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Optimal Capacity Analysis in the Cooperative Relay System

A two-hop decode-and-forward relay system is considered, which consists of one source, one destination and K relay stations and all the nodes are deployed with multiple antennas. The capacity expressions in the two hops are analyzed and the maximal capacity expressions when signal-to-noise ratio is sufficiently small and sufficiently large are deduced respectively. Based on the capacity expressions, the numerical relation between the relays and the antennas of source, relay and destination is concluded to get optimal data rate of the end to end link from source to destination. When signal-to-noise ratio is small, relay number increases linearly with the ratio of the antennas of source and destination, when signal-to-noise ratio is large, relay number increases exponentially with the ratio of the antennas of relay and destination. Simulation results verified our conclusions and showed that the simulation results are approximately equal to theoretical optimal results.