1. Chaudhari Sachin V, Prof.A M Deshmukh / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.1413-1415
Channel Estimation in OFDM
Chaudhari Sachin V, Prof.A M Deshmukh
Sinhghad College of Engineering, Pune
Sinhghad College of Engineering, Pune
ABSTRACT
Orthogonal frequency division single carrier modulation at a lower symbol rate.
multiplexing (OFDM) is a special case of multi- The symbol rate of each channel can be dropped to a
carrier transmission and it can support high data point that makes each symbol longer than the
rate requirement of multimedia based wireless channel’s impulse response, this eliminates ISI. The
systems. Since channel estimation is an integral two main drawbacks of OFDM are the large
part of OFDM systems, it is complicated to dynamic range of the signals being transmitted and
understand the basis of channel estimation the sensitivity to frequency errors.
techniques for OFDM systems so that the most
proper method can be applied. The estimation of Using Mat lab simulation we can
channel at pilot frequencies is based on LS and implement an OFDM transmission. Using the
MMSE estimation techniques by using BPSK simulation we can easily change the values of S/N
modulation scheme, and multi-path Rayleigh ratio and change the multi propagation effects on the
fading channels as channel models. The purpose transmission. Then we can analyze the results of
of this paper is to use a Mat lab simulation of each transmission and see how the BER is changed.
OFDM to see how the Bit Error Ratio (BER) of a The modulation scheme used is BPSK were we see
transmission varies when Signal to Noise Ratio the performance of LS & MMSE channel estimation
(S/N Ratio) and Multi propagation effects are techniques
changed on transmission channel.
1. OFDM SIMULATION
Index Terms— BER, ISI, OFDM, S/N Code used in this paper is for checking the
performance of LS & MMSE channel estimation
INTRODUCTION techniques by using BPSK Modulation scheme. A
Orthogonal Frequency Division scheme of every part of the implementation can be
Multiplexing (OFDM) has Presently been applied seen in Fig 1. In the end of the transmission, when
widely in wireless communication due to its high the receiver receives the data, a comparison of the
bandwidth efficiency and high data rate transmitted and the received data is done in order to
transmission capability and its robustness to multi- calculate the Bit Error Ratio (BER).This paper does
path delay. It has been used in wireless LAN not explain in detail the simulation Code but it
standards such as American IEEE802.11a and in focuses on the results which we get after simulation
multimedia wireless services such as Japanese
Multimedia Mobile Access Communications. A
proper estimation of channel is necessary before the
demodulation of OFDM signals since the radio
channel is frequency selective and time-varying for
wideband mobile communication systems [1].
In an OFDM scheme a large number of
sub channels or sub-carriers are used to transmit
digital data. Each sub-channel is orthogonal to every
other. They are closely spaced and narrow band.
The separation of the sub-channels is as minimal as
possible to obtain high spectral efficiency. OFDM is
being used because of its capability to handle with
multipath interference at the receiver the main
effects of multi propagation [2] is Frequency Fig.1: Mat lab Flow Chart
selective fading and Inter Symbolic Interference
(ISI). In OFDM the large number of narrow band 2. CHANNEL ESTIMATION
sub-carriers provides sufficiently “flat” channels. The two basic channel estimations in
Therefore the fading can be handled by simple OFDM systems are illustrated in Figure 2. The first
equalizing techniques for each channel. Furthermore one, block-type pilot channel estimation, is
