On Total Transmission Power Minimization Approach to Decentralized Beamforming in Single-Carrier Asynchronous Bidirectional Relay-Assisted Communication Networks

Abstract

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.

Proof of the Equivalency of MSE-Constrained and Rate-Constrained Power Optimization Approaches to Distributed Bi-Directional Beamforming

“…Such a relationship between the MSE at the output of a linear receiver and the data rate in the absence of a linear receiver does not hold in general. Using the notations used here, we can simplify the optimization problem (93) as [24] min…”

“…Using such a communication setting, our goal is, to first find the achievable MSE region for a single-carrier asynchronous bi-directional (two-way) AF relay network under a total transmit budget, and then, use this region to solve the problem of total power minimization under two constraints on the mean squared error (MSE) at the two transceivers. We prove rigorously that this power minimization leads to the very same solution that minimizes the total power under two constraints on the data rates at the two transceivers [24], if the MSE thresholds in the MSE-constrained total power minimization and the rate thresholds in the rate-constrained power minimization technique satisfy a logarithmic (or an exponential) relationship. In our study, we consider linear post-channel equalization and aim to characterize the frontier of the MSE region through optimally obtaining the relay beamforming weights, the transceivers' transmit powers, and the post-channel equalizers.…”

“…r The second contribution of this paper is optimally finding the transceivers' transmit powers and relay complex beamforming weights by solving the total power minimization problem under MSE constraints and showing how this solution is related to the solution of the rate-constrained power minimization problem. More specifically, we rely on our MSE region characterization to rigorously prove that in designing transceiver power allocation and distributed beamforming, our MSE-constrained total power minimization approach and the rate-constrained power minimization technique of [24] are equivalent, provided that the MSE thresholds in the former approach and the rate thresholds in the latter approach satisfy a logarithmic (or an exponential) relationship. The equivalence of these two approaches allows us to infer the un-coded MSE performance of the network from the rate-constrained problem, and conversely, the coded rate performance of the network can be inferred from the MSE-constrained total power minimization problem.…”

“…The design approach in [23] is sum-rate maximization method subject to a total power budget, while we consider a total power minimization technique subject to MSE constraints. In [24], the design approach is total power minimization subject to rate constraints without assuming any type of equalizations, while here, assuming linear post-channel equalization, we study a total power minimization approach subject to MSE constraints.…”

Cooperative Communications Based on Deep Learning Using a Recurrent Neural Network in Wireless Communication Networks

“…Tere is a transformation in the 5G networks regarding their speed, latency, and connectivity with the huge number of devices especially in the areas of IoT, VR, and artifcial intelligence (AI). Several researchers ofer AI-based solutions, especially deep learning (DL), due to their capacity to adapt to dynamic conditions, such as wireless network mobility; these approaches enable the efcient solution of challenging challenges [3]. In networking, machine learning is used to solve a variety of issues, including routing [4].…”