With the adoption of arbitrary and increasingly wideband signals, the design of modern radar systems continues to be limited by analog-to-digital converter technology and data throughput bottlenecks. ...Meanwhile, compressive sensing (CS) promises to reduce sampling rates below the Nyquist rate for some applications by constraining the set of possible signals. In many practical applications, detailed prior knowledge on the signals of interest can be learned from training data, existing track information, and/or other sources, which can be used to design better compressive measurement kernels. In this paper, we use an information-theoretic approach to optimize CS kernels for time delay estimation. The measurements are modeled via a Gaussian mixture model by discretizing the a priori probability distribution of the time delay. The optimal CS kernel that approximately maximizes the Shannon mutual information between the measurements and the time delay is then found by a gradient-based search. Furthermore, we also derive the Bayesian Cramér-Rao bound (CRB) for time delay estimation as a function of the CS kernel. In numerical simulations, we compare the performance of the proposed optimal sensing kernels to random projections and the Bayesian CRB. Simulation results demonstrate that the proposed technique for sensing kernel optimization can significantly improve performance, which is consistent with the Bayesian CRB versus signal-to-noise ratio (SNR). Finally, we use the Bayesian CRB expressions and simulation results to make conclusions about the usefulness of CS in radar applications. Specifically, we discuss CS SNR loss versus resolution improvement in SNR- and resolution-limited scenarios.
Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous ...works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the steering vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.
Coprime array offers a larger array aperture than uniform linear array with the same number of physical sensors, and has a better spatial resolution with increased degrees of freedom. However, when ...it comes to the problem of adaptive beamforming, the existing adaptive beamforming algorithms designed for the general array cannot take full advantage of coprime feature offered by the coprime array. In this paper, we propose a novel coprime array adaptive beamforming algorithm, where both robustness and efficiency are well balanced. Specifically, we first decompose the coprime array into a pair of sparse uniform linear subarrays and process their received signals separately. According to the property of coprime integers, the direction-of-arrival (DOA) can be uniquely estimated for each source by matching the super-resolution spatial spectra of the pair of sparse uniform linear subarrays. Further, a joint covariance matrix optimization problem is formulated to estimate the power of each source. The estimated DOAs and their corresponding power are utilized to reconstruct the interference-plus-noise covariance matrix and estimate the signal steering vector. Theoretical analyses are presented in terms of robustness and efficiency, and simulation results demonstrate the effectiveness of the proposed coprime array adaptive beamforming algorithm.
Massive multiple-input multiple-output (MIMO) is one of the most promising techniques for next generation wireless communications due to its superior capability to provide high spectrum and energy ...efficiency. Considering the very large number of antennas employed at the base station, however, the pilot overhead for downlink channel estimation becomes unaffordable in frequency division duplex (FDD) multiuser massive MIMO systems. In this paper, we propose an information-theoretic metric to design the pilot for downlink channel estimation in FDD multiuser massive MIMO systems. By exploiting the low-rank nature of the channel covariance matrix, we first derive the minimum number of pilot symbols required to ensure perfect channel recovery, which is much less than the number of antennas at the base station. Further, under a general channel model that the channel vector of each user follows a Gaussian mixture distribution, the pilot symbols are designed by maximizing the weighted sum of the Shannon mutual information between the measurements of the users and their corresponding channel vectors on the complex Grassmannian manifold. Simulation results demonstrate the effectiveness of the proposed information-theoretic pilot design for the downlink channel estimation in FDD massive MIMO systems.
Fuzzy arithmetic is of great significance in dealing with vague information, especially the basic arithmetic operations (i.e., ⊕, ⊖, ⊗, ⊙). However, the classical and widely accepted accurate and ...approximate approaches, the interval arithmetic approach and standard approximation method, cannot output accurate or well-approximated expressions of the membership function, which may prevent decision makers from making the right decisions in real applications. To tackle this problem, this paper first discusses the relationships among the membership function, the credibility distribution, and the inverse credibility distribution and summarizes the relationships as several theorems. Then, by means of the theorems and the newly proposed operational law, this paper proposes an inverse credibility distribution approach that can output the accurate expression of the membership function for continuous and strictly monotone functions of regular LR fuzzy intervals. To better demonstrate the effectiveness of the raised approach, the commonly-used LR fuzzy interval, the symmetric trapezoidal fuzzy number, is employed, and several comparisons with the other two methods are made. The results show that the proposed approach can output an exact or well-approximated expression of the membership function, which the others cannot. In addition, some comparisons of the proposed approach with other methods are also made on a completion time analysis of a construction project to show the effectiveness of the proposed approach in real applications.
