Source Precoding Research Articles

Antijamming Schemes for the Generalized MIMO Y Channel.

Signal space alignment (SSA) is a promising technique for interference management in wireless networks. However, despite the excellent work done on SSA, its robustness against jamming attacks has not been considered in the literature. In this paper, we propose two antijamming strategies for the SSA scheme applied in the multiple-input-multiple-output (MIMO) Y channel. The first scheme involves projecting the jamming signal into the null space of each source's precoding vectors, effectively eliminating it entirely. The second scheme removes interference originating from the jammer by subtracting the disturbance estimate from the incoming signal. The estimate is derived on the basis of the criterion of minimizing the received signal energy. The block error rate (BLER) performance of the proposed strategies in various channel configurations is verified by link level simulations and is presented to show the efficiency in mitigating jamming signals within the SSA-based MIMO Y channel.

Nonlinear Transceiver Design for Full-Duplex MIMO Relaying with Direct Link

This paper investigates the joint transceiver design for full-duplex (FD) multiple-input multiple-output relay systems where the direct link (DL) and nonlinear successive-interference-cancellation (SIC) detection are considered. The objective is to jointly optimize the source precoder, relay precoder, and receiver such that the resultant symbol-vector error rate (SVER) is minimized. The joint design is challenging since the coexistence of DL and FD relaying will introduce the inter symbol-vector interference. To address this problem, we first propose a novel QR-SIC receiver structure by performing the dual-filtering (DuF) and channel stacking before SIC. Then, the source and relay precoders are optimized for the proposed DuF-based QR-SIC receiver. Compared with the source precoder, optimizing the relay precoder is much more involved due to the complicated objective function. Hence, we transform the original optimization problem into a trace-minimization one, enabling a closed-form solution for the relay precoder. Furthermore, we theoretically show that the proposed design framework can be extended to the system with the DuF-based minimum mean-squared-error SIC receiver. Simulations show that our transceivers are indeed able to significantly improve the overall SVER performance.

Two-Way AF MIMO Multi-Relay System Design Using MMSE-DFE Techniques

Targeting at a better design of the analogue network coding (ANC)-assisted two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) multi-relay communication systems, we bring in the nonlinear minimal mean-squared error (MMSE)-decision feedback equalization (DFE) receiving technique to jointly optimize the source precoding, relay amplifying, feed-forward and feedback matrices. Under the transmission power constraints at both source nodes and each relay node, the two-way sum mean-squared error (MSE) of the signal waveform estimation of all data streams is minimized. To solve the complicated nonconvex optimization problem with four groups of system parameters, this paper develops an iterative block coordinate descent (BCD) algorithm, which converges to at least a Nash point. On the basis of it, for mitigating the error propagation in MMSE-DFE receivers, a group of permutation matrix variables, determining the detection orders of all data streams, are further introduced in our system optimization. Moreover, in case there is no sufficiently precise channel state information (CSI), we also make an extension of the developed algorithms, yielding a robust design scheme, to handle the channel uncertainties. Numerical simulation results show that, compared with the existing linear MMSE receiving-based algorithm, our proposed nonlinear ones provide improved MSE and bit-error-rate (BER) performance as well as good robustness against the imperfect CSI, indicating a promising application prospect of this research.

Finite-Order Source and Relay Filtering Design for Wideband Full-Duplex Amplify-and-Forward Relaying Networks

Compared with half-duplex relaying, the full-duplex relay (FDR) system provides higher spectral efficiency due to the concurrent transmission and reception at the relay node. As known, the full-duplex operation will introduce the self-interference (SI) that significantly degrades the system performance. Conventionally, SI is treated as a harmful signal that needs to be removed from the system as completely as possible. The conventional design concept, however, may not be efficient since SI is in fact a delayed version of the desired signal. Specifically, it is possible to have further performance improvement if SI can be exploited appropriately. In this paper, we will investigate the source/relay filter design problem where the source and relay are considered as finite impulse response (FIR) and infinite impulse response (IIR) filters, respectively. The design goal is to optimize the end-to-end performance for the linear minimum mean-square error (MMSE) and nonlinear MMSE decision-feedback equalizers. To reduce the implementation cost, we further propose a finite-order filter design for the source and relay precoders. Simulations demonstrate that our designs outperform the conventional ones.

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.

