正交匹配追踪(OMP)类算法是经典贪婪类稀疏重构算法,具有对空间中的相干信号不敏感和运算速度快的特点,但其本身寻优的过程与波束形成(CBF)算法相似,所以受到瑞利限的影响,无法分辨出相近角度.对此提出一种基于MUSIC的稀疏重构解相干算法(modified MUSIC OMP,MMO).该算法将MUSIC算法的思想引入到正交匹配追踪算法寻优中,解决了MUSIC算法不能直接解相干和正交匹配追踪算法无法实现超分辨的问题.仿真结果表明,与OMP解相干算法、CBF算法、MUSIC算法相比,MMO算法具有良好的性能.

在对市电的幅值及无功补偿场合,需对被补偿市电电压瞬时值进行过零检测.针对传统电网同步信号检测以及手动复位电路存在的问题,利用现场可编程逻辑门阵列(FPGA)板低电平复位的特点,提出了一种基于FPGA的电网同步信号检测电路.最后搭建实验平台进行了验证.实验结果表明,该电路具有结构简单、安全可靠等特点,解决了传统电网同步信号检测存在的电路复杂、可靠性差、安全性不高等问题,从而验证了本文所提出方法的可行性.

The mutual coupling problem of non-uniform linear array (NULA) is studied .Unlike uniform linear array (ULA) ,the mutual coupling matrix of NULA does not have the characteristics of banded symmet-ric Toeplitz ,so it is more complex to deal with .First of all ,according to the characteristics of the array struc-ture ,the mutual coupling matrix is transformed into the form of two ‘Toeplitz'matrix subtractions .Thus ,it is convenient to realize the decoupling of the angle and the mutual coupling coefficients .And then combining with the subspace principle ,the direction of arrival (DOA ) and the mutual coupling coefficient are estimated simulta-neously .The algorithm does not require additional auxiliary correction source ,and also it does not need non-lin-ear high-dimensional search and iterative process ,so the computation is small .Simulation results show that the proposed algorithm can estimate the signal angle and the mutual error coefficient well ,which has the character-istics of high precision and strong resolution ,hence ,it can effectively solve the mutual coupling problem of the NULA .

针对正交匹配追踪类算法具有对空间中的相干信号不敏感而解相干效果更好的特点,将矢量化引入到正交匹配追踪(OMP)算法的相干源处理中.为进一步降低矢量化的维数,对矢量化做了简化处理,提出一种新的解相干算法.该算法无需已知信号源数,与经典OMP算法、基于正交匹配追踪的奇异值分解(SVD)算法相比,解相干精度更高,算法鲁棒性更好.仿真结果验证了该算法的良好性能.

In this paper, the directional characteristics of two different placed dual circular arrays are studied, including the direction of radiation pattern, the beam width of the main lobe and the sidelobe level. Firstly, the array model of the dual circular array is established, the formula of the radiation pattern is deduced and extended to multi-circle circular array, and theoretical analysis is carried out. Secondly, a large number of simulation experiments are carried out by MATLAB software to analyze the relationship among the half-power beamwidth of the main lobe, the sidelobe peak level, the scanning angle and the number of array elements, as well as the relationship between the radius of the inner and outer elements. Finally, the theoretical analysis and simulation results are comprehensively sorted out. The conclusions are that the lowest level of the sidelobe exists when the radius ratio of inner and outer array is about 0. 5, and the beamwidth increases with the number of inner circular array elements but decreases with the number of outer circular array elements. The experimental results can provide theoretical reference for the reasonable setting of the number of elements and the location of the array elements.

针对非均匀九元十字阵的测频问题,提出一种基于波束预扫描的测频MUSIC算法,以提高非法线方向的测频精度.在构建特殊阵列空时两维模型的基础上,利用常规波束形成(CBF)算法对目标信号进行粗测角,确定信号方向,并将其转化为CBF权;再利用阵列合成MUSIC算法对信号进行测频,使测频波束指向目标信号方向,以解决阵列端线方向测频不准确的问题.最后进行了仿真.仿真结果表明,所提算法可实现对阵列端线方向单个和多个信号的频率估计,测频准确度高于不加权阵元组合算法,从而验证了本文所提算法的有效性.

In the estimation of direction-of-arrival (DOA) based on compressive seining,the construction of manifold matrix is the foundation of subsequent estimates.Firstly,this paper proposes the theoretical analysis about orthogonality of adjacent vector in manifold matrix.The results about the analysis show that the manifold matrix with equal angle interval is superior to that with equal sine interval in normal direction,and the manifold matrix with equal sine interval is superior to the one with equal angle interval in beam direction in the end.Respectively they both perform a better DOA estimation.Then this paper deduces systematically critical value of equal sine interval and equal angle interval,and discusses the influence of the number of array element and division number to the orthogonality.On this basis,a better sparsity model is designed,and a DOA estimation algorithm named sparse fusion in spatial domain (SFSD) is proposed based on the combination of equal sine interval and equal angle interval.Compared with the two other DOA estimation algorithms,the proposed algorithm has the better DOA estimation robustness,lower signal-to-noise ratio threshold and higher estimation precision.Finally,the superiority of the theoretical model and the efficiency of the algorithm are validated by computer simulation.

