A parametric direction finding technique

Abstract

The fundamental signal model for narrowband direction finding - the propagation of several sinusoidal planar wavefronts in a medium containing an array of sensors with additive Gaussian noise present - is assumed implicitly in most high resolution beamforming algorithms. The "natural" parameters for this problem - angles of arrival, signal strengths, inter-signal coherences, and noise strength - specify entirely the statistic used by many algorithms, the spatial correlation matrixR. Combining the relevant parameters for a given situation in a parameter vector p, an estimate of the true parameter vector can be obtained as the solution of an optimization problem:\min{\hat{p}}\max{\min}\parallel\hat{R} - R(\hat{p})\parallelwhere\hat{R}is an estimate ofR. The minimizing\hat{p}yields direct estimates of the relevant parameters rather than extracting them from an intermediate quantity such as a beampattern. This parametric method is an unbiased estimator which is capable of resolving closely spaced, completely coherent sources at low signal to noise ratios and low time-bandwidth product.