Routing and spectral efficiency in a wireless network with two parallel relays

This paper compares routing strategies in a simple four node network consisting of a source, a destination, and two parallel relays. Relay-to-relay communication is not considered, so there are three possible routing strategies: (1.) direct (source-to-destination) transmission; (2.) two-hop transmission that makes use of exactly one relay (i.e., the better-placed relay); and (3.) two-hop transmission wherein both relays are used during the second hop. The channel model assumes additive white Gaussian noise and attenuation due to path loss; for two-hop routing, time division multiple access is assumed for interference mitigation. Using simple capacity arguments, the paper first compares two-hop routing through one relay and two-hop routing through two relays and characterizes the relay placements for which one mode is preferable to the other. Then, two-hop transmission exploiting both relays is compared with direct transmission. It is shown that if the desired end-to-end rate is above a critical spectral efficiency, it is always preferable to transmit the signal directly no matter where the two relays are located.