The effect of a finite-distance signal source on a far-field steering Applebaum array-two dimensional array case

Approximate expressions are obtained for the output signal-to-noise ratio (SNR) expressed in terms of the finite signal distance and signal direction for a finite-distance signal source´s effect on the performance of a far-field steering two-dimensional Applebaum-type adaptive array. The expression is shown to be consistent with the actual simulated value. Using that expression, a simplified rule is obtained to determine the distance between the signal source and the array center at which the output SNR loss is given by a specific value. The SNR value so obtained varied with two-dimensional signal direction. The analysis for the case of an arbitrarily located array is presented, followed by the cases for rectangular, circular and elliptical arrays. It was found that this distance associated with the given SNR value is always less for a rectangular array than that of a linear array when the total number of array elements for both are equal and the performances of an elliptical array are similar to those of a circular array