non-Gaussian Noise Environments Research Articles

Fractional tap-length algorithm for adaptive filters under maximum correntropy criterion

Accurate estimation of the optimum tap-length for the adaptive filter provides a good balance between the steady-state performance and the complexity of the adaptive algorithm. The convergence performance of the variable tap-length least mean square( LMS) adaptive filters under the minimum mean square error( MMSE) criterion deteriorates in the non-Gaussian noise environment. A fractional tap-length( FT) algorithm for the maximum correntropy criterion( MCC) adaptive filters,named FT-MCC algorithm,is proposed to solve the above problem. The proposed algorithm is based on the concept of the optimum tap-length for the MCC adaptive filters. The difference of the correntropy between adaptive filters with different tap-lengths is used to achieve the tap-length update. Both theoretical analysis and simulation result show that the proposed algorithm has strong robustness in non-Gaussian noise environment compared with other variable tap-length LMS algorithm and the optimum tap-length can be well estimated with proper parameter selection.

음향 통신 채널 추정기를 이용한 대수학적 스텝크기 least mean fourth 알고리즘

ABSTRACT: The least-mean fourth (LMF) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the least mean square (LMS) algorithms with variable step size. It is because the variable step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a variable step-size LMF algorithm is proposed, which adopts an algebraic optimal step size as a variable step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.Keywords: Acoustic communication, Channel estimation, LMF, Algebraic optimal step-sizePACS numbers: 43.60.Dh, 43.60.Mn†Corresponding author: Jun-Seok Lim (jslim@sejong.ac.kr) Department of Electrical Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea(Tel: 82-2-3408-3299, Fax: 82-2-3408-4329)

Background modeling using Object-based Selective Updating and Correntropy adaptation

Background modeling is widely used in visual surveillance systems aiming to facilitate analysis of real-world video scenes. The goal is to discriminate between pixels from foreground objects and those ones from the background. However, real-world scenarios tend to have time and spatial non-stationary variations, being difficult to reveal the foreground and background entities from video data. Here, we propose a novel adaptive background modeling, termed Object-based Selective Updating with Correntropy (OSUC), to support video-based surveillance systems. Our approach that is developed within an adaptive learning framework unveils existing spatio-temporal pixel relationships, making use of a single Gaussian for the model representation stage. Moreover, we introduce a background updating scheme composed of an updating rule that is based on the stochastic gradient algorithm and Correntropy cost function. As a result, this scheme can extract the temporal statistical pixel distribution, at the same time, dealing with non-stationary pixel value fluctuations that affect the background model. Here, an automatic tuning strategy of the cost function bandwidth parameter is carried out that can handle both Gaussian and non-Gaussian noise environments. Besides, to include pixel spatial relationships in the background modeling processing, we introduce an object-based selective learning rate strategy for enhancing the background modeling accuracy. Particularly, an object motion analysis stage is presented to detect and track foreground entities based on pixel intensities and motion direction attained via optical flow computation. Testing is provided on well-known datasets for discriminating between foreground and background that include stationary and non-stationary behaviors. Achieved results show that the OSUC outperforms, in most of the considered cases, the-state-of-the-art approaches with an affordable computational cost. Therefore, the proposed approach is suitable for supporting real-world video-based surveillance systems.

Variable step-size diffusion least mean fourth algorithm for distributed estimation

The diffusion LMS (DLMS) is one of the most popular online distributed estimation algorithms, due to its simplicity and ease of implementation. However, it may suffer from large steady-state misalignment in some strong, non-Gaussian noise environments. To address this problem, this paper introduces a diffusion least mean fourth (DLMF) algorithm by using the mean-fourth error cost function in a diffusion strategy. Moreover, a variable step-size (VSS) method is developed to further reduce the steady-state misalignment of the DLMF. Simulation results show that the DLMF outperforms the DLMS with uniform or binary noise, and that the VSS-DLMF has a superior steady-state performance as compared to the DLMF.

