Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom

摘要

A new array geometry, which is capable of significantlyudincreasing the degrees of freedom of linear arrays, isudproposed. This structure is obtained by systematically nesting twoudor more uniform linear arrays and can provide O(N^2) degreesudof freedom using only physical sensors when the second-orderudstatistics of the received data is used. The concept of nesting isudshown to be easily extensible to multiple stages and the structureudof the optimally nested array is found analytically. It is possible toudprovide closed form expressions for the sensor locations and theudexact degrees of freedom obtainable from the proposed array as audfunction of the total number of sensors. This cannot be done forudexisting classes of arrays like minimum redundancy arrays whichudhave been used earlier for detecting more sources than the numberudof physical sensors. In minimum-input–minimum-output (MIMO)udradar, the degrees of freedom are increased by constructing audlonger virtual array through active sensing. The method proposedudhere, however, does not require active sensing and is capable ofudproviding increased degrees of freedom in a completely passiveudsetting. To utilize the degrees of freedom of the nested co-array, audnovel spatial smoothing based approach to DOA estimation is alsoudproposed, which does not require the inherent assumptions of theudtraditional techniques based on fourth-order cumulants or quasiudstationary signals. As another potential application of the nestedudarray, a new approach to beamforming based on a nonlinearudpreprocessing is also introduced, which can effectively utilize theuddegrees of freedom offered by the nested arrays. The usefulness ofudall the proposed methods is verified through extensive computerudsimulations.ud