Based on 8-shaped double circle circular array, a self-calibration algorithm is proposed in this paper for 2D angle estimation and calibration of mutual coupling coefficients. Through the analysis of array structure, the entire array is divided into two sub arrays. By observing the characteristics of mutual coupling matrix in each sub array and between two sub arrays, a reasonable reconstruction matrix is constructed, in order to realize the decoupling of the angle information and mutual coupling coefficient. First, the principle of rank loss is used to estimate the angle information, and then the mutual coupling coefficient is estimated by the estimated angle information. The high-dimensional search is not required in the whole process, so the amount of calculation is reduced. In addition, the algorithm does not require additional auxiliary correction source, hence, it is very simple to implement. Theoretical analysis and simulation results show that the proposed algorithm can solve the mutual coupling problem of 8-shaped double circle circular array reliably and effectively.

In order to solve the coherent problem of orthogonally matched pursuit(OMP) algorithm in sparse reconstruction, an improved de-coherent method is proposed by using vectorized autocorrelation matrix.The improved method reconstructs the angle only by the vectorized one-dimensional vector, which can reduce the influence of the noise and realize the decoherence without knowing the number of the signal source.Compared with the classical OMP algorithm, the sparse reconstruction effect is better.Theoretical analysis and simulation results verify the good performance of the algorithm.

In this paper, the characteristics of two different uniformly spaced circular arrays are analyzed, including the beam width, the sidelobe peak level, the resolution and the Cramer-Rao bound(CRB) of the array. Firstly, according to the structure of the dual circular array, the formula of array pattern, the formula of resolution and the formula of CRB are deduced. Secondly, the effects of the elements number and the radius of the array on the beam width, sidelobe level, resolution and CRB are analyzed theoretically. Thirdly, a lot of simulations are used to verify the validity of the theoretical analysis. All of these provide a theoretical reference for setting the number and the location of array elements in application reasonably.

In order to solve the coherent problem of Orthogonally Matched(OMP) Pursuit algorithm in sparse reconstruction, the feature vector corresponding to large eigenvalue of SVD is constructed by using received data, and two improved methods are proposed. Both methods reconstruct the angle through the feature vector, and can reconstruct the angle information accurately without knowing the number of the signal source. Compared with the classical OMP algorithm, the operation speed is faster and the sparse reconstruction effect is better. Theoretical analysis and simulation results verily the good performance of the algorithm.

Based on the dual uniform circular array, a self-calibration algorithm is proposed in the presence of mutual coupling, which can calibrate the mutual coupling in circular array and between two circular arrays at the same time. The algorithm utilizes the special mutual coupling matrix characteristic of dual uniform circular array to decouple angle information and mutual coupling coefficients. With less amount of calculation, the signal angle and the mutual coupling coefficients are estimated in turn. Finally, the cascade estimation is completed. The algorithm reduces the dimension of searching without any prior information about mutual coupling coefficient matrix and need not extra auxiliary source. So it can be easily implemented. Theory analysis and simulation results illustrate that the new algorithm has high precision and resolution, hence, it can effectively solve the problem of mutual coupling for the dual circular array.

针对稀疏重构中正交匹配追踪(OMP)算法解相干问题,利用接收数据构造目标矩阵奇异值分解(SVD)后的大特征值对应的特征矢量,提出了两种改进解相干算法(NSO算法和MNSO算法).首先根据稀疏重构的框架下的阵列DOA估计模型,理论上分析了经典OMP算法、NSO算法和MNSO算法的运算量和重构精度,然后给出了算法性能的仿真结果.仿真结果表明,相对于经典OMP算法,两种改进算法的运算速度更快,稀疏重构效果更优.理论分析和仿真结果验证了两种改进算法的良好性能.

To solve the problem of coherent sources using sparse reconstruction method, this paper proposes an improved method for solving coherent sources using the eigenvectors corresponding to the largest eigenvalues after Singular Value Decomposition (SVD) decomposition of received data. The method reconstructs the angle by iterating the feature vector, and reconstructs the angle information accurately without knowing the number of the signal source. Compared with the classical SVD algorithm, the operation speed is faster, and the sparse reconstruction effect is better. Theoretical analysis and simulation results verify the good performance of the algorithm.

A method dealing with direction of arrival(DOA) of coherent signals in the presence of mutual coupling is proposed .Firstly ,the generalized steering vector is obtained through DOA matrix method based on the second‐order statistics .Secondly ,subspace smoothing is applied to generalized steering vec‐tor and a linear constrained programming problem is obtained by matrix transform .So DOA and coeffi‐cients of mutual coupling can be estimated sequentially .Compared with the fourth‐order cumulant meth‐od ,the computation load is reduced with the second‐order statistics .And there is no loss of array ele‐ments ,which means less array elements are needed in this method .Computer simulations prove the ef‐fectivity of the proposed method .

The sparse UCA decorrelation root-MUSIC algorithm(SDR)is proposed to estimate the DOA of coherent signals of sparse uniform circular array.It improves traditional beamspace transform method by calibrating the phase of steering vector and eliminating the phase error.The steering vector of beamspace do-main is centric hermitian,so forward-backward average method and root-MUSIC can be applied.In this way,the computational burden is reduced by avoiding the search for the highest peaks and the decorrelation is achieved.Simulation results show that this method works well in sparse UCA even under low-SNR or low-snap situation.