Considered in this paper is a single-carrier asynchronous bidirectional cooperative network with amplify-and-forward relays helping two transceivers to exchange information. The network is asynchronous in the sense that the delays of propagation along different relaying paths are significantly different from each other. As a result, the channel between the two transceivers is best modeled with a multi-tap impulse response, which can cause interference between adjacent symbols at the end nodes. In a block-wise communication scheme, a cyclic prefix can be appended to each transmitted block of information symbols to avoid interference between adjacent blocks. To suppress interference within each block, however, the network parameters, namely, the relay complex weights and the transceivers' transmit powers should be judiciously chosen. To do so, we herein minimize, over these parameters, the total transmission power consumption throughout the network, under two constraints which ensure that the transceivers' data rates are above two given thresholds. It is herein proved that solving this total transmission power minimization problem leads to the impulse response of end-to-end channel having only a single non-zero tap. Indeed, our analysis shows that only the relays associated with this non-zero tap have to be selected to participate in the information exchange between the two transceivers. We present a simple 1-D integer search algorithm for optimally determining the index of the non-zero tap of the channel impulse response of the end-to-end channel. We also present computationally simple semi-closed-form expressions for the optimal values of the design parameters. Our numerical results show that under identical rate thresholds, in our power allocation scheme, for any channel realization, half of the power budget is allocated to the two transceivers and the remaining half is shared among all the relay nodes. INDEX TERMS Network beamforming, power control, two-way relay networks, bi-directional cooperative communication, distributed beamforming, power minimization.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.