Maximum directivity proof for three-dimensional arrays
Alan T. Parsons · The Journal of the Acoustical Society of America · 1987
A proof is presented for the following theorem: Given all possible three-dimensional (3-D) configurations of n omnidirectional acoustic sensors with vanishingly small separations, and given all possible weighting schemes and steer directions, the directivity index achieves an overall maximum value of n2 when the sensors are configured as a linear array steered to end-fire, it being immaterial whether or not the sensor spacings are equal.