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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. [ABSTRACT FROM AUTHOR]

This letter investigates the source and relay precoder design for full-duplex multiple-input multiple-output relay systems, where simultaneous wireless information and power transfer is enabled at the destination. The objective is to design the precoders such that the end-to-end performance can be optimized. Different from existing schemes, a novel dual-objective function is adopted in this letter. The proposed precoders yield closed-form solutions and avoid iterative algorithms. Moreover, our design is applicable when the system suffers from the residual loop-interference. Simulations show that the proposed scheme enables an efficient way to optimize information-decoding and energy-harvesting performances. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Full-duplex (FD) multiple-input multiple-output relaying has been considered an effective scheme to increase the spectral efficiency for wireless communications. As known, the main problem for the FD system is the cancellation of loop interference (LI). In this paper, we propose using the joint source/relay precoding to reduce the influence of LI. Therein, linear precoders are used at the source and relay, while the minimum mean-squared-error receiver is adopted at the destination. The joint precoder design is complicated when spatial multiplexing is exploited for signal transmission. To solve the problem, we propose an iterative method in which the original problem is split into two subproblems. With some matrix properties, we then show that each subproblem can be formulated as a convex optimization. Finally, a closed-form solution can be obtained with the Karush–Kuhn–Tucker conditions. Using a mean-squared-error upper bound, we also propose a low-complexity method to reduce the computational complexity. The proposed precoders have closed-form expressions, which is a great advantage in real-world implementation. Simulation results show that the proposed methods significantly outperform existing ones. [ABSTRACT FROM AUTHOR]

Joint source/relay precoding has been considered an effective method to improve the system performance of dual-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay systems. For practical implementations, the codebook-based limited-feedback precoding is widely exploited since the feedback bits can be effectively limited. As known, system performance strongly depends on the codeword selection criterion. In this paper, we will explore how to design the selection criterion when successive interference cancellation (SIC) receivers are adopted at the destination. Starting from the QR-SIC receiver, we first propose a centralized selection scheme by maximizing the minimum postprocessing signal-to-noise ratio (SNR). Next, a decentralized selection scheme is further developed to reduce the computational complexity. Furthermore, we demonstrate that our methods can be directly extended to the system with the minimum mean square error (MMSE)-SIC receiver. Simulation results show that the proposed designs can significantly improve system performance. [ABSTRACT FROM PUBLISHER]

Tomlinson–Harashima precoded (THP) multiple-input–multiple-output (MIMO) systems are developed to cancel the intersymbol interference (ISI) at the transmitter. However, the THP at least requires perfect channel direction information (CDI) to completely mitigate the interference at the transmitter, which is not practical in the real world. The limited feedback systems are then practically developed to convey the quantized CDI to the transmitter. Using the quantized CDI to conduct the THP, an unavoidable interference degrades the performance at the receiver. In this paper, we investigate the performance degradation resulted from the random vector quantization (RVQ), which is a kind of CDI-based limited feedback mechanism. Here, we measure the performance degradation as the excess mean-squared error (EMSE). Since the formulation of the EMSE is a complicated function of the quantization error, we proposed using the second-order Taylor expansion to derive an analytical result. Simulation results have also verified our proposed analysis, showing that the derived analysis can match the actual EMSE. [ABSTRACT FROM PUBLISHER]

In this paper, we study the codebook size design strategies in the multiple-input–multiple-output (MIMO) broadcast channel (BC) systems. We adopt the nonlinear Tomlinson–Harashima precoder (THP), which is designed by the imperfect channel direction information (CDI) acquired from the random vector quantization (RVQ) feedback mechanism. Under the limitation of the total feedback rate, we flexibly allocate the size of each user's codebook so that the overall channel capacity is maximized. Since the design problem is not convex, directly finding out the optimum allocation of codebook size is not attainable. However, by sophisticatedly using the discrete majorization theory, we can derive the codebook size allocation strategies for the high- and the low-signal-to-noise-ratio (SNR) regions. Interestingly, the results show that the equal size codebook is preferable in the low-SNR region, whereas the codebook allocates the whole available codebook size to a single user in the high-SNR region. Simulations certify the theoretical result of our design. [ABSTRACT FROM PUBLISHER]

We consider joint source/relay precoding in three-node two-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay systems. In our systems, linear precoders are used at the source and the relay, and the QR successive interference cancelation (SIC) receiver is used at the destination. Our design criterion is to minimize the block error rate (BLER) of the receiver. Since the BLER is a complicated function of the source and relay precoders, and the power constraints are coupled, the optimization problem is difficult to solve. To overcome the difficulty, we first apply the primal decomposition approach, transforming the original optimization to a subproblem and a master problem. In the subproblem, the optimum source precoder can be obtained with the geometric mean decomposition (GMD). In the master problem, however, the optimum relay precoder cannot be straightforwardly obtained. We theoretically prove that the optimum relay precoder exhibits a matrix diagonalization property. Using this property, we can then transform the master problem into a scalar-variable concave optimization problem. A closed-form solution can be derived by the Karuch–Kuhn–Tucker (KKT) conditions. Finally, we extend our method to the two-hop AF MIMO relay system with the minimum mean square error (MMSE) SIC receiver. Assuming a unitary source precoder, we obtain the optimum source and relay precoders in closed form. Simulations show that the proposed transceivers can significantly improve the system performance. [ABSTRACT FROM PUBLISHER]

