Accuracy of the Wiener-Hopf solution when based on sample statistics

Stephan Weiss; Ian K. Proudler; Yoann Altmann

doi:10.1109/LSP.2026.3667455

Accuracy of the Wiener-Hopf solution when based on sample statistics

Stephan Weiss, Ian K. Proudler, Yoann Altmann

Electronic And Electrical Engineering

Research output: Contribution to journal › Article › peer-review

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Abstract

This letter addresses the problem of an adaptive linear combiner when using sample statistics. In this case, the Wiener-Hopf solution can be based on sample covariance matrices and cross-correlation vectors. Despite these estimates being inaccurate, the calculated, approximate solution can be very precise. We explore why this is so by interpreting the Wiener-Hopf solution as coming from a least squares problem. We compare this solution to the case where we exploit knowledge about some of the statistics. Surprisingly this has very limited benefits and often is detrimental. We also show why it is disadvantageous to separately estimate the two statistics.

Original language	English
Pages (from-to)	1106-1110
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	33
DOIs	https://doi.org/10.1109/LSP.2026.3667455
Publication status	Published - 23 Feb 2026

Keywords

adaptive systems
least squares approximation
systems identification

Access to Document

10.1109/LSP.2026.3667455

Weiss-etal-IEEE-SPL-2026-Accuracy-of-the-Wiener-Hopf-solution-when-based-on-sample-statisticsAccepted author manuscript, 855 KBLicence: CC BY 4.0

Why can Wiener-Hopf reach accurate solutions with poor statistical estimates?
Weiss, S. & Proudler, I. K., 16 Jul 2025, 2025 IEEE Statistical Signal Processing Workshop (SSP). Piscataway, NJ: IEEE, p. 146-150 5 p. (IEEE/SP Workshop on Statistical Signal Processing (SSP)).
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23rd IEEE Statistical Signal Processing Workshop
Weiss, S. (Participant)
8 Jun 2025 → 11 Jun 2025
Activity: Presenting or Organising an Event › Organiser of major conference

Cite this

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abstract = "This letter addresses the problem of an adaptive linear combiner when using sample statistics. In this case, the Wiener-Hopf solution can be based on sample covariance matrices and cross-correlation vectors. Despite these estimates being inaccurate, the calculated, approximate solution can be very precise. We explore why this is so by interpreting the Wiener-Hopf solution as coming from a least squares problem. We compare this solution to the case where we exploit knowledge about some of the statistics. Surprisingly this has very limited benefits and often is detrimental. We also show why it is disadvantageous to separately estimate the two statistics.",

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author = "Stephan Weiss and Proudler, \{Ian K.\} and Yoann Altmann",

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AB - This letter addresses the problem of an adaptive linear combiner when using sample statistics. In this case, the Wiener-Hopf solution can be based on sample covariance matrices and cross-correlation vectors. Despite these estimates being inaccurate, the calculated, approximate solution can be very precise. We explore why this is so by interpreting the Wiener-Hopf solution as coming from a least squares problem. We compare this solution to the case where we exploit knowledge about some of the statistics. Surprisingly this has very limited benefits and often is detrimental. We also show why it is disadvantageous to separately estimate the two statistics.

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KW - least squares approximation

KW - systems identification

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JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

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Accuracy of the Wiener-Hopf solution when based on sample statistics

Abstract

Keywords

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Research output

Why can Wiener-Hopf reach accurate solutions with poor statistical estimates?

Activities

23rd IEEE Statistical Signal Processing Workshop

Cite this