AN ENHANCED CHANNEL ESTIMATION ALGORITHM FOR OFDM: COMBINED EM ALGORITHM AND POLYNOMIAL FITTING Xiaoqiang M a, Hisashi Kobayashi, and Stuart C . Schwartz Electrical Engineering Department, Princeton University Princeton, New Jersey 08544-5263 Email: xma, hisashi, [email protected]ABSTRACT Estimating a channel that is subject to frequency selec- tive Rayleigh fading is a challenging problem in an orthog- onal frequency division multiplexing (OFDM) system. In this paper we propose an enhanced channel estimation al- gorithm that combines the EM-based algorithms proposed previously and a Least Squares polynomial fitting (LSPF) approa ch. Th e combined algorithm can efficiently estimate the channel response of an OFDM system operating in an environment with multipath fading and additive white Gaus- sian noise (AWGN). The algorithm can improv e the channel estimate obtained from the EM-based algorithms by poly- nomial fitting. Simulation results show that t he hit error rate (BER) as well as the mean square error (MSE) of the channel can be improved by the algorithm. In particular, with these additional computation s and demodulation delay, the MSE can be made smaller than the Cramer-Rao lower bound (CRLB). 1. INTRODUCTION An efficient and accurate channel estimation procedure is necessary for coherent demodulation in OFD M systems. M any channel estimation algorithm s have been reported in the lit- erature [2]-[4]. Recently we proposed three different EM- based channel estimation algorithms (refer to [5]-[7]) that can achieve the CRLB in the high SNR region. In these al- gorithms the channel is estimat ed fra me by fram e by assum- ing the channel is changing from one frame to another. If we further assume the channel variation is smooth, then we might do a better job by considering several OFDM frames together. Obviously, if the channel does not change dur- ing several OFDM frames, we can certainly apply the EM- based algorithm [5]-[7] rjust average the channel estimates of those OFDM frames to obtain a better estimate. However, in a mobile environment with fast moving objects this as- sumption fails. Fortunately, the channel changes smoothly alone the time axis in a real mobile environment. This methods or time-domain smoothing), e.g., least squares poly- nomial fitting, in order to further improve the channel esti- mation accuracy. This basic idea is discussed in [SI and [9]. Similar time-frequency polynomial models are adopted in these two referenced papers. Both of them concentrate on the channel frequency response which contains many more components than the corresponding CIR in a typical OFDM system. Thus in their methods, the complexity to establish model coefficients is high. Furtherm ore, they need a large amount of pilot symbols in the time-frequency grid of the OFDM systems to minimize the model mismatch. This de- grades the overall system capacity or spectral efficiency. The main objective of this paper is to investigate the use of the polynom ial fi tti ng method in the time dom ain for chann el estimation of an OFDM system subject to slow time varying frequency selective fading. An EM-based channel estimation algorithm is carried out first to obtain near opti- mal chann el estimates using the information of the current OFDM frame only. Then, polynomial fitting is adopted by gathering channel estimates of several consecutive OFDM frames. By applying this concatenated channel estimation (EM-based algorithms followed by polynomial fitting), bet- ter channel estimates can be obtained. 2. EM-BASED CHANNEL ESTIMATION ALGORITHM The most important step in an EM-algorithm is determining what is known as “complete” data. Different selections of “complete” data result in different algorithms. T hree differ- ent EM-based channel estimation and signal detection al- gorithms have been proposed in [5]-[7] by carefully defin- ing different “complete” data for each algorithm. Their ad- vantages and disadvanta ges are discussed therein. Basi- cally, they have almost the same performance as measured by BE R and MSE. The only difference is the rate of conver- gence and computational burden. The second EM-based al- gorithm [6] has the fastest convergence speed as seen from - the simulations. Thus, we suggest using this algorithm as the first stage channel esti mation method. Furthermore, one moothness motivates us to use well designed curve fitting 0-7803-7663-3/03/$17.00 02003 IEEE IV - 68 ICASSP 2003
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8/12/2019 An Enhanced Channel Estimation Algorithm for OFDM - Combined EM Algorithm and Polynomial Fitting
AN ENHAN CED CHANN EL ESTIMATION ALGORITHM FOR OFDM: COMBINED EMALGORITHM AND POLYNOMIAL FITTING
Xiaoqiang M a, Hisashi Kobayashi, and Stuart C. Schwartz
Electrical Engineering Department, Princeton University
Princeton, New Jersey 08544-5263Email: xm a, hisashi, [email protected]
A B S T R A C T
Estimating a channel that is subject to frequency selec-
tive Rayleigh fading is a challeng ing problem in an orthog-
onal frequency division multiplexing (OFDM ) system. In
this paper we propose an enhanced channel estimation al-
gorithm that combines the EM-based algorithms proposed
previously and a Least Squares polynomial fitting (LSPF)
approa ch. Th e combined algorith m can efficiently estimate
the channel response of an OFDM system operating in anenviron ment with m ultipath fadin g and additive white Gaus-
sian noise (AWGN). The algor ithm can improv e the channel
estimate obtained from the EM-based algorithms by poly-
nomial fitting. Simula tion results show that the hit error
rate (BER) as well as the mean square error (MSE) of the
channel can be improved by the algorithm. In particular,
with these additional computation s and demodulation delay,
the MSE can be made smaller than the Cramer-Rao lower
bound (CRLB).
