Research On Direction Finding Techniques Using A Sparse Array

Sparse array is the array system whose element spacing exceeds a half wavelength. Compared with traditional full array, sparse array with the same number of sensors generally provides enlarged aperture size, and even increased degrees of freedom. These lead to sparse array possesses many performance advantages, such as stronger resolution performance, higher estimation accuracy and more processing capacity. Therefore, sparse array is a hot research topic in direction finding due to these advantages. This dissertation focuses on the direction-of-arrival (DOA) estimation method using a sparse array, including array geometry design, DOA estimation algorithms and their statistical performance analysis to demonstrate the advantages of sparse array over traditional full array quantitatively and theoretically. Works and contributions in the dissertation mainly include:1. The system tolerance of multi-level coprime array is studied, and two extended aperture-based DOA estimation algorithms using this array are presented. First, the system tolerances of three solving ambiguity algorithms are derived, and the capability that multi-level coprime array can offer a larger system tolerance is quantitatively demonstrated by both theoretical analysis and experimental results. Then, by using this array, a virtual ESPRIT algorithm based on modulo conversion (MC-VESPRIT) and a virtual PM algorithm based on modulo conversion (MC-VPM) are proposed, respectively. In the both algorithms, to break through the constraint that traditional algorithm needs the reference element spacing within a half-wavelength, the multi-level coprime relationship between the sensor spacings and the aperture extension in cumulant domain are used, and thus the DOA estimation accuracy is effectively improved. More importantly, the MC-VPM exploits a two-L-shaped configuration to avoid the estimation fails, and the VPM technique to achieve an automatically paired two-dimensional (2-D) DOA estimation.2. Two nested arrays and their accompanying2-D DOA estimation algorithms are proposed. A new two cross nested array geometry with three different inter-sensor spacings is designed to achieve enhanced degrees of freedom and doubled aperture length. The virtual matrix pencil method (VMPM) is proposed for this new array to estimate the2-D DOA of the signal sources, where the three different inter-sensor spacings are used to construct a virtual sparse two-parallel-shape array with much larger number sensors. Compared with the improved propagator method (PM), the VMPM has better angle estimation accuracy, and is capable of resolving O(P2/32) sources with P sensors. The statistical analyses of these two methods are studied, and the asymptotic variance expressions of their estimation errors are derived. Moreover, these asymptotic variance expressions are simplified for the case of one signal, and the quantitative comparisons are performed to demonstrate the performance advantage of the VMPM. Then, the idea of above nested arrays is generalized to multi-level. A multi-level nested L-shaped array is designed, and an arbitrary even order (2q) multiple signal classification (2g-MUSIC) algorithm based on2-D spatial smoothing is proposed. The proposed algorithm utilizes a2q statistics and M+N physical sensors to systematically construct the virtual uniform rectangular array (URA) with O(Mq×Nq) sensors. Thus, the estimation accuracy and the maximum number of resolvable signals are further improved. In addition, the optimal&suboptimal distribution of the multi-level nested L-shaped array also is derived to maximize the number of virtual sensors.3. Three sparse electromagnetic vector arrays and their accompanying2-D DO A estimation algorithms are studied. First, the coprime/nested scalar array is generalized to the joint domain of2-D space and polarization. A sparse coprime/nested electromagnetic vector arrays is designed, which not only contains the2-D coprime/nested characteristics, but also contains the polarization characteristice. By using the3-D characteristics of the array, a virtual URA with more difference co-vector-sensors is constructed to increase degree of freedom and extend doubled array aperture. To utilize these advantages to2-D DOA estimation and restore the electromagnetic vector sensor with6components, a polarization MUSIC algorithm based on3-D spatial smoothing (3DS-PMUSIC) is present. Compared with PMUSIC algorithm, the3DS-PMUSIC algorithm significantly improves several aspects of performances, and especially the maximum number of resolvable signals. The theoretical and simulation results show that the3DS-PMUSIC algorithm can resolve O(3P2) signals when P sensors is used. Then, the problem that the unknown spatially correlated noise severely degrades the2-D DOA and polarization estimation performance of traditional algorithms is considered. A matrix-reconstruction algorithm using an electromagnetic vector array with three-size spatial invariance is then proposed to deal with the problem. By exploiting the two cross-correlation matrices between some sensor data, the spatial-polarization characteristic of the array is fully employed, and the noise term is also eliminated. Compared with the traditional algorithms, the proposed algorithm provides a better estimation performance. In addition, the proposed algorithm does not need matrix prescribing and higher order statistics, and thus possess low computational complexity.4. Using a sparse uniform linear array (ULA) with distributed electromagnetic vector sensors, an2-D DOA estimation algorithm based on enhanced matrix and an parameters estimation algorithm based on PM and matrix reconstruction technique are proposed, respectively. The former is used to estimate the2-D DOA of coherent signals, while the latter is used to estimate the2-D DOA and polarization of mixed signals, which are a mixture of uncorrelated signals and coherent signals. The two algorithms not only keep the vector property of the electromagnetic vector sensors, but also extend the inter-sensor spacing and the spacing between the dipole-triad and loop-triad beyond a half-wavelength. Therefore, the two algorithms can provide a better estimation performance. In particular to the latter, the2-D DOA and polarization of the uncorrelated signals are first estimated, and the2-D DOA and polarization of the coherent signals are then estimated. This treatment leads to many advantages:more fully utilizing array aperture, improving estimation accuracy, increasing the maximum number of resolvable signal, and avoiding the performance degradation as the2-D DOA of uncorrelated signal is similar to that of coherent signal. In addition, the CRLB of2-D DOA and polarization estimations for the mixed-signal is also derived.