Sum Rate Optimization for Two Way Communications With Intelligent Reflecting Surface

In this letter, an intelligent reflecting surface (IRS) enhanced full-duplex MIMO two-way communication system is studied. The system sum rate is maximized through jointly optimizing the source precoders and the IRS phase shift matrix. Adopting the idea of Arimoto-Blahut algorithm, the non-convex optimization problem is decoupled into three sub-problems, which are solved alternatingly. All the sub-problems can be solved efficiently with closed-form solutions. In addition, practical IRS assumptions, e.g., discrete phase shift levels, are also considered. Numerical results verify the convergence and performance of the proposed scheme.

Beamforming Optimization for Intelligent Reflecting Surface Assisted MIMO: A Sum-Path-Gain Maximization Approach

Recently, intelligent reflecting surface (IRS) has emerged as an appealing technique that enables wireless communications with low hardware cost and low power consumption. In this letter, we consider an IRS-assisted point-to-point multi-input multi-output (MIMO) system, where a source communicates with its destination with the help of an IRS. Our goal is to maximize the spectral efficiency of this system by jointly optimizing the (active) precoding at the source and the (passive) phase shifters (PSs) at the IRS. However, this turns out to be an intractable mixed integer non-convex optimization problem. To circumvent the intractability, we propose a new sum-path-gain maximization (SPGM) criterion to obtain a high-quality and efficient suboptimal solution to this problem. Specifically, the PSs are first designed based on a simplified optimization problem, which aims to maximize the sum-gains of the spatial paths between the source and the destination. Then, a low-complexity alternating direction method of multipliers (ADMM) algorithm is utilized to solve this simplified problem. Finally, with the above obtained PSs, the source precoding is derived by performing the singular value decomposition (SVD) on the effective channel between the source and the destination. Numerical results demonstrate that the proposed scheme can achieve near-optimal performance.

Design of Cooperative MIMO Wireless Sensor Networks With Partial Channel State Information

Wireless sensor networks (WSNs) play a key role in automation and consumer electronics applications. This paper deals with joint design of the source precoder, relaying matrices, and destination equalizer in a multiple-relay amplify-and-forward (AF) cooperative multiple-input multiple-output (MIMO) WSN, when partial channel-state information (CSI) is available in the network. In particular, the considered approach assumes knowledge of instantaneous CSI of the first-hop channels and statistical CSI of the second-hop channels. In such a scenario, compared to the case when instantaneous CSI of both the first- and second-hop channels is exploited, existing network designs exhibit a significant performance degradation. Relying on a relaxed minimum-mean-square-error (MMSE) criterion, we show that strategies based on potential activation of all antennas belonging to all relays lead to mathematically intractable optimization problems. Therefore, we develop a new joint relay-and-antenna selection procedure, which determines the best subset of the available antennas possibly belonging to different relays. Monte Carlo simulations show that, compared to conventional relay selection strategies, the proposed design offers a significant performance gain, outperforming also other recently proposed relay/antenna selection schemes.

Design and performance analysis of multiple-relay cooperative MIMO networks

In this paper, we propose a closed-form (i.e., without the need of any iterative procedure) joint optimization framework of the source precoder, the amplify-and-forward relaying matrices, and the destination equalizer for a cooperative multiple-input multiple-output (MIMO) wireless network. We study in depth such a design and carry out its performance analysis in terms of average symbol error probability (ASEP), which allows one to calculate the diversity order of the cooperative system. The ASEP is also evaluated via Monte Carlo simulations and compared with recent competitive alternatives. Results show that the proposed design performs better than or comparably to recently proposed iterative approaches, with lower computational requirements.

Multiuser Multi-Hop AF MIMO Relay System Design Based on MMSE-DFE Receiver

To achieve a better long source-destination distance communication in uplink multiaccess scenarios, we propose a multiuser multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay technique with nonlinear minimal mean-squared error (MMSE)-decision feedback equalization (DFE) receiver. Under transmission power constraints, this paper focuses on the improvement of reliability, meanwhile, which doesn't lose the effectiveness or require higher complexity. We demonstrate that the optimal structures of relay amplifying matrices lead to a cascading construction for the mean-squared error (MSE) matrices of respective signal waveform estimations at the destination and each relay node. Hence, in (moderately) high signal-to-noise ratio (SNR) environment, the intractable nonconvex optimization problem can be decomposed into easier subproblems for separate optimizations of source precoding and relay amplifying matrices. The source precoding matrix, along with the decision feedback matrix, is obtained by an iterative process, which can converge to a Nash point within the reasonable time. As for the relay amplifying matrices, closed-form water-filling solutions are derived. The simulation and analysis results show that compared to other existing algorithms, which also utilize decomposition methods to simplify operations, the proposed algorithms have better MSE and bit-error-rate (BER) performance without increasing the computing time or signaling overhead, thus providing a new step forward in MIMO relay system design.

