Feng-Gang Yan

Low-Complexity DOA Estimation Based on Compressed MUSIC and Its Performance Analysis

This paper presents a new computationally efficient method for direction-of-arrival (DOA) estimation with arbitrary arrays. The total angular field-of-view is first divided into several small sectors and the original noise subspace exploited by the multiple signal classification (MUSIC) algorithm is mapped from one sector to the other sectors by a Hadarmard product transformation. This transformation gives a new noise-like subspace cluster (NLSC), whose intersection is found to be simultaneously orthogonal to the steering vectors associated with the true DOAs and several virtual DOAs. Based on such a multiple orthogonality, a novel compressed MUSIC (C-MUSIC) spatial spectrum at hand is derived. Unlike MUSIC with tremendous spectral search, C-MUSIC involves a limited search over only one sector, and hence it is computationally very attractive. To obtain the intersection of NLSC for more than two sectors, a low-complexity method is also proposed in the present work, which shows advantages over the existing alternative projection method (APM) and singular value decomposition (SVD) techniques. Furthermore, the mean square errors (MSEs) of the proposed estimator is derived. Simulation results illustrate that C-MUSIC trades-off MSEs by complexity and resolution as compared to the standard MUSIC efficiently.

Real-Valued MUSIC for Efficient Direction Estimation With Arbitrary Array Geometries

Most of the existing methods for direction-of-arrival (DOA) estimation are based on numerical characteristics behind the entire array output covariance matrix (AOCM). Since the AOCM is generally a complex matrix, those approaches require tremendous complex computations accordingly. This paper addresses the problem of DOA estimation with real-valued computations by considering the real part of AOCM (R-AOCM) and the imaginary part of AOCM (I-AOCM) separately. It is shown that the null space of R-AOCM and that of I-AOCM are the same subspace, which coincides with the intersection of the original noise subspace and its conjugate subspace. Using such a mathematical fact, a novel real-valued MUSIC (RV-MUSIC) estimator with a real-valued subspace decomposition on only R-ACOM (or I-AOCM) instead of the entire ACOM is derived. Compared with most state-of-the-art unitary algorithms suitable for only centro-symmetric arrays (CSAs), the proposed technique can be used with arbitrary array geometries. Unlike conventional MUSIC with exhaustive spectral search, RV-MUSIC involves a limited search over only half of the total angular field-of-view with a real-valued noise subspace, and hence reduces the complexity by 75%. Theoretical performance analysis on the mean square error (MSE) and numerical simulations demonstrate that RV-MUSIC shows a very close accuracy to the standard MUSIC.

Source localization based on symmetrical MUSIC and its statistical performance analysis

In this paper, a new method for fast direction-of-arrival (DOA) estimation with no dependance on array configurations is proposed, which is referred to as the symmetrical multiple signal classification (SMUSIC). Unlike the standard MUSIC, the S-MUSIC spatial spectrum is constructed by the intersection of the noise subspace and the conjugate noise subspace, and it hence generates spectral peaks at the true DOAs and the symmetrical virtual DOAs simultaneously. Such a characteristic allows fast DOA estimation by spectral search over only half of the total angular filed-of-view. Therefore, the new approach has a much lower computational complexity than the standard MUSIC. The statistical performance of S-MUSIC is studied and a close-form expression for the MSEs (mean square errors) of DOA estimation by the proposed estimator is derived. Numerical simulations are conducted to demonstrate the effectiveness of the new algorithm and to verify the theoretical analysis, and it is indicated that S-MUSIC makes a trade-off between MSEs and lower computational complexity as well as an improved resolution for closely-spaced sources as compared to the standard MUSIC.

MUSIC-like direction of arrival estimation based on virtual array transformation

In this paper, we propose a reduced-complexity algorithm to estimate the direction of arrivals (DOAs) of multiple uncorrelated narrow-band signals. We show that with an array of arbitrary configuration, the real part of the array covariance matrix can be equivalently reformulated as an entire array covariance matrix received by a virtual array with potential signal model available for DOA estimate. We provide in-depth insights into the eigenvalue decomposition (EVD) on the real part of the array covariance matrix, based on which we propose a novel virtual array transformation multiple signal classification (VAT-MUSIC) algorithm for DOA estimation with efficient real-valued computations. The new algorithm is able to reduce about 75% computational complexity and it has easy implementation advantages over state-of-the-art real-valued techniques. Furthermore, the performance of the proposed algorithm is theoretically analyzed and a closed-form expression is derived to predict the mean square error (MSE) of the new DOA estimator. Numerical simulations are conducted to demonstrate the advantages of the proposed algorithm and to verify the theoretical analysis.

