A COMPARATIVE PERFORMANCE STUDY OF OFDM SYSTEM WITH THE IMPLEMENTATION OF COMB PILOT-BASED MMSE CHANNEL ESTIMATION

International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.6, December 2013

A COMPARATIVE PERFORMANCE STUDY OF OFDM
SYSTEM WITH THE IMPLEMENTATION OF COMB
PILOT-BASED MMSE CHANNEL ESTIMATION
A. Z. M. Touhidul Islam
Department of Information and Communication Engineering
University of Rajshahi, Rajshai-6205, Bangladesh

ABSTRACT
This paper presents a comparative performance analysis of wireless orthogonal frequency division
multiplexing (OFDM) system with the implementation of comb type pilot-based channel estimation
algorithm over frequency selective multi-path fading channels. The Minimum Mean Square Error (MMSE)
method is used for the estimation of channel at pilot frequencies. For the estimation of channel at data
frequencies different interpolation techniques such as low-pass, linear, and second order interpolation are
employed. The OFDM system simulation has been carried out with Matlab and the performance is
analyzed in terms of bit error rate (BER) for various signal mapping (BPSK, QPSK, 4QAM, 16QAM, and
64QAM) and channel (Rayleigh and Rician) conditions. The impact of selecting number of channel taps on
the BER performance is also investigated.

KEYWORDS
OFDM, Multipath fading channels, Comb Pilot, MMSE estimation, Interpolation, Signal mapping.

1. INTRODUCTION
Orthogonal frequency division multiplexing (OFDM) is a parallel transmission technique and is
widely used in wireless communication systems because of its high rate transmission capability
and robustness against multipath fading, high spectral efficiency and so on [1]. However, as the
radio channel is frequency selective and time-variant, the channel transfer function in OFDM
systems looks unequal in both the time and frequency domains. Thus a dynamic estimation of the
channel is necessary before demodulating the OFDM signals for the coherent detection of the
information symbols.
Two basic training-based one dimensional (1D) channel estimation techniques can be adopted in
OFDM system are block type and comb type pilot-based channel estimation. In block type pilot
arrangement, the pilot signal is allocated to particular OFDM block and sent periodically in time
domain. Instead, in comb type pilot arrangement, the pilot signals are uniformly distributed
within each OFDM block. The comb pilot-based channel estimation consists of algorithms to
estimate the channel at pilot frequencies and to interpolate the channel at data frequencies. The
estimation of channel at pilot frequencies can be based on least square (LS), minimum mean
square error (MMSE) or least mean square (LMS) method, while different interpolation
techniques can be incorporated for the channel estimation at data frequencies [2, 3].
The aim of this paper is to evaluate the bit error rate (BER) performance of OFDM
communication system with the implementation of comb type pilot-based MMSE channel
DOI:10.5121/ijcsa.2013.3605

45


estimation algorithms and to compare the system performance for signal mapping with different
digital modulation schemes over Rayleigh and Rician multi-path fading channels. In addition, the
impact of selecting number of channel taps and different interpolation techniques such as lowpass, linear, and second order interpolation on the system performance are also examined. The
organization of the paper is as follows. Relevant studies of pilot-based channel estimation in
OFDM systems are discussed in Section 2. Section 3 describes a model of OFDM system used for
the implementation. Comb type pilot-based channel estimation algorithm is briefly explained in
Section 4. In section 5, simulation results are displayed in graphical form, analyzed and
compared. Conclusions of the present work are given in Section 6.

2. RELATED WORKS
In earlier studies the performance of different pilot-based channel estimation techniques both in
the time and frequency domains for wireless OFDM communication systems were investigated
[4-6]. The authors in [7] reviewed block type and comb type pilot-based channel estimation and
revealed that comb-type pilot based channel estimation with low-pass interpolation performs the
best among all channel estimation algorithms. Cai and Giannakis [8] studied the OFDM system
performance with M-PSK digital modulation over Raleigh frequency fading channel and
optimized the number of pilot symbols, the placement of pilot symbols and the power allocation
between pilot and information symbols.
In [9-11], OFDM channel estimation with MMSE estimator was investigated. The authors in [10]
shown that among the MMSE and ZF equalizers, the BER performance of MIMO OFDM system
is better for MMSE equalizer. Pramano and Triyono [12] found that the performance of MIMO
system is better than SISO system and the MMSE estimator produced better performance than
low complexity LS estimator. In another study [13], it was concluded that block type pilot-based
channel estimation is better for slow fading channel while comb type pilot-based channel
estimation shows better performance in fast fading environment.

