Construction of Projection Matrices Based on Non-Uniform Sampling Distribution for AoA Estimation

Abstract

A Non-Uniform Sampling (NUS) methodology is presented, which improves the Angle of Arrival (AoA) estimation accuracy. The proposed sampling methodology is applied to extract the collected data efficiently and to reduce the possible dependency within rows/columns of the Covariance / Correlation Matrix (CM). The new sampled matrix approach is utilized to form such a projection matrix in order to provide better resolution of angles of arrival for closely incident signals on the antenna array receiver and to increase Degrees of Freedom (DOFs) compared to the classical criterion. The new direction-finding method based on the NUS methodology is called a Non-Uniform Projection Matrix (NUPM). A theoretical analysis is presented to demonstrate the advantage of the NUS methodology in terms of the obtained energy of the eigenvalues that are associated with the signal eigenvectors. It is proved that the proposed matrix sampling approach can provide better estimation resolution and detection of higher numbers of angles of arrival compared to the classical sampling method, without increasing array aperture size and the complexity of computations. A reduced-dimension process is applied to the NUPM in order to decrease the computational burden at the grid-scanning step. A computer simulation, including many scenarios, is implemented to justify the expected improvements of the NUS methodology compared to the classical approach. It is found that the new sampling distribution enhances noise immunity and increases DOFs compared to the conventional criterion. The performance of the NUPM method is compared with several AoA methods, including the Cramer-Rao Lower Bound (CRLB), and the obtained results verify the effectiveness and robustness of the proposed NUPM technique. INDEX TERMS Antenna array, AoA estimation, covariance matrix, DOFs, projection matrix, non-uniform sampling. I. INTRODUCTION The number and size of communications-relevant data sets have increased concomitantly with the advancing development of communications bandwidth and power in several applications such as social networks, telecommunications, The associate editor coordinating the review of this manuscript and approving it for publication was Hasan S. Mir. and military [1], [2]. Currently, the fifth-generation (5G) mobile communication systems exploit a Massive Multiple-Input Multiple-Output (M-MIMO) technology to compensate path and penetration loss, and to satisfy high data-rate requirements [3]. Finding Angle or Direction of Arrival (AoA/DoA) parameters of the received/measured data within wireless communication systems has gained much attention, particularly in far-field signal applications [4]. With

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“…Once this goal is achieved, the next step is to sample N columns (i.e., the number of desired users) from the measured noise correlation matrix to construct the projection noise matrix. The challenge here is how to sample the N columns in such a way that can provide the best representation of the original matrix (i.e., R nn ) and extract the information about the signal parameters efficiently [32][33][34]. To this end, assume Q N represents the sampled matrix constructed by sampling N columns uniformly instead of sampling the first N columns straightforwardly.…”

“…It can be clearly seen that the DOFs number of the Array Factor (AF) based on the proposed sampling criterion is much higher than the produced ones that sample only the first N columns of a noise correlation matrix. Therefore, to find the null ratio number, R, between these two criteria, the number of produced nulls in (32) is divided by (28), which yields:…”