Digital Signal Processing 92 (2019) 20–25 Contents lists available at ScienceDirect Digital Signal Processing www.elsevier.com/locate/dsp Analytic performance investigation of signal level estimator based on empirical characteristic function in impulsive noise Sina Bakhshandeh Babarsad a , S. Mohammad Saberali a,∗ , Mahdi Majidi b a Department of Electrical Engineering, University of Isfahan, P. O. Box 81746-73441, Isfahan, Iran b Department of Electrical and Computer Engineering, University of Kashan, Kashan, Iran a r t i c l e i n f o a b s t r a c t Article history: Available online 4 May 2019 Keywords: Empirical characteristic function Estimation Impulsive noise Non-data aided Laplace noise Gaussian mixture noise In this paper, we evaluate the mean square error (MSE) performance of empirical characteristic function (ECF) based signal level estimator in a binary communication system. By calculating Cramér-Rao lower bound (CRLB) we investigate the performance of the ECF based estimator in the presence of Laplace and Gaussian mixture noises. We have derived an analytic expression for the variance of the ECF based estimator which shows that it is asymptotically unbiased and consistent. Simulation and analytic results indicate that the ECF based level estimator outperforms the previously proposed estimators in some signal to noise ratio (SNR) regions when the observation noise distribution is unknown.  2019 Elsevier Inc. All rights reserved. 1. Introduction The noise in many communication systems is impulsive [1–3] and consequently parameter estimation of the communication sig- nals in the presence of impulsive noise has attracted attention of many researchers [1,2,4–7]. One of the parameters that must be estimated in the presence of impulsive noises is the signal level which is very important from practical point of view [1]. It is well known that the implementation of the optimal commu- nication receivers requires an estimation of the signal level [1]. Previous works on this subject are either data-aided (DA) or non- data-aided (NDA) [1]. In the DA case, the estimation is based on some known training sequences transmitted through the chan- nel, whereas, the NDA estimation is carried out without any need for training sequences. Hence, NDA methods are also called blind methods. Although DA estimation methods are more accurate, they require more bandwidth compared to NDA methods. DA and NDA level estimators for a binary communication system in a noise with known Laplace distribution, namely the median estimator, have been proposed in [1] based on the maximum likelihood (ML) criterion. In [6], a method based on empirical characteristic func- tion (ECF) is proposed to estimate the signal level in the presence of unknown noise. In a communication system with completely known noise statistics, any unknown physical phenomena in the * Corresponding author. E-mail addresses: sina.bakhshande@gmail.com (S.B. Babarsad), sm.saberali@eng.ui.ac.ir (S.M. Saberali), m.majidi@kashanu.ac.ir (M. Majidi). channel or any change in the system components, alter the noise probability density function (PDF) to a different one. Hence, sta- tistical signal processing in unknown noise has attracted a lot of attention, recently [8–11]. It is well known that estimation meth- ods based on unknown PDF assumption are much more robust to the changes of the noise PDF. However, from estimation the- ory point of view, the possibility of signal level estimation with high accuracy without need to the complete knowledge about the noise PDF is questionable. It has been shown via simulation in [6] that ECF based method can estimate the signal level in unknown noise and has acceptable performance compared with ML based methods. ECF is previously used in a wide range of problems in- cluding parameter estimation of α-stable noise [12–14], testing for symmetry [15], test for multivariate normality [16] and Goodness- of-fit tests for multivariate stable distributions [17]. In this paper, we analytically show that the ECF based signal level estimator previously proposed in [6], works well when the PDF of the receiver noise is impulsive. In order to investigate the robustness of the proposed method, we evaluate its performance in the presence of Laplace and Gaussian mixture (GM) noises. ECF is an unbiased and consistent estimator for the characteristic func- tion (CF) [18]. By using the ECF, we obtain the required informa- tion for NDA estimation of the signal level in unknown impulsive noise. We compare the performance of the ECF based estimator with that of ML based method in [1], for Laplace noise. We exam- ine the efficacy of the ECF based estimator by obtaining the mean square error (MSE) index of performance and comparing it with the Cramér-Rao lower bound (CRLB). We also derive an analytic ex- https://doi.org/10.1016/j.dsp.2019.04.009 1051-2004/ 2019 Elsevier Inc. All rights reserved.