Sparse Antenna Array Design for MIMO Radar Using Multiobjective Differential Evolution

A two-stage design approach is proposed to address the sparse antenna array design for multiple-input multiple-output radar. In the first stage, the cyclic algorithm (CA) is used to establish a covariance matrix that satisfies the beam pattern approximation for a full array. In the second stage, a sparse antenna array with a beam pattern is designed to approximate the desired beam pattern. This paper focuses on the second stage. The optimization problem for the sparse antenna array design aimed at beam pattern synthesis is formulated, where the peak side lobe (PSL) is weakly constrained by the mean squared error. To solve this optimization problem, the differential evolution (DE) algorithm with multistrategy is introduced and PSL suppression is treated as an inequality constraint. However, in doing so, a new multiobjective optimization problem is created. To address this new problem, a multiobjective differential evolution algorithm based on Pareto technique is proposed. Numerical examples are provided to demonstrate the advantages of the proposed approach over state-of-the-art methods, including DE and genetic algorithm.

Two-Step Root-MUSIC for Direction of Arrival Estimation without EVD/SVD Computation

Most popular techniques for super-resolution direction of arrival (DOA) estimation rely on an eigen-decomposition (EVD) or a singular value decomposition (SVD) computation to determine the signal/noise subspace, which is computationally expensive for real-time applications. A two-step root multiple signal classification (TS-root-MUSIC) algorithm is proposed to avoid the complex EVD/SVD computation using a uniform linear array (ULA) based on a mild assumption that the number of signals is less than half that of sensors. The ULA is divided into two subarrays, and three noise-free cross-correlation matrices are constructed using data collected by the two subarrays. A low-complexity linear operation is derived to obtain a rough noise subspace for a first-step DOA estimate. The performance is further enhanced in the second step by using the first-step result to renew the previous estimated noise subspace with a slightly increased complexity. The new technique can provide close root mean square error (RMSE) performance to root-MUSIC with reduced computational burden, which are verified by numerical simulations.

Reduced-Complexity Direction of Arrival Estimation Using Real-Valued Computation with Arbitrary Array Configurations

A low-complexity algorithm is presented to dramatically reduce the complexity of the multiple signal classification (MUSIC) algorithm for direction of arrival (DOA) estimation, in which both tasks of eigenvalue decomposition (EVD) and spectral search are implemented with efficient real-valued computations, leading to about 75% complexity reduction as compared to the standard MUSIC. Furthermore, the proposed technique has no dependence on array configurations and is hence suitable for arbitrary array geometries, which shows a significant implementation advantage over most state-of-the-art unitary estimators including unitary MUSIC (U-MUSIC). Numerical simulations over a wide range of scenarios are conducted to show the performance of the new technique, which demonstrates that with a significantly reduced computational complexity, the new approach is able to provide a close accuracy to the standard MUSIC.

Computationally efficient direction of arrival estimation with unknown number of signals

Abstract In this paper, we investigate the problem of direction of arrival (DOA) estimation with unknown number of signals in the framework of beamforming. We show that the real part of the array output covariance matrix (R-AOCM) can be reformulated as an entire AOCM of a virtual array with available signal model for fast DOA estimate. By introducing an optimization problem to minimize the variance of the weighted output of this virtual array, DOA can be found by a novel real-valued real part Capon (R-Capon) estimator accordingly. Moreover, we prove that the rank of the R-AOCM is always no less than that of the entire AOCM, which suggests that R-Capon outperforms the standard Capon in scenarios with small numbers of snapshots. We also prove that the inverse of the R-AOCM can be equivalently jointed by those of two sub-matrices of about half sizes, and hence R-Capon has a significantly reduced computational complexity. These advantages as well as the theoretical analysis are finally verified by numerical simulations over a wide range of scenarios.

An improved polarization and DOA estimation algorithm

In order to reduce the computation complexity during the multi-dimension iterative search of the MUSIC algorithm used to estimate the polarization and DOA of incident signal, an improved algorithm for estimating the polarization and DOA is proposed based on a polarization sensitive uniform array. Firstly, the polarization and DOA of the incident signal are coarsely estimated by a beam forming method based on FFT operation, then the traditional MUSIC algorithm is adapted to get the multi-dimension iterative search. By this method, the searching area for the multi-dimension full space is reduced to a smaller size, and the computation complexity is effectively reduced. The availability of the algorithm has been verified by the simulation.

Reduced-order root-MUSIC based on Schur spectral factorization

The root multiple signal classification (Root-MUSIC) has recently drawn a considerable attention, by using a polynomial rooting instead of spectral searching to reduce the complexity. The Root-MUSIC is computationally efficient in conjunction with a uniform linear array (ULA) composed of M sensors. Compared with traditional multiple signal classification (MUISC) algorithm, Root-MUSIC is more advantaged but also has a redundancy by solving a (2M-2) order polynomial. The polynomial is intensely complex when large number of sensors is used, and consequently, tremendous computations are required. A reduced-order Root-MUSIC based on the Schur spectral factorization is presented in this paper, which only need to calculate a (M-1) order polynomial. Simulations are conducted to support the validity of the algorithm. The results show that reduced-order Root-MUSIC has a similar root mean square error (RMSE) performance as Root-MUSIC with less computation.