Noncooperative iterative MMSE beamforming algorithms for ad hoc networks

• Published in: IEEE transactions on communications Vol. 54; no. 4; pp. 748 - 759
• Main Authors: Iltis, R.A., Seung-Jun Kim, Hoang, D.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Algorithms; Applied sciences; Array signal processing; Beamforming; Detection, estimation, filtering, equalization, prediction; Distortion; Exact sciences and technology; game theory; Games; Information, signal and communications theory; Interference; Iterative algorithms; Lagrangian functions; least-mean-square (LMS) methods; MIMO; Miscellaneous; Multiplexing; Networks; Operation, maintenance, reliability; Optimization; Physical layer; Power efficiency; Quality of service; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Wireless networks; Performance evaluation; Mobile radiocommunication; least-mean- square (LMS) methods; Array signal processing; Eigenvector; Wireless telecommunication; Time division multiplexing; Iterative method; networks; Algorithm; Game theory; Beam forming; Optimization; Mean square error; Necessary condition; Simulation; First order; Ad hoc network; Service quality; Least mean squares methods; Signal to noise ratio; Fixed point
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2006.873095

An asynchronous unicast ad hoc network is considered, where each node i is equipped with a receive/transmit beam-former pair (W/sub i/, g/sub i/) designed under a quality-of-service (QoS) SNR constraint. It is first shown that the minimum sum-power beamformers for the network satisfy a weak duality condition, in which the pairs ((g/sub i//sup opt/)*, (W/sub i//sup opt/)*) achieve the same sum power as the primal network. However, the optimum receive beamformer w/sub i//sup opt/ is not in general equal to (g/sub i//sup opt/)*, in contrast to the case of cellular and time-division duplexing networks. Iterative minimum mean-square error (IMMSE) beamforming algorithms are then proposed in which w/sub i/ = g/sub i/* is enforced. These algorithms are shown to be instances of the Power Algorithm in which gi is the maximizing eigenvector of an SNR-related objective matrix. The IMMSE algorithm can also be viewed as a noncooperative beamforming game, in which the payoff includes normalized SNR, and the tax is related to interference caused at other nodes. The existence of fixed points (Nash equilibria) is proved for IMMSE. Furthermore, fixed points of IMMSE are shown to satisfy the first-order necessary conditions for optimization using a network Lagrangian. The IMMSE game is modified to yield a sequential distortionless-response beamforming algorithm, which is shown to be convergent using a Total Interference Function. Extensive simulation results illustrate that IMMSE yields better power efficiency than a greedy noncooperative SNR-maximizing game.