“A Robust Approach to Linearly-Constrained Adaptive Array Processing”

by George Thomas Zunich

May 1991

Minimum variance beamforming is a powerful technique in adaptive array processing that allows the reception of a signal of interest while nulling unwanted interfering signals. In the presence of a high input signal-to-noise ratio (SNR), however, the technique is very sensitive to amplitude and phase perturbations of the array processing system and the processor may attempt to null the signal of interest as if it were an interfering signal. The result is a substantial degradation of the output SNR of the beamformer over that achieved for the error-free system.

This dissertation presents and analyzes robust constraints that protect a minimum variance beamformer from the effects of small phase anomalies resulting from factors such as random channel phase errors, array placement errors, steering errors, and/or frequency miscalibration.The use of robust constraints is shown to eliminate the need for precise phase calibration of the array. This is an important contribution because, in most practical applications, precise phase calibration is more difficult than is accurate amplitude calibration.

The approach taken in this thesis is to first demonstrate that the robust constraints can be deriveddirectly from an analysis of the beamformer output power. A critical parameter which depends on both the beamformer weighting coefficients and the phase errors is identified. It is shown that performance degradation will only occur when this parameter lies within a circular region in the complex plane. Robust constraints for the array weights are then identified which force the parameter value to be external to the circular region, regardless of the specific values of sufficiently small phase errors. An identical set of robust constraints is shown to arise whenderivative constraints are placed on individual array elements.

A closed-form solution for the weight coefficients achieved with robust constraints is derived for the specific case of a narrowband adaptive array processor. Equations are developed that predict SNR performance resulting from the use of the robust constraints. An adaptive processor for the robust system is developed using a modified Generalized Sidelobe Canceller structure. Performance of the robust system is illustrated using both simulation experiments with synthesized input data and computations on actual array data. The results obtained confirm the effectiveness of the constraints in phase-perturbed environments.