Multiple Single-antenna Relays Research Articles

Joint source and relay beamforming design and time allocation for wireless powered multi-relay multi-user network

This paper studies joint source and relay beamforming optimization and time allocation for a wireless powered multi-relay multi-user network, where a multi-antenna base station (BS) transmits information to users with the assistance of multiple single-antenna relays. Considering that the relays are energy-constrained, which are powered by the BS wirelessly, we aim to maximize the minimum rate among the users by jointly optimizing the information and energy beamforming at the BS, the distributed beamforming at the relays, and the time allocation under the power constraints and the energy causality constraints at the BS and relays, respectively. In order to tackle the formulated optimization problem, we propose an iterative algorithm by alternatively solving two subproblems. Numerical results show that the proposed joint optimization scheme obviously outperforms other schemes.

Cooperative Beamforming for Hybrid Satellite-Terrestrial Relay Networks

This paper addresses the cooperative beamforming (BF) problem for hybrid satellite-terrestrial relay networks (HSTRNs), where a geostationary satellite transmits signals to a terrestrial mobile terminal (MT) with the help of multiple single-antenna relays. Specifically, we first formulate a constrained optimization problem to maximize the achievable rate of MT while satisfying the total power constraint of relays and the interference-to-noise ratio (INR) constraint at the earth stations (ESs). Then, based on Rayleigh-Ritz method, we propose an iterative BF algorithm to obtain the optimal analytical expressions of weight vector. Furthermore, to reduce computational complexity and transmission delay, we design MRT-based BF scheme as the suboptimal scheme. Finally, numerical results are given to confirm the validity and superiority of the proposed cooperative BF schemes.

Jointly Optimal Pre- and Post-Channel Equalization and Distributed Beamforming in Asynchronous Bidirectional Relay Networks

We consider an asynchronous bi-directional relay network (consisting of two single transceivers and multiple single-antenna relays) where the transceiver-relay paths are subject to different relaying and/or propagation delays. In such a network, the end-to-end link can be viewed as a multipath channel which can cause intersymbol-interference (ISI) in the signals received by the two transceivers. Assuming a block transmission/reception scheme, we consider both pre- and post-channel equalization at both transceivers to combat the interblock-interference (IBI) induced due to ISI. Considering amplify-and-forward relays, we study the problem of optimal design of pre- and post-channel linear equalizers and optimal power loading at the two transceivers as well as optimal network beamforming. To do so, assuming a limited total transmit power budget, we minimize the total mean square error of the linearly estimated signals at both transceivers by optimally obtaining the transceivers’ powers and relay beamforming weights as well as block pre- and post-channel linear equalizers at the two transceivers. We prove rigorously that this minimization leads to a certain relay selection scheme, where only a subset of the relays will be turned on. We also provide semiclosed form solutions to the design parameters.

Diagonal Amplifying Matrix Design in Multihop Distributed Relay Networks

In this paper, we study a multihop distributed relay network consisting of a single source–destination pair and multiple nonregenerative single-antenna relay nodes, which are arranged in different layers. Due to the distributed deployment, the amplifying matrix of the relay nodes at each layer has to be a diagonal matrix. We adopt a layer-by-layer approach to compute the relay amplifying matrices with the objective of maximizing the end-to-end transmission rate. The amplifying matrix of each layer is derived from a per-layer sum-rate maximization problem. When there is only one receiving node at the direct forward layer, the nonconvex per-layer sum-rate maximization problem is equivalently converted into a convex quadratically constrained quadratic program and could be efficiently solved. When there are multiple receiving nodes at the direct forward layer, the nonconvex per-layer sum-rate maximization problem is more challenging. We then transform it into a difference-of-convex program and design iterative convex programing to yield an approximate solution. The analysis shows that the proposed iterative algorithm will converge to local optima of the per-layer sum-rate maximization problem. Simulation results confirm that the proposed scheme outperforms the existing works in terms of the end-to-end transmission rate and is more effective in suppressing noise propagation.

Performance analysis of joint relay selection and transmission schemes in multiple-antenna two-way relay systems

In this paper, we consider a two-way relay system with two multi-antenna sources and multiple single-antenna relays and study the performances for various transmission schemes with the assumption that perfect channel state information (CSI) is available at both the sources and the relays. Although a transmission scheme that combines source beamforming and relay selection (BF-RS) is known to improve a system performance, its performance has not been theoretically analyzed yet. In the paper, we focus on the performance analysis in terms of the symbol error probability (SEP) for the BF-RS scheme. The analytical upper and lower bounds of the end-to-end system SEP are derived in the closed form, and the asymptotic SEP expression is given in high SNR regime. By both analytical and simulation results, it is clearly shown that a full transmit and relay selection diversity gain can be achieved without code rate loss. The SEP curves from simulations show that our derived bounds can predict the performance accurately. Based on the derived analytical results, we propose an individual power allocation (IPA) scheme to save the total transmit power. We show that the IPA scheme can result in considerable energy saving with a comparable SEP performance.

Probabilistic-Constrained Simultaneous Wireless Information and Power Transfer for Multiple-Relay Networks

Simultaneous Wireless Information and Power Transfer (SWIPT) potentially offers great convenience to prolong the lifetime of energy-constrained nodes in wireless networks. This paper considers multiple-relay network that incorporates SWIPT where the Base Station (BS) communicates with the user through the help of multiple single-antenna relays. A relay beamforming and energy harvest design is proposed to maximize the probability of the Signal-to-Noise-Ratio (SNR) of the user larger than a pre-defined threshold while not violating the power constraint of relays and guaranteeing the energy of the user received from probabilistic perspective. Then, we use S-lemma transform probabilistic-constrained problem into non- probability. An iteration-based algorithm is devised to solve this problem. Simulation results verify the effectiveness of the proposed scheme, which can achieve better tradeoff between the power consumption of relays and the user's SNR.

