Abstract
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.
Highlights
A RRAY processing has been extensively applied to the diverse engineering applications including radar, sonar, wireless communication and seismic prospecting and so forth
As a physical parameter containing the unknown DoAs, phase-difference can be treated as a result of difference operation on phases of the same source impinging upon the adjacent sensors
Except for the rotational-invariance structure of array manifold proposed by the ESPRIT which was used to wholly extract the propagators of the incident sources, in accordance with the above definition, here we provide the other manner of explicit extraction of phase-difference
Summary
A RRAY processing has been extensively applied to the diverse engineering applications including radar, sonar, wireless communication and seismic prospecting and so forth. It is beneficial and meaningful to study array processing from the fused perspective of physical and signal properties of the incident sources. As a physical parameter containing the unknown DoAs, phase-difference can be treated as a result of difference operation on phases of the same source impinging upon the adjacent sensors Once such a connection is made, except for the rotational-invariance structure of array manifold, by making use of difference operation on phases, phase-difference can be individually extracted out from the ULA representation and explicitly expressed for the subsequent estimation. By fusing difference operation on phases with the appropriate signal assumption on source and noise, here we take the azimuth-only ULA as an object and probe the DoA estimation in theory and method.
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