Robust Transceiver Research Articles

Source/relays/destination combined MMSE-based optimization for AF-MIMO multiple-relay systems with correlated channel uncertainties

In this paper, source/relays-precoders and destination-equalizer combined optimization are proposed as a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) multiple-relay system with Gaussian random and correlated channel uncertainties in both hops. Taking correlated channel uncertainties into account, a robust transceiver joint optimization design is developed based on the minimum mean-squared error (MMSE) criterion under individual power constraints at the source and the relays. Simulation results illustrate that the robust multiple relays/transceiver joint design architecture for an AF-MIMO system equipped with multiple relays substantially outperforms a nonrobust transceiver design that assumes estimated channels as actual channels.

Non-Iterative Symbol-Wise Beamforming for MIMO-OFDM Systems

In this paper, we propose a non-iterative symbol-wise beamforming scheme for MIMO-OFDM systems, which can provide the performance approaching that of the iterative symbol-wise beamforming scheme and can reduce the computational complexity significantly for channels with a small number of strong channel taps. Simulation results show that our proposed scheme leads to a negligible performance loss compared with the iterative symbol-wise beamforming scheme regardless of spatial correlation or presence of co-channel interference. For realistic situations, we also consider the system designs to manage imperfect channel knowledge at the transmitter or receiver. First, we propose a limited feedback technique and a codebook design algorithm for symbol-wise beamforming in a spatially correlated frequency selective channel. Simulation results show that the proposed limited feedback technique can provide insignificant outage capacity loss compared with the symbol-wise beamforming scheme with perfect channel knowledge when the proposed codebook is adopted with a moderate number of feedback bits. Second, we propose a robust transceiver optimization for symbol-wise beamforming under channel uncertainty. From simulation results, we confirm that our proposed robust transceiver optimization can incur less degradation than the iterative and proposed symbol-wise beamforming schemes under the assumption of a bounded channel uncertainty model.

Robust Transceiver with Tomlinson-Harashima Precoding for Amplify-and-Forward MIMO Relaying Systems

In this paper, robust transceiver design with Tomlinson-Harashima precoding (THP) for multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying systems is investigated. At source node, THP is adopted to mitigate the spatial intersymbol interference. However, due to its nonlinear nature, THP is very sensitive to channel estimation errors. In order to reduce the effects of channel estimation errors, a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. With novel applications of elegant characteristics of multiplicative convexity and matrix-monotone functions, the optimal structure of the nonlinear transceiver is first derived. Based on the derived structure, the transceiver design problem reduces to a much simpler one with only scalar variables which can be efficiently solved. Finally, the performance advantage of the proposed robust design over non-robust design is demonstrated by simulation results.

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.

The Sign-Definiteness Lemma and Its Applications to Robust Transceiver Optimization for Multiuser MIMO Systems

We formally generalize the sign-definiteness lemma to the case of complex-valued matrices and multiple norm-bounded uncertainties. This lemma has found many applications in the study of the stability of control systems, and in the design and optimization of robust transceivers in communications. We then present three different novel applications of this lemma in the area of multi-user multiple-input multiple-output (MIMO) robust transceiver optimization. Specifically, the scenarios of interest are: (i) robust linear beamforming in an interfering adhoc network, (ii) robust design of a general relay network, including the two-way relay channel as a special case, and (iii) a half-duplex one-way relay system with multiple relays. For these networks, we formulate the design problems of minimizing the (sum) MSE of the symbol detection subject to different average power budget constraints. We show that these design problems are non-convex (with bilinear or trilinear constraints) and semi-infinite in multiple independent uncertainty matrix-valued variables. We propose a two-stage solution where in the first step the semi-infinite constraints are converted to linear matrix inequalities using the generalized sign-definiteness lemma, and in the second step, we use an iterative algorithm based on alternating convex search (ACS). Via simulations we evaluate the performance of the proposed scheme.

