Abstract
Several works show that the linear Angle of Arrival (AoA) methods such as Projection Matrix (PM) have low computational complexity compared to the subspace methods. Although the PM method is classified as a subspace method, it does not need decomposition of the measured matrix. This work investigates the effect of the sampled columns within the covariance matrix on the projection matrix construction. To the authors’ knowledge, this investigation has not been addressed in the literature. Unlike the subspace methods such as Multiple Signal Classification (MUSIC), Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Minimum Norm, Propagator, etc., which have to use a specific number of columns, we demonstrate this aspect is not applicable in the PM method. To this end, the projection matrix is formed based on a various number of sampled columns to estimate the arrival angles. A theoretical analysis is accomplished to illustrate the relationship between the number of the sampled columns and the degrees of freedom (DOFs). The analysis shows that with the same aperture size, the DOFs can be increased by increasing only the number of sampled columns in the projection matrix calculation step. An intensive Monte Carlo simulation for different scenarios is presented to validate the theoretical claims. The estimation accuracy of the PM method, based on the proposed selected sampling methodology outperforms all the other techniques with less complexity compared to the Capon and MUSIC methods. The estimation accuracy is evaluated in terms of Root Mean Square Error (RMSE) and the Probability of Successful Detection (PSD). The results are presented and discussed.
Highlights
The major application of a sensor array is to estimate parameters of a signal or signals impinging on the array [1,2,3]
Unlike the subspace methods such as Multiple Signal Classification (MUSIC), Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Minimum Norm, Propagator, etc., which have to use a specific number of columns, we demonstrate this aspect is not applicable in the Projection Matrix (PM)
It was proven that the way of sampling the rows/columns of a matrix has a substantial influence on the performance of the PM algorithm
Summary
The major application of a sensor array is to estimate parameters of a signal or signals impinging on the array [1,2,3]. A Multiple Signal Classification (MUSIC) method is an Eigenstructure technique, which provides fairly estimates for the angles of arrival, the number of signals, and their strengths [19,20] This algorithm conceptually depends on the orthogonality between the noise subspace and steering vector of the antenna array to generate the spatial spectra of received array signals. In Reference [34], the authors presented a Maximum Signal Subspace (MSS) AoA method, which depends on the orthogonality between the manifold vector and the eigenvector that is associated with the highest eigenvalue regardless of the number of incoming signals This method reduced the computational load in the grid-searching step; it is only suitable for ULAs. Later, the authors proposed an algorithm called Subtracting Signal Subspace (SSS), which is based on the orthogonality between the manifold vector and signal subspace and can estimate signal directions of arrival in both.
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