Robust Optimization for Amplify-and-Forward MIMO Relaying From a Worst-Case Perspective

Shen, Hong; Wang, Jiaheng; Levy, Bernard C.; Zhao, Chunming

doi:10.1109/tsp.2013.2278819

Cited by 35 publications

(41 citation statements)

References 42 publications

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“…complex Gaussian random variables with zero mean and unit variance. Suppose that the uncertainty sizes are related to the quality of channels [22], [35], [36], e.g., the radius of uncertainty regions can be set to 1). Simulation results are averaged over 1000 independent channel realizations, and 5000 QPSK symbols are transmitted for each data stream per realization.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In [32]- [34], the norm-bounded CSI errors were considered in a multipointto-multipoint system and the MIMO relay was designed to minimize the consumed power under different quality of service (QoS) constraints. The authors in [35], [36] proved that the robust design for single user MIMO AF relay leads to the channel-diagonalizing structure, and the optimal solution can be obtained only through the scalar operations. The signdefiniteness lemma was generalized to the case of complexvalued variables and multiple semi-infinite constraints, and its applications to robust optimization were investigated in [37].…”

Section: Robust Transceiver Design For Downlinkmentioning

confidence: 99%

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Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

Gao

Qiu

2015

IEEE Trans. Wireless Commun.

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In this paper, we investigate the robust transceiver design for a downlink multiuser multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay system with imperfect channel state information (CSI). We consider that the actual channel is within the neighborhood of a nominal channel and formulate two optimization problems following the philosophy of worst-case robustness, i.e., minimizing the sum mean-square-error (SMSE) and minimizing the total transmit power for any channel realization in the uncertainty region. In order to efficiently find the solutions, we transform the original problems into suitable forms using the sign-definiteness lemma and then propose an alternating iterative algorithm with guaranteed convergence. To further reduce the computational complexity, the cutting-set method is developed, which alternates between transceiver design and channel determination steps. Moreover, some interesting extensions of the proposed methods are discussed, including various types of uncertainty models and transmit power constraints, nonlinear transceiver structure, and uncertain noise covariance. Simulation results are presented to demonstrate the effectiveness of the proposed robust designs.Index Terms-Amplify-and-forward, relay, multiuser, MIMO, transceiver design, imperfect channel state information, worstcase robustness.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Robust Transceiver Design For Downlinkmentioning

confidence: 99%

Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

Gao

Qiu

2015

IEEE Trans. Wireless Commun.

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“…Details of transformation from (11) to (13) are presented in Appendix B. The optimization problem (13) is easier to solve than (11). Once the optimal 1 is derived, Q opt and W opt are computed using (12) and (10), respectively.…”

Section: Minimum Conditional Mse Criterionmentioning

confidence: 99%

Optimization of a MIMO amplify-and- forward relay system with channel state information estimation error and feedback delay

Zhang

Zhao

et al. 2016

EURASIP J. Adv. Signal Process.

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This paper addresses the robust design of a multiple-input multiple-output amplify-and-forward relay system against channel state information (CSI) mismatch due to estimation error and feedback delay. The estimation error and feedback delay are expressed using appropriate models, from which we derive the conditional mean square error (MSE) between the desired and the received signals upon the estimated CSI. The conditional MSE is then minimized to optimize the relay beamforming matrix with relay transmission power constraint. It is shown that the proposed optimization problem reduces to the conventional minimum MSE problem when CSI mismatch vanishes. By analyzing the structure of the optimal beamforming matrix, the optimization problem is simplified so that it can be directly solved using the genetic algorithm (GA). To further reduce the computational load, we develop a relaxed version of the optimization problem. It is found that the relaxation enables us to efficiently solve the problem using water filling strategy. Computer simulations show that both GA and water filling solutions are superior to conventional solutions without CSI mismatch consideration, while the water filling is 1000 times faster than the GA.

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“…As pointed out in [33]- [35], the errors caused by quantization is bounded. Furthermore, there are several ways to determine ε j in practice [36], such as measuring the difference between the true and estimate of channel gain generated by a channel emulator or calculating ε j based on the specific distribution of channel errors to guarantee that the norms of possible errors are upper bounded with a certain probability [33]. Furthermore, we can choose M j based on the specific shape of G j , such as the identity matrix corresponding to a circle.…”

Section: B Robust Problem Formulationmentioning

confidence: 99%

Robust Energy Efficiency Maximization in Cognitive Radio Networks: the Worst-Case Optimization Approach

Wang

Sheng

Zhang

et al. 2014

IEEE Trans. Commun.

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Energy efficiency (EE) is very crucial for future wireless communication systems, especially for cognitive radio networks (CRNs). The EE performance relies on channel state information (CSI) of channels. Besides, the interference from secondary users (SUs) to primary users (PUs) also closely depends on CSI in underlay CRNs. However, available works on EE usually assume that CSI is perfect, which is often inaccurate in practical systems. Thus, in this paper we investigate the robust EE maximization problem in underlay CRNs with multiple SUs and PUs. Assuming CSI error to be bounded, we consider that all channels lie in some bounded uncertainty regions. From the perspective of worst-case optimization, we formulate it as the max-min problem with infinite constraint, which is nontrivial even without this constraint. This is because that the outer-maximization problem is non-convex and the inner-minimization problem is a concave minimization problem known as NP-hard in general. We propose a scheme to handle this problem via the fractional programming and global optimization techniques. Particularly, we efficiently solve this problem in two special cases. Simulation results validate that our proposed scheme can improve the worst-case EE of SUs distinctly and strictly guarantee the quality-of-service (QoS) of PUs under all parameters' uncertainties.Index Terms-Cognitive radio networks, energy efficiency, worst-case optimization, general norm uncertainty.

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Robust Optimization for Amplify-and-Forward MIMO Relaying From a Worst-Case Perspective

Cited by 35 publications

References 42 publications

Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

Robust Transceiver Design for Downlink Multiuser MIMO AF Relay Systems

Optimization of a MIMO amplify-and- forward relay system with channel state information estimation error and feedback delay

Robust Energy Efficiency Maximization in Cognitive Radio Networks: the Worst-Case Optimization Approach

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