Single-Channel Spatial Spectrum Estimation Direction Finding by the Time-Modulated Linear Array

A novel single-channel direction finding (DF) method with spatial spectrum estimation is proposed based on 1 bit time-modulated array (TMA). Its performance is analyzed from theoretical derivation to numerical simulations and compared with other existing DF methods. The proposed DF method is implemented as follows. First, the received sideband signals from the 1 bit modulated single-channel signal are deduced, followed by the detailed analysis of the received noise distribution. Second, the harmonic recovery (HR) method with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2} $ </tex-math></inline-formula> -norm approximation is utilized to recover the original array signals. Finally, conventional spatial spectrum estimation methods are easily applied for high-accuracy DF. Meanwhile, The DF accuracy of the proposed 1 bit method is analyzed under the Gaussian noise model, and its Cramér–Rao lower bounds (CRLBs) are deduced for the first time and compared with conventional arrays and other DF TMA systems. Numerical simulations are provided to show that the proposed 1 bit TMA system and HR method can achieve better accuracy performance over the existing TMA systems when the circuit noise is predominant in the received noises. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -band 1 bit TMA system is fabricated and implemented to experimentally verify the feasibility of the proposed method under circumstances of a single incident source and two coherent sources.

This paper presents a method for high resolution multiple source direction finding with an antenna array. Unlike previously developed algorithms, the proposed approach can achieve high resolution direction finding with only one receiver, thereby, offering significant hardware savings. The proposed approach requires the signal received by the antenna array to be pre-processed by a beamformer network where each of the beamformer output ports are sequentially sampled by a RF switch. As the power of each beamformer output port is a function of the array covariance matrix, we derive a Kronecker form that leads to an unique least squares estimates of the array covariance matrix using the power measured from all the beamformer output ports. With the array covariance matrix estimated, conventional high resolution DF algorithms can be applied to determine the direction of arrival estimation of the multiple sources impinging the antenna array.

The present algorithms on 2-D temporal-spatial spectrum estimation are deteriorated when the number of signals become close to the dimension of the array. The expenses of the hardware and the software have to be increased to alleviate this degradation. In this paper, a kind of new signal model and approach for 2-D temporal-spatial spectrum estimation is proposed. Through the temporal projection, the maximal number of the signals this method can deal with is much more than present algorithms. Simulation results are presented to demonstrate the performance of the proposed algorithm

Partial discharge is an important symbol of insulation defects. Partial discharge detection system based on UHF antenna array can realize partial discharge location in air-insulated substation. Using spatial spectrum estimation can reduce the antenna array and achieve high-precision positioning with smaller array size. This paper discusses the direction finding accuracy of different antenna arrays with the help of Cram&#x00E9;r-Rao lower bound. Through theoretical derivation and numerical calculation, the influence of array structure on direction finding performance is studied, which provides guidance for optimizing antenna array. The results show that in order to achieve high direction finding accuracy, the offset B in the analytical expression of array factor q should be as large as possible, and the amplitude A and initial phase $\gamma$ should be selected reasonably according to the application requirements. The farther a single burst deviates from the original equilibrium position, the more drastic the change of the Cram&#x00E9;r-Rao lower bound with the variable azimuth angle, and the worse the comprehensive direction finding performance.

This paper addresses the problem of spatial spectrum estimation in dynamic environments with a maneuverable sensor array. Estimation of the time-varying acoustic field directionality is of fundamental importance in passive sonar. In this paper, mobility of the array is treated as a feature allowing for left-right disambiguation as well as improved resolution toward endfire. Two new methods for on-line spatial spectrum estimation are presented: (1) recursive maximum likelihood estimation using the EM algorithm and (2) time-varying spatial spectrum estimation via derivative-based updating. A multi-source simulation is used to compare the proposed algorithms in terms of their ability to suppress ambiguous array backlobes. A broadband method is presented utilizing knowledge of the source temporal spectrum. Detection performance of weak high-bearing rate sources in interference-dominated environments is evaluated for a flat spectrum. [This work was supported by ONR under grant N000140810947.]

The most prominent subspace decomposition methods for spatial spectrum estimation include multiple signal classification algorithm (MUSIC) as well as estimation signal parameter via rotational invariance technique (ESPRIT). However, the drawbacks of MUSIC is that estimating the number of source signals are constraint by the following two aspects: array aperture and a large number of sampling data. After carefully investigating the theory of compressive sensing (CS), this paper constructs the model for spatial spectrum estimation on the basis of the sparsity of source signals in the angle spectrum. According to the principle of CS, spatial signals can be sampled with much less sensors, which leads to small sampling data. Furthermore, the source signals can be reconstructed accurately by some recovery algorithms. The approaches are compared with MUSIC and three numerical simulation experiments are programmed with MATLAB. The reconstruction results are found to be approximately to the original signals. The most attractive merits of our proposed method not only reduces the number of elements which are needed for sampling as well as decreases the amount of sampling data, but also the source signals can be reconstructed in terms of their amplitude and bearing simultaneously.