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Coprime arrays can achieve an increased number of degrees of freedom by deriving the equivalent signals of a virtual array. However, most existing methods fail to utilize all information received by ...the coprime array due to the non-uniformity of the derived virtual array, resulting in an inevitable estimation performance loss. To address this issue, we propose a novel virtual array interpolation-based algorithm for coprime array direction-of-arrival (DOA) estimation in this paper. The idea of array interpolation is employed to construct a virtual uniform linear array such that all virtual sensors in the non-uniform virtual array can be utilized, based on which the atomic norm of the second-order virtual array signals is defined. By investigating the properties of virtual domain atomic norm, it is proved that the covariance matrix of the interpolated virtual array is related to the virtual measurements under the Hermitian positive semi-definite Toeplitz condition. Accordingly, an atomic norm minimization problem with respect to the equivalent virtual measurement vector is formulated to reconstruct the interpolated virtual array covariance matrix in a gridless manner, where the reconstructed covariance matrix enables off-grid DOA estimation. Simulation results demonstrate the performance advantages of the proposed DOA estimation algorithm for coprime arrays.
In this letter, we propose a coprime array interpolation approach to provide an off-grid direction-of-arrival (DOA) estimation. Through array interpolation, a uniform linear array (ULA) with the same ...aperture is generated from the deterministic non-uniform coprime array. Taking the observed correlations calculated from the signals received at the coprime array, a gridless convex optimization problem is formulated to recover all the rows and columns of the unknown correlation matrix entries corresponding to the interpolated sensors. The optimized Hermitian positive semidefinite Toeplitz matrix functions as the covariance matrix of the interpolated ULA, which enables to resolve off-grid sources. Simulation results demonstrate that the proposed array interpolation-based DOA estimation algorithm achieves improved performance as compared to existing coarray-based DOA estimation algorithms in terms of the number of achievable degrees-of-freedom and estimation accuracy.
Direction-of-arrival (DOA), power, and achievable degrees-of-freedom (DOFs) are fundamental parameters for source estimation. In this paper, we propose a novel sparse reconstruction-based source ...estimation algorithm by using a coprime array. Specifically, a difference coarray is derived from a coprime array as the foundation for increasing the number of DOFs, and a virtual uniform linear subarray covariance matrix sparse reconstruction-based optimization problem is formulated for DOA estimation. Meanwhile, a modified sliding window scheme is devised to remove the spurious peaks from the reconstructed sparse spatial spectrum, and the power estimation is enhanced through a least squares problem. Simulation results demonstrate the effectiveness of the proposed algorithm in terms of DOA estimation and power estimation as well as the achievable DOFs.
In this paper, we study binary signature codes for the weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let <inline-formula> <tex-math notation="LaTeX">A(n, t) ...</tex-math></inline-formula> denote the maximum size of a <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula>-signature code of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">A(n, w, t) </tex-math></inline-formula> denote the maximum size of a <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula>-signature code of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> and constant-weight <inline-formula> <tex-math notation="LaTeX">w </tex-math></inline-formula>. First, we derive asymptotic and general upper bounds on <inline-formula> <tex-math notation="LaTeX">A(n,t) </tex-math></inline-formula> by relating signature codes to <inline-formula> <tex-math notation="LaTeX">B_{t} </tex-math></inline-formula> codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of <inline-formula> <tex-math notation="LaTeX">A(n,2,2) </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">A(n,3,2) </tex-math></inline-formula> for infinitely many <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> by connecting signature codes with <inline-formula> <tex-math notation="LaTeX">C_{4} </tex-math></inline-formula>-free graphs and union-free families, respectively. Third, we provide two explicit constructions for <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula>-signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from a geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.
Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in the training data. In this paper, we reconstruct the interference-plus-noise covariance matrix ...in a sparse way, instead of searching for an optimal diagonal loading factor for the sample covariance matrix. Using sparsity, the interference covariance matrix can be reconstructed as a weighted sum of the outer products of the interference steering vectors, the coefficients of which can be estimated from a compressive sensing (CS) problem. In contrast to previous works, the proposed CS problem can be effectively solved by use of a priori information instead of using l1-norm relaxation or other approximation algorithms. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always equal to the optimal value.
•The interference-plus-noise covariance matrix is sparsely reconstructed for adaptive beamforming.•The proposed compressive sensing problem can be solved by use of a priori information instead of l1-norm relaxation.•The proposed beamformer offers a fast convergence and almost equals to the optimal performance.
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