A Novel Spatial Sampling Scheme for DOA Estimation With Movable Arbitrary Sparse Arrays

Sparse arrays have been an important concept in the study of direction of arrival (DOA) estimation since they can obtain the number of degrees of freedom (DOFs) is much larger than that of the number of physical sensors. However, the missing lags in the difference co-array reduce the DOF that is expected. Recently, array motion has received considerable attention, since this operation can fill the missing lags, increase the DOF, and enlarge the array aperture without adding extra physical sensors. In this study, we investigate the DOA estimation of array mounted on a moving platform and propose the condition and corresponding spatial sampling scheme that can result in a complete consecutive difference co-array. Specifically, we first explore the general expression of the synthetic array, which is generated by collecting the sampling data of a moving array at different times. After that, the closed-form expression for the difference co-array corresponding to the synthetic array is derived. Thirdly, we introduce the condition that must be satisfied to generate a hole-free difference co-array for movable arbitrary arrays. Then, based on this condition, we develop a non-uniform sampling method that can fill all the missing lags and lead to a fully consecutive difference co-array regardless of the physical geometry, which can therefore improve uniform DOFs (uDOFs). Finally, several classical arrays, including uniform linear array, coprime array, nested array, etc., are adopted to apply the proposed sampling scheme, and the closed-form expressions of the resulting uDOFs are analyzed in detail. Numerical simulations are presented to illustrate the effectiveness and superiority of the proposed sampling scheme in DOA estimation performance.