Jointly optimal distributed beamforming and power control in asynchronous two-way relay networks

Abstract

In this paper, we consider an asynchronous two-way relay network, where multiple single-antenna relay nodes enable bi-directional communication between two single-antenna transceivers using amplifyand-forward (AF) signaling in a multiple access broadcast channel (MABC) protocol. We assume that each relaying path, which originates from one transceiver, goes through one of the relays, and ends at the other transceiver, causes a delay which can be significantly different from the delays caused by other relaying paths. Such a two-way relay channel can produce inter-symbol-interference at the two transceivers. Assuming a block transmission scheme, we use cyclic prefix insertion to eliminate inter-block-interference. Aiming to optimally obtain the relay beamforming weights and the transceivers' transmit powers, we minimize the total consumed power in the network, subject to two constraints on the transceivers' data rates. We rigorously prove that at the optimum, the end-to-end channel impulse response (CIR) must have only one non-zero tap, and hence, only those relays which contribute to that non-zero tap are switched on. We propose a simple search algorithm to optimally determine which tap of the end-to-end CIR is non-zero. Finally, we present a semi-closed-form solution for the optimal the relays' beamforming weights and the transceivers' transmit powers.