An average stochastic gradient method for time delay and multipath estimation

An average stochastic gradient method is proposed to iteratively solve the minimization problem of a quadratic criterion, in terms of the delays and amplitudes of a multipath channel. It is shown that the minimization of a quadratic error criterion leads to partly nonlinear gradient equations, which are analyzed from the viewpoint of solution unicity and attraction domain. The initial guess was that the gradient must be chosen no further from the solution than one correlation radius of the input process. An expression of a stochastic gradient is derived, yielding a simple algorithm that is able to converge to the solution with short data samples. Simulation results are given to help understand the behavior of various versions of the algorithm