变冲噪声中近最优的恒虚警率检测方法
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本文探讨了在不断变化的脉冲干扰环境中，基于α稳定分布的近似最优检测方法，尤其是针对其常数误报率(CFAR, Constant False Alarm Rate)设计。α稳定分布作为一种重要的非高斯统计模型，因其对描述突发干扰的广泛适用性而备受关注。然而，除了少数特殊情况外，它没有封闭形式的概率密度函数(PDF)，这给理论分析和实际应用带来了一定挑战。
传统的做法是采用子优化的零记忆非线性函数（ZMNL），如经典的卡塞尔(Cauchy)分布和高斯分布作为近似，来设计局部最优的检测器。这些非线性函数能够在一定程度上捕捉到α稳定分布的特性，尽管它们并非完全精确。设计这样的检测器时，关键在于找到一个能够在面对脉冲噪声背景下既能保持较低的误报率又能保持较高检测效率的函数形式。
研究者们通过Xutao Li、Jun Sun、Shouyong Wang和Lisheng Fan的合作，着重于在Shantou University和Huazhong University of Science and Technology的电子工程系以及Wuhan Radar Institute的关键实验室，针对这一问题进行了深入研究。他们的工作可能涉及信号处理领域的算法优化，例如改进的滤波器设计、统计测试理论或者基于机器学习的数据驱动方法，以提升在脉冲干扰环境中的检测性能。
文章可能包括以下几个部分：
1. **引言**：介绍α稳定分布和CFAR原则在无线通信、雷达或信号处理中的重要性，以及现有技术的局限性。
2. **理论背景**：回顾α稳定分布的特性，讨论其PDF的特殊性质以及为什么它在脉冲干扰中的应用具有挑战性。
3. **ZMNL函数的选择与优化**：详细阐述如何选择和调整ZMNL函数以逼近α稳定分布，以及这种方法如何用于设计CFAR检测器。
4. **方法与策略**：提出新的设计方法或算法，可能是基于迭代优化、蒙特卡洛模拟或统计估计，以求在近似和性能之间找到平衡。
5. **仿真与实验结果**：展示在不同参数下，新设计的检测器相比于传统方法在误报率和检测效率上的改善。
6. **结论与未来方向**：总结研究成果，指出潜在的改进空间，并讨论可能的应用领域和未来的研究挑战。
这篇发表在《IET Signal Processing》的研究论文，不仅为解决脉冲干扰环境下的近似最优检测问题提供了新的视角，也为相关领域的工程师和研究人员提供了一个实用且有效的设计框架。通过深入理解和利用α稳定分布的特性，它有助于提高无线通信系统的稳健性和可靠性。
Published in IET Signal Processing
Received on 24th December 2011
Revised on 29th March 2013
Accepted on 22nd April 2013
doi: 10.1049/iet-spr.2013.0024
ISSN 1751-9675
Near-optimal detection with constant false alarm ratio
in varying impulsive interference
Xutao Li
1
, Jun Sun
2
, Shouyong Wang
3
, Lisheng Fan
1
, Li Chen
1
1
Department of Electronic Engineering, Shantou University, Shantou, Guangdong, People’s Republic of China
2
Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, Hubei,
People’s Republic of China
3
Key Laboratory, Wuhan Radar Institute, Wuhan, Hubei, People’s Republic of China
E-mail: lixt@stu.edu.cn
Abstract: As an important class of non-Gaussian statistic model, α-stable distribution has received much attention because of its
generality to represent impul sive interference. Unfortunately, it does not have a closed-form probability density function (PDF)
except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an
approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To
enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α-stable. In
particular, a simplified version of Cauchy–Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is
detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture
model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using
BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form.
Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and
achieves near-optimal performance in varying impulsive interference.
1 Introduction
The signal processing systems often encounter noise and
interference [1–5], among which the impulsive interference
has received much attention in recent years. A remarkable
nature of impulsive interference is that its density function
in the tail is heavier than that of Gaussian density [6, 7]. In
recent two decades, there has been a tremendous interest in
studying the symmetric α-stable (SαS) distribution which is
considered as a generalisation of Gaussian distribution [1–
3]. Moreover, it has been tested and found to match the real
data with excellent fidelity [8–11], similar to that of the
broadly accepted Middleton models [12, 13].
As a classical problem, signal detection in noisy
observation is usually viewed as the hypothesis testing in
inference [14] and has been implemented in a variety of
scenario, such as radar, sonar and communications [15–17].
In most of the previous work, the signal is assumed to be
corrupted by the Gaussian noise because of the central limit
theorem, and the linear detectors have been well developed.
However, when the impulsive interference appears, the
linear detector designed under the Gaussian assumption
loses its performance severely [18, 19].
The analytically optimal detector is feasible only when the
probability density function (PDF) of interference is
analytical known. Unfortunately, there are no closed forms
for the probability densities of SαS except for two special
cases, say Gaussian and Cauchy distributions [1].
In consistent with the scale mixtures in modelling
heavy-tailed distributions [6, 7], several approximation
mixture models have been proposed to approximate the
actual SαS’s PDF, such as Gaussian mixture model (GMM)
[20–22] derived from the subGaussian theory [1] and
Cauchy–Gaussian mixture (CGM) model [23, 24].
However, the GMM cannot capture the algebraic tails of
SαS with small number of Gaussian components M while
loses analytical convenience with large M. The CGM model
is computationally expensive in evaluating triple
parameters. To develop a tractable form, in [25], we have
briefly introduced a simplifi
ed CGM model with
bi-parameter called bi-parameter CGM (BCGM) model,
which is a valid approximation for SαS with α ∈ [1, 2].
Since too impulsive interference with α < 1 is infrequent in
practice, α ∈ [1, 2] is hereby taken as the practical
consideration. In this paper, we will detail the fact that th e
mixture of Cauchy densities can be regarded as another
approximation for SαS PDF. Such a fact gives a reasonable
support to the BCGM model.
In a real radar or sonar system, to achieve adaptive
detection with constant false alarm ratio (CFAR) [26, 27],
the test threshold should be adjusted according to the
preset false alarm ratio (FAR) in varying circumstance.
An analytical PDF of interference is expected in
solving such a problem. By using BCGM model, a
concise PDF, the relation between test threshold and FAR
can be evaluated handily, which indicates that the adaptive
www.ietdl.org
824 IET Signal Process., 2013, Vol. 7, Iss. 9, pp. 824–832
&
The Institution of Engineering and Technology 2013 doi: 10.1049/iet-spr.2013.0024
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