IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2019 1
Kalman Filter based Recursive Estimation of
Channel and Impulsive Noise for OFDM Systems
Xinrong Lv, Youming Li, Yongqing Wu, and Hui Liang
Abstract—In this paper, we propose a compressed sensing
based joint channel estimation and impulsive noise mitigation
method for OFDM systems. Firstly the channel impulse response
and impulsive noise are jointly viewed as an unknown sparse
vector, which are estimated from sparse Bayesian learning (SBL)
theory by utilizing pilot subcarriers. Then a novel recursive
Kalman filtering based SBL algorithm for joint channel and
impulsive noise estimation is proposed by using the first order
autoregressive model for tracking slowly time varying wireless
channel. This algorithm can be extended also to quasi-static,
block-fading scenario conveniently. Simulation results illustrate
the efficiency of the proposed techniques in terms of the mean
square error and bit error rate performance.
Index Terms—OFDM, sparse Bayesian learning(SBL), Kalman
filtering and smoothing, channel estimation, impulsive noise.
I. INTRODUCTION
Orthogonal frequency division multiplexing(OFDM) is al-
ready adopted as modulation technique for many emerging
communication standards, since it can effectively mitigate the
multipath distortion of the wireless channel [1]. OFDM-based
communication systems provide optimal performance in Ad-
ditive Gaussian White Noise(AGWN) environment. However,
in some scenarios, such as vehicular networks [2], smart grid
[3], and shallow sea underwater networks [4], the presence
of impulsive noise (IN) makes the performance of OFDM
systems deteriorate sharply.
Many methods have been developed to remove the im-
pulsive noise at the receiver. The memoryless nonlinearity
preprocessor, for example clipping, blanking and their combi-
nation etc., is the widely used IN mitigation scheme [5] [11].
This class of methods eliminate the IN in the received time
domain OFDM signal by setting a threshold, which exploits
the feature that the amplitude of IN is significantly higher
than that of the background noise. However, it is very hard to
This work was supported in part by the National Natural Science Foundation
of China under Grant No. 61571250 and No.61531018, Key Laboratory
of Mobile Internet Application Technology of Zhejiang Province, Ningbo
Natural Science Foundation under Grant 2015 A610121, Foundation of
Ningbo Jiangbei District Science and Technology Bureau under Grant 011-
201801B20013, K. C. Wong Magna Fund of Ningbo University, and the
Science Foundation of Zhejiang Business Technology Institute under Grant
No. 2017Z01.
Xin-Rong Lv is with the Faculty of Information Science and Engineering,
Ningbo University, China, and also with the College of Intelligent Electronics
Engineering, Zhejiang Business Technology Institute , Ningbo ,China, 315211
(e-mail: lxrnet@zbti.edu.cn).
Youming Li is with the Faculty of Information Science and Engineering,
Ningbo University, China, 315211 (liyouming@nbu.edu.cn).
Yongqing Wu is with the Institute of Acoustics, Chinese Academy of
Science, Beijing, China (e-mail: wyq@mail.ioa.ac.cn).
Hui Liang is with the Ningbo Sanxing Electric Co. Ltd., China, 315211
(e-mail: lianghui@mail.sanxing.com)
obtain the optimal threshold which relies on the priori statistics
of impulsive noise and background noise. So in practice the
threshold is usually set as empirical value, which may destroy
the orthogonality among OFDM subcarriers [6]. Another class
of mitigation methods is to estimate the time-domain impulsive
noise and remove it based on compressed sensing (CS) theory
as the impulsive noise shows the sparsity in the time domain.
However, the performance of these methods is dependent on
the number of available null tones which is usually limited
by the bandwidth [7]. Furthermore these impulsive noise mit-
igation methods are usually based on the assumption that the
channel impulse response is known to the receiver. However in
practice it is not easy to acquire the channel state information,
especially in the presence of impulsive noise.
Recently joint channel and impulsive noise estimation meth-
ods have attract attention. The proposed method in [8] applies
the CS to estimate jointly the channel and IN by superimposing
the channel impulse response onto the impulsive noise, which
assumes that the nonzero components in the channel impulse
response are not contaminated by the impulsive noise. The
authors of [9] adopt the generalized approximate message
passing (GAMP) to jointly estimate the channel and IN,
but this method requires a priori statistics about the channel
and impulsive noise. A least-squares (LS) based algorithm is
proposed to jointly estimate the channel and impulsive noise
for underwater acoustic OFDM systems [10], which requires
the accurate positions of IN in received OFDM signal.
In this work, we propose a recursive compressed sensing
(CS) algorithm incorporating Kalman Filter and Smoother (K-
FS) to tackle the problem of channel estimation in the presence
of impulsive noise for OFDM systems. Firstly, we formulate
a CS framework to estimate simultaneously the channel and
impulsive noise by exploiting the joint sparsity of both them.
Then we use all OFDM symbols in a frame to promote
the estimation performance by incorporating KFS in the CS
framework. The main contribution of our work is that: (i) we
use the first autoregressive (AR) model to track the random
behaviour of the channel and impulsive noise in an OFDM
frame; and (ii) we develop an Expectation Maximization (EM)
based algorithm to estimate the parameters of joint probability
density function (pdf) of the channel and impulsive noise in an
OFDM frame. To the best of our knowledge, there is no related
research on the joint channel and IN estimation based on the
AR model by using CS theory. Simulation results show that
our proposed algorithm can lead to a significant improvement
in the mean square error (MSE) of channel estimation and bit
error rate (BER) performance.
The rest of the paper is organized as follows. The OFDM