Robust Design for Linear Non-Regenerative MIMO Relays With Imperfect Channel State Information

Rong, Yue

doi:10.1109/tsp.2011.2113376

Cited by 66 publications

(96 citation statements)

References 10 publications

(12 reference statements)

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“…complex Gaussian variables with zero mean and unit variance. Moreover, for the above schemes, the worst-case channel error changes witĥ H rd according to (14) which can be readily verified from the proof of Theorem 1. Fig.…”

Section: Simulation Resultsmentioning

confidence: 62%

“…We can achieve the lower bound in the above expression by selecting the worst-case CSI error ∆ w rd as indicated in (14) and letting the relay precoder beF opt r in (15). Therefore, we conclude that (∆ w rd ,F opt r ) is the optimal solution to the minimax problem (13) and its optimal value is (17 …”

Section: Appendix II Proof Of Propositionmentioning

confidence: 92%

“…It can be found from (14) that, the worst-case CSI uncertainty ∆ w rd has the similar SVD structure as the nominal channel H rd and it decreases the ith singular value ofĤ rd by min{σ rd,i , ϵ rd }, which, intuitively, can be explained by the fact that the worst-case CSI perturbation shall attempt to degrade the nominal channel as much as possible. From (15), we observe that the optimal relay precoder has a channel-diagonalizing structure, where the unitary matrices U H sr andV rd match the eigen-directions of the source-relay channel H sr and the nominal relaydestination channelĤ rd , respectively.…”

Section: Lemma 2 ( [39 Chapter 3 Theorem A8])mentioning

confidence: 99%

“…Proposition 1: The worst-case CSI error ∆ w rd and the optimal relay precoderF opt r that together solve the minimax problem (13) are given respectively by (14) and…”

Section: Worst-case MI Maximization For Af Mimo Relayingmentioning

confidence: 99%

See 3 more Smart Citations

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

Shen

Wang

Levy

et al. 2013

IEEE Trans. Signal Process.

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Abstract-In this paper, we consider robust optimization of amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay precoders in presence of deterministic imperfect channel state information (CSI), when the CSI uncertainty lies in a norm bounded region. Two widely used performance metrics, mutual information (MI) and mean square error (MSE), are adopted as design objectives. According to the philosophy of worst-case robustness, the robust optimization problems with respect to maximizing the worst-case MI and minimizing the worstcase MSE are formulated as maximin and minimax problems, respectively. Due to the fact that these two problems do not have a concave-convex or convex-concave structure, we cannot rely on the conventional saddle point theory to find the robust solutions. Nevertheless, by exploiting majorization theory, we show that the formulated maximin and minimax problems both admit saddle points. We further analytically characterize the saddle points, and provide closed-form solutions to robust relay precoder designs. Interestingly, we find that, under both MI and MSE metrics, the robust relay optimization leads to a channeldiagonalizing structure, meaning that eigenmode transmission is optimal from the worst-case robustness perspective. The proposed robust designs can improve the spectral efficiency and reliability of AF MIMO relaying against CSI uncertainties at the similar cost of computational complexity as the existing non-robust schemes.Index Terms-Multiple-input multiple-output (MIMO) cooperative transmission, mutual information (MI), mean square error (MSE), worst-case robust design, relay precoding, imperfect channel state information (CSI).

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Section: Simulation Resultsmentioning

confidence: 62%

Section: Appendix II Proof Of Propositionmentioning

confidence: 92%

Section: Lemma 2 ( [39 Chapter 3 Theorem A8])mentioning

confidence: 99%

“…Proposition 1: The worst-case CSI error ∆ w rd and the optimal relay precoderF opt r that together solve the minimax problem (13) are given respectively by (14) and…”

Section: Worst-case MI Maximization For Af Mimo Relayingmentioning

confidence: 99%

See 2 more Smart Citations

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

Shen

Wang

Levy

et al. 2013

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…In [36], an iterative algorithm based on alternate optimization approach has been proposed for an AF MIMO relay channel with direct link. A statistically robust design has been presented for linear AF MIMO relays for two imperfect CSI scenarios in [37], whereas this approach has been extended for the same network with a direct link in [38]. In [39], a robust joint relay precoder and destination receive filters design has been considered for an AF relay network with two models of CSI error, namely, stochastic and norm-bounded errors.…”

Section: A Related Work: Mse Based Robust Designsmentioning

confidence: 99%