Two-way Multi-relay Networks Research Articles

Spectrum-Energy Efficiency Tradeoff in Decode-and-Forward Two-Way Multi-Relay Networks

Owing to its high spectrum efficiency (SE), two-way relaying has aroused tremendous research interests. In this paper, the spectrum-energy efficiency (SE-EE) trade-off in decode-and-forward (DF) two-way multi-relay networks is studied by considering non-ideal power amplifiers and non-negligible circuit. Firstly, we consider the scenario of several relay nodes. To achieve better performance, the relay node with the highest energy efficiency (EE) is selected as the optimal one. Secondly, we design the optimal power allocation method to allocate each node with the optimal transmission power to enhance EE and SE. Finally, we evaluate the performance of our method and additionally analyze how the change of relay nodes’ relative position influences the EE and SE. Simulation results show that: 1) the proposed method can achieve higher SE than optimal relay equal power allocation, random relay equal power allocation, and optimal power allocation only; 2) the proposed method can achieve higher EE than optimal relay equal power allocation, random relay equal power allocation, and optimal power allocation only; and 3) EE and SE increase at first and then decrease when relay nodes move from the middle of the source node and destination node to both ends.

Joint Power Allocation and Distributed Equalization Design for OFDM-Based Filter-and-Forward Two-Way Multi-Relay Networks

We consider multi-carrier two-way relaying networks consisting of two user transceivers and multiple filter-and-forward (FF) relays. The FF relaying technique along with the multi-carrier schemes at the transceivers are utilized to suppress the inter-symbol-interference caused by the frequency-selectivity of the end-to-end channel. We jointly optimize subcarrier power allocation at the transceivers and the FIR filters at the FF relays to minimize the total transmit power subject to two quality of service constraints measured by sum-rates at the transceivers. We propose two approaches to tackle this problem: a gradient steepest descent technique, and a semi-closed-form method, which enforces a new constraint on the optimization such that at the optimum, the frequency-selective end-to-end channel is turned into a frequency-flat one. Furthermore, we show that the second method can be used as an initial point for the gradient steepest descent technique. Aiming to evaluate the performance of the proposed methods with a benchmark, we obtain a lower bound for the minimum transmit power at the network. We show that the proposed techniques are within 3 dB of this lower bound. Our numerical results further show that the proposed methods outperform existing solutions for similar networks.

Power-Optimal Distributed Beamforming for Multi-Carrier Asynchronous Bidirectional Relay Networks

We consider the problem of joint power allocation and distributed beamforming design for asynchronous two-way multi-relay networks, where two transceivers rely on an orthogonal frequency division multiplexing (OFDM) scheme to exchange information through multiple amplify-and-forward relay nodes. The network is assumed to be asynchronous in the sense that different relaying paths are subject to different propagation delays. This assumption renders the end-to-end channel between the two transceivers frequency-selective. The impulse response of such a channel can be modeled as a finite impulse response (FIR) system with multiple taps. We present a simple semi-closed-form solution for the problem of minimization of the total transmission power consumed in such networks subject to two quality of service constraints on the transceivers rates. We show that at the optimum, the end-to-end channel must be frequency-flat, which means only one tap of the end-to-end channel impulse response is non-zero. As a result, our semi-closed-form solution leads to a relay selection scheme, in which only those relays associated with the non-zero tap of the end-to-end channel impulse response are switched on, and the rest of the relays are kept off. The simulation results demonstrate that using the proposed semi-closed-form algorithm significantly outperforms the traditional best relay selection method.

Performance Analysis of Relay Selection with Enhanced Dynamic Decode-and-Forward and Network Coding in Two-Way Relay Channels

In this paper, we adopt the relay selection (RS) protocol proposed by Bletsas, Khisti, Reed and Lippman (2006) with Enhanced Dynamic Decode-and-Forward (EDDF) and network coding (NC) system in a two-hop two-way multi-relay network. All nodes are single-input single-output (SISO) and half-duplex, i.e., they cannot transmit and receive data simultaneously. The outage probability is analyzed and we show comparisons of outage probability with various scenarios under Rayleigh fading channel. Our results show that the relay selection with EDDF and network coding (RS-EDDF&NC) scheme has the best performance in the sense of outage probability upon the considered decode-and-forward (DF) relaying if there exist sufficiently relays. In addition, the performance loss is large if we select a relay at random. This shows the importance of relay selection strategies.

Joint Beamforming Design and Time Allocation for Wireless Powered Asymmetric Two-Way Multirelay Network

This paper studies the joint beamforming design and time allocation for a two-way energy harvesting (EH) relay network, where a single-antenna base station and a single-antenna user communicate with each other through multiple-single antenna EH relay nodes, and an external multiantenna power beacon wirelessly power the relays. Unlike the existing studies that assumed the symmetric two-way relaying scenario, we assume a more practical scenario of asymmetric two-way relaying considering different traffic demands on the downlink and uplink. In this paper, we design the optimal beamforming vectors at the relays and at the power beacon jointly with the time allocation between information and EH transmissions, in the sense of maximizing the sum rate of the asymmetric information transmission under the EH constraints at the relays, and the power constraint at the power beacon. The formulated optimization problem is nonconvex, and thus, it is difficult to solve. To solve this challenging problem, we propose an iterative algorithm based on the semidefinite relaxation and the successive convex approximation techniques. Also, to reduce the computational complexity, we propose an efficient noniterative scheme based on the maximum-ratio transmission. The performance of the proposed schemes is demonstrated through simulations.

