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The frequency diverse array-multi-input multi-output (FDA-MIMO) radar can locate target in angle and range dimensions by transmitting little frequency offset across the transmit sensors. In this paper, a joint space-time-frequency domain optimization scheme is designed to estimate the direction of departure (DOD), direction of arrival (DOA) and range of target. We propose synthetic aperture-multi coprime frequency offset (SA-MCFO) framework which synthesizes all subarrays generated by array motion to expand array aperture and signal bandwidth. We also propose reduce dimension multiple signal classification with decoupling (RDMD) algorithm to detect target by combining reduce dimension (RD) transformation and subarray based estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which results in decoupling of DOD and range as well as fine estimation accuracy. The proposed SA-MCFO framwork enjoys remarkable system flexibility but with lower system cost. The proposed RDMD algorithm significantly reduce computational complexity but with ignorable performance degradation compared with the conventional 3D multiple signal classification (3D-MUSIC) algorithm. We also provide the Cramer-Rao bounds (CRBs) of DOD, DOA and range as performance benchmark, and numerical simulations are conducted to verify the superiorities and effectiveness of the proposed SA-MCFO framework and RDMD algorithm.

The frequency diverse array (FDA) is mainly applied to achieving target localization under the complicated electromagnetic jamming condition. The bistatic multiple-input-multiple-output (MIMO) radar with FDA has gained comprehensive attention in recent years. An innovative method covering the transmitting subarray scheme and the unitary estimation of signal parameters via rotational invariance technology (ESPRIT) is proposed for joint direction of departure (DOD), direction of arrival (DOA), and range estimation. First, a non-overlapping subarray scheme is designed for the transmitting array to decouple DOD and range. For the purpose of enhancing the estimation accuracy and reducing the computational complexity, the real-valued rotational invariance matrix is obtained via applying the unitary transformation to the extended data. The removal method is proposed to avoid the periodic phase ambiguity. The pairing method is put forward to achieving the match of three-dimensional parameter (DOD, DOA and range) for multiple targets. The computational complexity of the proposed algorithm and conventional ESPRIT algorithm are also provided. Finally, extensive experiment results indicate that the proposed algorithm shows the superior performance than the ESPRIT algorithm.

In a complex-valued phasor Hopfield neural network with a training pattern, only the rotated patterns are fixed points, while in a complex-valued K-state Hopfield neural network, there exist K fixed points. In the case of a quaternionic Hopfield neural network (QHNN) with a continuous activation function, again only the rotated patterns are fixed points. We consider a QHNN with a split activation function, which is a 16-state activation function. This type of QHNN is referred to as a split QHNN (SQHNN). It is expected to have 16 fixed points, all of which are global minima. The rate at which the training pattern would be recalled from random initial states would thus be expected to be 1/16. However, the rate was higher in our computer simulations. We investigate the reasons for this discrepancy. HighlightsRotated patterns of training patterns are fixed points.Quaternionic Hopfield neural networks have rotational invariance.Rotational invariance reduces noise tolerance.Rotational invariance is caused by association law of quaternions.Quantization reduces rotational invariance.

Recently, nested arrays have received considerable interest because such array configurations can be systematically designed and their degrees of freedom (DOFs) can be expressed in closed form. Compared with uniform linear arrays, they have obvious advantages in array aperture and DOFs. In this paper, we introduce nested subarray structure to cylindrical conformal array to form a nested conformal array, and develop a corresponding algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation. By vectorizing the covariance matrices of the nested subarray outputs, we firstly generate the three-parallel difference coarray signal and derive the rotational invariance structures between three coarray manifolds. An augmented covariance matrix of the coarray outputs is then constructed via three-dimensional spatial smoothing processing. Finally, the 2-D DOAs of the sources are estimated by the total least squares (TLS)-ESPRIT method. Compared with the traditional schemes with uniform conformal arrays, our algorithm fully exploits the extended aperture of the nested subarrays, and thus enhances the DOA estimation accuracy. Numerical results demonstrate the superiority of the proposed algorithm in comparison to the existing methods.

AMP and VAMP are two different algorithms that solve high-dimensional standard linear regression problems effectively and efficiently. In previous studies, they were long observed to have identical fixed points in their state evolutions (SEs), however, a formal justification is still missing. This issue is addressed in the paper. Instead of looking directly into the problem, we consider a scope more ambitious which puts aside all assumptions underlying the proven SEs. We then show that: 1) Having the spectrum of a Marchenko-Pastur law is a necessary and sufficient condition for the AMP-style and VAMP-style SEs to share an identical fixed point; 2) As the zero-mean i.i.d. Gaussian ensemble have a Marchenko-Pastur spectrum and satisfies all conditions required by the proven AMP SE and VAMP SE, this particular ensemble is the first example of having an identical fixed point. After that, we conjecture the proven VAMP SE might be extended to cover ensembles that break the right rotational invariance, among which the i.i.d. zero-mean sub-Gaussian ensemble could be a second example to yield identical fixed points. This conjecture is supported by experiments from wireless communications and compressive sampling.

