Deploying an amplify-and-forward (AF) relay and a reconfigurable intelligent surface (RIS) can significantly enhance the quality of received signals in wireless communication systems. However, most existing studies focus on beamforming design at the relay and phase-shift design at the RIS under fixed device locations, neglecting the substantial impact of geometric placement on communication performance. Moreover, in practical systems, the phase gain of RIS elements varies with the applied phase shift. This paper considers the physical characteristics of practical RIS phase shifters and jointly optimizes the deployment of the relay and RIS under geometric and power constraints to maximize the signal-to-interference-plus-noise ratio (SNR) at the receiver. The associated optimization problem is highly nonlinear and non-convex, making it difficult to obtain satisfactory suboptimal solutions using traditional convex approximation techniques. To address this challenge, we propose two numerical approaches, deep deterministic policy gradient (DDPG) and particle swarm optimization (PSO), to approximate the optimal solution. Simulation results verify that the proposed approaches can effectively achieve near-optimal performance, as benchmarked by exhaustive grid search. Furthermore, the optimal deployment places both the relay and the RIS closer to the transmitter, outperforming the conventional midpoint deployment strategy.

Integrating large-scale antenna arrays is essential for overcoming capacity limitations in wireless communications. In this work, we examine a novel sixth-generation (6G) secure simultaneous wireless information and power transfer (SWIPT) system, where a transmitter equipped with an extremely large-scale antenna array (ELAA) operates in the near-field region. In our design, the transmitter concurrently delivers confidential data to information receivers and energy to zero-energy devices (ZEDs) via non-orthogonal multiple access (NOMA). A key innovation of our approach is the specialized near-field beamfocusing technique derived from a three-dimensional spherical channel model, which explicitly accounts for the unique propagation characteristics of near-field communications and distinguishes our method from traditional far-field designs. We formulate a non-convex optimization problem aimed at maximizing the secrecy rate while satisfying minimum quality-of-service and energy harvesting requirements. To solve this problem, we develop an iterative algorithm based on weighted sum-rate maximization and sequential convex approximations that effectively mitigate interference and enhance beamfocusing performance. Numerical simulations demonstrate that, with a 64-element uniform linear array and 40 dBm transmit power, our near-field NOMA system achieves an 18.41% higher secrecy rate than near-field spatial division multiple access (SDMA) and a 36.78-fold improvement over near-field orthogonal multiple access (OMA), along with a 6.39 dBm increase in harvested power relative to SDMA. These results underscore the critical role of specialized near-field design in next-generation 6G networks and its significant implications for industrial internet-of-things (IoT) and Industry 4.0 applications.

Pinching-antenna systems (PASS) route energy through low-loss dielectric waveguides and radiate via reconfigurable pinching antennas (PAs), enabling large, shapeable apertures with minimal radio chains. We study a near-field multicast downlink network that extends single-waveguide PASS to a coordinated multi-waveguide array and jointly optimizes PA positions and beams. We first develop a cascaded channel that couples in-waveguide and free-space propagation, and pose a worst-case multicast objective under spacing, coupling span, and power constraints. A two-stage co-design then follows. Stage I performs layout planning as a constrained bi-objective placement that maximizes the worst-user signal-to-noise ratio (SNR) while minimizing a wrapped-phase residual; when solved with the non-dominated sorting genetic algorithm (NSGA) II, it yields feasible Pareto layouts. Stage II fixes a knee layout obtained from Stage I and refines the multicast beam via a convex semi-definite relaxation (SDR)-successive convex approximation (SCA) formulation with a feasibility warm start, thereby recovering rank-one beams. Numerical results reveal that over wide ranges of transmit power, coupling span, PA per waveguide, number of waveguides, user count, user range, and base-station height, the proposed design outperforms a single-waveguide PASS and$\boldsymbol {x}$or$\boldsymbol {y}$-aligned uniform linear arrays, delivering higher worst-user rates as well as sharply lowering the per-user rate variance. The study also identifies broad coupling-length ranges where gains saturate and shows that a moderate number of pinches and additional waveguides help improve spatial coverage until a geometry-limited plateau is reached. These effects arise from in-waveguide proximity and lateral phase control, positioning multi-waveguide PASS as a practical, flexible antenna option for next-generation communication.

