Yiyu Zhou

Direction-of-Arrival Estimation of Wideband Signals via Covariance Matrix Sparse Representation

This paper focuses on direction-of-arrival (DOA) estimation of wideband signals, and a method named wideband covariance matrix sparse representation (W-CMSR) is proposed. In W-CMSR, the lower left triangular elements of the covariance matrix are aligned to form a new measurement vector, and DOA estimation is then realized by representing this vector on an over-complete dictionary under the constraint of sparsity. The a priori information of the incident signal number is not needed in W-CMSR, and no spectral decomposition or focusing is introduced. Simulation results demonstrate the satisfying performance of W-CMSR in wideband DOA estimation in various settings. Moreover, theoretical analysis and numerical examples show how many simultaneous signals can be separated by W-CMSR on typical array geometries, and that the half-wavelength spacing restriction in avoiding ambiguity can be relaxed from the highest to the lowest frequency of the incident wideband signals.

An Efficient Maximum Likelihood Method for Direction-of-Arrival Estimation via Sparse Bayesian Learning

The computationally prohibitive multi-dimensional searching procedure greatly restricts the application of the maximum likelihood (ML) direction-of-arrival (DOA) estimation method in practical systems. In this paper, we propose an efficient ML DOA estimator based on a spatially overcomplete array output formulation. The new method first reconstructs the array output on a predefined spatial discrete grid under the sparsity constraint via sparse Bayesian learning (SBL), thus obtaining a spatial power spectrum estimate that also indicates the coarse locations of the sources. Then a refined 1-D searching procedure is introduced to estimate the signal directions one by one based on the reconstruction result. The new method is able to estimate the incident signal number simultaneously. Numerical results show that the proposed method surpasses state-of-the-art methods largely in performance, especially in demanding scenarios such as low signal-to-noise ratio (SNR), limited snapshots and spatially adjacent signals.

A Unified Framework and Sparse Bayesian Perspective for Direction-of-Arrival Estimation in the Presence of Array Imperfections

Self-calibration methods play an important role in reducing the negative effects of array imperfections during direction-of-arrival (DOA) estimation. However, the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios, such as low signal-to-noise ratio (SNR) and limited snapshots. This paper aims at formulating a unified framework and sparse Bayesian perspective for array calibration and DOA estimation. A comprehensive model of the array output is presented first when a single type of array imperfection is considered, with mutual coupling, gain/phase uncertainty, and sensor location error treated as typical examples. The spatial sparsity of the incident signals is then exploited, and a Bayesian method is proposed to realize array calibration and source DOA estimation. The array perturbation magnitudes are assumed to be small according to most application scenarios, and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear. Cramer-Rao lower bounds (CRLBs) for the array calibration and DOA estimation precisions are also obtained. The sparse Bayesian method is finally extended to deal with the DOA estimation problem when more than one type of array perturbation coexists.

Sparsity-Inducing Direction Finding for Narrowband and Wideband Signals Based on Array Covariance Vectors

Among the existing sparsity-inducing direction-of-arrival (DOA) estimation methods, the sparse Bayesian learning (SBL) based ones have been demonstrated to achieve enhanced precision. However, the learning process of those methods converges much slowly when the signal-to-noise ratio (SNR) is relatively low. In this paper, we first show that the covariance vectors (columns of the covariance matrix) of the array output of independent signals share identical sparsity profiles corresponding to the spatial signal distribution, and their SNR exceeds that of the raw array output when moderately many snapshots are collected. Thus the SBL technique can be used to estimate the directions of independent narrowband/wideband signals by reconstructing those vectors with high computational efficiency. The method is then extended to narrowband correlated signals after proper modifications. In-depth analyses are also provided to show the lower bound of the new method in DOA estimation precision and the maximal signal number it can separate in the case of independent signals. Simulation results finally demonstrate the performance of the proposed method in both DOA estimation precision and computational efficiency.