This paper proposes robust beamforming designs for a multiple-input–single-output (MISO) interference channel (IC). Considering the random vector quantization (RVQ) feedback mechanism, we first derive the closed-form expression for the mean-squared-error (MSE) metric by averaging over the noise, the quantization error, and the channel amplitude. With the derived MSE result, we devise the robust beamformer by minimizing total MSEs and by minimizing the maximum per-user MSE. Since the optimizations of both designs are not convex, we first propose an iterative method to find out the solutions for the minimum total MSE criterion, where the transmitter beamforming vectors and the receiver decoding scalars are iteratively obtained. For the other design criterion, we propose an exhaustive search that can transfer the design problem into a feasible search problem. With the same design criterion, we propose another iterative method to find out the solutions, where the decoding scalars and the beamforming vectors are iteratively derived by minimizing MSE and second-order cone programming (SOCP), respectively. The simulation results verify the robustness of both designs when the quantization error exists. [ABSTRACT FROM PUBLISHER]

In this paper, we propose cognitive overlay transceiver designs, where a primary transceiver pair and a secondary transceiver pair coexist in a network, and the primary user (PU) allows the secondary user (SU) to concurrently transmit its signals at the price of reducing the power of the PU's signal relayed by cooperative amplify-and-forward (AF). Since the considered transceiver design is mainly to devise the precoders both for the PU and the SU at the secondary transmitter (ST), the channel state information (CSI) has to be known at the ST. We therefore consider the limited feedback scheme with random vector quantization (RVQ), where the ST can only know the quantized channel direction information (CDI). Considering the statistics of the CSI quantization error and the linear minimum mean square error (LMMSE) receiver, we derive the closed-form MSE expressions corresponding to the PU and the SU. With the derived MSEs, we propose two robust design criteria. One criterion is to minimize the ST's power consumption under the constraint that the PU's and SU's quality-of-service (QoS; i.e., MSE) can be met. The other criterion is to minimize the SU's MSE when the PU's QoS can be controlled under a certain value and the ST satisfies the limitation of its transmission power consumption. Both the optimization problems of the proposed design criteria are not convex, and the corresponding solutions cannot be directly obtained. We then propose transfering the original optimization problems into two subproblems, where each of them is eventually formulated as a convex optimization problem, and the solutions are iteratively obtained, which is effective. Thus, the results can be obtained with the interior-point method. Simulations certify the robustness of our designs. [ABSTRACT FROM PUBLISHER]

In this letter, we propose a robust design for a two-stage Tomlinson- Harashima precoder (THP) multiple-input multiple-output (MIMO) system, where the THP cascaded with a unitary precoder is deployed at the transmitter and a linear minimum mean-square error decoder is adopted at the receiver. With the random vector quantization (RVQ) feedback scheme, only the channel direction information (CDI) is quantized and fed back to the transmitter. Applying the THP directly at the transmitter will cause unavoidable interference at the destination due to the quantization error. We herein design a robust THP with the minimum mean-squared error (MMSE) criterion by taking the quantization error into account to mitigate the effect of the quantization error. Simulation results show that the proposed robust THP scheme provides the better performance compared to the non-robust one. [ABSTRACT FROM PUBLISHER]

In this paper, we study a far-end channel estimation problem in a three-node multiple-input–multiple-output (MIMO) relay system. The estimation is accomplished in two phases. In the first phase, the source node keeps silence, the relay transmits pilots, and the destination estimates the relay-to-destination channel. In the second phase, the source transmits pilots, and the relay amplifies the received pilots with a precoder and forwards the resultant pilots to the destination. The destination then estimates the source-to-relay channel based on the received signals and the estimated relay-to-destination channel in the first phase. We aim to conduct a robust design deriving the optimum source pilots and precoding matrix with the minimum mean square error (MMSE) criterion. The design can be easily formulated as an optimization problem; however, the problem is not convex and is difficult to solve. We then propose using a lower bound of the objective function in the optimization problem. We show that the optimization of the lower bound is equivalent to the original problem when channel correlation matrices have certain structures. With the correlation matrices, we can derive optimum pilot structures so that the proposed optimization can be transferred to a scalar-valued concave optimization, and a closed-form solution can be obtained via Karush–Kuhn–Tucker (KKT) conditions. Simulations show that our proposed method outperforms existing nonrobust methods. [ABSTRACT FROM PUBLISHER]

We consider the precoding problem in an amplifyand-forward (AF) multiple-input-multiple-output (MIMO) relay system in which multiple antennas are equipped at the source, the relay, and the destination. Most existing methods for this problem only consider the design of the relay precoder, and some even ignore the direct link. In this paper, we consider a joint source/relay precoder design problem, taking both the direct and the relay links into account. Using a minimum-mean-square-error (MMSE) criterion, we first formulate the problem as a constrained optimization problem. However, it is found that the mean square error (MSE) is a highly nonlinear function of the precoders, and a direct optimization is difficult to conduct. We then design the precoders to diagonalize the MSE matrix in the cost function. To do that, we pose certain structural constraints on the precoders and derive an MSE upper bound. It turns out that minimization with respect to this bound becomes simple and straightforward. Using the standard Lagrange technique, we can finally obtain the solution with an iterative water-filling method. Simulation results show that the proposed method, with an additional precoder, outperforms the existing methods, in terms of either the MSE or the bit error rate (BER). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]