Relay Precoding Matrix Research Articles

Optimal Energy-Efficient Source and Relay Precoder Design for Two-Way MIMO-AF Relay Systems

Energy efficiency (EE) is a key figure of merit for designing the next generation of communication systems. Meanwhile, relay-based cooperative communication, through machine-to-machine and other related technologies, is also playing an important part in the development of these systems. This paper designs an energy efficient precoding method for optimizing the EE/energy consumption of two-way multi-input multi-output (MIMO)-amplify-and-forward (AF) relay systems by using pseudo-convexity analysis to design EE-optimal precoding matrices. More precisely, we derive an EE-optimal source precoding matrix in closed-form, design a numerical approach for obtaining an optimal relay precoding matrix, prove the optimality of these matrices, when treated separately, and provide low-complexity bespoke algorithms to generate them. These matrices are then jointly optimized through an alternating optimization process that is proved to be systematically convergent. Performance evaluation indicates that our method can be globally optimal in some scenarios and that it is significantly more energy efficient (i.e., up to 60% more energy efficient) than existing EE-based one-way or two-way MIMO-AF precoding methods.

Joint Power Allocation and Relay Beam-forming in Orbital Angular Momentum Amplify-and-Forward Relay Networks

Orbital Angular Momentum (OAM) is a promising technology that can effectively improve the spectral efficiency of wireless communications. However, it is important for OAM to keep the antenna alignment of transmitter and receiver. The alignment requirements greatly increases the difficulty of the practical application of OAM, especially when there is a barrier or a large turning angle between uniform circular arrays (UCAs). In this letter, we studied the application of amplify-and-forward (AF) relay in multiple-input multiple-output (MIMO) OAM system to solve the problem caused by the existence of UCAs corners. In this work, our goal is to achieve the maximum achievable rate by jointly optimizing the source power allocation matrix and the relay pre-coding matrix, constrained by the power of the source and the relay. The problem is expressed as a convex problem by mathematical operations, and then based on the Lagrange dual method, we solved it by proposing an iterative algorithm. Numerical simulations show the superiority of the algorithm.

Multi-objective optimization design for multi-source multicasting MIMO AF relay systems

In this paper, we consider a multi-source multicasting two-hop multi-input multi-output amplify-forward (AF) relay system, where multiple source nodes multicast their own messages to a group of receivers with the cooperation of an AF relay node. In particular, we aim at minimizing the transmission power consumption and the mean-squared error (MSE) of the receiver estimated signal simultaneously. However, the two objectives are coupled and even conflicting. In view of this, a multi-objective optimization (MOO) framework is adopted to achieve the trade-off between the two objectives. The formulated MOO problem (MOOP) takes into account the constraints of the MSE upper bound and the maximum transmission power budget. Since the MOOP is non-convex and hard to tackle, we propose a resource allocation algorithm by exploiting the weighted Tchebycheff approach and the optimal structure of the relay precoding matrix. Simulation results not only demonstrate the effectiveness of the proposed algorithm, but also unveil an important trade-off between the total power consumption and the MSE at receivers.

Optimal Energy-Efficient Source and Relay Precoder Design for Cooperative MIMO-AF Systems

Energy efficiency (EE) is a key design criterion for the next generation of communication systems. Equally, cooperative communication is known to be very effective for enhancing the performance of such systems. This paper proposes a breakthrough approach for maximizing the EE of multiple-input-multiple-output (MIMO) relay-based nonregenerative cooperative communication systems by optimizing both the source and relay precoders when both relay and direct links are considered. We prove that the corresponding optimization problem is at least strictly pseudoconvex, i.e., having a unique solution, when the relay precoding matrix is known, and that its Lagrangian can be lower and upper bounded by strictly pseudoconvex functions when the source precoding matrix is known. Accordingly, we then derive EE-optimal source and relay precoding matrices that are jointly optimized through alternating optimization. We also provide a low-complexity alternative to the EE-optimal relay precoding matrix that exhibits close to optimal performance, but with a significantly reduced complexity. Simulations results show that our joint source and relay precoding optimization can improve the EE of MIMO-AF systems by up to ∼ $50\%$ when compared to direct/relay link only precoding optimization.

Energy Efficient Precoder Design for Non-Regenerative MIMO-CRN

This letter presents a problem of designing a relay precoding matrix for a multi-input multi-output cognitive relay network, where a secondary system (SS) works in an underlay mode and communicates through a non-regenerative relay. An optimization problem is formulated to maximize the energy efficiency of the SS subject to a transmit power constraint and an interference constraint. An efficient scheme based on the fractional programming and augmented Lagrangian multiplier method is proposed to solve the resultant problem. Numerical results are provided to show the effectiveness of the proposed scheme.