In this article, we investigate the performance of a holographic active reconfigurable intelligent surface (HARIS)-aided near-field (NF) uplink non-orthogonal multiple access (NOMA) secure communication system with an imperfect channel state information (iCSI) in the presence of an eavesdropper (Eve). In order to provide efficient resource utilization, a sum secrecy rate (SSR) maximization problem is formulated, where the combining vector at base station (BS), power allocation at each uplink user, and the HARIS phase profile are jointly optimized under the strict constraints of quality of service (QoS) requirement and limited power budget at each uplink user and HARIS considering norm-bounded CSI uncertainty. In order to tackle the non-convex nature of the formulated problem, we propose an alternating optimization (AO)-based algorithm that adopts an iterative approach and uses optimization techniques such as semidefinite programming (SDP), convex upper bound approximation, and semidefinite relaxation (SDR) to optimize all three design variables simultaneously. Then, extensive simulations are performed to validate the efficacy and convergence of the proposed algorithm. Furthermore, we also demonstrate the impact of key system parameters, such as HARIS elements, minimum QoS corresponding to each user, the total power budget at uplink users, and maximum amplification factor at the HARIS. It is shown that the use of NOMA can achieve up to 45% higher performance compared to SDMA, OMA, and TDMA. It is also highlighted that, under the proposed algorithm with NF assumptions, the achieved average SSR is around 65% higher compared to the hybrid and far-field (FF) assumptions.

This work investigates the performance of rate splitting multiple access (RSMA) in a holographic reconfigurable intelligent surface (HRIS)-aided near-field (NF) driven downlink secure communication system under imperfect channel state information (iCSI) in the presence of an eavesdropper (Eve). We formulate a weighted sum secrecy rate (WSSR) while ensuring a minimum quality of service (QoS) at each node under the available resource constraints, such as the total power budget at the base station (BS). Since the optimization problem is nonconvex due to the coupling of the variables, we propose an iterative algorithm based on alternating optimization (AO) that jointly optimizes transmit beamforming at BS and phase shift at HRIS. Numerical results are shown to validate the effectiveness and convergence of the proposed algorithm. Furthermore, we also discuss the impact of the key system parameters, such as HRIS reflecting elements, minimum QoS constraint, transmit power budget, and number of users. The dominance of RSMA over conventional multiple-access technologies such as non-orthogonal multiple access (NOMA) and space division multiple access (SDMA) is also demonstrated.

This article proposes a holographic active reconfigurable intelligent surface (HARIS)-aided near-field (NF)-driven uplink non-orthogonal multiple access (NOMA) secure communication system under imperfect channel state information (iCSI) in the presence of an eavesdropper (Eve). To ensure efficient resource utilization, a sum secrecy rate (SSR) maximization problem is formulated by jointly optimizing the combined vector at the base station (BS), the power allocation for each uplink user, and the HARIS phase profile under strict quality of service (QoS) requirements and limited power budgets at both the uplink users and HARIS. Due to the non-convex nature of the problem, an alternating optimization (AO)-based algorithm is proposed, which uses semidefinite programming (SDP), convex upper bound approximation, and semidefinite relaxation (SDR) techniques to optimize all variables iteratively. Extensive simulations validate the performance and convergence of the proposed algorithm. In addition, the effects of system parameters, such as the number of HARIS elements, minimum QoS per user, maximum BS receive power, and the HARIS amplification factor, are investigated.

