A Non-Asymptotic Analysis on the Additional Bias of Capon's Method

IF 3.2 2区工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Signal Processing Letters Pub Date : 2025-04-28 DOI:10.1109/LSP.2025.3565131

Jian Dong;Jinzhi Xiang;Wei Cui;Yulong Liu

引用次数: 0

Abstract

The Capon method is one of the classical direction-of-arrival (DOA) estimation methods in array signal processing. The standard analysis of the additional bias of this method is asymptotic, which assumes the number of snapshots

$K$

goes to infinity. This paper provides a non-asymptotic analysis for the additional bias by employing some tools from high-dimensional probability and perturbation analysis of optimization problems. We establish upper bounds for the additional bias in both expectation and tail forms, which reveal that the additional bias has an error rate of

$O(K^{-\frac{1}{2}})$

when the number of snapshots satisfies a certain condition. We demonstrate our results by some numerical experiments.

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Capon方法附加偏差的非渐近分析

Capon方法是阵列信号处理中经典的到达方向估计方法之一。该方法的附加偏差的标准分析是渐近的，它假设快照的数量K趋于无穷大。本文利用优化问题的高维概率和摄动分析中的一些工具，给出了附加偏差的非渐近分析。我们建立了期望和尾形式下附加偏差的上界，表明当快照数量满足一定条件时，附加偏差的错误率为$O(K^{-\frac{1}{2}})$。通过一些数值实验验证了我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Signal Processing Letters 工程技术-工程：电子与电气

CiteScore

7.40

自引率

12.80%

发文量

339

审稿时长

2.8 months

期刊介绍： The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.