On stochastic approximation and the hierarchy of adaptive array algorithms

Stochastic approximation is used to illustrate the connection between several recently proposed recursive algorithms for adaptation of array processing structures. The development illustrates the manner in which incorporation of a priori statistical information leads from one algorithm to another. This link establishes a hierarchy among the algorithms. Sufficient conditions are established to ensure convergence of the algorithms and the conditions are shown to be universal in the sense that they are independent of the particular algorithm implemented. The signal processing problem considered throughout the paper is one of estimating (in real time) the time history of a stochastic, propagating signal that is immersed in additive, propagating and nonpropagating noise. The propagating noise is sometimes called interference.