In this paper, we develop a group of spatial difference smoothing (SDS) techniques in multiple-input multiple-output (MIMO) radar to facilitate the directions-of-departure (DODs) and directions-of-arrival (DOAs) estimation of coherent signals under unknown correlated noise. The conventional SDS technique, which exploits the difference between the forward spatially smoothed covariance matrix and the backward one, has been used to reduce noise for coherent sources location. However, it fails when the number of sources is odd. To solve the problem, we refine the SDS technique into asymmetric SDS (A-SDS) technique. Meanwhile, two smoothing methods exist in MIMO radar, which are transmit-receive spatial smoothing relying on the rotational invariance property of array and transmit-receive diversity smoothing brought by waveform diversity. Then the general SDS and A-SDS techniques using the spatial smoothing are specialized into transmit-receive diversity SDS (TRD-SDS) and asymmetric TRD-SDS (A-TRD-SDS) techniques using the diversity smoothing. Further, the forward, backward, and combined forward-backward forms of these four kinds of smoothing techniques are discussed. Based on them, eigenstructure algorithms are applied for DOD and DOA estimation. The proposed techniques can be used in bistatic or monostatic MIMO radar under spatially colored or white noise, and their effectiveness is confirmed by simulations. Four kinds of spatial difference smoothing (SDS) techniques in MIMO radar are developed to estimate the DOD and DOA of coherent sources under unknown spatially colored noise.The failure of conventional SDS is analyzed, and modified techniques are proposed.The diversity smoothing in MIMO radar is incorporated in SDS techniques.The forward, backward, and combined forward-backward forms of these SDS techniques are introduced.The aforementioned techniques are compared and extended from bistatic to monostastic MIMO radar.

In this paper, a novel conjugate ESPRIT (C-ESPRIT) method for direction of arrival (DOA) estimation in monostatic MIMO radar is proposed. Firstly, a reduced-dimensional matrix is employed to transform the data matrix into a low dimensional space. Then the properties of noncircular signals are utilized to construct a new virtual array, whose elements are twice that of the monostatic MIMO radar virtual array with distinct elements. The rotational invariance properties of the new virtual array are figured out to estimate DOA through ESPRIT. Compared with the reduced-dimensional ESPRIT (RD-ESPRIT), the proposed method improves the angular estimation accuracy significantly and detects more targets. Simulation results verify the effectiveness of the proposed method.

Fractal dimension measures the geometrical complexity of images. Lacunarity being a measure of spatial heterogeneity can be used to differentiate between images that have similar fractal dimensions but different appearances. This paper presents a method to combine fractal dimension (FD) and lacunarity for better texture recognition. For the estimation of the fractal dimension an improved algorithm is presented. This algorithm uses new box-counting measure based on the statistical distribution of the gray levels of the ''boxes''. Also for the lacunarity estimation, new and faster gliding-box method is proposed, which utilizes summed area tables and Levenberg-Marquardt method. Methods are tested using Brodatz texture database (complete set), a subset of the Oulu rotation invariant texture database (Brodatz subset), and UIUC texture database (partial). Results from the tests showed that combining fractal dimension and lacunarity can improve recognition of textures.

In this paper, we present a fast algorithm for joint estimation of the two-dimensional (2-D) directions of arrival (DOAs) and frequencies of the incoming signals in wireless communications using a hierarchical space-time decomposition (HSTD) technique. Based on the HSTD, the proposed algorithm makes use of a sequence of one-dimensional (1-D) Unitary estimation of signal parameters via rotational invariance technique (ESPRIT) algorithms to estimate these parameters alternatively in a hierarchical tree structure. Also, in between every other 1-D Unitary ESPRIT algorithm, a temporal filtering process or a spatial beamforming process is invoked to partition the incoming signals into finer groups stage by stage to enhance the estimation accuracy as well as to alleviate the contaminated noise. Furthermore, with such a tree-structured estimation scheme, the pairing of these parameters is automatically determined without extra computational overhead. Simulation results show that the new algorithm provides satisfactory performance but with drastically reduced computations compared with previous works.

This paper addresses the two-dimensional (2-D) frequency estimation embedded in additive Gaussian noise. By use of the biorthogonality of matrices and rotational invariance property, we construct an interesting cost function and propose a novel iterative algorithm for 2-D frequency estimation, which obtains one column of the Vandermonde matrix containing 1-D frequencies and the corresponding column of the Vandermonde matrix containing the other 1-D frequencies at each stage. Therefore, the proposed algorithm can pair the 2-D frequencies automatically. The convergence of the proposed iterative algorithm is also proven. Moreover, all the columns of the frequency matrices can be obtained by systematically multistage decomposition and multistage reconstruction. Simulation results are provided to show the good performance of the proposed algorithm.

This paper proposes a computationally efficient 2-D direction-of-arrival estimation method for the single source case. In this method, the array outputs are regarded as the pixel values and then transformed into the Zernike moments (ZMs). The rotation-invariant feature of ZMs allows us to estimate azimuth angles independently of elevation angles, without performing the eigenvalue decomposition. Obtained the azimuth estimate, the elevation angle is estimated by applying the MUSIC technique to the Correlation matrix of the ZM Vector that is smaller than that of the original array input vector. Therefore the computational complexity of the eigenvalue decomposition and the sweeping operation can be reduced. Several simulation results are presented to show the effectiveness of the proposed method.