Search Results (62)

For meter-wave multiple-input multiple-output (MIMO) radar, the multipath of target echoes may cause severe errors in height measurement, especially in the case of complex terrain where terrain fluctuation, ground inclination, and multiple reflection points exist. Inspired by a sparse array with greater degrees of freedom and low mutual coupling, a height measurement method based on a sparse array is proposed. First, a practical signal model of MIMO radar based on a sparse array is established. Then, the modified multiple signal classification (MUSIC) and maximum likelihood (ML) estimation algorithms based on two classical sparse arrays (coprime array and nested array) are proposed. To reduce the complexity of the algorithm, a real-valued processing algorithm for generalized MUSIC (GMUSIC) and maximum likelihood is proposed, and a reduced dimension matrix is introduced into the real-valued processing algorithm to further reduce computation complexity. Finally, sufficient simulation results are provided to illustrate the effectiveness and superiority of the proposed technique. The simulation results show that the height measurement accuracy can be efficiently improved by using our proposed technique for both simple and complex terrain. Full article

In this paper, an artificial neural network (ANN) has been proposed to estimate the required values of the adjustable parameters of a Semi-Coprime array with staggered steering (SCASS), which was proposed recently. By adjusting the amount of staggering and the sidelobe attenuation (SLA) factor of Chebyshev weights, SCASS can promise a quite small half-power beamwidth (HPBW) and a high peak-to-side-lobe ratio (PLSR), even when the beam is steered away from broadside direction. However, HPBW and PSLR cannot be improved simultaneously. There is always a trade-off between the two performance metrics. Therefore, in this paper, a mechanism has been introduced to minimize HPBW for a desired PSLR. The proposed ANN takes the array of architectural parameters, the required steering angle, and the desired performance metric, i.e., PSLR, as input and suggests the values of the adjustable parameters, which can promise the minimum HPBW for the desired PSLR and steering angle. To train the ANN, we have developed a dataset in Matlab by calculating HPBW and PSLR from the beampattern generated for a large number of combinations of all the variable parameters. It has been shown in this work that the trained ANN can suggest the optimum values of the adjustable parameters that promise the minimum HPBW for the given steering angle, PSLR, and array architectural parameters. The trained ANN can suggest the required adjustable parameters for the desired performance with mean absolute error within just 0.83%. Full article

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method. Full article

More recently, the ability of the coprime array to yield large array apertures and high degrees of freedom in comparison with the uniform linear array (ULA) has drawn an enormous amount of attention. In light of this, we propose a low-rank matrix completion algorithm via minimization of the ratio of the nuclear norm and the Frobenius norm (N/F) to solve the two-dimensional (2D) direction finding problem for the L-shaped coprime array (LsCA). Specifically, we first interpolate the virtual co-array signal related to the cross-correlation matrix (CCM) and utilize the interpolated virtual signal for Toeplitz matrix reconstruction. Then, the N/F method is employed to perform low-rank matrix completion on the reconstructed matrix. Finally, exploiting the conjugate symmetry characteristics of the completed matrix, we further develop a direction-finding algorithm that enables 2D angle estimation. Remarkably, the 2D angles are able to be automatically paired by the proposed algorithm. Numerical simulation findings demonstrate that the proposed N/F algorithm generates excellent angular resolution and computational complexity. Furthermore, this algorithm yields better estimation accuracy compared to the competing algorithms. Full article

This paper presents a robust adaptive beamforming algorithm based on an attention convolutional neural network (ACNN) for coprime sensor arrays, named the CAWE-ACNN algorithm. In the proposed algorithm, via a spatial and channel attention unit, an ACNN model is constructed to enhance the features contributing to beamforming weight vector estimation and to improve the signal-to-interference-plus-noise ratio (SINR) performance, respectively. Then, an interference-plus-noise covariance matrix reconstruction algorithm is used to obtain an appropriate label for the proposed ACNN model. By the calculated label and the sample signals received from the coprime sensor arrays, the ACNN is well-trained and capable of accurately and efficiently outputting the beamforming weight vector. The simulation results verify that the proposed algorithm achieves excellent SINR performance and high computation efficiency. Full article

For target detection and recognition in a complicated electromagnetic environment, the two-dimensional direction-of-arrival and polarization estimation using a polarization-sensitive array has been receiving increased attention. To efficiently improve the performance of such multi-parameter estimation in practice, this paper proposes a parallel synthetic coprime array with reduced mutual coupling and hardware cost saving and then presents a dimension-reduction compressive sensing-based estimation method. For the proposed array, the polarization types, numbers, and positions of antennas in each subarray are jointly considered to effectively mitigate mutual coupling in the physical array domain and to both enhance degrees of freedom and extend the aperture in the difference coarray domain with the limited physical antennas. By exploring the array configuration, the parameter estimation can be formulated as a block-sparse signal reconstruction problem, and then the one-dimensional sparse reconstruction algorithm is only used once to achieve multi-parameter estimation with automatic pair-matching. The theoretical analysis and simulation results are provided to demonstrate the superior performance of the proposed array and method over the existing techniques. Full article

