractive protocol with low-complexity that provides excellent performance relative to other known methods.