Random Beam Patterns from Linear Arrays

The design of linear microphone arrays with randomly spaced elements is investigated.The probability distribution function for the element positions is derived in the continuum limit by matching the response of the array to an objective beam function.An analysis of the expected value and variance of the beam is presented as a function of the angular direction.Comparison of these metrics to those generated from uniformly distributed array positions is conducted.The number of elements and random ensembles required to meet a desired sidelobe level is obtained.It is found that using a probability density function of a particular beam pattern can reduce the side lobe levels of the random samples of the transducer position.