Unlike uniform linear arrays (ULAs), coprime arrays require fewer physical sensors yet provide higher degrees of freedom (DOF) and larger array apertures. However, due to the existence of “holes” in the differential co-array, the target detection performance deteriorates, especially in adaptive beamforming. To address these challenges, this paper proposes an efficient and robust adaptive beamforming algorithm leveraging coprime array interpolation. The algorithm eliminates unwanted signals and uses the Gauss–Legendre quadrature method to reconstruct an Interference-plus-Noise Covariance Matrix (INCM), thereby obtaining the beamforming coefficients. Unlike previous techniques, we utilize a virtual interpolated ULA to expand the aperture, enabling the acquisition of a high-dimensional covariance matrix. Additionally, a projection matrix is constructed to eliminate unwanted signals from the received data, greatly enhancing the accuracy of INCM reconstruction. To address the high computational complexity of integral operations used in most INCM reconstruction algorithms, we propose an approximation based on the Gauss–Legendre quadrature, which reduces the computational load while maintaining accuracy. This algorithm avoids the array aperture loss caused by using only the ULA segment in the difference co-array and improves the accuracy of INCM reconstruction. Simulation and experimental results show that the performance of the proposed algorithm is superior to the compared beamformers and is closer to the optimal beamformer in various scenarios. Full article

Deep learning techniques have made certain breakthroughs in direction-of-arrival (DOA) estimation in recent years. However, most of the current deep-learning-based DOA estimation methods view the direction finding problem as a grid-based multi-label classification task and require multiple samplings with a uniform linear array (ULA), which leads to grid mismatch issues and difficulty in ensuring accurate DOA estimation with insufficient sampling and in underdetermined scenarios. In order to solve these challenges, we propose a new DOA estimation method based on a deep convolutional generative adversarial network (DCGAN) with a coprime array. By employing virtual interpolation, the difference co-array derived from the coprime array is extended to a virtual ULA with more degrees of freedom (DOFs). Then, combining with the Hermitian and Toeplitz prior knowledge, the covariance matrix is retrieved by the DCGAN. A backtracking method is employed to ensure that the reconstructed covariance matrix has a low-rank characteristic. We performed DOA estimation using the MUSIC algorithm. Simulation results demonstrate that the proposed method can not only distinguish more sources than the number of physical sensors but can also quickly and accurately solve DOA, especially with limited snapshots, which is suitable for fast estimation in mobile agent localization. Full article

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of coherent sources. To overcome this limitation, we propose an enhanced coprime array in this paper. By increasing the number of array sensors in the coprime array, it is feasible to enlarge the aperture of the array and these additional array sensors can be utilized to achieve spatial smoothing, thus enabling estimation of the DOA for coherent sources. Additionally, applying the spatial smoothing technique to the signal subspace, instead of the conventional spatial smoothing method, can further improve the ability to reduce noise interference and enhance the overall estimation result. Finally, DOA estimation is accomplished using the MUSIC algorithm. The simulation results demonstrate improved performance compared to traditional algorithms, confirming its feasibility. Full article

In this paper, we introduce a Reduced-Dimension Multiple-Signal Classification (RD-MUSIC) technique via Higher-Order Orthogonal Iteration (HOOI), which facilitates the estimation of the target range and angle for Frequency-Diverse Array Multiple-Input–Multiple-Output (FDA-MIMO) radars in the unfolded coprime array with unfolded coprime frequency offsets (UCA-UCFO) structure. The received signal undergoes tensor decomposition by the HOOI algorithm to get the core and factor matrices, then the 2D spectral function is built. The Lagrange multiplier method is used to obtain a one-dimensional spectral function, reducing complexity for estimating the direction of arrival (DOA). The vector of the transmitter is obtained by the partial derivatives of the Lagrangian function, and its rotational invariance facilitates target range estimation. The method demonstrates improved operation speed and decreased computational complexity with respect to the classic Higher-Order Singular-Value Decomposition (HOSVD) technique, and its effectiveness and superiority are confirmed by numerical simulations. Full article

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is −8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér–Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than $4°$, the estimation accuracy can reach over 90%. Full article

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability. Full article

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios. Full article

Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests. Full article

A split-aperture array (SAA) is an array of sensors or antenna elements in which the array is split into two or more sub-arrays (SAs). Recently proposed SAAs, namely coprime and semi-coprime arrays, offer to attain a small half-power beamwidth (HPBW) with a small number of elements, compared to most conventional unified-aperture arrays, at the cost of reduced peak-to-side-lobe ratio (PSLR). To reduce HPBW and increase PSLR, non-uniform inter-element spacing and excitation amplitudes have proven helpful. However, all the existing arrays and beam-formers suffer increased HPBW, degraded PSLR or both when the main beam is steered away from the broadside. In this paper, we propose staggered beam-steering of SAs, a novel technique for decreasing HPBW. In this technique, we steer the main beams of the SAs of a semi-coprime array to angles slightly different from the desired steering angle. In conjunction with staggered beam-steering of SAs, we have utilized Chebyshev weights to suppress the side lobes. The results show that the beam-widening effect of Chebyshev weights can be mitigated considerably by staggered beam-steering of the SAs. Ultimately, the unified beam-pattern of the whole array offers HPBW and PSLR better than the existing SAAs, uniform and non-uniform linear arrays, especially when the desired steering angle is away from the broadside direction. Full article