A Degenerate Spatial ARMA Process of External Sources Impinging Upon an Azimuth-Only ULA and the Estimation of Doas and Noise Variances

Array processing is an interdisciplinary topic of both physics and signal processing. Physical basis of array processing is the orderly-setup of sensors in space that induces regular change of the phase of external sources incident upon sensor array. In the current paper the direction-of-arrival (DoA) estimation of an azimuth-only uniform linear array (ULA) is investigated in theory and method from the fused perspective of signal and physical properties of the incident sources. By organically fusing the stationary assumption on source signals and noises with difference operation on the phases, a distinctive system of linear equations satisfied by the incident sources is theoretically derived for the azimuth-only ULA with the Hankel-block-matrix of signal correlations as coefficient matrix and the elementary power-sum symmetric functions of the propagators of incident sources as the unknowns. Based on the derived system of linear equations, signal model of the incident sources is first proved as a degenerate spatial ARMA process subject to the identical autoregressive and moving average parameters and simultaneously obeying the dimensional homogeneity principle (DHP) in physics. The explicit root-finding polynomial is proposed with the unknowns of the system of linear equations as polynomial coefficients and the propagators as the roots. No extraneous roots and conjugate symmetry constraint on polynomial coefficients are involved. The DoAs and noise variances can be separately estimated under the backgrounds of spatially white and colored noises, which are numerically analyzed with the different coherent lengths of noises. A simple sound experiment is designed and performed to verify the proposed DoA estimation method. It is promising to investigate the DoA estimation of the ULA model, particularly of the ULAs of the multi-dimensional array from the fused perspective of physical and signal properties of the incident sources.