The Sign-Definiteness Lemma and Its Applications to Robust Transceiver Optimization for Multiuser MIMO Systems

• Published in: IEEE transactions on signal processing Vol. 61; no. 2; pp. 238 - 252
• Main Authors: Gharavol, E. A., Larsson, E. G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2013; Institute of Electrical and Electronics Engineers
• Subjects: 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; 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
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2012.2222379

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.