This article investigates a near-field secure simultaneous wireless information and power transfer (SWIPT) network employing a non-orthogonal multiple access (NOMA) scheme. In this network, a base station equipped with an extremely largescale array antenna (ELAA) communicates with and transfers power to multiple single-antenna zero-energy devices (ZEDs) within the near-field region, while an eavesdropper attempts to wiretap the communication by intercepting the information signals. Specifically, we aim to maximize the overall secrecy sum rate of the ZEDs while ensuring a minimum energy harvesting criterion at the ZEDs. Consequently, a non-convex resource optimization problem is formulated and solved using an iterative approach, leveraging weighted sum-rate maximization via minorization-maximization (WSR-MM) with second-order cone programming (SOCP) transformation and general convex approximations. Finally, numerical results are presented to demonstrate the performance of the proposed near-field secure SWIPT system under varying network parameters.

Deep reinforcement learning (DRL) has recently found comprehensive application in communication systems to address complex resource allocation problems. However, conventional DRL algorithms suffer from slow convergence, severely limiting their utility in dynamic communication environments. In this paper, we present a novel approach, namely hybrid model-based and data-driven DRL (HM-DRL) optimization, to tackle these challenges. In the HM-DRL, the original problem is split into inner and outer optimization tasks. The inner optimization is accomplished using low-complexity model-based methods, while the outer optimization employs DRL techniques. The HM-DRL scheme reduces the number of optimized parameters in outer optimization, thereby improving convergence. As a case study, we apply HM-DRL to optimize reflector configurations in a reconfigurable intelligent surface (RIS)-assisted orthogonal frequency division multiplexing (OFDM) system. By jointly optimizing the activation of antennas and associated reflectors at the RIS, our HM-DRL approach significantly accelerates learning speed, facilitating the discovery of near-optimal solutions.

Reconfigurable Intelligent Surface (RIS) devices inherently lack A/D and D/A converters and power amplifiers, resulting in limited signal processing capability and effective radiation range. The design of RIS reflectors typically requires channel state information (CSI). Conventional RIS designs for far-field transmission simplify the process by considering only the direction of radiation. However, in near-field RIS-assisted mmWave transmissions, the near-field effect necessitates consideration of both the direction of propagation and the distance between the transmitter and receiver in the near-field model. Consequently, complete CSI is essential for accurately configuring reflectors for near-field propagation. However, acquiring complete CSI is impractical, especially in mmWave RIS-assisted massive MIMO systems. In this paper, we propose a method for jointly optimizing beamforming and RIS reflectors in RIS-assisted multiple-input single-output (MISO) systems using Deep Deterministic Policy Gradient (DDPG) reinforcement learning (RL) with and without CSI. When near-field CSI is unavailable, the proposed design directly configures the reflectors by leveraging the received signal power corresponding to pilot signals. Alternatively, with near-field CSI, the proposed joint design can explore a more feasible solution set through the DDPG framework, achieving superior performance. Simulation results provide valuable insights into beamforming and RIS design in near-field channels, demonstrating that the proposed methods outperform existing approaches. Furthermore, the proposed beamforming and RIS design without CSI eliminates the need for explicit channel estimation, significantly enhancing its practicality for real-world system applications.

The estimation of channel state information (CSI) is a well-known challenge in reconfigurable intelligent surface (RIS)-assisted communication systems due to the limited signal processing capabilities of the RIS node. Conventional methods often resort to employing a substantial number of pilot sequences to obtain the necessary degrees of freedom, leading to a significant reduction in the data transmission rate. In this study, we present deep learning-based channel estimator designed for scenarios with limited pilots in an RIS-assisted single-input-multiple-output (SIMO) orthogonal frequency division multiplexing (OFDM) system. Specifically, we introduce an untrained deep neural network (DNN) based on the deep image prior (DIP) network. This DIP-based DNN is employed to denoise the estimated channel using orthogonal matching pursuit (OMP), ultimately achieving a more accurate channel estimation. Numerical results from our experiments demonstrate that the proposed untrained DIP-based DNN estimator offers significant improvements in accuracy when compared to both conventional OMP-based approaches and training-based DNN estimators.

