Fast WL Beamforming Using Toeplitz Covariance 


Vol. 51,  No. 1, pp. 112-120, Jan.  2026
10.7840/kics.2026.51.1.112


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  Abstract

When the signals impinging on a uniform linear array (ULA) are strictly noncircular and uncorrelated with each other, this paper proposes a WL (widely linear) beamforming method that can provide fast convergence. As the incident signals are uncorrelated the elements along each diagonal of the array covariance matrix, which has a Toeplitz form, are equal while the elements along each antidiagonal of the relation matrix become identical. In this paper, the extended sample matrix (ESM) conventionally used is rectified according to the properties of equality. It is shown that in terms of the -norm the rectified ESM has less error than the conventional one and that it is transformed into a real matrix by using a unitary matrix. The eigenvalues and eigenvectors of the ESM are efficiently obtained from the eigen-decomposition of the real matrix. The extended steering vector for the desired signal is estimated based on the fact that it is orthogonal to the noise subspace. Then, the weight vector is found such that it lies in an estimated signal subspace. Simulation results demonstrate that the proposed WL beamforming method provides much faster convergence speed to the steady state than the conventional ones, thereby showing the effectiveness of the rectification.

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  Cite this article

[IEEE Style]

Y. Choi, "Fast WL Beamforming Using Toeplitz Covariance," The Journal of Korean Institute of Communications and Information Sciences, vol. 51, no. 1, pp. 112-120, 2026. DOI: 10.7840/kics.2026.51.1.112.

[ACM Style]

Yang-Ho Choi. 2026. Fast WL Beamforming Using Toeplitz Covariance. The Journal of Korean Institute of Communications and Information Sciences, 51, 1, (2026), 112-120. DOI: 10.7840/kics.2026.51.1.112.

[KICS Style]

Yang-Ho Choi, "Fast WL Beamforming Using Toeplitz Covariance," The Journal of Korean Institute of Communications and Information Sciences, vol. 51, no. 1, pp. 112-120, 1. 2026. (https://doi.org/10.7840/kics.2026.51.1.112)
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pISSN : 1226 - 4717
eISSN : 2287 - 3880