An analytical model for the constrained stochastic gradient algorithm

This paper presents an analytical model for the constrained stochastic gradient (CSG) algorithm. This algorithm is used to obtain the weights of antenna arrays for mobile communications, aiming to maximize the signal-to-interference-plus-noise ratio (SINR) of such systems. For the algorithm performance evaluation, several operating conditions are considered by combining a wide variety of angles-of-arrival for both desired and interfering signals. To have an analytical model describing the system behavior is very useful, since it permits efficient evaluation of the algorithm performance under different working conditions. Thus, analytical expressions for the first moment of the weight vector and the SINR characteristic are derived here. The proposed model is obtained under a small step-size condition, resulting in smooth behavior for both the weight and SINR characteristics. The accuracy of the proposed model is assessed through numerical simulations.