Imposing pattern nulls on broadband array responses

This paper considers the problem of altering a quiescent design for an array of omni-directional sensors so that the altered design rejects a far- field broadband signal from a given direction. This problem occurs where microphone arrays are to be used to acquire speech signals for telecommunication and interferring signals must be rejected. Three main results are presented in this paper. First, conditions for imposing an exact broadband null upon any given quiescent array response are derived. Second, an analysis of the sensitivity of exact nulling array responses to sensor position error is presented. Third, frequency domain formulations for broadband nulls are obtained and it is shown that these are less restrictive than the exact null conditions which are imposed in the time domain. A Lagrange multiplier approach is used to impose the null conditions upon a quiescent array response to minimize the square error between the quiescent and nulled responses. A design example is given.