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