Effects of motion on adaptive arrays

Abstract
Adaptive beamforming procedures based on linear least-squares estimation of a wanted signal, such as the sample matrix inverse (SMI) algorithm, have been shown to successfully excise unwanted interference from the beamformer output. It is usually assumed that the signal environment is stationary, however under nonstationary conditions, such as those experienced by an array mounted on a rapidly moving platform, performance may be significantly degraded. The paper examines the effects of array motion on the structure of the sample covariance matrix and derives expressions for the resulting eigenvalues. These results are used to show that even when the same data is used both to compute the adaptive weights and to form the beamformer output, the performance can be sensitive to extremely small movements of the array. In particular, simple closed-form expressions are derived for the limiting angular displacements of linear arrays which can be tolerated without significant performance degradation during the time taken to acquire sufficient data to update the weights.