The imperfect array degrades the direction finding performance. In this paper, we investigate the direction finding problem in uniform linear array (ULA) system with unknown mutual coupling effect between antennas. By exploiting the target sparsity in the spatial domain, the sparse Bayesian learning (SBL)-based model is proposed and converts the direction finding problem into a sparse reconstruction problem. In the sparse-based model, the off-grid errors are introduced by discretizing the direction area into grids. Therefore, an off-grid SBL model with mutual coupling vector is proposed to overcome both the mutual coupling and the off-grid effect. With the distribution assumptions of unknown parameters including the noise variance, the off-grid vector, the received signals and the mutual coupling vector, a novel direction finding method based on SBL with unknown mutual coupling effect named DFSMC is proposed, where an expectation-maximum (EM)-based step is adopted by deriving the estimation expressions for all the unknown parameters theoretically. Simulation results show that the proposed DFSMC method can outperform state-of-the-art direction finding methods significantly in the array system with unknown mutual coupling effect.

Detecting direction of arrival (DoA) using array antenna is considered as common challenge in different typeS of applications, such as sonar, radar, wireless communications. DoA estimation plays an important role in direction finding applications. Further, effective DoA estimation technique is the primary requirements for smart antenna system to realize beam forming technique. Multiple signal classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance (ESPRIT) algorithms have been widely studied, and they are considered as fundamental for the majority of the DoA methods in literature. In this paper, the principal of DoA estimations is presented. The main focus of the current paper is on the classical methods (Bartletts and MVDR), MUSIC and ESPRIT algorithms. Review of various efforts that have been made to enhance the performance of these algorithms was acheived. Then compared their performances using simulation results. Further, applying MUSIC algorithm to estimate the frequency of the multiple incident signals. The results show that MUSIC algorithm has higher resolution compared to other presented techniques. It is also shown that the accuracy of ESPRIT method is mainly rely on the number of antenna elements. Finally, the principle of Eigenvalues-based method was proposed. It is shown that this method has good resolution with very low complexity as it does not need decomposition of covariance matrix.

Direction finding for electronic warfare application should provide a wider field of view as possible. But the maximum unambiguous field of view for conventional direction finding methods is a hemisphere. It cannot distinguish the direction of arrival of the signals from the back lobe of the array. In this paper, a full 3-D direction finding method based on aperture synthesis radiometry is proposed. The model of the direction finding system is illustrated, and the fundamentals are presented. The relationship between the outputs of the measurements of a 3-D array and the 3-D power distribution of the point sources can be represented by a 3-D Fourier transform, and then the 3-D power distribution of the point sources can be reconstructed by an inverse 3-D Fourier transform. And in order to display the 3-D power distribution of the point sources conveniently, the whole spherical distribution is represented by two 2-D circular distribution images, one of which is for the upper hemisphere, and the other is for the lower hemisphere. Then a numeric simulation is designed and conducted to demonstrate the feasibility of the method. The results show that the method can estimate the arbitrary direction of arrival of the signals in the 3-D space correctly.

Electronic support measures (ESM) systems use different methods for direction finding (DF). Performance of a DF antenna array is an essential measure of the overall ESM system. A common DF method of phase interferometry using a circular interferometer is discussed. Typically a circular interferometer employs a polarizer to match the desired incident polarizations to the polarization of the antenna array. This paper describes a simulation method for evaluation of polarizer impact on direction finding performance of a circular interferometer. Simulation of DF antenna performance of a circular interferometer with and without a polarizer, using method-of-moments antenna simulation and spreadsheet based post-processing. The benefits of simulation include being a cost effective way of performance prediction for a new design or for the influence of installation structures on an existing system. Sample DF accuracy results are discussed and compared to previously published specifications. This work is based on analysis conducted on the ESM system for the surface combatant force guided missile frigates (FFG ) upgrade project.

