Investigation of Scalable Approximation of the Minimum Variance Distortionless Response Beamformer

The minimum variance distortionless response (MVDR) beamformer is commonly used with phased arrays to perform adaptive spatial filtering - preserving array gain in a desired direction while minimizing in-band interference from other directions. This constrained optimization problem is traditionally solved by regularly constructing and inverting the array covariance matrix, resulting in computational complexity of order O(N<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>), where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> is the number of elements in the array. This paper explores a beamspace approximation, using a combination of the spatial fast Fourier transform (FFT) and iterative search, to achieve linear-logarithmic complexity. We investigate the signal to interference-plus-noise ratio (SINR) and complexity tradeoffs associated with this approach to examine its suitability for large array systems,