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...
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| Published in | IEEE transactions on signal processing Vol. 61; no. 2; pp. 238 - 252 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.01.2013
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 1941-0476 |
| DOI | 10.1109/TSP.2012.2222379 |
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| Abstract | 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. |
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| AbstractList | 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 semiinfinite 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 signdefiniteness 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. 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. |
| Author | Larsson, E. G. Gharavol, E. A. |
| Author_xml | – sequence: 1 givenname: E. A. surname: Gharavol fullname: Gharavol, E. A. email: ebrahim@isy.liu.se organization: Electr. Eng. Dept. (ISY), Linkoping Univ., Linkoping, Sweden – sequence: 2 givenname: E. G. surname: Larsson fullname: Larsson, E. G. email: erik.larsson@isy.liu.se organization: Electr. Eng. Dept. (ISY), Linkoping Univ., Linkoping, Sweden |
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| Keywords | Performance evaluation Relay Relay network robust transceiver optimization Iterative method Beam forming Optimization Transceiver Mean square error Duplex process Linear matrix inequality Ad hoc network MIMO system Multiple access Multistage method Two channel system Control system multi-user MIMO relay networks Ad hoc networks Algorithm Complex variable method Symbol detection Relay channel Simulation One way sign-definiteness lemma Signal processing robust design beamforming |
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| SubjectTerms | Ad hoc networks Adhoc Networks Applied sciences Array signal processing Beamforming Detection, estimation, filtering, equalization, prediction Exact sciences and technology Information, signal and communications theory MIMO Multi-user MIMO Optimization Receivers Relay Networks Relays Robust Design Robust Transceiver Optimization Robustness Sign-definiteness Lemma Signal and communications theory Signal, noise Telecommunications and information theory Uncertainty |
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| Title | The Sign-Definiteness Lemma and Its Applications to Robust Transceiver Optimization for Multiuser MIMO Systems |
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