Selective Relay-Activation for Conditional DF Relaying

This paper considers a conditional decode-and-forward (DF) based cooperative system where a source (S) with multiple (M) antennas transmits information to a single-antenna destination (D) with the help of multiple (L ≤ M - 1) single-antenna relays ({R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> }). The optimal transmit weighting vector at the source is not available in the literature due to the non-linear conditional DF operation, which renders the problem non-convex. To solve this problem, we first show that the optimal transmit vector for the single-relay system can be determined by comparing the S-D beamformer (maximum-ratio-transmit beamforming vector for the S-D link) with the one that utilizes “just sufficient” energy to activate the relay-link. However, it is difficult to directly apply the above idea to the multi-relay system, due to the fact that the S-R and S-D links are normally not orthogonal. To tackle this issue, we propose to utilize basis functions that are orthogonal to the S-D and S-R links, respectively, which enables the activating of one S-R link without considering the S-D link and the other S-R links. We then apply the new basis functions to the multi-relay system and propose a selective relay-activation algorithm, where the optimal solution is obtained by comparing the S-D beamformer with schemes that selectively activate different combinations of the relay-links. The selective relay-activation algorithm is different from the conventional water-filling in the sense that the energy is filled to discrete levels to activate the S-R links, a unique feature arising from the conditional DF operation.

Bidirectional Cellular Relay Network with Distributed Relaying

In this paper, we consider a bidirectional cellular relay network with distributed relays where a single base station exchanges information with multiple independent users through multiple single-antenna relays. We design the transceivers at the base station, the relays, and the users. The related optimization problems are generally non-convex and difficult to solve. In this paper, we propose a unified framework to design the transceiver algorithms based on two criteria, i.e. weighted sum MSE minimization and sum rate maximization. Specifically, we show that the sum rate maximization problem can be converted into an iterative weighted sum MSE minimization problem. Low-complexity iterative algorithms are developed for both weighted sum MSE minimization and sum rate maximization optimization problems. However, the convergence points of the proposed iterative algorithms are sensitive to the initial conditions, especially in the high signal-to-noise ratio (SNR) regime. For this reason, we further derive the high-SNR asymptotically optimal solutions and use them as the initials for the proposed iterative algorithms. Simulation results show that the proposed scheme can approximately double the system throughput, compared to the conventional four-stage transmission schemes.

Multi-Carrier Asynchronous Bi-Directional Relay Networks: Joint Subcarrier Power Allocation and Network Beamforming

We consider an asynchronous bi-directional relay network, consisting of two single-antenna transceivers and multiple single-antenna relays, where the transceiver-relay paths are subject to different relaying and/or propagation delays. Such a network can be viewed as a multipath channel which can cause inter-symbol-interference (ISI) in the signals received by the two transceivers. Hence, we model such a communication scheme as a frequency selective multipath channel which produces ISI at the two transceivers, when the data rates are high. To tackle ISI, the transceivers can employ an orthogonal frequency division multiplexing (OFDM) scheme to diagonalize the end-to-end channel. The relays use simple amplify-and-forward relaying, thereby materializing a distributed beamformer. For such a scheme, we propose two different algorithms, based on the max-min fair design approach, to calculate the subcarrier power loading at the transceivers as well as the relay beamforming weights. We develop computationally efficient solutions to these two approaches. Simulation results are presented to show that our proposed schemes outperform equal or maximum power allocation schemes.

Distributed Beamforming for Relay Assisted Multiuser Machine-to-Machine Networks

We consider signal transmission with the aid of multiple half-duplex single-antenna relay nodes using the amplify-and-forward (AF) strategy for a multiuser wireless machine-to-machine (M2M) communication system. In such a scenario, relay beamforming has been proved to be an effective way to improve system performance by employing spatial diversity gains. Early works have mostly focused on various centralized relay beamforming schemes based on global channel state information (CSI). Since global CSI is often unavailable due to geometric locations, power limitation, or other constraints of the relay nodes in M2M networks, our work aims to develop distributed algorithms that each relay node individually learns its own beamforming weights with local CSI. We propose two suboptimal relay beamforming schemes that only require local CSI to minimize mean square error (MSE) for all the users with nonorthogonal channels. For multiuser systems with orthogonal channels, we divide the optimization problem into multiple single user problems which then can be solved by each relay independently. Numerical simulations for the proposed algorithms are presented showing the performance of the proposed schemes is close to that of the optimal scheme with global CSI in terms of bit error rate (BER) criterion.

Selection based inter-relay power allocation for multiple AF single-antenna relays

This article deals with inter-relay power allocation for multiple-input multiple-output systems with multiple single-antenna relays. It is difficult to derive an optimal solution in a closed form for the case of multiple multi-antenna relays as well as the case of multiple single-antenna relays. In this article, we propose an approximate solution which is effective only for the case of multiple single-antenna relays. A key contribution of this article is a low complexity inter-relay power allocation method which is based on relay selection. This approach also reduces the feedback information of the gain factors of all the relays. An incremental greedy search algorithm is also proposed to further reduce the complexity of the relay selection process with negligible performance degradation. Simulations indicate that the performance is comparable to the optimal exhaustive search algorithm.