Precoding Design for Correlated MIMO-AF Relay Networks With Statistical Channel State Information

An iterative precoding design of a two-hop amplify-and-forward (AF) multiple-input multiple-output relay network with one source, multiple relays, and one destination is presented. To provide a solution for general scenarios, the source-to-destination direct link and double correlated Kronecker Rician fading channels are considered. Statistical channel state information is used for the average capacity formulation for the sake of its robustness and infrequent update. The source and relay precoders are optimized to maximize a closed-form upper bound of the average capacity giving a suboptimal design. The non-convex design problem is divided into three sub-problems: source precoder, relay beamforming, and relay power allocation (PA). For optimizing the source precoder subject to multiple power constraints, rather than using computationally expensive penalty type algorithms, an efficient design procedure as a type of water-filling with multiple water levels is developed. Its negative PA is handled by a simple method of determining the eigen-modes of positive power. Using the Riemannian steepest descent method and a newly proposed power adaptation to optimize the relay beamforming and relay PA, respectively, the constrained optimization problems become unconstrained. Simulations show that the developed design procedure with trivial initialization provides nearly global optimum performance with fast convergence and efficient computation. The developed methods for the source precoder and relay PA outperform upon the augmented Lagrangian method with respect to convergence and computing time. Furthermore, the generality of the proposed scheme makes the design procedure applicable to AF relay networks with different simplified Kronecker channel models and with/without the direct link.

Successive relaying for large MIMO amplify‐and‐forward relay networks

SummaryIn this paper, we consider a large relay network with one source, K relays and M users, where the source and relays are equipped with W and N antennas, respectively. We propose an amplify‐and‐forward successive relaying protocol in which the relays are divided into 2 groups to successively help transmission to M users. Achievable sum rate of the proposed protocol is derived and found to scale as when N and M are fixed and K→∞ . On the other hand, when M and K are fixed and N→∞, the achievable sum rate scales as . Therefore, the scaling law of the achievable sum rate coincides with the capacity scaling law of the considered network. Then, both precoding at the source and grouping of the relay nodes are jointly optimized to further improve the proposed protocol. Numerical results show that the proposed successive relaying protocol can outperform the conventional 2‐slot relaying protocol and the proposed joint optimization scheme for source precoding and relay grouping bring considerable rate gain.

Nonlinear Transceiver Designs for Full-Duplex MIMO Relay Systems

This paper investigates nonlinear transceiver design for full-duplex multiple-input multiple-output (FD-MIMO) relay systems. A dual-hop amplify-and-forward relaying protocol is considered. At the destination, nonlinear successive-interference-cancellation (SIC) is used for signal detection. The goal is to find the source and relay precoders such that the symbol-vector error rate (SVER) can be minimized. Due to the loop interference (LI), optimizing the relay precoder in FD systems is much more involved. In this paper, we propose novel designs to solve this problem. Starting from the QR-SIC receiver, we theoretically show that the relay precoder can be solved with a closed-form expression even when the system incurs LI. Then, we consider the system with a minimum mean-squared-error SIC receiver, where the relay precoder design entails a different problem formulation and introduces new challenges. We propose a novel iterative method, with closed-form solutions in each iteration, to solve this problem. Simulations show that our designs can significantly improve the SVER performance for FD-MIMO relay systems.

Joint MMSE Transceiver Designs for MIMO AF Relaying Systems With Direct Link

In this paper, we provide minimum mean-squared error-based source-relay-destination transceiver designs for multiple-input multiple-output amplify-and-forward relaying systems, where direct link between the source and the destination is non-negligible. In an earlier work, a local optimal technique was introduced which employs a projected gradient method and an interior point method. Since these methods may have quite high computational complexity, we investigate a new local optimal solution for the source-relay-destination transceiver which has low complexity. To this end, we first introduce the optimal closed-form solution for the relay transceiver for given source and destination filters. Then, for given relay and destination transceivers, the optimal source precoder design is derived, which requires only 1-D bisection search. Based on these solutions, we propose a joint optimization algorithm which iteratively finds a local optimal solution. Also, we introduce a simple non-iterative algorithm which computes filters in closed-forms with low complexity. Furthermore, since perfect channel knowledge may not be feasible in practical systems, a joint transceiver technique which is robust to channel uncertainties is provided. It is confirmed by simulation results that the proposed schemes outperform conventional techniques with significantly reduced complexity.