Robust MMSE Transceiver Design for Nonregenerative Multicasting MIMO Relay Systems

In this paper, we investigate the transceiver design for nonregenerative multicasting multiple-input multiple-output (MIMO) relay systems, where one transmitter broadcasts common message to multiple receivers with the aid of a relay node. The transmitter, relay, and receivers are all equipped with multiple antennas. We assume that the true (unknown) channel matrices have Gaussian distribution, with the estimated channels as the mean value, and the channel estimation errors follow the well-known Kronecker model. We first develop an iterative robust algorithm to jointly design the transmitter, relay, and receiver matrices to minimize the maximal mean-squared error (MSE) of the signal waveform estimation among all receivers. Then, we derive the optimal structure of the relay precoding matrix and show that the MSE at each receiver can be decomposed into the sum of the MSEs of the first-hop and second-hop channels. Based on this MSE decomposition, we develop a simplified transceiver design algorithm with a low computational complexity. Numerical simulations demonstrate the improved robustness of the proposed transceiver design algorithms against the mismatch between the true and estimated channels. Interestingly, compared with the iterative algorithm, the simplified transceiver design has only negligible performance loss with significantly reduced computational complexity.

New Results on Transceiver Design for Two-Hop Amplify-and-Forward MIMO Relay Systems With Direct Link

Conventional amplify-and-forward (AF) protocol for half-duplex two-hop multiple-input-multiple-output (MIMO) relay systems assumes that the source node transmits the signal only at the first time slot. While making the source node silent at the second time slot simplifies the system design, it is strictly suboptimal. To improve the system performance, in this paper, we consider that the source node transmits signals during both time slots. We develop two novel iterative algorithms to optimize the source, relay, and receiver matrices in this new AF MIMO relay system. Both algorithms are based on the minimum mean-square error (MMSE) criterion. In particular, the first algorithm is applicable for general MIMO relay systems with multiple concurrent data streams, where the source, relay, and receiver matrices are optimized in an alternating fashion until convergence. The second algorithm is developed for MIMO relay systems with a single data stream, where the source precoding vectors and the relay precoding matrix are optimized iteratively and the receiver matrix is obtained after the convergence of the source vectors and the relay matrix. Simulation results show that compared with conventional AF MIMO relay systems, the proposed system provides better bit-error-rate performance for both multiple-data-stream and single-data-stream cases.

User-Centric Precoding Designs for the Non-Regenerative MIMO Two-Way Relay Systems

In this letter, we jointly design the source and relay precoders for non-regenerative multi-input multi-output two-way relay systems from the user-centric perspective. The two sources are assumed to be both energy efficiency (EE) desirable and spectral efficiency (SE) desirable. We aim at studying the EE–SE tradeoff between the two sources. The resulting problem is a non-convex multi-objective problem. To address this issue, an iterative algorithm is proposed to design the relay precoding matrix and source beamforming vectors alternatively. We also show that the proposed iterative algorithm is guaranteed to converge.

Wireless Information Surveillance via Proactive Eavesdropping with Spoofing Relay

Wireless information surveillance, by which suspicious wireless communications are closely monitored by legitimate agencies, is an integral part of national security. To enhance the information surveillance capability, we propose in this paper a new proactive eavesdropping approach via a spoofing relay, where the legitimate monitor operates in a full-duplex manner with simultaneous eavesdropping and spoofing relaying to vary the source transmission rate in favor of the eavesdropping performance. To this end, a power splitting receiver is proposed, where the signal received at each antenna of the legitimate monitor is split into two parts for information eavesdropping and spoofing relaying, respectively. We formulate an optimization problem to maximize the achievable eavesdropping rate by jointly optimizing the power splitting ratios and relay precoding matrix at the multiantenna monitor. Depending on the suspicious and eavesdropping channel conditions, the optimal solution corresponds to three possible spoofing relay strategies, namely constructive relaying, jamming, and simultaneous jamming and destructive relaying. Numerical results show that the proposed technique significantly improves the eavesdropping rate of the legitimate monitor as compared to the existing passive eavesdropping and jamming-assisted eavesdropping schemes.

Simplified MMSE Precoding Design in Interference Two-Way MIMO Relay Systems

We investigate the transceiver design for interference two-way amplify-and-forward multiple-input multiple-output relay communication systems. A novel algorithm with a closed-form solution is developed to optimize the relay precoding matrix based on its optimal structure and a modified transmission power constraint at the relay node. An iterative algorithm is proposed to minimize the sum mean-squared error of the signal waveform estimation. Simulation results demonstrate that the proposed algorithm achieves a better performance-complexity tradeoff compared with existing techniques.

