A method of calculating average array signal response in a two-path medium

A method is described for calculating average signal array gain for cw acoustic signals in a multipath medium. The two-path case is considered; the extension to many paths is straightforward but tedious. Only phase fluctuations are treated; the signals arriving along the two paths may have different amplitudes, but these amplitudes are assumed constant in time and uniform across the array aperture. It is suggested that for beam formation by delay and sum the array signal gain for single path represents the upper limit of performance for multipath.