Efficient direction of arrival estimation using low rank approximation

Abstract

A novel and useful system and method for direction of arrival (DOA) estimation having a complexity of order O(N log N), which allows a DOA dependent calibration. In one embodiment, the architecture comprises several fast Fourier transform (FFT) machines operating in parallel with coefficient multiplications before and after the FFT operations. These pre and post coefficients are computed using an optimal low rank approximation of a distortion matrix using singular value decomposition. The values of the pre and post calibration coefficients before and after the FFT operations for each rank are computed from the singular value decomposition of the distortion matrix C=B/F, where B is the digital beam forming (DBF) matrix and F is the ideal FFT matrix. A method of acquiring the beamforming matrix B is also disclosed. The architecture implements K×N×logN operations which for relatively low rank is significantly smaller than the Noperations required for the complete matrix multiplication, where K is the rank of the approximation and N is the length of the FFT. A circuit and method for computing the calibration coefficients and a simple proof that this approximates a general beam forming matrix is disclosed.