Two-Dimensional Frequencies Estimation Using Two-Stage Separated Virtual Steering Vector-Based Algorithm

Abstract

In this paper, we develop a novel two-stage separated virtual steering vector-(SVSV-) based algorithm without association operation to estimate 2D frequencies. The key points of this algorithm are (i) in the first stage, this paper rearranges the measurement data as virtual rectangular array data matrix and obtains the propagator from the data matrix using least-squares operator. In addition, the virtual steering vector can be separated into two parts using the introduced electric angle that combines 2D frequencies (to avoid incorrect association especially when multiple 2D frequencies have the same frequency at some dimension), and thus the electric angle and the first part of separated steering vector can be estimated using the derived rank-reduction propagator method; (ii) in the second stage, this paper estimates the second part of separated steering vector using another least-squares operator and obtains 2D frequencies from the recovered steering vector. The resultant SVSV algorithm does not require spectral search or pairing parameters or singular value decomposition (SVD) of data matrix. Simulation results are presented to validate the performance of the proposed method.

Two-dimensional frequency estimation using a modified version of the two-stage separated virtual steering vector-based algorithm

“…The signal model used for proposed method is similar to the one used by SVSV in [1]. Only, the difference is that the modified SVSV's signal model can also have the similar 2…”

“…Where, 1 2 . So to solve this problem, we have incorporated a different approach at the second stage of SVSV.…”

“…As the noise subspace is orthogonal to the signal subspace (second part of steering vector given in [1, Eq. (17)]), so we construct a polynomial ( ) ρ γ as given (8) is its hermitian transpose [1,8]. Term T is used for transpose and H for hermitian transpose.…”

“…These methods either use eigen value decomposition (EVD) of the data covariance matrix or singular value decomposition (SVD) of the data matrix to separate the noise subspace from the signal subspace. D. Liu & J. Liang has recently proposed a novel 2D frequency estimation algorithm called two-stage separated virtual steering vectorbased algorithm (SVSV) [1]. The method is based on the propagator method, so it does not require EVD or SVD of the data of received signal to estimate frequencies.…”

“…As the proposed method is a modified version of SVSV, so all the mathematical expressions of SVSV given in [1] are equally applicable to the Modified SVSV and our subsequent discussion would frequently use the mathematical expressions of SVSV. Hence, the readers are referred to [1] for the mathematical framework detail of the SVSV before going through forthcoming sections of this paper.…”