Absolutely optimum array filters for sensor arrays

A family of array filters is derived for processing the recorded measurements of an array of sensors with the purpose of attenuating coherent noise interfering with a desired signal. One member of this family is the absolutely optimum array filter (AOAF), which minimizes the magnitude squared of the array rejection response subject to an all-pass condition for the desired signal. The AOAF is shown to have an array rejection response where both the width of the main lobes and the height of the sidelobes are reduced to zero.