Gaussian Orthogonal Relay Channels: Optimal Resource Allocation and Capacity

A Gaussian orthogonal relay model is investigated, where the source transmits to the relay and destination in channel 1, and the relay transmits to the destination in channel 2, with channels 1 and 2 being orthogonalized in the time–frequency plane in order to satisfy practical constraints. The total available channel resource (time and bandwidth) is split into the two orthogonal channels, and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized. The main focus of the analysis is on the case where the source-to-relay link is better than the source-to-destination link, which is the usual scenario encountered in practice. A lower bound on the capacity (achievable rate) is derived, and optimized over the parameter $theta$, which represents the fraction of the resource assigned to channel 1. It is shown that the lower bound achieves the max-flow min-cut upper bound at the optimizing $theta$, the common value thus being the capacity of the channel at the optimizing $theta$ . Furthermore, it is shown that when the relay-to-destination signal-to-noise ratio (SNR) is less than a certain threshold, the capacity at the optimizing $theta$ is also the maximum capacity of the channel over all possible resource allocation parameters $theta$ . Finally, the achievable rates for optimal and equal resource allocations are compared, and it is shown that optimizing the resource allocation yields significant performance gains.