Recently, the full-duplex multiple-input multiple-output relay (FD-MIMO-R) has been widely considered a promising way to increase the spectrum efficiency of a cooperative communication network. Under frequency-selective fading channels, an FD-MIMO-R system simultaneously exhibits the self-interference (SI) and inter-symbol interference (ISI). Most existing transceiver designs aim to cancel or mitigate these two interferences by treating them as harmful signals. However, SI and ISI are inherently generated from the desired signal, which implies that further performance improvement is possible if they can be properly exploited. This concept motivates us to propose novel finite-order space-time source and relay filters so that the end-to-end mean-square error can be minimized. Our design is based on the following two phases. First we derive the optimum spectrums of the source and relay filters with a majorization theory and alternating optimization. The finite-order filters are then developed by applying the weighted least-square criterion. Numerical experiments show that our proposed filters are indeed able to significantly improve the system performance in either flat or frequency-selective fading channels.

In this paper, novel finite-order filter designs for source and multiple full-duplex relays (FDRs) are proposed to improve the spectrum efficiency and link reliability of amplify-and-forward cooperative communication networks. In contrast to the single relay, FDRs suffer not only self-interference (SI), but inter-relay interference (IRI). By taking SI and IRI into consideration, this work aims at the joint design of the source filter, relay filters, and the linear minimum squared error (LMMSE) receiver. The finite-order filters are conducted in two stages. In the first stage, the spectrums of the source and FDRs are computed. Since the optimization problem involves the nonlinear equality constraint, we adopt the generic nonlinear equality alternating direction method of multipliers (neADMM) with a damping procedure to find the stationary solution. In the second stage, the filter coefficients are developed to approach the derived spectrums by using a weighted least square criterion. The numerical results justify the validity of the proposed designs. Interestingly, the results show that preserving a certain amount of SI at the FDRs not only reduces the implementation cost but improves the end-to-end signal-to-interference-plus-noise ratio (SINR).

This paper studies the joint common beamforming (CB) and the superposition coding (SC) design for a two-user massive multiple-input single-output (MISO) system with non-orthogonal multiple access (NOMA). Conventional beamforming design has to estimate the uplink channel state information (CSI) of the near and the far users separately. By the channel reciprocity, the CB is then constructed by combining two uplink CSIs together with certain rules. The design needs two training phases to separately estimate the CSI of the two users but combine them subsequently. In this paper, we propose a model adopting common pilots for the near and far users to estimate an uplink combined channel. In this model, only one training phase is required, and the CB is then constructed by the estimated combined channel directly. With the estimated combined channel, the joint CB and SC design is equivalent to optimizing the pilot power allocation and SC factor. However, the associated optimization is not convex. We then adopt the majorization-minimization approach to conduct the optimization problem and numerically find that the solutions meet the optimum points. Simulations verify the effectiveness of our joint design and show the superior performance not only for the transmission rate but also the reduced overhead.

This paper considers the finite-order filter design problem for the source and multiple full-duplex (FD) relays in a cooperative communication system under frequency-selective fading channels. The goal is to optimize the source and relay filters such that the end-to-end signal-to-interference-plus-noise ratio (SINR) of minimum mean-squared error decision-feedback equalizer (MMSE-DFE) can be maximized. The resultant design problem is very difficult since we need to deal with self interference (SI), inter-relay interference (IRI), and inter-symbol interference (ISI) at the same time. Novel designs are then proposed to overcome the difficulty in this work. Transforming the signals into the frequency domain and using some optimization techniques, we first theoretically derive the power spectrum of the source filter and the spectrums of the relay filters. Then, the finite-order design is developed to approach the derived spectrums. Based on the weighted least-square (WLS) criterion, the Steiglitz-McBride method is exploited to obtain the filter coefficients in finite lengths. Numerical results demonstrated that complete removal of SI may not be a good strategy; preserving a certain amount of SI at each relay instead provides better SINR performance.

