Wireless Communications and Mobile Computing

Volume 2019, Article ID 8107176, 12 pages

https://doi.org/10.1155/2019/8107176

## Median-Difference Correntropy for DOA under the Impulsive Noise Environment

Correspondence should be addressed to Xiaotong Zhang; nc.ude.btsu.sei@txz

Received 25 May 2019; Revised 21 August 2019; Accepted 16 September 2019; Published 3 October 2019

Guest Editor: Peio Lopez-Iturri

Copyright © 2019 Fuqiang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The source localization using direction of arrival (DOA) of target is an important research in the field of Internet of Things (IoTs). However, correntropy suffers the performance degradation for direction of arrival when the two signals contain the similar impulsive noise, which cannot be detected by the difference between two signals. This paper proposes a new correntropy, called the median-difference correntropy, which combines the generalized correntropy and the median difference. The median difference is defined as the deviation between the sampling value and the median of the signal, and it intuitively reflects the abnormality of impulsive noise. Then, the median difference is combined with the generalized correntropy to form a new weighting factor that can effectively suppress the amplitude level of impulsive noise. To improve the robustness of the algorithm, an adaptive kernel size is also integrated into the weighting factor to obtain the optimal local feature. The influence of adaptive kernel sizes on the proposed algorithm is simulated, and the comparison between three typical direction-of-arrival estimation algorithms is conducted. The results show that the accuracy of the median-difference correntropy is significantly superior to the correntropy-based correlation and the phased fractional lower-order moment for a wide range of alpha-stable distribution noise environments.

#### 1. Introduction

The source localization using direction of arrival (DOA) of target is an important research in the field of Internet of Things (IoTs). The direction-of-arrival (DOA) approaches based on acoustics have many applications including radar, sonar, seismic exploration, navigation, and sound source tracking [1–3]. DOA estimation is usually regarded as a problem of signal matching, and the performance is significantly influenced by noise. A majority of existing DOA estimations are based on the concept that noise follows Gaussian distribution [4, 5]. Since the Gaussian process has second-order and higher-order statistics, the traditional DOA algorithms can easily evaluate the signal characteristics according to second-order statistics [6]. The multiple signal classification (MUSIC) algorithm [7, 8] and estimation method of signal parameters via rotational invariance techniques (ESPRIT) are the basic subspace algorithms which have good performance [9, 10]. MUSIC is the representative of the noise subspace algorithm, and ESPRIT is the representative of the signal subspace algorithm.

Because of atmospheric noise, electromagnetic interference, sea clutter, car ignitions, and office equipment, the signal is corrupted by the extremely impulsive noise that exhibits irregularity in time domain. In addition, the probability density functions of impulsive noise decay with heavy tails and do not follow a common Gaussian distribution [11]. Therefore, alpha-stable distribution is usually used to define impulsive noise [12]. The conventional covariance matrix is calculated from the second-order statistics of the signal, which may be infinite when the data are corrupted by the extremely impulsive noise [13, 14]. In addition, the conventional DOA algorithms cannot be decomposed into the signal subspace and the noise subspace with covariance matrix. Thus, it has become increasingly important to study DOA under the impulsive noise environment.

The relevant statistical algorithms mainly focus on the existence of statistics. The fractional lower-order statistics (FLOS) algorithms [15] exhibit a more desirable performance than the second-order statistics for alpha-stable distribution [16]. When the signal contains impulsive noise, the signal bears the fractional lower-order statistics. The FLOS algorithms employ the minimum dispersion (MD) criterion to suppress impulsive noise, such as the robust covariation in ROC-MUSIC [17], the fractional lower-order statistics- (FLOM-) based MUSIC, and the phased fractional lower-order moment (PFLOM). The FLOM algorithm-based MUSIC obtains a finite covariance by suppressing one of two cross-correlation signals when the characteristic exponent of alpha-stable distribution ranges from 1 to 2 [18]. The PFLOM algorithm gets the accurate DOA estimation with circular symmetrical signals, embedded in the additive impulsive noise [19]. However, investigators demonstrate that the performance of FLOM and PFLOM algorithms depends on the relationship between the parameter of fractional lower-order moment and the characteristic exponent of alpha-stable distribution. If the characteristic exponent is unknown, the performance of FLOM and PFLOM algorithms seriously decreases.

The correntropy criterion [20] is a relatively simple method that can measure the local similarity between two signals [21, 22]. Because it has the properties of M-estimation, the correntropy has been widely used in the impulsive noise environment [23]. Zhang et al. [24] investigated a narrowband model based on the generalized correntropy which is called the correntropy-based correlation (CRCO) in impulsive noise environment. The CRCO algorithm imposes a correntropy operator on the covariance matrix to depress impulsive noise. The generalized correntropy is suitably for dealing with the template matching between the received signal and the template signal [25]. Since DOA estimation is a matching problem between two signals, the generalized correntropy is incapable of measuring the difference between the outliers and fails to suppress impulsive noise. Thus, when data contain the similar impulsive noise, the cross-correlation of the generalized correntropy is infinite.

In order to solve the problem that correntropy cannot distinguish the similar impulsive noise, we propose a median-difference correntropy (MDCO) algorithm. The MDCO depending on the inner product of vectors measures the similarity of multidimensional properties from input space. A weighting factor of a median difference is defined and evaluates the similarity between the sample value and the median of the signal. The median difference intuitively reflects the abnormality of impulsive noise to guarantee that the autocorrelation is finite. Then, MDCO derives the weighting factor of the generalized correntropy from the correntropy criterion which suppresses the larger impulsive noise. Hence, the weighted covariance function of signal employs the generalized correntropy instead of second-order statistics. These two criteria map the signal from the low-dimensional space to an infinite-dimensional reproducing kernel Hilbert space (RKHS) with impulsive noise, thus including higher-order signal statistics. The adaptive kernel size is applied to the weighting factor for MDCO which can obtain the optimal local feature. At convergence, MDCO is unbiased and it is applicable to achieve CRLB under various parameters. The main work is summarized as follows:(1)We propose a median-difference correntropy (MDCO) algorithm, which can effectively combine the generalized correntropy and the median difference to suppress impulsive noise(2)To improve the robustness of MDCO, we also introduce a novel adaptive kernel size into the weighting factor of the generalized correntropy and the median difference

The rest of this paper is organized as follows: The problem model is defined with DOA in Section 2. In Section 3, we present the median-difference correntropy (MDCO) for DOA estimation under impulsive noise environment. The performance evaluation is presented in Section 4. Finally, conclusions are drawn in Section 5.

#### 2. Problem Formulation

It is considered that a uniform linear array of *M* isotropic acoustic sensors receives the far-field signal generated by narrowband sources. Then, Figure 1 illustrates the linear array model.