Robust Optimization for Amplify-and-Forward MIMO Relaying From a Worst-Case Perspective
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...
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| Vydáno v: | IEEE transactions on signal processing Ročník 61; číslo 21; s. 5458 - 5471 |
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| Jazyk: | angličtina |
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01.11.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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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 worst-case 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 channel-diagonalizing 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. |
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| AbstractList | 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 worst-case 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 channel-diagonalizing 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. |
| Author | Jiaheng Wang Hong Shen Levy, Bernard C. Chunming Zhao |
| Author_xml | – sequence: 1 surname: Hong Shen fullname: Hong Shen email: shenhongseu@gmail.com organization: Nat. Mobile Commun. Res. Lab., Southeast Univ., Nanjing, China – sequence: 2 surname: Jiaheng Wang fullname: Jiaheng Wang email: jhwang@seu.edu.cn organization: Nat. Mobile Commun. Res. Lab., Southeast Univ., Nanjing, China – sequence: 3 givenname: Bernard C. surname: Levy fullname: Levy, Bernard C. email: bclevy@ucdavis.edu organization: Dept. of Electr. & Comput. Eng., Univ. of California, Davis, Davis, CA, USA – sequence: 4 surname: Chunming Zhao fullname: Chunming Zhao email: cmzhao@seu.edu.cn organization: Nat. Mobile Commun. Res. Lab., Southeast Univ., Nanjing, China |
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| Keywords | Performance evaluation multiple-input multiple-output (MIMO) cooperative transmission Relaying Parameter estimation Relay Imperfect channel state information (CSI) Worst case method mutual information (MI) Closed form equation Optimization Mean square error Channel estimation mean square error (MSE) Routing protocols Robustness Deterministic approach MIMO system Maximin problem Coding circuit Eigenmode Channel structure Transmission protocol relay precoding Saddle point Minimax method Signal processing Metric Reliability worst-case robust design Mutual information |
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| SubjectTerms | Amplification Applied sciences Coding, codes Detection, estimation, filtering, equalization, prediction Exact sciences and technology Imperfect channel state information (CSI) Information, signal and communications theory Mathematical analysis Mathematical models mean square error (MSE) Mean square errors MIMO Minimax technique multiple-input multiple-output (MIMO) cooperative transmission mutual information (MI) Optimization Relay relay precoding Relays Robustness Saddle points Signal and communications theory Signal, noise Telecommunications and information theory Transceivers Uncertainty worst-case robust design |
| Title | Robust Optimization for Amplify-and-Forward MIMO Relaying From a Worst-Case Perspective |
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