Robust Transceiver Optimization for Downlink Coordinated Base Station Systems: Distributed Algorithm

This paper considers the joint transceiver design for downlink multiuser multiple-input single-output (MISO) systems with coordinated base stations (BSs) where imperfect channel state information (CSI) is available at the BSs and mobile stations (MSs). By incorporating antenna correlation at the BSs and taking channel estimation errors into account, we solve two robust design problems: (1) minimizing the weighted sum of mean-square-error (MSE) with per BS antenna power constraint, and (2) minimizing the total power of all BSs with per user MSE target and per BS antenna power constraints. These problems are solved as follows. First, for fixed receivers, we propose centralized and novel computationally efficient distributed algorithms to jointly optimize the precoders of all users. Our centralized algorithms employ the second-order-cone programming (SOCP) approach, whereas, our novel distributed algorithms use the Lagrangian dual decomposition, modified matrix fractional minimization and an iterative method. Second, for fixed BS precoders, the receivers are updated by the minimum mean-square-error (MMSE) criterion. These two steps are repeated until convergence is achieved. In all of our simulation results, we have observed that the proposed distributed algorithms achieve the same performance as that of the centralized algorithms. Moreover, computer simulations verify the robustness of the proposed robust designs compared to the nonrobust/naive designs.

A 1.0625 $\sim$ 14.025 Gb/s Multi-Media Transceiver With Full-Rate Source-Series-Terminated Transmit Driver and Floating-Tap Decision-Feedback Equalizer in 40 nm CMOS

A robust transceiver designed for NRZ signaling beyond 10Gb/s over long-range physical media (including electrical backplanes, copper cables and optical modules) must contend with significant challenges from insertion loss, crosstalk, and reflection. For inter-symbol interference (ISI) cancellation, half-rate decision-feedback equalizer (DFE) with unrolled first tap [1–3] is widely used to avoid noise amplification and to relax timing for data sampling/feedback. However, tap-unrolling increases slicer count and entails half-rate multiplexers eating into timing margin. To remove reflection-induced ISI due to impedance discontinuities in the media, the DFE must cover tap positions higher than 30UI which is beyond tap range of the DFEs reported in previous work [1–4]. Fig. 1 shows an example of bumpy channel with reflection energy up to 40UI.

Robust linear transceivers for downlink multi-user multiple-input multiple-output systems using second-order cone programming optimisation

This study addresses the joint robust linear transceiver design problems for a downlink multi-user multiple-input multiple-output (MIMO) antenna system in the presence of imperfect channel state information (CSI). The uncertainty in the channel is characteried by a norm-bounded region, and two robust optimal design problems are considered. One is aimed at minimising the total transmitter power subject to users' mean square error (MSE) constraints in the presence of channel uncertainty, the other is to minimise the worst-case sum-mean square error (sum-MSE) under power constraints for all admissible uncertainties. For these two problems, the authors propose two iterative algorithms based on second-order cone programming (SOCP) formulations, which can be efficiently solved and have less computational complexity than their semi-definite programming (SDP) counterparts. Simulation results also illustrate that the proposed robust design approaches can significantly reduce the computational complexity while achieving almost the same performance as the robust SDP methods.

Robust sum-MSE transceiver optimisation for multi-user non-regenerative MIMO relay downlink systems

Presented is transceiver optimisation for multi-user non-regenerative MIMO relay downlink systems. By taking the channel uncertainties into account, a robust scheme is proposed to minimise the sum mean square error (SMSE) of the system under the power constraints, where the transceiver is obtained by using the Karush-Kuhn-Tucker conditions and realised through an iterative algorithm. Simulation results verify the robustness of the proposed scheme against the estimation errors.