Decoupled beamforming techniques for distributed MIMO two-way multi-relay networks with imperfect CSI

This paper investigates decoupled beamforming techniques for the distributed multi-input multi-output (MIMO) two-way relay networks (TWRN) with imperfect channel state informations (CSIs). The objective of this paper is to maximize the weighted sum rate (SR) with semi-infinite relay power constraints. Since the objective problem is difficult to be solved directly, considering the high signal-to-residual-interference-plus-noise ratio (SRINR) and employing the Cauchy-Schwarz inequality and S-lemma, the problem can be approximately converted into a source beamforming decoupled one. In addition, with the optimal relay beamforming design and maximum ratio combining (MRC) at the receiver, the MIMO channels are decoupled into parallel single-input single-output (SISO) channels. By this way, the suboptimal relay beamforming matrix can be efficiently obtained with minimal relay power constraint. Specifically, the semi-infinite constraints can be reformulated into a linear matrix inequality (LMI), which can be efficiently solved by using an alternating optimization algorithm. Numerical results demonstrate that our proposed decoupled beamforming scheme outperforms the existing works in terms of the SR and the computational complexity with satisfactory convergence.

Semiblind Channel Estimation and Precoding Scheme in Two-Way Multirelay Networks

A low-complexity precoding scheme and semiblind channel estimation method are proposed for amplify-and-forward two-way relay networks with multiple relays and frequency-selective fading channels. In the proposed approach, precoding is performed using a rotation-based matrix and the composite channel impulse response of each source-relay-destination link is estimated based on the second-order statistics of the received signals. The ambiguity in the proposed channel estimates caused by the channel information of the direct link is eliminated using a small number of training blocks. The accuracy of the proposed semiblind channel estimates is examined by deriving the mean square error of the channel estimates for two asymptotic cases, namely an infinite number of data blocks and a high signal-to-noise ratio (SNR) regime. The two cases, thus, provide a useful insight into the effects on the estimation performance of imperfect direct link information and statistical errors of the ensemble correlations, respectively. The asymptotic analyses are confirmed by the simulation results, which show that the normalized mean square error of the channel estimates varies inversely with the SNR and the number of data blocks.

Enhanced beamforming design and sum-rate maximization for two-way multi-relay networks

In this paper, we investigate an enhanced relay beamforming design for two-way relay networks (TWRN). In order to reduce the computational complexity, we derive a sum of the inverse of the signal-to-noise ratio (SI-SNR) problem equivalent to the objective sum-rate (SR) problem. The SI-SNR problem can be reformulated as a simple optimization problem by using the Cholesky decomposition and Cauchy-Schwarz inequality, and solved by the interior-point method. The numerical results show that the proposed SI-SNR method can not only reduce the computational complexity but also have the same SR performance as that of the conventional works.

Distributed Concatenated Recursive Alamouti-Circulant STBC for Two-Way Multi-Relay Networks

A general distributed multi-antenna two-way relaying network with multiple relays is considered in this paper. We first obtain a tight lower bound of pairwise error probability (PEP) of a maximum likelihood detector for the general distributed linear dispersion code for a half-duplex amplify-and-forward two-way relaying network (TWRN) consisting of two sources with each having single antenna and $N$ relays with each having two antennas. Furthermore, by jointly considering signal precoding at the sources and signal processing at the relays, a general distributed concatenated recursive Alamouti-circulant space-time block code is proposed for the considered TWRNs. Our design ensures that the equivalent channel matrices at both source nodes are the so-called the recursive Alamouti-circulant matrices, with each block being a product of the two Alamouti channel matrices. Based on a lower–upper bound strategy and an induction method, asymptotic PEP formula is attained to show that given the optimal angle rotation matrix and the precoding matrix, the code can meet the lower bound of the diversity gain, as well as the maximum coding gain. In addition, the proposed rate one code turns to be effectively decodable.

Training Designs for Estimation of Spatially Correlated Fading Channels in MIMO Amplify-and-Forward Two-Way Multi-Relay Networks

In this letter, we present training designs for estimation of spatially correlated multiple-input multiple-output amplify-and-forward two-way multi-relay channels. An optimal training structure is initially derived to minimize total mean-square-error of the channel estimation and, then, source training power and relay amplification parameters are optimized numerically. For the purpose of complexity reduction and implementation simplicity, an upper bound-based power allocation is also proposed in a closed form. Simulation results show that the proposed schemes considerably outperform the conventional schemes.

Network coding-based channel quality indicator reporting for two-way multi-relay networks

This paper considers channel quality indicator CQI reporting for data exchange in a two-way multi-relay network. We first propose an efficient CQI reporting scheme based on network coding, where two terminals are allowed to simultaneously estimate the CQI of the distant terminal-relay link without suffering from additional overhead. In addition, the transmission time for CQI feedback at the relays is reduced by half while the increase in complexity and the loss of performance are negligible. This results in a system throughput improvement of 16.7% with our proposed CQI reporting. Upper and lower bounds of the mean square error MSE of the estimated CQI are derived to study performance behaviour of our proposed scheme. It is found that the MSE of the estimated CQI increases proportionally with the square of the cardinality of CQI level sets although an increased number of CQI levels would eventually lead to a higher data rate transmission. On the basis of the derived bounds, a low-complexity relay selection RS scheme is then proposed. Simulation results show that, in comparison with optimal methods, our suboptimal bound-based RS scheme achieves satisfactory performance while reducing the complexity at least three times in case of large number of relays. Copyright © 2012 John Wiley & Sons, Ltd.