Sparse Array Design And DOA Estimation Based On Fourth Order Cumulants

The direction of arrival(DOA)estimation is widely used in radar,sonar,communications,speaker positioning,seismic exploration,and other related fields.Compared to a uniform array,a sparse array has a larger array aperture with the same number of sensors,providing more degrees of freedom and higher estimation accuracy.Conventional sparse array-based DOA estimation methods mostly focus on the second-order cumulants,which fail to fully utilize all the virtual lags generated by sparse arrays.However,the fourth-order cumulants-based DOA estimation methods effectively utilize more lag information,thereby further improving estimation performance.Therefore,this article takes nested arrays as the research object,and combines fourth-order cumulants with sparse arrays to design new sparse arrays.The main work includes:1.Under the condition of far-field sources,using fourth-order cumulants to analyze the virtual sensor layout of nested arrays,a new sparse array-the expanded nested array is proposed,and its mathematical expressions of hole locations,consecutive lags,and unique lags are analyzed,providing a theoretical basis for the proposed another sparse array in the future.2.Under the condition of far-field sources,in order to solve the problem of holes in the proposed expanded nested array,a hole-free expanded nested array is proposed by adding and moving a sensor.The mathematical expressions related to the consecutive lags and virtual sensor redundancy are derived.Simulation experiments verify the effectiveness and superiority of the proposed array.3.Under the condition of mixed sources in the far-field and near-field,the virtual sensor redundancy of symmetric nested arrays is analyzed based on the fourth-order cumulants,and a symmetric switched nested array is proposed.The mathematical expression related to the consecutive lags of the proposed symmetric switched nested array is derived,laying a foundation for further improvement of the proposed sparse array.4.Under the condition of mixed sources in the far-field and near-field,an shifted symmetric switched nested array is proposed by moving subarrays of the symmetric switched nested array,and the mathematical expression of the consecutive lags of the shifted symmetric switched nested array is derived.Simulation experiments verify the effectiveness and superiority of the proposed array.