On Sum-Rate Maximization Approach to Network Beamforming and Power Allocation for Asynchronous Single-Carrier Two-Way Relay Networks

Abstract

We study the sum-rate maximization problem, under a total power budget, for asynchronous single-carrier bi-directional relay networks, consisting of two transceivers and multiple amplify-and-forward relays. When different transceiver-relay links cause significantly different propagation delays in the signal they convey, the end-to-end channel is not amenable to a frequency-flat modeling; rather, a multi-path channel model is appropriate. Such a multi-path channel model results in inter-symbol-interference at the transceivers. Aiming to maximize the sum-rate of this channel over the relay weights and transceivers' powers, we rigorously prove that such a sum-rate maximization problem leads to a relay selection scheme, where only those relays, which contribute to one of the taps of the end-to-end channel impulse response (CIR), are turned on. Indeed, we prove that the optimal end-to-end CIR has only one non-zero tap, rendering the end-to-end channel frequency-flat. Our proof shows that the mean-squared-error (MSE) optimal joint post-channel equalization, network beamforming, and power allocation scheme is sum-rate-optimal. The equivalence of MSE-optimal and sum-rate-optimal solutions is interesting, as MSE minimization promotes end-to-end reliability, while sum-rate maximization advocates for multiplexing gain. These approaches often pull the design of communication systems in different directions. For the aforementioned scenario, these approaches are identical as we prove.