The Selected Samples Effect on the Projection Matrix to Estimate the Direction of Arrival

Abstract

The way and size of matrix sampling have significant effects on the obtained eigen/singular values and the corresponding eigen/singular vectors of the sample matrix. Thus, this work analyzes and investigates these effects on the Angle of Arrival (AoA) estimation accuracy. To this end, the covariance matrix is sampled with different sub-matrices sizes. The obtained sampled matrices are used to construct the projection matrices. At each formed projection matrix, the Singular Value Decomposition (SVD) is applied to calculate the singular values of the signal subspace to show the sampling impact. It is demonstrated with the same array aperture size, output Signal to Noise Ratio (SNR) and the number of snapshots, the power can be increased by increasing only number of sampled rows/columns in the matrix projection construction stage. This, in turn, improves the estimation accuracy of the AoA methods. Numerical simulation examples are given to justify this claim. The results are presented and discussed.