A NEURAL NETWORK APPROACH TO MVDR BEAMFORMING PROBLEM

Abstract

A Hopfield-type neural network approach which leads to an analog circuit for implementing the real-time adaptive antenna array is presented. An optimal pattern of the array can be steered by updating the weights across the array in order to maximize the output signal-to-noise ratio (SNR). Furthermore, it is shown that the problem of adjusting the array weights can be characterized as a constrained quadratic nonlinear programming. Practically, the adjustment of settings is required to respond to a rapid time-varying environment. Many numerical algorithms have been developed for solving such problems using digital computers. The main disadvantage of these algorithms is that they generally converge slowly. To tackle this difficulty, a neural analog circuit solution is particularly attractive in real-time applications with minimization of a cost function subject to constraints. A novel Hopfield-type neural net with a number of graded-response neurons designed to perform the constrained quadratic nonlinear programming would lead to such a solution in a time determined by RC time constants, not by algorithmic time complexity. The constrained quadratic programming neural net has associated it with an energy function which the net always seeks to minimize. A fourth-order Runge-Kutta simulation is conducted to verify the performance of the proposed analog circuit. It shows that the circuit operates at a much higher speed than conventional techniques and the computation time of solving a linear array of 10 elements is about 0.1 ns for RC = 5 x 10(-9).