To boost the spectral efficiency of cooperative communication systems, full duplex relays (FDRs) have been widely considered due to the concurrent signal transmission and reception at the relay. However, the self-interference (SI) is always a main problem that deteriorates the system performance. Most conventional FDR designs focus on narrowband transmission and treat SI as a harmful signal, consequently aiming to cancel SI as clear as possible. However, the relay transceiver can be inherently modeled as an infinite impulse response (IIR) filter by recognizing SI as a delayed desired signal. Based on this concept, we propose a novel design where the finite-length source, FDR filters, and the linear minimum mean-squared error (MMSE) equalizer are jointly optimized for frequency-selective fading channels. Simulations demonstrate the effectiveness of our design that preserving partial SI indeed enables further performance improvement.

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.

In this paper, we investigate the robust beamforming design for simultaneous wireless information and power transfer (SWIPT)-enabled hierarchical cognitive radio (HCR) where the primary receiver (PR) is allowed to harvest energy when the secondary system (SS) radiates its information to the secondary receiver (SR). The design objective is to maximize the transmission rate of SS provided that the harvested energy and outage probability of the primary system (PS) are guaranteed. The optimization problem, however, is not convex due to the probability-based constraints introduced by the imperfect channel state information (CSI). To obtain the tractable solution, we apply the Bernstein-type inequality and sphere bounding so that the problem can be approximated by convex formulations. Then, the resultant problems can be efficiently solved with CVX tools. Simulation results demonstrate that the designs can effectively improve the system performance under imperfect CSI environments.

In this paper, the outage performance is studied for a full-duplex (FD) relay network that adopts an amplify-and-forward (AF) scheme. The residual self- interference (RSI) generated by a relay node is treated as a useful signal, rather than noise as in the existing works, at a destination node. We provide a new approximate closed-form expression for the outage probability with the knowledge of the instantaneous source-relay (SR) channel gain, and an optimal power allocation (OPA) scheme to further improve the performance by minimizing the derived outage probability in hand. The analytical results are validated through numerical simulations, which reveals that the proposed FD scheme can outperform the conventional half-duplex (HD) and FD schemes in the AF relay networks.

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.

Full-duplex (FD) relaying has been considered an effective scheme to increase the spectral efficiency of multiple- input multiple-output (MIMO) relay systems. As well-known, the main concern for the FD system is the cancellation of loop interference (LI). In this paper, we consider the joint source/relay precoding to mitigate the LI problem in FD-MIMO relay systems. In our system, spatial multiplexing is exploited for the signal transmission, and the QR successive-interference-cancellation (SIC) receiver is adopted at the destination. Linear precoders are considered at the source and relay, and the block error rate is used as the criterion for the precoders design. To facilitate the optimization, we propose using the primal decomposition, translating the original problem into a subproblem and a master problem. In the subproblem, the source precoder is first solved with the geometric mean decomposition (GMD) method. Then, the master problem can be formulated as a convex optimization so that the relay precoder can be solved with Karush-Kuhn-Tucker (KKT) conditions. The proposed precoders have closed-form expressions, facilitating real- world implementation. Simulation results show that the proposed method significantly improves the performance of FD-MIMO relay systems.

A bit-adaptive precoding matrix index (PMI) feedback mechanism is proposed in Long Term Evolution-Advanced (LTE-A). In Coordinated Multipoint Transmission (CoMP) scenarios, the number of feedback PMI bits for all channel state information (CSI) processes at the same time may be larger than that the current LTE-A system can support. However, in some environments like slow-fading channels, the number of feedback PMI bits is thus reduced at the cost of limited performance loss without changing the codebook in LTE-A. To carry out this concept, we build up a candidate set for each PMI in the codebook of LTE-A. Based on the previous selected PMI, the current selected PMI belongs to the candidate set of the previous selected PMI. The candidate set is defined as a subset of precoder indices in the codebook of LTE-A. Since the number of elements in the candidate set is smaller than that of all precoders in the codebook, the number of feedback PMI bits can be reduced. Simulations show that the feedback PMI overhead can be reduced at the cost of limited performance loss. When the mobility speed is 20 km/h, the SNR loss is about 0.25 dB for block error rate is 10-2and the overhead reduction ratio is 25%.