Extended 2q-MUSIC algorithm for noncircular signals

The NC-2q-MUSIC algorithm proposed in this paper is an extension of the 2q-MUSIC algorithm to the case of noncircular signals which are widely used in communication systems. The computational complexity of the NC-2q-MUSIC algorithm is analyzed in this paper and the NC-2q-MUSIC algorithm for uniform linear array (ULA), which, called NC-2q-MUSIC/ULA algorithm, needs much less computation, is also proposed. Due to the utilization of noncircular information of signals, the root mean square error (RMSE) performance of NC-2q-MUSIC algorithm is better than 2q-MUSIC algorithm for noncircular signals. And the NC-2q-MUSIC algorithm can handle more signals than 2q-MUSIC algorithm. It is proved that the robustness to modeling errors of NC-2q-MUSIC algorithm increases with q. Simulation results validate the better performance of NC-2q-MUSIC over 2q-MUSIC.

A Method for Blind Recognition of Convolution Code Based on Euclidean Algorithm

The key equation (KE) plays an important role in cryptography and communication. In this paper, a new generalization of KE is introduced. By the problem of convolution code blind recognition, a multi-order key equation (MKE) is introduced. It is proved that the MKE can be used for blind recognition of convolution code with any code rate. A fast algorithm based on Euclidean algorithm is achieved which can solve 2-order KE. A new method for blind recognition of convolution code with 1/2 code rate is given, and an example is given in detail, then the computation load is analyzed. The computation load of our algorithm not more than L times N/2, where L is the length of the shortest linear feedback shift register to generate it, N is code length.

Array Signal Processing via Sparsity-Inducing Representation of the Array Covariance Matrix

A method named covariance matrix sparse representation (CMSR) is developed to detect the number and estimate the directions of multiple, simultaneous sources by decomposing the array output covariance matrix under sparsity constraint. In CMSR the covariance matrix elements are aligned to form a new vector, which is then represented on an overcomplete spatial dictionary, and the signal number and directions are finally derived from the representation result. A hard threshold, which is selected according to the perturbation of the covariance elements, is used to tolerate the fitting error between the actual and assumed models. A computation simplification technique is also presented for CMSR in special array geometries when more than one pair of sensors has equal distances, such as the uniform linear array (ULA). Moreover, CMSR is modified with a blind-calibration process under imperfect array calibration to enhance its adaptation to practical applications. Simulation results demonstrate the performance of CMSR.

Direction-of-Arrival Estimation of Noncircular Signals via Sparse Representation

This correspondence addresses the problem of direction-of-arrival (DOA) estimation of noncircular signals, and a new method named noncircular covariance matrix sparse representation (NC-CMSR) is proposed. NC-CMSR realizes DOA estimation by jointly representing the covariance and elliptic covariance matrices of the array output on overcomplete dictionaries subject to sparsity constraint. The new method relies less on the a priori information of the incident signal number than its subspace-based counterparts, and also achieves identification of simultaneous circular and noncircular signals without any extra processes. Simulation results demonstrate the performance of NC-CMSR in DOA estimation and circular-and-noncircular signal identification.

DOA estimation with uniform linear arrays in the presence of mutual coupling via blind calibration

Direction-of-arrival (DOA) estimation in the presence of mutual coupling is a widely studied problem in the field of array signal processing. Most of the previous methods tried to estimate the DOAs by compensating the effect of mutual coupling with measured antenna impedances, which is not an effective way because the impedances are often time-variant. A blind calibrating method is proposed in this paper to deal with the problem of DOA estimation with uniform linear arrays in the presence of mutual coupling. This method exploits the complex symmetric Toeplitz form of the mutual coupling matrix (MCM) of unitary linear arrays (ULA), and transforms conventional direction finding methods from testing the orthogonality between the signal and noise subspaces to checking the rank deficiency of a projected matrix, eliminating most of the influence brought in by the effect of mutual coupling. Simulation results are presented to show the satisfying performance of the new method.

Research of Satellite-to-Satellite Passive Tracking Using Bearings-Only Measurements In J2000 ECI Frame

Based on the problems of singularity while using classic orbit elements in satellite bearings-only passive tracking and the lack of physical meanings in measurement equations variables and their corresponding coordinate transformation, a new passive extended Kalman filtering tracking method using bearings-only measurements in J2000 ECI frame is put forward. An explicit definition of the variables and their coordinate transformation in measurement equation are submitted. Moreover, the state propagation stage, state transfer matrix and measurement Jacobi matrix are deducted in detail. Performance is validated through simulated data from STK6.0. Simulation indicates that it is possible to passively track low earth circular orbit satellite (e=0) by a high earth orbit satellite using bearings-only measurements. Furthermore, this method can reach good convergence even when the initial errors are relatively large