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Power system dynamic state estimation (DSE) has always been a critical problem in studying power systems. One of the essential parts of power systems are synchronous machines. In this work, we dealt with the problem of DSE of a synchronous machine by introducing a novel state space-based least mean fourth (SSLMF) algorithm. The rationale behind the proposed algorithm is the fact that a power system may encounter non-Gaussian disturbances/state errors and the least mean fourth algorithm is proven to be better in such environments. Moreover, we have also introduced a normalized version of the proposed algorithm, namely state space normalized least mean fourth (SSNLMF) algorithm to deal with the stability issue under Gaussian disturbances. Another motivation for developing the SSLMF algorithm is its simplicity as compared to other model-based nonlinear filtering algorithms such as Kalman filter, extended Kalman filter (EKF). Moreover, we also investigate the performance of the recently introduced state space least mean square (SSLMS). Performance of the SSLMF and the SSLMS is compared with existing EKF in both Gaussian and non-Gaussian noise environments. Extensive simulation results are presented which show superiority of the proposed algorithms, and hence, it verifies our rationale behind the work.

Robust correntropy ICA based blind channel estimation for MIMO-OFDM systems

Purpose – The purpose of this paper is to propose a robust correntropy assisted blind channel estimator for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) for improved channel gains estimation and channel ordering and sign ambiguities resolution in non-Gaussian noise channel. Design/methodology/approach – The correntropy independent component analysis with L1-norm cost function is used for blind channel estimation. Then a correntropy-based method is formulated to resolve the sign and order ambiguities of the channel estimates. Findings – Simulation study on Gaussian noise scenario shows that the proposed method achieves almost the same performance as the conventional L2-norm based method. However, in non-Gaussian noise scenarios performance of the proposed method significantly outperforms the conventional and other popular estimators in terms of mean square error (MSE). To solve the ordering and sign ambiguities problems, an auto-correntropy-based method is proposed and compared with the extended cross-correlation-based method. Simulation study shows improved performance of the proposed method in terms of MSE. Originality/value – This paper presents for the first time, a correntropy-based blind channel estimator for MIMO-OFDM as well as simulated comparison results with traditional correlation-based methods in non-Gaussian noise environment.

Automatic Modulation Classification for Low SNR Digital Signal in Frequency-Selective Fading Environments

In this research, a classifier is proposed for automatic modulation classification of some common modulation schemes, i.e., BPSK, QPSK, 8-PSK and 16-QAM. Our proposed classifier considers multipath fading effects on the received signal in a non-Gaussian noise environment. Automatic modulation classification is very challenging in real-world scenarios due to fading effects and additive Gaussian mixture noise on modulation schemes. Most of the available modulation classifiers do not consider the fading effects which results in degradation of classification in a blind channel environment. In our work, the channel is supposed to be suffering from excessive additive Gaussian mixture noise and frequency selective fading resulting in low signal SNR. The estimation of the unknown channel along with noise parameters is performed using ECM algorithm and then used in maximum-likelihood classifier for the classification of modulation schemes. Simulation results are presented that show 2 dB improvement in performance than classifier which considers only Gaussian noise in the received signal.

Goodness‐of‐fit‐based non‐parametric spectrum sensing under Middleton noise for cognitive radio

A novel goodness-of-fit-based non-parametric spectrum sensing scheme in a non-Gaussian noise environment, modelled by Middleton class A distribution, is proposed. The sampling distribution of the proposed test statistic is derived and the detection performance is shown using Monte Carlo simulations. Results are presented and it is concluded that the performance is degraded if the Gaussian component in the Middleton noise is higher than the non-Gaussian component.

