Design Collaborative Systems with Multiple AF-Relays for Asynchronous Frequency-Selective Fading Channels

Distributed systems with multiple amplify-and-forward (AF) relays are very appealing, due to their, ease of implementing space diversity. Although their performance on synchronous flat-fading channels was well understood, the corresponding design and optimization in asynchronous frequency selective fading (AFSF) channels remains unsolved. In this paper, we tackle the problem in the information-theoretic framework, revealing that multi-relay amplify-and-forward (MR-AF) systems over AFSF channels can be better understood through the concept of virtual sub-channels Each relay node virtually performs two functions, appropriately amplifying sub-channel signals on one hand and serving as a local switching center on the other. System design, therefore, reduces to the determination of optimal amplification factors, switching matrices, and power allocation among the source, relays and relevant sub-channels. The optimization is implemented in a layered structure. The effects of asynchronism and knowledge of channel information on mutual information are also investigated.