Erratum for ‘Robust sum-MSE transceiver optimisation for multi-user non-regenerative MIMO relay downlink systems’

Erratum for ‘Robust sum-MSE transceiver optimisation for multi-user non-regenerative MIMO relay downlink systems’

Robust Transceiver Design for K-Pairs Quasi-Static MIMO Interference Channels via Semi-Definite Relaxation

In this paper, we propose a robust transceiver design for the K-pair quasi-static MIMO interference channel. Each transmitter is equipped with M antennas, each receiver is equipped with N antennas, and the k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> transmitter sends L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> independent data streams to the desired receiver. In the literature, there exist a variety of theoretically promising transceiver designs for the interference channel such as interference alignment-based schemes, which have feasibility and practical limitations. In order to address practical system issues and requirements, we consider a transceiver design that enforces robustness against imperfect channel state information (CSI) as well as fair performance among the users in the interference channel. Specifically, we formulate the transceiver design as an optimization problem to maximize the worst-case signal-to-interference-plus-noise ratio among all users. We devise a low complexity iterative algorithm based on alternative optimization and semi-definite relaxation techniques. Numerical results verify the advantages of incorporating into transceiver design for the interference channel important practical issues such as CSI uncertainty and fairness performance.

Robust MMSE Transceiver Designs for Downlink MIMO Systems with Multicell Cooperation

Therobust-generalized iterative approach(Robust-GIA),robust-fast iterative approach(Robust-FIA), androbust-decoder covariance optimization approach(Robust-DCOA) are proposed for designing MMSE transceivers of downlink multicell multiuser MIMO systems with per-cell and per-antenna power constraints and possibly imperfect channel state information. TheRobust-DCOAis the most restrictive but is always optimum, theRobust-GIAis the most general, and theRobust-FIAis the most efficient. When theRobust-DCOAis applicable and the decoder covariance matrices are full rank, the three proposed approaches are equivalent and all provide the optimum solution. Numerical results show that the proposed robust approaches outperform their non-robust counterparts in various single-cell and multicell examples with different system configurations, channel correlations, power constraints, and cooperation scenarios. Moreover, performances of the robust approaches are insensitive to estimation errors of channel statistics (correlations and path loss). With cell-cooperation, cell edge interference problems can be remedied without reducing the number of data streams by using the proposed robust approaches.

Game Theory in Signal Processing and Communications

Game theory is a branch of mathematics aimed at the modeling and understanding of resource conflict problems. Essentially, the theory splits into two branches: noncooperative and cooperative game theory. The distinction between the two is whether or not the players in the game can make joint decisions regarding the choice of strategy. Noncooperative game theory is closely connected to minimax optimization and typically results in the study of various equilibria, most notably the Nash equilibrium. Cooperative game theory examines how strictly rational (selfish) actors can benefit from voluntary cooperation by reaching bargaining agreements. Another distinction is between static and dynamic game theory, where the latter can be viewed as a combination of game theory and optimal control. In general, the theory provides a structured approach to many important problems arising in signal processing and communications, notably resource allocation and robust transceiver optimization. Recent applications also occur in other emerging fields, such as cognitive radio, spectrum sharing, and in multihop-sensor and adhoc networks.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

In this paper, we present robust joint non-linear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust i) minimum SMSE, ii) MSE-constrained, and iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semi-definite programs (SDP). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints.

Game theory in signal processing and communications [From the Guest Editors

Game theory is a branch of mathematics aimed at the modeling and understanding of resource conflict problems. Essentially, the theory splits into two branches: noncooperative and cooperative game theory. The distinction between the two is whether or not the players in the game can make joint decisions regarding the choice of strategy. Noncooperative game theory is closely connected to minimax optimization and typically results in the study of various equilibria, most notably the Nash equilibrium. Cooperative game theory examines how strictly rational (selfish) actors can benefit from voluntary cooperation by reaching bargaining agreements. Another distinction is between static and dynamic game theory, where the latter can be viewed as a combination of game theory and optimal control. In general, the theory provides a structured approach to many important problems arising in signal processing and communications, notably resource allocation and robust transceiver optimization. Recent applications also occur in other emerging fields, such as cognitive radio, spectrum sharing, and in multihop-sensor and adhoc networks.