Transceiver Design for Interference MIMO Relay Systems with Direct Links

In this paper, we consider interference multiple-input multiple-output (MIMO) relay systems where multiple pairs of transmitters–receivers simultaneously communicate through a single relay node and where all nodes are equipped with multiple antennas. We propose a new iterative algorithm to jointly optimize the relay precoding matrix and the receiver matrices of such a system based on the minimum sum mean-squared error (MSE) criterion. The optimal structure of the relay precoding matrix is developed to decrease the computational complexity of transceiver optimization. Simulation results demonstrate that the proposed transceiver optimization algorithm has a better MSE and bit-error-rate (BER) performance and a faster convergence rate than existing works.

MMSE-Based Transceiver Design Algorithms for Interference MIMO Relay Systems

In this paper, we investigate the transceiver design for amplify-and-forward interference multiple-input multiple-output (MIMO) relay communication systems, where multiple transmitter-receiver pairs communicate simultaneously with the aid of a relay node. The aim is to minimize the mean-squared error (MSE) of the signal waveform estimation at the receivers subjecting to transmission power constraints at the transmitters and the relay node. As the transceiver optimization problem is nonconvex with matrix variables, the globally optimal solution is intractable to obtain. To overcome the challenge, we propose an iterative transceiver design algorithm where the transmitter, relay, and receiver matrices are optimized iteratively by exploiting the optimal structure of the relay precoding matrix. To reduce the computational complexity of optimizing the relay precoding matrix, we propose a simplified relay matrix design through modifying the transmission power constraint at the relay node. The modified relay optimization problem has a closed-form solution. Simulation results demonstrate that the proposed algorithms perform better than the existing techniques in terms of both MSE and bit-error-rate.

Tomlinson-Harashima Precoding Based Transceiver Design for MIMO Relay Systems With Channel Covariance Information

In this paper, we investigate the performance of the Tomlinson-Harashima (TH) precoder based nonlinear transceiver design for a nonregenerative multiple-input multiple-output (MIMO) relay system assuming that the full channel state information (CSI) of the source-relay link is known, while only the channel covariance information (CCI) of the relay-destination link is available at the relay node. We first derive the structure of the optimal TH precoding matrix and the source precoding matrix that minimize the mean-squared error (MSE) of the signal waveform estimation at the destination. Then we develop an iterative algorithm to optimize the relay precoding matrix. To reduce the computational complexity of the iterative algorithm, we propose a simplified precoding matrices design scheme. Numerical results show that the proposed precoding matrices design schemes have a better bit-error-rate performance than existing algorithms.

Robust Design for Amplify-and-Forward MIMO Relay Systems With Direct Link and Imperfect Channel Information

In this paper, we propose statistically robust design for multiple-input multiple-output (MIMO) relay systems with the direct source-destination link and imperfect channel state information (CSI). The minimum mean-squared error (MMSE) of the signal waveform estimation at the destination node is adopted as the design criterion. We develop two iterative methods to solve the nonconvex joint source, relay, and receiver optimization problem. In particular, we derive the structure of the optimal relay precoding matrix and show the effect of CSI mismatch on the structure of the optimal robust source and relay matrices. The proposed algorithms generalize the transceiver design of MIMO relay systems with the direct link to the practical scenario of imperfect CSI knowledge. Simulation results demonstrate an improved performance of the proposed algorithms with respect to the conventional methods at various levels of CSI mismatch.

非对称双向中继X网络中基于最大化和速率的干扰对齐与中继处理算法

Two-way relay X networks offer a higher degrees of freedom, in contrast to traditional wireless communication networks. The relay processing based on zero forcing only considers the interference, ignoring the desired signal, so that the sum rate of the network to be improved. Specifically, the lower user transmission power, the greater disadvantages. The interference alignment scheme was researched for asymmetric two-way relaying X networks, moreover the relay beamforming technique based on the desired signal and interference signal was also presented. Firstly, a mathematical model was obtained for the network sum rate by the spatial relationship between user signal vectors. Then, the relay beamforming scheme based on sum rate maximization was transformed into a linear search for the optimal value through the matrix analysis and numerical analysis theory, and the objective function of the network was approximated by the limitation. Furthermore, the objective function was approximated by the linear combinations of parameters of one-way network. Finally, the relay precoder matrix to maximize the sum rate was obtained. Simulation results show that the proposed scheme significantly improved the network rate compared with existing relay processing scheme, while simplifying the complexity of the algorithm.

Transceiver Design for SC-FDE Based MIMO Relay Systems

In this paper, we propose a joint transceiver design for single-carrier frequency-domain equalization (SC-FDE) based multiple-input multiple-output (MIMO) relay systems. To this end, we first derive the optimal minimum mean-squared error linear and decision-feedback frequency-domain equalization filters at the destination along with the corresponding error covariance matrices at the output of the equalizer. Subsequently, we formulate the source and relay precoding matrix design problem as the minimization of a family of Schur-convex and Schur-concave functions of the mean-squared errors at the output of the equalizer under separate power constraints for the source and the relay. By exploiting properties of the error covariance matrix and results from majorization theory, we derive the optimal structures of the source and relay precoding matrices, which allows us to transform the matrix optimization problem into a scalar power optimization problem. Adopting a high signal-to-noise ratio approximation for the objective function, we obtain the global optimal solution for the power allocation variables. We illustrate the excellent performance of the proposed system and compare it to that of conventional orthogonal frequency-division multiplexing MIMO relay systems based on computer simulations.

