Coherent Signal Parameter Estimation by Exploiting Decomposition of Tensors

Long Liu,Jian Xie,Ling Wang,Zhaolin Zhang,Yuexian Wang

doi:10.1155/2019/5794791

Abstract

The problem of parameter estimation of coherent signals impinging on an array with vector sensors is considered from a new perspective by means of the decomposition of tensors. Signal parameters to be estimated include the direction of arrival (DOA) and the state of polarization. In this paper, mild deterministic conditions are used for canonical polyadic decomposition (CPD) of the tensor-based signal model; i.e., the factor matrices can be recovered, as long as the matrices satisfy the requirement that at least one is full column rank. In conjoint with the estimation of signal parameters via the algebraic method, the DOAs and polarization parameters of coherent signals can be resolved by virtue of the first and second factor matrices. Hereinto, the key innovation of the proposed approach is that the proposed approach can effectively estimate the coherent signal parameters without sacrificing the array aperture. The superiority of the proposed algorithm is shown by comparing with the algorithms based on higher order singular value decomposition (HOSVD) and Toeplitz matrix. Theoretical and numerical simulations demonstrate the effectiveness of the proposed approach.

Highlights

We present a signal model based on the third-order tensor, with three dimensions corresponding to the temporal, spatial, and polarized information of the signal
The mild deterministic conditions [22] are used for canonical polyadic decomposition (CPD) of the tensor-based signal model; i.e., as long as the coherent signals comply with any one of the spatial and polarized diversities, the proposed approach can effectively estimate the parameters of the coherent signals. e parameters to be estimated mainly include the direction of arrival (DOA) and polarization parameters delivered by the signal
Set the number of electromagnetic (EM) vector sensors in the array as L, and the components measured by an EM vector sensor are indexed as 1, . . . , J separately. e spatial steering vector for the array with DOA (θ, φ) is given by as(θ, φ) where fl bTl ε/λ, ε − 􏼂 sin φr cos θr sin φr sin θr cos φr]T, and bl ∈ R3 indicates the spatial location of the lth sensor, l 1, . . . , L

Summary

Signal Model

Let θ ∈ [0, 2π) and φ ∈ [0, π] serve as the indications of the azimuth angle and the elevation angle. E spatial steering vector for the array with DOA (θ, φ) is given by as(θ, φ). Where fl bTl ε/λ, ε − 􏼂 sin φr cos θr sin φr sin θr cos φr]T, and bl ∈ R3 indicates the spatial location of the lth sensor, l 1, . Let Ψ (θ, φ, c, η) indicate the spatial-polarization parameter, where c ∈ [0, π/2] symbolizes the polarization auxiliary angle and η ∈ [− π, π) symbolizes the polarization-phase difference. R􏼉 are assumed to be received by the array. R 1 where the additive prewhitening noise n(k) is assumed to have a Gaussian complex circular. The noise tensor N ∈ CJ×L×K is yielded by tensorization with respect to the noise matrix N [n(1), . The noise tensor N ∈ CJ×L×K is yielded by tensorization with respect to the noise matrix N [n(1), . . . , n(k)]

The Proposed Approach

Simulation Results

Conclusions

Construction of the Intermediate Matrix