Fan-Shuo Tseng

Linear MMSE Transceiver Design in Amplify-and-Forward MIMO Relay Systems

We consider the precoding problem in an amplify-and-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).

Joint Tomlinson–Harashima Source and Linear Relay Precoder Design in Amplify-and-Forward MIMO Relay Systems via MMSE Criterion

Existing minimum-mean-square-error (MMSE) transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems all assume a linear precoder at the source. Nonlinear precoders in such a system have yet to be considered. In this paper, we study a nonlinear transceiver in AF MIMO relay systems in which a Tomlinson-Harashima (TH) precoder is used at the source, a linear precoder is used at the relay, and an MMSE receiver is used at the destination. Since two precoders and three links are involved, the transceiver design, which is formulated as an optimization problem, is difficult to solve. We first propose an iterative method to overcome the problem. In the method, the two precoders are separately optimized in an iterative step. To further improve the performance, we then propose a non-iterative method that can yield closed-form solutions for the precoders. This method uses the primal decomposition technique in which the original optimization can first be decomposed into a master and a subproblem optimization. In the subproblem, the optimum source precoder is solved as a function of the relay precoder. In the master problem, the optimization is then transferred to a relay-precoder-only problem. However, the optimization is not convex, and the primal decomposition cannot be directly applied. We then propose cascading a unitary precoder after the TH precoder so that the optimization in the subproblem and the master problem can be conducted. Furthermore, using a relay precoder structure, we can transfer the master problem to a convex optimization problem and obtain a closed-form solution by the Karuch-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceivers can significantly outperform existing linear transceivers.

Nonlinear Transceiver Designs in MIMO Amplify-and-Forward Relay Systems

Various linear transceiver design methods have been developed in three-node amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems. Nonlinear designs in such systems, however, have yet to be investigated. In this paper, we propose nonlinear transceiver designs for a linear source and relay precoded system with the QR successive-interference-cancellation (SIC) receiver and another linear source and relay precoded system with the minimum-mean-squared-error (MMSE) SIC receiver. Our designs minimize the criterion of the block error rate, which is a complicated function of the source and relay precoders. Solving the two precoders simultaneously is not feasible. To overcome the difficulties, we first resort to the primal decomposition approach, i.e., transferring the original optimization to a subproblem and a master problem and solving the two precoders individually. However, since two power constraints are mutually coupled, the decomposition cannot actually be conducted. We then propose a unitary structure for the source precoder and show that the power constraints can be decoupled. As a result, the source precoder can be solved as a function of the relay precoder in the subproblem. With a proposed relay precoder structure, the master problem can further be transferred to a scalar-valued concave optimization problem. A closed-form solution can finally be derived by the Karuch-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceivers can significantly outperform the existing linear transceivers.

Robust Tomlinson-Harashima Source and Linear Relay Precoders Design in Amplify-and-Forward MIMO Relay Systems

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.

Robust Far-End Channel Estimation in Three-Node Amplify-and-Forward MIMO Relay Systems

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.

Robust Tomlinson-Harashima Precoder Design with Random Vector Quantization in MIMO Systems

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.

Optimum Transceiver Designs in Two-Hop Amplify-and-Forward MIMO Relay Systems With SIC Receivers

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.

Robust Beamforming Design in MISO Interference Channels With RVQ Limited Feedback

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.

Robust Multiple-Antenna Cooperative Spectrum Sharing Design With Random Vector Quantization

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 PUs 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 STs power consumption under the constraint that the PUs and SUs quality-of-service (QoS; i.e., MSE) can be met. The other criterion is to minimize the SUs MSE when the PUs 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.

Channel estimation for OFDM systems with subspace persuit algorithm

Signal recovery techniques for compressive sampling, such as matching pursuit (MP), orthogonal MP (OMP), and linear programming (LP), have been developed and applied to the spare channel estimation problem in orthogonal-frequency-division-multiplexed (OFDM) systems. In this paper, we first propose using a newly developed algorithm, subspace pursuit (SP), for the channel estimation problem. It is shown that the SP algorithm can outperform the MP, OMP, and LP algorithms. However, the SP algorithm will fail if the number of the pilots is small. We then propose a decision-feedback method, referred to as the pseudo-pilot assisted (PA) SP, which can be used in low pilot-density scenarios. Simulations show that the proposed PASP can significantly improve the performance of channel estimation when the number of pilots is small.