New Steady-State Analysis Results of Variable Step-Size LMS Algorithm With Different Noise Distributions

The step-size in well-known variable step-size least mean square (VSSLMS) is updated as μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sub> = αμ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> + γe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with , γ > 0, and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sub> is set to μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> or μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> when it falls below or above these lower and upper bounds, respectively. It provides fast convergence at early stages of adaptation while ensuring small steady-state misalignment. This paper considers the steady-state performance of the VSSLMS in non-Gaussian noise environments. The contribution of the paper to the VSSLMS is threefold; (1) when γ ≪ 1 - α, the VSSLMS has low steady-state misalignment. (2) when α ≪ 1, the VSSLMS achieves different steady-state misalignments for different noise distributions. (3) In theory, there are different optimal values α for different noise distributions, i.e., 0.17 (Gaussian distribution), 0.21 (Student distribution), 0.38 (Laplace distribution), 0 (Binary and Uniform distributions). Analytical results are compared with simulations and are shown to agree well.

ML-Based Blind Frequency Offset Estimation Schemes for OFDM Systems in Non-Gaussian Noise Environments

This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments. Keywords—Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.

Spatial Sign and Rank Cyclic Detectors

This letter proposes robust nonparametric cyclic detectors based on the spatial sign and magnitude rank concepts. The proposed detectors are single-cycle detectors exploiting the known (conjugate) cyclic autocorrelation of the signal of interest. Cyclostationarity allows distinguishing among different signals and emitters that exhibit distinct cyclostationary properties. The asymptotic distributions of the proposed cyclic detectors are established under the null hypothesis when only noise is present. Simulation results demonstrate the robust performance of the proposed detection algorithms in both Gaussian and heavy-tailed non-Gaussian noise environments.

비가우시안 노이즈가 존재하는 수중 환경에서 2차원 위치추정

본 논문은 비가우시안 노이즈가 존재하는 수중환경에서 비선형 필터 기법에 따른 2차원 위치 추정에 관한 연구 내용이다. 최근 위치 추정을 위한 필터로 확장형 칼만필터(EKF: Extended Kalman filter)가 많이 사용되고 있다. 하지만, 수중과 같은 비가우시안 노이즈가 존재하는 비선형 시스템에서는 많은 문제점을 가지고 있다. 따라서 본 논문에서는 상태변이의 예측을 기반으로한 EKF를 대신하여 통계적 발생인자 에 기반을 둔 분포 재해석 기법을 이용한 2차원 파티클필터 (TDPF: Two-Dimension Particle Filter)를 제안한다. 모의 실험을 통하여 Non-Gaussian Noise 가 존재하는 수중환경에서 제안하는 TDPF의 성능을 EKF와 비교분석하였으며 TDPF가 EKF보다 정확한 위치 추정결과를 제공하는 것을 확인하였다. This paper has considered the location estimation problem in two dimension space by using a non-linear filter under non-Gaussian noise in underwater acoustic sensor networks(UASNs). Recently, the extended Kalman filter (EKF) is widely used in location estimation. However, the EKF has a lot of problems in the non-linear system under the non-gaussian noise environment like underwater environment. In this paper, we propose the improved Two-Dimension Particle Filter (TDPF) using the re-interpretation distribution techniques based on the maximum likelihood (ML). Through the simulation, we compared and analyzed the proposed TDPF with the EKF under the non-Gaussian underwater sensor networks. Finally, we determined that the TDPF's result shows more accurate localization than EKF's result.

A Modified Nonparametric Message Passing Algorithm for Soft Iterative Channel Estimation

Based on the factor graph framework, we derived a Modified Nonparametric Message Passing Algorithm (MNMPA) for soft iterative channel estimation in a Low Density Parity-Check (LDPC) coded Bit-Interleaved Coded Modulation (BICM) system. The algorithm combines ideas from Particle Filtering (PF) with popular factor graph techniques. A Markov Chain Monte Carlo (MCMC) move step is added after typical sequential Important Sampling (SIS) -resampling to prevent particle impoverishment and to improve channel estimation precision. To reduce complexity, a new max-sum rule for updating particle based messages is reformulated and two proper update schedules are designed. Simulation results illustrate the effectiveness of MNMPA and its comparison with other sum-product algorithms in a Gaussian or non-Gaussian noise environment. We also studied the effect of the particle number, pilot symbol spacing and different schedules on BER performance.