the large amount of carriers can provide same data developed under the assumption of slow fading
rates of a channel, and it is performed by inserting pilot tones
1413 | P a g e

2. Chaudhari Sachin V, Prof.A M Deshmukh / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.1413-1415
R̲
into all subcarriers of OFDM symbols within a ̅ ̅H
YY=E{YY }= ̲ ̲ ̲ ̲ ̲ ̲
XFRgg FH XH+ σ2NIN (4)
specific period. The second one, comb-type pilot
̲
channel estimation, is introduced to satisfy the need Assume Rgg thus (RHH ) and σ2N are known
̲
for equalizing when the channel changes even from as receiver in advance, MMSE estimator of g is ̅
̲ ̲
one OFDM block to the subsequent one. It is thus given ĝMMSE= RgY RYY -1 YHH note that g is not
̅ ̅
performed by inserting pilot tones into certain Gaussian , ĝMMSE it is not necessarily a minimum
subcarriers of each OFDM symbol, mean-square error estimator, but it is still the best
where the interpolation is needed to estimate the linear estimator in the mean-square error sense. At
conditions of data subcarriers [1]. last, it is calculated that
̲ ̲ ̲ ̲ ̲
ĤMMSE= F ĝMMSE F[(FH XH )-1 Rgg-1 σ2N+ XF]-1Y̅
̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
=F Rgg[(FH XHXF)-1 σ2N+ Rgg] F-1 ĤLS (5)
̲ ̲ ̲ ̲
=RHH[RHH+ σ2N(X XH)-1 ĤLS
3. PLOTS OF BER AS A FUNCTION OF S/N
RATIO
PLOT OF SNR V/S0BER FOR AN OFDM SYSTEM WITHOUT & WITH MMSE/LS ESTIMATOR BASED RECEIVERS
10
Bit Error Rate
-1
10
Fig.2: Pilot arrangement.
In block-type pilot-based channel mmse
estimation, as shown in Figure 2, OFDM channel ls
actual
estimation symbols are transmitted periodically, and -2
10
5 10 15 20 25 30
all subcarriers are used as pilots. Since LS estimate SNR in DB
is susceptible to noise and ICI, MMSE is proposed
while compromising complexity. Since MMSE
includes the matrix inversion at each iteration [3]. Fig.3: SNR V/S BER for an OFDM system without
& with MMSE/LS estimation based receiver using
2.1 LS Estimator BPSK modulation scheme
The LS estimator minimizes the parameter
̅ ̲ ̅ ̅ ̲ ̅
( Y-XH)H ( Y-XH) where (•)H means the conjugate Conclusion
transpose operation. It is shown that the LS The estimators given in this paper can be
̅
estimator of H is given by [1]. used to efficiently estimate the channel in the
̲
ĤLS= X-1Y=[(XK/ YK)]T (1) OFDM system giving us certain knowledge about
the channel statistics. Moreover its complexity of
2.2 MMSE Estimator MMSE is large as compared to LS estimator. The
The MMSE estimator employs the second- above results of simulation are done by using 64
order statistics of the channel conditions to subcarriers in OFDM system. We can also see the
minimize the mean-square error .Denoted by R gg,, ̲ effect of implementing the estimators such as the
R̲ R̲ LS & MMSE in the OFDM system. The above
̅
HH , YY the auto covariance matrix of g , H and Y
̅ ̅
,respectively and R gy the cross covariance matrix
̲ results show us the SNR VS BER plot for with and
̅
between g and Y .[1]Also denoted by σ2N the noise
̅ without MMSE/LS based receiver using BPSK
̅
variance E{(| N|2}.Assume the channel vector g and̅ modulation scheme
̅
the noise N are uncorrelated it is derived that
R ̲
̅ ̅H ̲ ̅ ̲ ̅ H ̲ ̲ ̲H
HH= E{HH } = E{(Fg) ( Fg) }= F Rgg F (2) Acknowledgement
This work is done under the valuable
̲ ̅ ̅ ̅ ̲ ̲ ̅ ̅ ̲ ̲ ̲
RgY = E{g YH}=E{ g(XF g+ N)H}= Rgg FH XH (3) guidance of Prof A.M Deshmukh.
1414 | P a g e

3. Chaudhari Sachin V, Prof.A M Deshmukh / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.1413-1415
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[3] Jan-Jaap van de Beek, Ove Edfors, Magnus
Sandell, Sarah Kate Wilson and Per Ola
B.rjesson," On Channel Estimation In
OFDM Systems," In Proceedings of
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Ô95), vol. 2, pp. 815-819, Chicago, USA,
September 1995.
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