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems

We study robust transceiver optimization in a downlink, multiuser, wireless system, where the transmitter and the receivers are equipped with antenna arrays. The robustness is defined with respect to imperfect knowledge of the channel at the transmitter. The errors in the channel state information are assumed to be bounded, and certain quality-of-service targets in terms of mean-square errors (MSEs) are guaranteed for all channels from the uncertainty regions. Iterative algorithms are proposed for the transceiver design. The iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions. The framework supports robust counterparts of several MSE-optimization problems, including transmit power minimization with per-user or per-stream MSE constraints, sum MSE minimization, min-max fairness, etc. Although the convergence to the global optimum cannot be claimed due to the intricacy of the problems, numerical examples show good practical performance of the presented methods. We also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure, the uncertainty modeling, and a multicellular setup.

Robust QoS-Constrained Optimization of Downlink Multiuser MISO Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The knowledge of the channel at the transmit side of a communication system can be exploited by using precoding techniques, from which the overall transmission quality might benefit significantly. However, in practical wireless systems, the channel state information is prone to errors, which sometimes deteriorates the performance drastically. In this paper, we address the problem of robust transceiver design in a downlink multiuser system, with respect to the erroneous channel knowledge at the transmitter. The base station is equipped with an antenna array, while users have single antennas. The transceiver optimization is performed under a set of predefined users' quality-of-service constraints, defined as maximum mean square errors, or minimum signal-to-interference-plus-noise ratios (SINRs), which must be satisfied for all disturbances that belong to given, bounded uncertainty sets. Efficient numerical solutions are obtained using semidefinite programming methods from convex optimization theory. The proposed algorithms are found to outperform related approaches in the literature in terms of the achieved performance, while maintaining low computational complexity. The studied uncertainty models are applicable in mitigating typical errors that emerge as a result of quantization or channel estimation. </para>

Robust Transceiver Design for Multiuser MIMO Downlink with Channel Uncertainties

This letter addresses the problem of robust transceiver design for the multiuser multiple-input-multiple-output (MIMO) downlink where the channel state information at the base station (BS) is imperfect. A stochastic approach which minimizes the expectation of the total mean square error (MSE) of the downlink conditioned on the channel estimates under a total transmit power constraint is adopted. The iterative algorithm reported in [2] is improved to handle the proposed robust optimization problem. Simulation results show that our proposed robust scheme effectively reduces the performance loss due to channel uncertainties and outperforms existing methods, especially when the channel errors of the users are different.

Statistically Robust Design of Linear MIMO Transceivers

The treatment of channel state information (CSI) is critical in the design of MIMO systems. Accurate CSI at the transmitter is often not possible or may require high feedback rates. Herein, we consider the robust design of linear MIMO transceivers with perfect CSI either at the transmitter or at both sides of the link. The framework considers the design problem where the imperfect CSI consists of the channel mean and covariance matrix or, equivalently, the channel estimate and the estimation error covariance matrix. The robust transceiver design is based on a general cost function of the average MSEs as well as a design with individual MSE based constraints. In particular, a lower bound of the average MSE matrix is explored for the design when only the CSI at the transmitter is imperfect. Under different CSI conditions, the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect CSI, but with a different equivalent channel and/or noise covariance matrix.

On the Design of Linear Transceivers for Multiuser Systems with Channel Uncertainty

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on downlink systems with a single antenna at each receiver. For systems with uplink-downlink reciprocity, we consider a stochastic model for the channel uncertainty, and we propose an efficient algorithm for the joint design of the linear preceding matrix at the base station and the equalizing gains at the receivers so as to minimize the average mean-square-error (MSE) over the channel uncertainty. The design is based on a generalization, derived herein, of the MSE duality between the broadcast and multiple access channels (MAC) to scenarios with uncertain CSI, and on a convex formulation for the design of robust transceivers for the dual MAC. For systems in which quantized channel feedback is employed, we consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst- case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a "system-wide" uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the "per-user" uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed approaches to robust linear transceiver design can significantly reduce the sensitivity of the downlink to uncertain CSI, and can provide improved performance over that of existing robust designs.