1. INTRODUCTION
An efficient and accurate channel estimation procedure is
necessary for coherent demod ulation in OFD M systems. M any
channel estimation algorithm s have been reported in the lit-
erature [2]-[4]. Recently w e proposed three different EM-
based channel estimation algorithms (refer to [5]-[7]) that
can achieve the CRL B in the high SNR region. In these al-
gorithms the channel is estimated fra me by fram e by assum-
ing the channel is changing from o ne frame to another. If
we further assum e the channel variation is smo oth, then we
might do a better job by considering several OFDM frames
together. Obviously, if the channel does not change dur-
ing several OFD M frames, w e can certainly apply the EM -
based algorithm [5]-[7] rju st average the channel estimates
of those OFDM frames to obtain a better estimate. However,
in a mobile environment with fast moving objects this as-
sumption fails. Fortunately, the channel chan ges smoothly
alone the time axis in a real mobile environment. This
methods or time-domain smoothing), e.g., least squares poly-
nomial fitting, in order to further improve the channel esti-
mation accuracy. Th is basic idea is discussed in [SI and [9].
Similar time-frequency polynomial mode ls are adopted in
these two referenced papers. Both of them concentrate on
the channel frequency response which contains many morecomp onents than the corresponding CIR in a typical OFDM
system. Thus in their methods, the complexity to establish
model coefficients is high. Furtherm ore, they need a large
amount of pilot symbols in the time-frequency grid of the
OFDM systems to minimize the model mismatch. This de-
grades the overall system capacity o r spectral efficiency.
The main objective of this paper is to investigate the
use of the polynom ial fitting method in the time dom ain for
chann el estimation of an OF DM system subject to slow time
varying frequency selective fading. An EM-based channel
estimation algorithm is carried out first to obtain near opti-
mal chann el estimates using th e information of the current
OFDM frame only. Then, polynomial fitting is adopted by
gathering channel estimates of several consecutive OFDMframes. By applying this concatenated channel estimation(EM-based algorithms followed by polynomial fitting), bet-
ter channel estimates can be obtaine d.
2. E M - B AS E D C H A N N E L E S T I M A T I O N
A L G O R I T H M
The most important step in an EM-algori thm is determining
what is known as “complete” data. Different selections of
“com plete” data result in different algorithms. T hree d iffer-
ent EM-based channel estimation and signal detection al-
gorithm s have been proposed in [5]-[7] by ca refully defin-
ing different “complete” data for each algorithm. Their ad-
vantages and disadvanta ges are discussed therein. Basi-
cally, they have almost the sam e performance as measured
by BE R and MSE . The only difference is the rate of conver-
gence and computational burden. The second EM-based al-
gorithm [6] has the fastest convergence speed as seen from
- the simulations. Thus, w e suggest using this algorithm as
the first stage channel estimation method. Furthe rmore, onemooth ness motivates us to use well designed curve fitting
0-7803-7663-3/03/$17.00 02 00 3 IEEE IV - 68 ICASSP 2003
Fig. 3. MSE of channel estimates for OFDM systems EM-
based algorithm concatenated with LSPF.
Y 1 0 m Y I . O Y m 7 0 m w n I m
r ,ms
0 s , I , ,
Fig. 4. The realization of the am plitude of hl when SNR
equals to IOdB.
a) PDFs of the estimate of
W h i ) Q h i )
(b) PDFs of the estimate of
Fig. 5 . Simulated and analytical PDFs of the estimate of
R(hl) and D ( h l ) when S NR equals to 1OdB.
dures. Another merit of EM-base algorithms is the good
MSE performance that is close to the CRLB. Otherwise, a
MSE lower than the CRLB could not be achieved. That
is why the c oncatenated channel estimation algorithm with
the variou s EM-based algorithms in the first stage will yield
similar final performance after applying the LSPF.
6. CONCLUSION
In this paper we proposed a concatenated channel estima-
tion algorithm for OFDM systems in order to enhance sys-
tem performance. In particular, EM-based channel estima-
tion algorithms followed by LSPF is proposed and tested.
Simulation results show a significant MSE improvement,
compared to the EM -based algori thm alone. The proposed
concatenated channe l estimation method can he used in other
applications such as single carrier systems with frequency
domain c hannel estimation. In order to make the concate-
nated channel estimation work, G aussian-like estimation er-
rors should be generated from the first stage.
Note: Additional details in a longer paper and large r fig-
ures can be found at http://www.ee.princeton.edurxmdfit.pdf.
7. REFERENCES
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[5] X. Ma, H. Kobayashi and S . Schwartz, "EM-Based C hannelEstimation for OFDM," in Proc. of PACRIM 2001, vol. 2,pp. 449-452.
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