SPSA-Based Tracking Method for Single-Channel-Receiver Array

A novel tracking method in the phased antenna array with a single-channel receiver for the moving signal source is presented in this paper. And the problems of the direction-of-arrival track and beamforming in the array system are converted to the power maximization of received signal in the free-interference conditions, which is different from the existing algorithms that maximize the signal to interference and noise ratio. The proposed tracking method reaches the global optimum rather than local by injecting the extra noise terms into the gradient estimation. The antenna beam can be steered to coincide with the direction of the moving source fast and accurately by perturbing the output of the phase shifters during motion, due to the high efficiency and easy implementation of the proposed beamforming algorithm based on the simultaneous perturbation stochastic approximation (SPSA). Computer simulations verify that the proposed tracking scheme is robust and effective

On the Choice of Random Directions for Stochastic Approximation Algorithms

We investigate variants of the Kushner-Clark Random Direction Stochastic Approximation (RDSA) algorithm for optimizing noisy loss functions in high-dimensional spaces. These variants employ different strategies for choosing random directions. The most popular approach is random selection from a Bernoulli distribution, which for historical reasons goes also by the name Simultaneous Perturbation Stochastic Approximation (SPSA). But viable alternatives include an axis-aligned distribution, a normal distribution, and a uniform distribution on a spherical shell. Although there are special cases where the Bernoulli distribution is optimal, there are other cases where it performs worse than other alternatives. We find that for generic loss functions that are not aligned to the coordinate axes, the average asymptotic performance is depends only on the radial fourth moment of the distribution of directions, and is identical for Bernoulli, the axis-aligned, and the spherical shell distributions. Of these variants, the spherical shell is optimal in the sense of minimum variance over random orientations of the loss function with respect to the coordinate axes. We also show that for unaligned loss functions, the performance of the Keifer-Wolfowitz-Blum Finite Difference Stochastic Approximation (FDSA) is asymptotically equivalent to the RDSA algorithms, and we observe numerically that the pre-asymptotic performance of FDSA is often superior. We also introduce a "quasirandom" selection process which exhibits the same asymptotic performance, but empirically is observed to converge to the asymptote more rapidly