비정규 잡음에 강인한 ML기반 OFDM 블라인드 주파수 옵셋 추정기

본 논문에서는 비정규 잡음에 강인한 직교 주파수 분할 다중화 (orthogonal frequency division multiplexing: OFDM) 블라인드 주파수 옵셋 추정기들을 제안한다. 먼저 복소 등방성 코시 과정으로 모델링 된 비정규 잡음 환경에서 최대 우도 (maximum likelihood: ML) 추정기를 제안한다. 또한, ML 기반의 보다 간단한 추정기를 제안한다. 모의실험을 통해 제안한 추정기들이 비정규 잡음에 강인하며 기존 추정기보다 우수한 주파수 옵셋 추정 성능을 가짐을 보인다. In this paper, we propose robust blind estimators for the frequency offset of orthogonal frequency division multiplexing in non-Gaussian noise environments. We first propose a maximum likelihood (ML) estimator in non-Gaussian noise modeled as a complex isotropic Cauchy process, and then, a simpler estimator based on the ML estimator is proposed. From numerical results, we confirm that the proposed estimators are robust to the non-Gaussian noise and have a better estimation performance over the conventional estimator in non-Gaussian noise environments.

비-가우시안 잡음하의 통신을 위한 바이어스된 오차 분포의 유클리드 거리

비-가우시안 잡음 환경의 적응 시스템을 위해, 평행 이동한 오차 분포와 오차 0에 위치한 델타 함수 사이의 유클리드 거리를 새로운 성능기준으로 제안하였다. 또한, 이 성능 기준에 근거하여 적응 알고리듬을 개발하였고, 얕은 바다에서 구한 수중 통신 다경로 채널에 충격성 잡음과 직류 바이어스 잡음이 더해진 환경으로 등화 성능을 시뮬레이션한 결과, 제안한 알고리듬이 기존의 MEDE 알고리듬 보다 5 dB 이상 향상된 MSE 성능을 보이며 오차 분포의 중심 위치가 정확히 0에 위치하였다. In this paper, the Euclidean distance between the probability density functions (PDFs) for biased errors and a Dirac-delta function located at zero on the error axis is proposed as a new performance criterion for adaptive systems in non-Gaussian noise environments. Also, based on the proposed performance criterion, a supervised adaptive algorithm is derived and applied to adaptive equalization in the shallow-water communication channel distorted by severe multipath fading, impulsive and DC-bias noise. The simulation results compared with the performance of the existing MEDE algorithm show that the proposed algorithm yields over 5 dB of MSE enhancement and the capability of relocating the mean of the error PDF to zero on the error axis.

비가우시안 노이즈가 존재하는 수중 환경에서 MBK 시스템의 위치 추정

본 논문은 노이즈가 비 정규 분포를 따르는 수중 환경에서 비 선형 필터 기법에 따른 Mass-Damper-Spring (MBK) 시스템 위치추정에 관한 연구 내용이다. 최근 위치 추정에 사용되는 필터는 확장 칼만 필터 (EKF: Extended Kalman Filter) 와 파티클 필터(Particle Filter)가 주목 받고 있다. EKF는 가우시안 잡음 (Gaussian Noise) 이 존재하는 비선형 시스템에서 정확도가 높은 알고리즘으로 널리 사용되고 있지만, 수중 환경과 같이 비 가우시안 잡음이 존재하는 경우 사용에 많은 제약이 따른다. 이에 본 논문에서는 상태예측을 기반으로 둔 EKF와 비교하여, 통계적 발생 가능성 인자 (Maximum Likelihood) 에 기반한 분포 재해석 기법을 이용한 개선된 ODPF (One-Dimension Particle Filter)를 제안한다. 모의 실험을 통하여 non-Gaussian noise가 존재하는 수중 환경에서 EKF와 제안한 Particle filter를 사용한 위치 추정 결과를 비교 분석하였으며, 계산 용량 및 통계 샘플이 충분한 경우 ODPF가 EKF 대비 정확한 위치 추정 결과를 제공하는 것을 확인하였다.