Most nonlinear transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems assume that instantaneous perfect channel state informations (CSIs) are available. Transceiver design with imperfect CSIs have rarely been addressed. In this paper, we consider an AF MIMO system in which a Tomlinson-Harashima precoder (THP) is used at the source, a linear precoder at the relay, and a minimum-mean-squared-error (MMSE) receiver at the destination. With the imperfect CSIs, we propose a new robust transceiver design method. It is shown that the optimization problem for the design is difficult due to the fact that the objective function is a nonlinear function of the source and relay precoders and yet the constraints are coupled. To overcome the problem, we adopt the primal decomposition technique, decomposing the original optimization into a subproblem and a master problem. To facilitate the derivation of the solution, we propose cascading THP with a unitary precoder and using a lower bound of the objective function. In this way, we can translate the original matrix-valued optimization into the scalar-valued concave optimization. Using the Karush-Kuhn-Tucker (KKT) conditions, we can finally obtain the closed-form solutions for the relay and source precoders. Simulations show that the proposed design is effective against the imperfect CSIs.

Existing transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems often assume the availability of perfect channel state informations (CSIs). Robust designs for imperfect CSI have less been considered. In this paper, we propose a robust nonlinear transceiver design for the system with a Tomlinson-Harashima precoder (THP), a linear relay precoder, and a minimum-mean-squared-error (MMSE) receiver. Since two precoders and imperfect CSIs are involved, the robust transceiver design is difficult. To overcome the difficulty, we first propose cascading an additional unitary precoder after the THP. The unitary precoder can not only simplify the optimization but also improve the performance of the MMSE receiver. We then adopt the primal decomposition dividing the original optimization problem into a subproblem and a master problem. With our formulation, the subproblem can be solved and the two-precoder problem can be transferred to a single relay precoder problem. The master problem, however, is not solvable. We then propose a lower bound for the objective function and transfer the master problem into a convex optimization problem. A closed-form solution can then be obtained by the Karush-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceiver can significantly outperform existing linear transceivers with perfect or imperfect CSIs.

Existing precoding schemes in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems use linear precoders. In this paper, we consider a precoding scheme in which a Tomlinson-Harashima (TH) precoder (THP) is used at the source and a linear precoder at the relay. With a minimum-mean-squared-error (MMSE) receiver at destination, we propose a new joint precoders design method. Since two precoders are involved, the transceiver design, formulated as an optimization problem, is difficult to solve. To overcome the problem, we propose cascading an additional unitary precoder with the TH precoder. The unitary precoder can not only simplify the optimization problem but also improve the MMSE performance. With the specially designed unitary precoder at the source, we can then adopt the primal decomposition method to solve this problem. With the method, the original optimization problem can first be decomposed into a master and a subproblem optimization problems, and then transferred to a relay precoder optimization problem. However, the optimization is not a convex problem and the solution is not obtainable. We then propose a method being able to transfer it to a convex optimization problem. A closed-form solution can then be obtained by the Karuch-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceiver can significantly outperform existing linear transceivers.

