# Uniform Sampling Methodology to Construct Projection Matrices for Angle-of-Arrival Estimation Applications

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School of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK

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Department of Communication and Informatics Engineering, Basra University College of Science and Technology, Basra 61004, Iraq

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Instituto de Telecomunicações, Campus Universitário, 3810-193 Aveiro, Portugal

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School of Engineering, University of South Wales, Pontypridd, CF37 1DL, UK

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Faculty of Art, Science and Technology, Wrexham Glyndwr University, Wrexham LL11 2AW, UK

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Author to whom correspondence should be addressed.

Received: 31 October 2019 / Revised: 18 November 2019 / Accepted: 19 November 2019 / Published: 21 November 2019

(This article belongs to the Special Issue Theory and Applications in Digital Signal Processing)

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.