This manuscript firstly proposes a reduced size, low-complexity Angle of Arrival (AoA) approach, called Reduced Uniform Projection Matrix (RUPM). The RUPM method applies a Uniform Sampling Matrix (USM) criterion to sample certain columns from the obtained covariance matrix in order to efficiently find the directions of the incident signals on an antenna array. The USM methodology is applied to reduce the dependency between the adjacent sampled columns within a covariance matrix; then, the sampled matrix is used to construct the projection matrix. The size of the obtained projection matrix is reduced to minimise the computational complexity in the searching grid stage. A theoretical analysis is presented to demonstrate that the USM methodology can increase the Degrees of Freedom (DOFs) with the same aperture size and number of sampled columns compared to the classical sampling criterion. Then, a polynomial root is constructed as an alternative efficient computational solution of the UPM method in a one-dimensional (1D) array spectrum peak searching problem. It is found that this distribution increases the number of produced nulls and enhances noise immunity. The advantage of the RUPM method is that it is appropriate to apply for any array configuration while the Root-UPM offers better estimation accuracy with less execution time under a uniform linear array condition. A computer simulation based on various scenarios is performed to demonstrate the theoretical claims. The proposed direction-finding methods are compared with several AoA methods in terms of the required execution time, Signal-to-Noise Ratio (SNR) and different numbers of data measurements. The results verify that the new methods can achieve significantly better performance with reduced computational demands.
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