This paper addresses the linear transceiver design with quality of service (QoS) constraints in an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system. Taking both the direct and the relay links into account and using the minimum-mean-squared-error (MMSE) receiver at the destination, we jointly design the source/relay precoders such that the transmitted power is minimized and QoS constraints are satisfied. The optimization problem such formulated, however, is a highly nonlinear formulation of the source and relay precoders, and the optimum solution is difficult to derive. To solve the problem, we then propose to use a constrained structure for the precoders, and derive mean-squared-error (MSE) upper bounds. Using the primal decomposition method, we can then translate the original optimization problem into two scalar-valued convex optimization problems. The closed-form solutions for the precoders can then be derived by corresponding Karush-Kuhn-Tucker (KKT) conditions. Using the solution, we further provide a sufficient condition to determine if the system is proper to be operated in the cooperative mode or not. Simulations show that the proposed precoded MIMO relay system can significantly reduce the transmission power, compared to a non-cooperated one.

Most precoding schemes in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems only consider the relay precoder, and the receiver is often linear. In this paper, we propose a joint source/relay precoders design method for a nonlinear minimum-mean-squared-error successive interference cancellation (MMSE-SIC) receiver. It is shown that a direct minimization of the average bit-error-rate (BER) is not feasible. Using the uniform channel decomposition (UCD) method, we can design the source and relay precoders such that the signal-to-interference-plus-noise ratio (SINR) for each layer is equal and the block BER (BLER) can be minimized. Unlike UCD in conventional MIMO systems, two precoders have to be optimized simultaneously and the optimum solution is still difficult to derive. We then propose to adopt the primal decomposition method decomposing the original problem into a master and a subproblem optimizations. To facilitate the optimization, we propose a unitary source precoder such that the subproblem can be analytically solved, and the source precoder can be expressed as a function of the relay precoder. Then, with a proposed relay precoder structure, the master problem can be translated into a standard concave optimization problem. By Karush-Kuhn-Tucker (KKT) conditions, we can finally obtain the closed-form solutions for the relay and source precoders. Simulations show that the proposed design can outperform existing precoding methods in AF MIMO relay systems.

Existing precoder designs for an amplify-and-forward (AF) cooperative system often assume a linear receiver at the destination, and a precoder at the relay. The performance enhancement of such a system is then limited. In this paper, we consider a nonlinear successive interference cancellation (SIC) receiver, and at the same time take the source precoder into consideration. Using the geometric mean decomposition (GMD), we propose a joint source/relay precoders design method, fully exploring information provided by direct and relay links. With our method, the design problem can be transformed to a standard scalar concave optimization problem, and a closed-form solution can be obtained. Simulations show that the proposed design can significantly enhance the performance of a MIMO AF cooperative system.

This paper addresses the joint source/relay precoder design problem in amplify-and-forward (AF) cooperative communication systems where multiple antennas are equipped at the source, the relay, and the destination. Existing solutions to the problem only consider the relay link and, thus, do not fully exploit all the available link resource. Using a minimum-mean- squared-error (MMSE) criterion, we propose a joint precoder design method, taking both the direct and relay links into account. It is shown that the MMSE is a highly nonlinear function of the precoder matrices, and a direct minimization is not feasible. To facilitate analysis, we propose to design the precoders toward first diagonalizing the MSE matrix of the relay link. This imposes certain structural constraints on both precoders that allow us to derive an analytically tractable MSE upper bound. By conducting minimization with respect to this upper bound, the solution can be obtained by an iterative water- filling technique. Simulations show that the proposed design can significantly enhance the performance of MIMO AF cooperative systems.

This paper considers transmitter precoding in an amplify-and-forward cooperative system where multiple antennas are equipped at the source, the relay, and the destination. Existing methods for the problem only consider the design of the relay precoder. To further improve the performance, we include the source precoder into the design. Using a minimum-meansquare- error (MMSE) criterion, we propose a joint source/relay precoder design method, taking both the direct and relay links into account. It is shown that the MMSE is a highly nonlinear function of the precoding matrices, and a direct minimization is not feasible. To facilitate analysis, we propose to design the precoders toward first diagonalizing the MSE matrix of the relay link. This imposes certain structural constraints on both precoders that allow us to derive an analytically tractable MSE upper bound. By conducting minimization with respect to this bound, the solution can be obtained by an iterative water-filling technique.