편이 확률밀도함수 사이의 거리측정 기준과 비 가우시안 잡음 환경을 위한 등화 알고리듬

이 논문에서는 편이된 확률밀도함수 간 거리 측정이라는 새로운 거리 측정 기준을 제안하고 이에 관련된 등화 알고리듬을 도출하여 충격성 잡음과 시변 직류 잡음이 있는 다경로 채널에 적용하였다. 이러한 비 가우시안 잡음 환경에서 시행한 시뮬레이션의 결과로부터, 제안한 알고리듬이 충격성 잡음에 강인성을 보일 뿐 아니라 시변 직류 잡음도 제거하는 탁월한 능력을 가짐을 입증하였다. In this paper, a new distance measure for biased PDFs is proposed and a related equalizer algorithm is also derived for supervised adaptive equalization for multipath channels with impulsive and time-varying DC bias noise. From the simulation results in the non-Gaussian noise environments, the proposed algorithm has proven not only robust to impulsive noise but also to have the capability of cancelling time-varying DC bias noise effectively.

비정규 잡음 환경에서 협력 무선인지 네트워크를 위한 순서 기반 스펙트럼 센싱 기법

본 논문에서는 비정규 충격성 잡음 환경에서 협력 무선인지 네트워크를 위한 순서 기반 스펙트럼 센싱 기법을 제안한다. 구체적으로는 잡음을 이변수 등방형 대칭 알파 안정 (bivariate isotropic symmetric <TEX>${\alpha}$</TEX>-stable) 분포를 따르는 것으로 모형화하고, 그에 알맞은 관측 샘플의 순서와 일반화된 우도비 검정 기반 협력 스펙트럼 센싱 기법을 제안한다. 모의실험을 통해 비정규 잡음 환경에서 제안한 기법이 기존의 기법에 비해 더 좋은 스펙트럼 센싱성능을 가짐을 보인다. In this paper, we propose a novel spectrum sensing scheme based on the order statistic for cooperative cognitive radio network in non-Gaussian noise environments. Specifically, we model the ambient noise as the bivariate isotropic symmetric <TEX>${\alpha}$</TEX>-stable random variable, and then, propose a cooperative spectrum sensing scheme based on the order of observations and the generalized likelihood ratio test. From numerical results, it is confirmed that the proposed scheme offers a substantial performance improvement over the conventional scheme in non-Gaussian noise environments.

Some Analysis of the LPI Concept for Active Sonar

A low probability of intercept (LPI) waveform is designed to appear to the target it probes as noise, and consequently the robust target receiver can detect only a rise in random energy. It can be recalled by the transmitter (platform), and matched to what is received; however, the platform pays a heavy two-way attenuation penalty: its signal-to-noise ratio (SNR) is far lower than that at the target. How these two factors trade off against one another is the topic of this paper. It will be shown that the sonar's time-bandwidth product is generally unfavorable to LPI. For most cases of interest in a Gaussian noise environment, LPI sonar does not favor covert observation for sonar signals shorter than 1 min at ranges greater than 100 yards. However, LPI sonar may have a key role in non-Gaussian heavy-tailed noise environments. Specifically, LPI may play a role in environments where the ambient noise has a kurtosis of around 10.

비정규 잡음에 강인한 OFDM 주파수 옵셋 추정 기법

In this paper, we propose robust estimators for the frequency offset of orthogonal frequency division multiplexing in non-Gaussian noise environments. We first propose a maximum-likelihood (ML) estimator in non-Gaussian noise modeled as a complex isotropic Cauchy process, and then, we present a simpler suboptimal estimator based on the ML estimator. From numerical results, it is demonstrated that the proposed estimators not only outperform the conventional estimators, but also have a robustness in non-Gaussian noise environments.