Nizar Tayem

Conjugate ESPRIT (C-SPRIT)

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 well-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) /spl Phi//sup */ while ESPRIT uses /spl Phi/ with no conjugate for the second subarray geometry.

Azimuth and elevation angle estimation with no failure and no eigen decomposition

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, Wus method has some drawbacks, such as pair matching between the azimuth and elevation angle estimations for multiple different sources. Furthermore, Wus 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.

Two-Dimensional DOA Estimation Using Cross-Correlation Matrix With L-Shaped Array

Two dimensional (2-D) direction-of-arrival (DOA) elevation and azimuth angles estimation for uncorrelated sources using L-shaped array is presented in this letter. The key points of the proposed method are the following: 1) The proposed scheme obtains the cross-correlation matrix between the subarrays data to construct a data matrix with free noise; 2) employ only linear operations on the data matrix hence low computational complexity; 3) it has better angle estimation with no failure in practical mobile elevation angle range (70°-90°). Simulation results demonstrate that the proposed method has better performance and lower computational complexity compared to the existing schemes.

Joint Time Delay and Frequency Estimation Without Eigen-Decomposition

In this letter, we addressed the problem of estimating the time delay and the frequencies of noisy sinusoidal signals received at two spatially separated sensors. We employ the Propagator Method (PM) in conjunction with the well-known MUSIC/root-MUSIC algorithm; the proposed method would generate estimates of the unknown parameters. Such estimates are based on the observation and/or covariance matrices. Moreover, the PM does not require the eigenvalue decomposition (EVD) or singular value decomposition (SVD) of the cross-spectral matrix (CSM) of received signals; therefore, a significant improvement in computational load is achieved. Computer simulations are also included to demonstrate the effectiveness of the proposed method.

Conjugate Music for Non-Circular Sources

This paper proposes a method for the direction of arrival (DOA) estimation for non-circular sources, such as binary phase shift keying (BPSK) and M-ary amplitude shift keying (MASK). The proposed scheme can be applied to both scenarios; the sources are noncoherent or coherent. Comparisons that are made with the well-known classical subspace algorithms, such as MUSIC and forward/backward smoothing by Pillai et al., show that the proposed method has several advantages. First, no forward/backward spatial smoothing for the covariance matrix is needed, whereas the Pillai method requires it, which increases the computational load and is time-consuming. Second, the proposed method can detect N-1 coherent sources when N antennas are used, whereas the well-known Pillai method can only detect 2N/3 coherent sources. Third, the proposed method is more suitable for real-time implementation since it only requires a single or few snapshots in order to give an accurate DOA estimation. However, both MUSIC and Pillai require a high number of snapshots, which increases the computational cost and memory storage. Simulation results show that the proposed method has better performance, compared to the forward/backward spatial smoothing by the Pillai and MUSIC algorithm

Propagator Method for joint time delay and frequency estimation

A novel method of estimating the differential delay of a sinusoidal signal is considered. The new method utilizes the propagator method (PM) which does not require the eigen-decomposition of the cross-spectral matrix (CSM) in estimating the delay of a signal received at two separated sensors. Moreover, the proposed method would generate estimates of the signal frequencies. Such estimates of time delay and frequencies are based on the observation and/or covariance matrices. Computer simulation is performed to validate the new procedure.

HARDWARE IMPLEMENTATION OF A PROPOSED QR- TLS DOA ESTIMATION METHOD AND MUSIC, ESPRIT ALGORITHMS ON NI-PXI PLATFORM

In this paper, we present an experimental veriflcation of a novel QR-TLS algorithm. Two other algorithms for direction of arrival (DOA) estimation of multiple incident source signals called multiple signal classiflcation (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) are implemented on a National Instruments (NI) PXI platform. The proposed method is based on subspace decomposition of a received data into a signal and a noise space using QR decomposition. The angle of the signal arrival information is extracted from the signal subspace by using the method of total least squares (TLS). The algorithms are implemented in LabView NI hardware. The experimental procedures are discussed in details which includes interfacing of the uniform linear array (ULA) of antennas with the NI-PXI platform, calibrating phase difierences between the RF receivers, and selecting transmitter and receiver parameters, for determining the DOAs of the multiple incident source signals. The experimental results are shown for a single and two sources lying at arbitrary angles from the array reference to verify the successful real time implementation of the proposed and other DOA estimation algorithms.

Reply to “Comments on `L-Shape Two-Dimensional Arrival Angle Estimation With Propagator Method'”

In this reply to the paper by Shu, Liu and Lu (see ibid., p.1502-3, 2008), a novel method with low-complexity, but showing neither estimation failure nor the pair-matching problems, is described for the two-dimensional DOA estimation. The authors in the previous papers (Kikuchi et al., 2006; Gu et al, 2008)also proposed two methods different from that in (Van der Veen et a., 1992) to achieve the automatic pair matching by employing the L-shaped array configuration. The method in this reply is also different from the ones in (Kikuchi et al., 2006; Gu et al, 2008). In this reply, an independently developed algorithm is presented by using the unitary root MUSIC and unitary MUSIC and changing the L-shape to a cross-shaped array configuration.

Covariance Matrix Differencing for Coherent Source DOA Estimation Under Unknown Noise Field

In this paper, we propose an algorithm to estimate the one- and two-dimensional direction of arrival angles (DOAs) from the coherent incident sources. We can apply our proposed algorithm for more practical situations even when the unknown noise covariance matrix is in a complex symmetric Toeplitz form; whereas the Prasads method requires that the unknown noise should be in a real symmetric Toeplitz form. Our proposed method is based on the difference between the forward/backward spatial smoothing for the data covariance matrix and the Hermition of the backward spatial smoothing. This covariance matrix difference is introduced to eliminate the noise components from the array structure. The numerical results verify that the proposed method gives more accurate estimation and superior performance than the conventional root MUSIC of the forward/backward spatial smoothing.

L-shape 2-dimensional arrival angle estimation with propagator method

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/spl deg/ and 90/spl deg/. 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 in signal to noise ratio for the parameters used in this paper.