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In this paper, the problem of estimating the two-dimensional direction of arrival angles with automatic pair matching for multiple non-coherent sources is presented. The proposed method employs Cholesky factorization for a Hermitian positive-definite covariance matrix in conjunction with parallel factor (PARAFAC) and trilinear alternative least squares method. The proposed method offers several advantages compared with well-known eigenvalue decomposition (EVD)-based methods. First, it provides fast execution since Cholesky factorization requires O( $$n^{3}$$ /6) number of operations, whereas EVD requires $$O(n^{3})$$ . Second, it is suitable for hardware implementation using field-programmable gate arrays. Third, it provides significantly lower memory requirements since only the lower triangular matrix of Cholesky factorization requires to be stored. Fourth, it applies PARAFAC model to the signal space with a smaller dimension compared with the conventional PARAFAC model that is applied directly to noise data without preprocessing. Hence, the proposed method provides better performance and less computational cost and processing time compared with the conventional PARAFAC model. Computer simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present six subspace decomposition based methods for joint time of arrival (TOA) and frequency of arrival (FOA) estimation of multiple incident sources. These are LU-TLS, QR-TLS, direct TSQR-TLS, direct TSLU-TLS, parallel TSQR-TLS, and parallel TSLU-TLS. The direct and parallel TSQR/TSLU-TLS are recently developed methods in subspace decomposition and are employed in this work for time and frequency estimation. The proposed methods employ a pair of spatially separated sensors to receive multiple incident source signals. A data matrix is constructed in the form of a Hankel matrix from multiple snapshots of the received signal. The information of both TOA and FOA of multiple incident sources is extracted from the data matrix by applying LU/QR techniques (in the first set of the methods) and a tall skinny TSLU/TSQR factorization in the second set. The estimates of the TOA and FOA are obtained from the signal subspace by applying the total least squares (TLS) method. Simulation results are presented to assess the performance of the proposed methods. The effect of parametric variations on the performance has also been analyzed for all the proposed methods. Further, the computational times and complexities of the proposed methods are also computed and compared with each other. [ABSTRACT FROM AUTHOR]

A response by Nizar Tayem and Hyuck M. Kwon to a letter to the editor about their article "L-Shape Two-Dimensional Arrival Angle Estimation With Propagator Method" that was published in the previous issue is presented.

Abstract: Recently, Wu et al. proposed a scheme for two-dimensional direction of arrival angle estimation for azimuth and elevation angles, using the propagator method. An advantage of this method over the classical subspace based algorithms, such as ESPRIT and MUSIC, is that it does not apply any eigenvalue decomposition (EVD) to the cross spectral matrix or singular value decomposition (SVD) to the received data. This significantly reduces the computational complexity, compared to the EVD and SVD. However, Wu''s method has some drawbacks, such as pair matching between the azimuth and elevation angle estimations for multiple different sources. Furthermore, Wu''s method has an estimation failure problem in the range of practical mobile elevation angles. The objectives of this paper are two-fold: (1) to overcome these two problems with less arithmetic operation counts than Wu used; and (2) to improve the performance significantly. To achieve these objectives, we propose an antenna array configuration which avoids these problems. Simulation results verify that the proposed scheme can remove these problems and give much better performance. [Copyright &y& Elsevier]

It is known that computational loads of the propagator method (PM) can be significantly smaller, e.g., one or two order, than those of MUSIC and ESPRIT because the PM does not require any eigenvalue decomposition (EVD) of the cross-correlation matrix and singular value decomposition (SVD) of the received data. However, the PM of the parallel shape array has nonnegligible drawbacks such as 1) requirement of pair matching between the 2-D azimuth and elevation angle estimation which is an exhaustive search and 2) estimation failure problems when elevation angles are between 70° and 90°. The purpose of this paper is to show a way to remove these problems in the PM without additional computational loads. This paper will employ one or two L-shape arrays because the parallel shape used in the PM may cause the aforesaid problems. Simulation results verify that the PM with one or two L-shape configurations can remove these problems and improve the performance of the PM significantly, e.g., almost 5 dB hi signal to noise ratio for the parameters used in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm to estimate the direction of the arrival angles (DOAs) from noncoherent one-dimensional (1-D) signal sources such as binary phase shift keying (BPSK) and M-ary amplitude shift keying (MASK) The proposed algorithm can provide a more precise DOA estimation and can detect more signals than we D-known classical subspace.methods MUSIC and ESPRIT for the 1-D signals. The complexity is the same as that of ESPRIT since the proposed algorithm uses the same array geometry and subarray processing that ESPRIT does. The main differences between the proposed algorithm and the ESPRIT algorithm are as follows: 1) the number of overlapping array elements between two subarrays is equal to M in the proposed algorithm, while in ESPRIT the maximum number of overlapping elements is M - 1, where M denotes the total number of array elements, and 2) the proposed algorithm employs the conjugate of rotation matrix (CRM) V while ESPRIT uses 1 with no conjugate for the second subarray geometry. [ABSTRACT FROM AUTHOR]

A response by Jean-Pierre Delmas to a letter to the editor about the article on Conjugate ESPRIT is presented.