On the Constrained Stochastic Gradient Algorithm: Model, Performance, and Improved Version

• Published in: IEEE transactions on signal processing Vol. 57; no. 4; pp. 1304 - 1315
• Main Authors: Kolodziej, J.E., Tobias, O.J., Seara, R., Morgan, D.R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive antenna arrays; Algorithm design and analysis; algorithm modeling; Algorithms; Antenna arrays; Applied sciences; Communication system control; constrained stochastic gradient algorithm; Constraints; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Gaussian noise; Information, signal and communications theory; Interference; Interference constraints; Mathematical analysis; Mathematical models; Miscellaneous; Mobile antennas; Mobile communication; Signal analysis; Signal and communications theory; Signal processing; Signal to noise ratio; Signal, noise; Spreads; Stochastic processes; Stochasticity; Studies; Telecommunications and information theory; Performance evaluation; Stochastic model; Parameter estimation; Wireless telecommunication; Signal estimation; Adaptive antenna arrays; Mobile communication; Stochastic method; Algorithm; Modeling; algorithm modeling; Signal interference; Accuracy; constrained stochastic gradient algorithm; Constructive geometry; Algorithm performance; Gaussian signal; Arrival angle; Analytical method; Signal processing; Numerical simulation; Signal to interference plus noise ratio; Antenna array; Gradient method
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.2010375

This paper discusses the constrained stochastic gradient (CSG) algorithm used for controlling antenna arrays, aiming to maximize the signal-to-interference-plus-noise ratio (SINR) in mobile communications. Firstly, analytical expressions for the first moment of the weight vector and the SINR characteristic of the standard CSG algorithm are derived for two interferer signals, considering small step-size conditions and assuming Gaussian signal, interference, and noise. From these model expressions, the CSG algorithm performance is assessed, which predicts undesired behavior (termed here unbalanced behavior, pertaining to an unbalance between maximizing signal power and minimizing interference power) when one or more interference angles-of-arrival are close to the signal angle-of-arrival and the angle-of-arrival spreads of the involved signals are small. Finally, by using the model expressions, an improved CSG (ICSG) algorithm is proposed to compensate the unbalanced behavior of the standard CSG algorithm. The accuracy of the proposed model and the effectiveness of the modified algorithm are assessed through numerical simulations.