Analysis of Nonuniformly Spaced Linear Arrays

In this work. the design of linear microphone arrays with nonuniform element spacing is investigated. Both deterministic and random transducer location selection approaches to realizing the linear array is outlined. The probability distribution function for element positions is derived in the continuum limit by matching the response of the array to an objective beam function. The target response is designed to exhibit uniform sidelobe levels of prescribed amplitude. Random beam profiles constructed by sampling the positions of a fixed number of elements from the derived distribution function are analyzed with respect to the mean and variance in the sidelobe amplitudes. It is shown that in comparison to the uniformly distributed case. nonuniform spacing can lead to a higher variance in the sidelobe amplitudes if the number of elements is small. However. with increase in the element size. the variance approaches that of the uniform case. The advantage of nonuniform spacing is in control of the mean sidelobe amplitudes which remain below the specified amplitude in the visible range of the observation parameter.