Geometry Of Array With High Resolution In Direction Finding

In such fields as communication,radar,sonar,seismology and biomedicalengineering,the estimation of Direction of Arrival(DOA) is a very important subject.Sensors array is often employed as the equipment of Direction Finding(DF) because thephase difference of impinging signals between the sensors of array can be used toestimate DOA.The impinging signals coming from different DOAs exhibit different spatialfrequencies,the estimation of DOAs can be implemented by estimating spatialfrequencies.The sensors of array are sampling points arranged spatially,samples fromthe sensors can be used to estimate the spatial frequencies,i.e.,the DOAs,so,thearrangement of the spatial sampling points,namely,the array geometry,exerts greatinfluence on the performance of DF system.The study of array geometry is an essentialtopic in array signal processing.The influence of array geometry on the performance of DF system depends onDOA estimation algorithms.Subspace algorithms are popular for their high resolutionand low complexity.For the nonlinearity of those algorithms,the relationship betweenarray geometry and the performance of the DF system adopting the algorithms iscomplex.Even though,as the criteria of design and optimization of array geometry,therelationship needs to be studied.One problem which subspace algorithms suffer is ambiguity.Manifoldambiguities occur when there are linear dependent steer vectors on array manifold.Manifold is a function of array geometry,so the ambiguities are determined by arraygeometry.The study of ambiguity consists of two parts:1.Studying the relationship between the array geometry and ambiguity;Findingthe existence condition of ambiguity on certain array geometry and locating theambiguities.2.Determining if the ambiguities can be resolved;Designing method to resolvethe ambiguities.About the geometry of array,the following novel results are presented in this thesis.1.Based on minimal manifold length,an index is suggested,the index can beused to evaluate the accuracy performance of given linear array.Conventionally,aperture is often used as an index to compare the performance ofdifferent linear arrays,but it does not take into account the number of sensor and thearray geometry.We propose an index to evaluate accuracy of linear array,the indexconsiders the whole information of array geometry.2.The CRLB of DOA estimation on volume array is deduced.Planar array can be used to estimate azimuth and elevation,but in the zone of lowelevation,the estimation of elevation becomes worse.To overcome the shortcoming,the application of volume array is suggested.In this thesis,we deduce the relationshipbetween the CRLB of DOA estimation on volume array and the geometry of the volumearray.The CRLB verify the experience that volume array outperform planar array inlow elevation zone3.The relationship between the geometry errors of array and errors of DOAsestimated by subspace algorithm is deduced.The sensitivity of several planar arrayswith respect to geometry errors is studied.In practice,the arrays suffer geometry errors,this leads to DF errors,so therelationship between them is very important in DF system implementation.Based on thestudy of array manifold,we derive the relationship.4.Based on specifications on two independent cone angles,an approach of planararray design is suggested.The planar array can estimate two dimensional independent angles,but knowndesign technique of planar array only considers specifications of elevation,so the designapproach that considers the specifications of two dimensional angles is needed.Afterparameters transform from azimuth-elevation to cone angles,one such design approachis proposed.5.We identify the linear array free of rank-2 ambiguity and planar array free ofrank 2 elevation ambiguity on given azimuth.Because the array manifold is nonlinear function of array geometry,the resultsabout relationship between array geometry and ambiguity are not sufficient.Low rankambiguity is more harmful to DF system,so we identify the linear array free of rank 2 ambiguity,and then,we identify the planar array free of rank 2 elevation ambiguity ongiven azimuth.6.Based on steepest descent method,a robust approach to resolve ambiguity isproposed.Sparse arrays have advantages of high performance and low cost,but they arecertain to suffer ambiguities,so the methods resolving manifold ambiguities arenecessary.Because the known methods are based on linear programming technique,they are sensitive to coefficient error,a robust method based on steepest descent methodis proposed,simulation results verify the robustness of the proposed method.