Improved Uniform Linear Array Fitting Scheme with Increased Lower Bound on Uniform Degrees of Freedom for DOA Estimation

Recently, uniform linear array (ULA) fitting (UF) principle is proposed for sparse array (SA) design using pseudo-polynomial equations. Typically, it is verified that the designed SAs via UF enjoy a lower bound on uniform degrees of freedom (uDOF), which is approximately $0.5N^2$ with $N$ sensors. Herein, an improved UF (IUF) scheme is proposed to significantly increase the lower bound on uDOF, which is realized by introducing two sub-ULAs, with name of adjoint transfer arrays (ATAs), on both sides of a transfer sub-ULA. The ATAs together with the transfer sub-ULA serve as a new layer to construct an adjoint transfer layer (ATL) that has improved aperture in comparison with traditional transfer layer to improve the lower bound on uDOF, which is derived in detail. Furthermore, two novel SAs are developed based on the ATL to verify the effectiveness of the proposed IUF scheme to increase the uDOF. Numerical simulations verify the superiority of devised SAs for direction-of-arrival (DOA) estimations.