Sensor arrays have been successfully applied to many engineering fields and the theoretical as well as applied aspects of senor array processing have received intensive research interest. Practically, sensor array systems usually suffer from uncertainties such as unknown gains and phases, mutual coupling, and look direction mismatch. In this thesis, problems of direction finding and beamforming in the presence of array uncertainties are addressed, and new algorithms to tackle these problems are developed.&#13;\n&#13;\nIn certain applications, senor arrays are only partly calibrated. Hence, the exact responses of some sensors are unknown, which degrades the performance of traditional direction finding techniques. To tackle this problem, a new method for direction finding with partly calibrated uniform linear arrays (ULAs) is proposed. It generalizes the estimation of signal parameters via rotational invariance techniques (ESPRIT) by modeling the imperfection of the ULA as gain and phase uncertainties. For a fully calibrated array, it reduces to the standard ESPRIT algorithm. In this method, the direction-of-arrivals (DOAs), unknown gains and phases of the uncalibrated sensors can be estimated in closed-form without performing spectral grid search. Moreover, it can be further improved by a refining scheme proposed. Its superiority over existing methods is demonstrated by simulation results.&#13;\n&#13;\nApart from unknown gains and phases, the mutual coupling caused by interactions among sensors also seriously deteriorate the performance of array processing techniques. In ULAs, the mutual coupling matrix (MCM) can be approximated as a banded symmetric Toeplitz matrix. Using this specific property, a new parameterization of the steering vector is proposed and the corresponding method for joint estimation of DOAs and MCM is derived. Compared with the conventional subarray-based method, the proposed one makes use of the whole array and achieves better performance especially for weak signals. On the other hand, the specific property is further employed to develop a new approach to calibrate the steering vector. By incorporating the calibrated steering vector with a diagonally loaded robust beamformer, a new adaptive beamformer for ULAs with mutual coupling is obtained. It is found that the resultant steering vector estimate considerably improves the robustness of the beamformer against mutual coupling.&#13;\n&#13;\nAnother common uncertainty in sensor array systems is the look direction mismatch. Though numerous robust beamformers have been developed accordingly, most of them cannot offer sufficient robustness against large look direction errors. To this end, a new robust beamforming method which can flexibly control the magnitude response in the look direction is proposed. By linearizing the nonconvex constraints in the original problem, the resultant problem is convex and can be solved using second-order cone programming (SOCP). Moreover, to further improve the robustness against array covariance uncertainties, this method is extended by optimizing its worst-case performance. Unlike some conventional methods restricted to specific arrays, the proposed method is applicable to arbitrary array geometries. Simulation results show that the proposed method offers comparable performance to the optimal solution for uniform linear arrays, and also achieves good results under different array specifications and geometries.

In this paper, the implementation of real time direction finding method on FPGA platform for the direction finding systems that have four coherent channels and linear antenna array is presented. If the signals that are received from same direction and distance between antennas are processed by a FPGA card, different antenna pair combinations can be generated. Direction finding is achieved by the comparison of possible angle of arrival values that is calculated using measured fundamental phase and overlapping replicas. The developed real time algorithm and implemented structure on FGPA platform, which includes phase difference calculation, overlapped phase differences and angle calculation blocks, finally ambiguity resolution method and direction finding results are presented.

Two-dimensional multiple signal classification (MUSIC) algorithm based on polarization sensitive array (PSA) has excellent performance. However, it suffers a high computational complexity due to a multitude of complex operations. In this paper, we propose a real-valued two-dimensional MUSIC algorithm based on conjugate centrosymmetric signal model, which is applicable to arbitrary centrosymmetric polarization sensitive array. The modified forward/backward averaging, which can be applied to the PSA, is presented. Hence, the eigen-decomposition analysis process and spectrum function computation are converted into real domain, prominently reducing the computational complexity. Then, the direction-of-arrival (DOA) estimation is decoupled from the polarization parameter estimation so that the four-dimensional spectral peak search process is avoided. The theoretical computational complexity is discussed and the Cramer-Rao bound (CRB) of DOA estimation is derived in this paper. The simulation results indicate that the proposed algorithm achieves superior accuracy in DOA estimation and has low computational complexity.

In recent research, spatial processing technique based on antenna array has been considered as one of the most effective anti-spoofing methods. This paper provides a novel spoofing suppression scheme based on the Cyclic Multiple Signal Classification (MUSIC) algorithm. In this method, the cyclostationarity of navigation signals are fully excavated to estimate the spatial power spectrum before the despreading process of the receiver. Then, based on the assumption that the spoofing signals with different spurious pseudo random noise (PRN) codes come from one single-antenna source, the spoofing attack can be detected if the power of a certain direction is significantly larger than other directions. Finally, the subspace projection is adopted to eliminate the spoofing signals and beamforming for each satellite ensures that the power of the authentic signals is not attenuated. The proposed technique has lower computational complexity than the post-despreading methods because all the operations are performed on the digitized baseband samples without any modification to the receiver. In addition, different with other pre-despreading methods, this method can accurately estimate the DOAs of the spoofing and authentic signals, which can not only provide higher gain for the authentic signals but also be helpful for the interference source positioning in some applications.

In this paper, we deal with the multiple carrier frequency offsets (CFOs) estimation issues for orthogonal frequency-division multiple access (OFDMA) based uplink system. In such system, the interleaved carrier assignment scheme (CAS) has gained much attention for it brings maximum frequency diversity though it undergoes severe CFO problem than other schemes. The multiple-CFO estimation problem in this scheme uses a similar signal structure as that of Direction of Arrival (DOA) estimation problem in array signal processing, so subspace based multiple signal classification (MUSIC) algorithm can be exploited to estimate multiple CFOs. Compared with the conventional MUSIC algorithm utilizing eigenvalue decomposition of complex-value covariance matrix, the proposed unitary MUSIC and unitary root-MUSIC CFO estimation algorithms have comparable performance but lower computational complexity because of real-value covariance matrix used, which is verified by computer simulation.