Joint Source and Relay Precoder Design in Amplify-and-Forward MIMO Relay Systems with Direct Link

This paper investigates the precoder design problem in a two-hop amplify-and-forward multiple-input-multiple-output relay system. Many previous works on this problem are based on the minimum mean-square error criterion and the presence of a direct link between the source and the destination is ignored. In this paper, we propose a new method for joint source and relay precoder design based on maximizing the mutual information between the source and the destination, taking both the relay link and the direct link into account. In contrast to previous works, which consider the transmit power constraints of the source and the relay independently, we assume a total power constraint on the sum transmit power of the source and the relay instead to study also the optimal power distribution over the two nodes. A constrained optimization problem with respect to the unknown source precoder matrix and relay precoder matrix is then formulated, which is nonconvex and very difficult to solve directly. We propose a structural constraint on the precoders by analyzing the structure of the problem and referring to related works. With the proposed precoders' structure and by applying the Hadamard's inequality, the original problem is simplified from a matrix-valued problem to a scalar-valued one. However, the new scalar-valued problem is still nonconvex and we manage to convert it into two subproblems and solve it in an iterative fashion. By using the Karash---Kuhn---Tucker (KKT) conditions, we give out the closed-form solutions to the subprobelms. Simulation results demonstrate that the proposed design method converges rapidly and significantly outperforms the existing methods.

Precoding Design for MIMO Relay Multicasting

In this paper, we consider a two-hop multicasting multiple-input multiple-output (MIMO) relay system where one transmitter multicasts common message to multiple receivers with the aid of a relay node, and all nodes are equipped with multiple antennas. Joint transmit and relay precoding design problems are investigated for multicasting multiple data streams based on two design criteria. In the first scheme, we aim at minimizing the maximal mean-squared error (MSE) of the signal waveform estimation among all receivers subjecting to power constraints at the transmitter and the relay node. This problem is highly nonconvex with matrix variables and the exactly optimal solution is very hard to obtain. We develop an iterative algorithm to jointly optimize the transmitter, relay, and receiver matrices through solving convex subproblems. By exploiting the optimal structure of the relay precoding matrix, we then propose a low complexity solution which decouples the optimization of the transmitter and relay matrices under the (moderately) high first-hop signal-to-noise ratio (SNR) assumption. In the second scheme, we propose a total transmission power minimization strategy subjecting to quality-of-service (QoS) constraints. By using the optimal structure of the relay precoding matrix and the (moderately) high first-hop SNR assumption, we show that this problem can be solved using the semidefinite programming (SDP) technique. Numerical simulations demonstrate the effectiveness of the proposed algorithms. Interestingly, we show that for the special case of single data stream multicasting, the relay precoding matrix optimization problem can be equivalently converted to the transmit beamforming problem for single-hop multicasting systems.

Joint source and relay design for two-hop amplify-and-forward relay networks with QoS constraints

Abstract In this paper, we consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meet pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using majorization theory, we simplify the matrix-valued optimization problem into a scalar-valued one. We then propose a lower bound and an upper bound of the original problem, both in convex forms. Specifically, the latter is solved by a multi-level water-filling algorithm that is much efficient than directly applying the interior point method. Numerical examples corroborate the proposed studies and also demonstrate the tightness of both bounds to the original problem.

다중 안테나 다중 중계 시스템을 위한 가중치 대각화 기반의 저 복잡도 전력 할당 기법

본 논문에서는 증폭 후 재전송 프로토콜 기반의 다중 안테나 다중 중계 시스템에서 저 복잡도의 전력 할당 기법을 제안한다. 기존의 다중 안테나 전처리 기법이 복소수로 구성 된 꽉 찬 행렬을 전처리 필터로 사용하였다면, 제안 하는 기법은 각 중계 노드에서 안테나 별 전력으로 구성 된 실수 대각 행렬을 전처리 필터로 사용한다고 볼 수 있다. 추가적으로 복소수 꽉 찬 행렬로 유효 채널을 대각화 하지 못함에서 발생하는 오차를 감소시키기 위해 가중치 벡터를 각 스트림에 적용시켜 안테나 수와 상관없이 낮은 복잡도로 최적 성능에 근접한 성능을 얻을 수 있다. 마지막으로 모의실험을 통해 제안하는 기법이 상호정보량 측면에서 기존의 기법들보다 우수함을 보인다.