Non‐linear transceiver design for secure communications with artificial noise‐assisted MIMO relay

This study investigates the problem of physical layer security for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems operating in the presence of a passive eavesdropper. Specifically, the authors consider the robust design of an artificial noise (AN)-assisted non-linear transceiver employing Tomlinson–Harashima precoding (THP), with imperfect knowledge of the legitimate channel states. The design problem can be reformulated as a two-level optimisation, where the outer problem aims to optimise the source precoder as a function of the relay precoder, while the inner problem at the relay aims to jointly optimise the relay precoder as well as the power allocation between the AN and the information-bearing signals. To solve the inner problem, the authors adopt a bisection method which attempts to maximise the AN power level, to confuse the eavesdropper, while satisfying the mean-squared-error requirement for the intended user. Some relaxation for the objective function is applied to transform the problem into a standard convex optimisation one. Regarding the outer problem, closed-form solutions for the precoders can be derived by an iterative method based on the Karush–Kuhn–Tucker conditions. Simulation results illustrate the superior secrecy performance provided by the proposed non-linear transceiver design with AN and THP.

Joint source and relay precoding for generally correlated MIMO with full and partial CSIT

In this paper, we jointly design linear source and relay precoders for two-hop MIMO relaying. The involved channels encounter spatially correlated fading, the source data symbols are mutually correlated, and the noises are colored not only at the destination but also at the relay. Two different scenarios of channel state information (CSI) are assumed to be available at the transmitters: full CSI of both hops (the full CSIT) and full CSI of the source-relay hop only plus the covariance information of the relay-destination hop (the partial CSIT). First, with the full CSIT, we derive optimal precoders by maximizing the instantaneous mutual information (MI). Secondly, with the partial CSIT knowledge we derive suboptimal precoders by maximizing the average MI. For both the CSIT cases, we propose an iterative algorithm to perform power allocation iteratively and alternatively between the source antennas and the relay antennas. Its simplified version in which the power allocation is performed separately between the source antennas and the relay antennas is also developed. Simulation results show that our proposed precoding schemes with the full CSIT provide significantly higher capacity than the existing schemes. Besides, the proposed schemes with the partial CSIT also perform well especially when the channels are spatially correlated at the transmit sides and at medium-to-high signal-to-noise ratios (SNRs), while they require much lower computational complexity and less feedback overhead.

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.

Relaying Strategies for Wireless-Powered MIMO Relay Networks

This paper investigates relaying schemes in an amplify-and-forward multiple-input multiple-output relay network, where an energy-constrained relay harvests wireless power from the source information flow and can be further aided by an energy flow (EF) in the form of a wireless power transfer at the destination. However, the joint optimization of the relay matrix and the source precoder for the energy-flow-assisted (EFA) and the non-EFA (NEFA) schemes is intractable. The original rate maximization problem is transformed into an equivalent weighted mean square error minimization problem and optimized iteratively, where the global optimum of the nonconvex source precoder subproblem is achieved by semidefinite relaxation and rank reduction. The iterative algorithm finally converges. Then, the simplified EFA and NEFA schemes are proposed based on channel diagonalization, such that the matrices optimizations can be simplified to power optimizations. Closed-form solutions can be achieved. Simulation results reveal that the EFA schemes can outperform the NEFA schemes. Additionally, deploying more antennas at the relay increases the dimension of the signal space at the relay. Exploiting the additional dimension, the EF leakage in the information detecting block can be nearly separated from the information signal, such that the EF leakage can be amplified with a small coefficient.

Joint Relay/Antenna Selection and Precoding Design for Two-Way MIMO Amplify-and-Forward Relaying Systems

In this paper, a unified framework of relay/antenna subset selection and transceiver design is proposed for a dual-hop two-way amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relaying system in correlated fading channels. By making use of the singular value decomposition (SVD) technique, the joint design of two-source transceivers and multirelay precoders is developed based on the minimum-mean-square-error (MMSE) criterion. This MMSE-based optimization leads to a highly nonlinear objective function of sources and relaying precoders under power constraints so that an iterative search algorithm is applied to explore the optimal power allocation. Simulation results show that the SVD-based joint design of relay and source precoders, in conjunction with the SVD-based relay-and-antenna selection scheme, is capable of achieving superior performance in terms of bit error rate (BER) with an alleviated demand on relays and associated antenna pairs.