An efficient algorithm for direction finding against unknown mutual coupling

DOA Estimation and Self-Calibration under Unknown Mutual Coupling

In practical applications, the assumption of omnidirectional elements is not effective in general, which leads to the direction-dependent mutual coupling (MC). Under this condition, the performance of traditional calibration algorithms suffers. This paper proposes a new self-calibration method based on the time-frequency distributions (TFDs) in the presence of direction-dependent MC. Firstly, the time-frequency (TF) transformation is used to calculate the space-time-frequency distributions (STFDs) matrix of received signals. After that, the estimated steering vector and corresponding noise subspace are estimated by the steps of noise removing, single-source TF points extracting and clustering. Then according to the transformation relationship between the MC coefficients, steering vector and MC matrix, we deduce a set of linear equations. Finally, with two-step alternating iteration, the equations are solved by least square method in order to estimate DOA and MC coefficients. Simulations results show that the proposed algorithm can achieve direction-dependent MC self-calibration and outperforms the existing algorithms.

ESPRIT-Like Two-Dimensional DOA Estimation for Monostatic MIMO Radar with Electromagnetic Vector Received Sensors under the Condition of Gain and Phase Uncertainties and Mutual Coupling

In this paper, we focus on the problem of two-dimensional direction of arrival (2D-DOA) estimation for monostatic MIMO Radar with electromagnetic vector received sensors (MIMO-EMVSs) under the condition of gain and phase uncertainties (GPU) and mutual coupling (MC). GPU would spoil the invariance property of the EMVSs in MIMO-EMVSs, thus the effective ESPRIT algorithm unable to be used directly. Then we put forward a C-SPD ESPRIT-like algorithm. It estimates the 2D-DOA and polarization station angle (PSA) based on the instrumental sensors method (ISM). The C-SPD ESPRIT-like algorithm can obtain good angle estimation accuracy without knowing the GPU. Furthermore, it can be applied to arbitrary array configuration and has low complexity for avoiding the angle searching procedure. When MC and GPU exist together between the elements of EMVSs, in order to make our algorithm feasible, we derive a class of separated electromagnetic vector receiver and give the S-SPD ESPRIT-like algorithm. It can solve the problem of GPU and MC efficiently. And the array configuration can be arbitrary. The effectiveness of our proposed algorithms is verified by the simulation result.

Improved Spatial Differencing Scheme for 2-D DOA Estimation of Coherent Signals with Uniform Rectangular Arrays

This paper proposes an improved spatial differencing (ISD) scheme for two-dimensional direction of arrival (2-D DOA) estimation of coherent signals with uniform rectangular arrays (URAs). We first divide the URA into a number of row rectangular subarrays. Then, by extracting all the data information of each subarray, we only perform difference-operation on the auto-correlations, while the cross-correlations are kept unchanged. Using the reconstructed submatrices, both the forward only ISD (FO-ISD) and forward backward ISD (FB-ISD) methods are developed under the proposed scheme. Compared with the existing spatial smoothing techniques, the proposed scheme can use more data information of the sample covariance matrix and also suppress the effect of additive noise more effectively. Simulation results show that both FO-ISD and FB-ISD can improve the estimation performance largely as compared to the others, in white or colored noise conditions.

Performance Analysis of the Direct Position Determination Method in the Presence of Array Model Errors

The direct position determination approach was recently presented as a promising technique for the localization of a transmitting source with accuracy higher than that of the conventional two-step localization method. In this paper, the theoretical performance of a direct position determination estimator proposed by Weiss is examined for situations in which the array model errors are present. Our study starts from a matrix eigen-perturbation result, which expresses the perturbation of eigenvalues as a function of the disturbance added to the Hermitian matrix. The first-order asymptotic expression of the positioning errors is presented, from which an analytical expression for the mean square error of the direct localization is available. Additionally, explicit formulas for computing the probabilities of a successful localization are deduced. Finally, Cramér–Rao bound expressions for the position estimation are derived for two cases: (1) array model errors are absent and (2) array model errors are present. The obtained Cramér-Rao bounds provide insights into the effects of the array model errors on the localization accuracy. Simulation results support and corroborate the theoretical developments made in this paper.

DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays

A fast direction of arrival (DOA) estimation method using a real-valued cross-correlation matrix (CCM) of coprime subarrays is proposed. Firstly, real-valued CCM with extended aperture is constructed to obtain the signal subspaces corresponding to the two subarrays. By analysing the relationship between the two subspaces, DOA estimations from the two subarrays are simultaneously obtained with automatic pairing. Finally, unique DOA is determined based on the common results from the two subarrays. Compared to partial spectral search (PSS) method and estimation of signal parameter via rotational invariance (ESPRIT) based method for coprime arrays, the proposed algorithm has lower complexity but achieves better DOA estimation performance and handles more sources. Simulation results verify the effectiveness of the approach.

A Channelization-Based DOA Estimation Method for Wideband Signals

In this paper, we propose a novel direction of arrival (DOA) estimation method for wideband signals with sensor arrays. The proposed method splits the wideband array output into multiple frequency sub-channels and estimates the signal parameters using a digital channelization receiver. Based on the output sub-channels, a channelization-based incoherent signal subspace method (Channelization-ISM) and a channelization-based test of orthogonality of projected subspaces method (Channelization-TOPS) are proposed. Channelization-ISM applies narrowband signal subspace methods on each sub-channel independently. Then the arithmetic mean or geometric mean of the estimated DOAs from each sub-channel gives the final result. Channelization-TOPS measures the orthogonality between the signal and the noise subspaces of the output sub-channels to estimate DOAs. The proposed channelization-based method isolates signals in different bandwidths reasonably and improves the output SNR. It outperforms the conventional ISM and TOPS methods on estimation accuracy and dynamic range, especially in real environments. Besides, the parallel processing architecture makes it easy to implement on hardware. A wideband digital array radar (DAR) using direct wideband radio frequency (RF) digitization is presented. Experiments carried out in a microwave anechoic chamber with the wideband DAR are presented to demonstrate the performance. The results verify the effectiveness of the proposed method.

A Modified Rife Algorithm for Off-Grid DOA Estimation Based on Sparse Representations

In this paper we address the problem of off-grid direction of arrival (DOA) estimation based on sparse representations in the situation of multiple measurement vectors (MMV). A novel sparse DOA estimation method which changes MMV problem to SMV is proposed. This method uses sparse representations based on weighted eigenvectors (SRBWEV) to deal with the MMV problem. MMV problem can be changed to single measurement vector (SMV) problem by using the linear combination of eigenvectors of array covariance matrix in signal subspace as a new SMV for sparse solution calculation. So the complexity of this proposed algorithm is smaller than other DOA estimation algorithms of MMV. Meanwhile, it can overcome the limitation of the conventional sparsity-based DOA estimation approaches that the unknown directions belong to a predefined discrete angular grid, so it can further improve the DOA estimation accuracy. The modified Rife algorithm for DOA estimation (MRife-DOA) is simulated based on SRBWEV algorithm. In this proposed algorithm, the largest and sub-largest inner products between the measurement vector or its residual and the atoms in the dictionary are utilized to further modify DOA estimation according to the principle of Rife algorithm and the basic idea of coarse-to-fine estimation. Finally, simulation experiments show that the proposed algorithm is effective and can reduce the DOA estimation error caused by grid effect with lower complexity.

Real-Valued Covariance Vector Sparsity-Inducing DOA Estimation for Monostatic MIMO Radar

In this paper, a real-valued covariance vector sparsity-inducing method for direction of arrival (DOA) estimation is proposed in monostatic multiple-input multiple-output (MIMO) radar. Exploiting the special configuration of monostatic MIMO radar, low-dimensional real-valued received data can be obtained by using the reduced-dimensional transformation and unitary transformation technique. Then, based on the Khatri–Rao product, a real-valued sparse representation framework of the covariance vector is formulated to estimate DOA. Compared to the existing sparsity-inducing DOA estimation methods, the proposed method provides better angle estimation performance and lower computational complexity. Simulation results verify the effectiveness and advantage of the proposed method.

Sparse Bayesian learning for DOA estimation with mutual coupling

Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.