Routing and Spectral Efficiency in Fading with Alamouti Coding at Two Parallel Relays

This paper compares direct and relayed transmission in a simple four node configuration with a source, a destination and two parallel relays. The channel model assumes additive white Gaussian noise, attenuation from path loss, and slow Rayleigh fading. The two parallel relays use the Alamouti code to relay data to the destination. Using outage probability as a metric, we investigate the relative advantage of relaying as a function of relay placement and the required end-to-end spectral efficiency. We first quantify the benefit derived from adding a second relay to a one-relay network; we then calculate the "critical" rate, above which direct transmission always yields a lower outage probability. It is seen that the critical rate for a two- relay system (with diversity combining) is only modestly higher than that of a one-relay system - suggesting that the addition of more parallel relays is not an effective means of increasing the range of end-to-end rates over which relaying provides an advantage over direct transmission.