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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 61; no. 21; pp. 5458 - 5471
Main Authors: Hong Shen, Jiaheng Wang, Levy, Bernard C., Chunming Zhao
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.11.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
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
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2013.2278819