3. OFDM SYSTEM DESCRIPTION
Figure 1 shows a typical block diagram of OFDM communication system with comb type pilotbased MMSE channel estimation. The binary data (information) from the input are first grouped
and mapped into multi-amplitude and multi-phase signals according to the type of modulation
(BPSK, QPSK, 4QAM, 16QAM, and 64QAM) used at the signal mapper. After serial to parallel
conversion of the modulated data, comb type pilots are inserted uniformly between the
information data sequence. The IFFT block is used for transforming and multiplexing the
complex data sequence into time domain signal. Following the IFFT block, a cyclic prefix is
added to avoid possible inter-symbol interference (ISI) in OFDM systems. After the parallel to
serial conversion, the signal is transmitted through a frequency selective multi-path Rayleigh or
Rician fading channel.
At the receiver, after serial to parallel conversion of the received signal, the cyclic prefix is
removed first and then fed to an FFT block for de-multiplexing the multi-carrier signals.
Following the FFT block, the pilot signals are extracted from the demultiplexed samples. The
channel estimation at pilot subcarriers is performed by MMSE while the estimation of channel at
data subcarriers is achieved by different interpolation techniques. After signal demodulation at the
signal demapper, the information binary data is reconstructed at the receiver output.

4. COMB PILOT-BASED CHANNEL ESTIMATION
Comb type pilot-based channel estimation is suitable for fast-fading channel where the channel
condition changes between adjacent OFDM symbols. The comb type pilot arrangement is shown
in Fig. 2 in which the pilot signals are uniformly distributed within each OFDM block. In comb
46


type channel estimation, after extracting the pilot signals from the received signal, the channel
transfer function is estimated from the received pilot signals and the known pilot signals. The
channel responses of data subcarriers can be estimated with the interpolation of the neighboring
pilot channel responses.

Fig. 1 OFDM system block diagram with Comb pilot-based
MMSE channel estimation.

Pilot

Frequency (Sub Carriers)

Data

Time (OFDM Symbols)
Fig. 2 Comb type pilot arrangement.

Comb type pilot-based channel estimation can be based on least square (LS), minimum mean
square error (MMSE) or least mean square (LMS) method. Here only MMSE channel estimator is
employed for the estimation of channel at pilot subcarriers because of its superior performance as
compared to LS estimator. Pilot signal estimation and channel interpolation algorithms are
discussed in the following subsections.
47


4.1 Channel estimation at Comb pilot subcarriers by MMSE
Suppose Npi comb pilot signals X pi n, where n  0,1,, N pi  1 , are uniformly added into
X(m) data signals. If the OFDM signal modulated on the m-th subcarrier, X(m) can be expressed
as
X m  X nLs  i 
(1)

 X n , i  0
  pi
Information data , i  1, 2,, Ls  1

Here the total N subcarriers are divided into Npi groups, each with

Ls  N / N pi adjacent

subcarriers. The least squares (LS) estimate of pilot signal is given by [3, 4]

ˆ
H pi, LS  X pi1Ypi

where

(2)





H pi  H pi 0 H pi 1H pi N pi  1

T

(3)

is the channel frequency response at pilot subcarriers,





Ypi  Ypi 0Ypi 1Ypi N pi  1

T

(4)

is the vector of the received pilot signals. It can also be expressed as

Ypi  X pi. H pi  I pi  Wpi

(5)

 X pi 0

0



where X pi  
,
 0
X pi N pi  1


Ipi is the ICI vector and Wpi is the Gaussian noise vector at pilot subcarriers.
The

ˆ
H pi, LS can also be expressed as H pi, LS  H pi, LS 0 H pi, LS 1H pi, LS N pi  1T .

The estimate of pilot signals based on minimum mean square error (MMSE) is given by [4],

ˆ
ˆ
H pi, MMSE  RH pi H pi, LS RH1pi H pi, LS H pi, LS



(6)



2
H
 RH pi H pi RH pi H pi   n X pi X pi



ˆ
H

1 1

pi, LS

,

2
ˆ
where H pi, LS is the LS estimate of H pi ,  n is the noise variance of Wpi , and the

covariance matrices are defined by,






.



H
H
RH pi H pi  E H pi H pi , RH pi H pi, LS  E H pi H pi, LS , and



H
RH pi, LS H pi, LS  E H pi, LS H pi, LS

48


4.2 Channel estimation at data subcarriers by Interpolation
A highly efficient interpolation technique is necessary for the estimation of channel at data
subcarriers using the channel information at pilot subcarriers. Three interpolation techniques:
low-pass, linear and second order interpolations are employed for the present study. In low-pass
interpolation, at first zeros are added to the original sequence. Then a low-pass finite impulse
response (FIR) filter is applied to pass the original data sequence without any change and to
interpolate between such that it can minimize the mean square error (MSE) between the
interpolated points and their ideal values.
In linear interpolation, two successive pilot subcarriers that are located in between the pilots are
used to determine the channel response for data subcarriers. It is implemented with the usage of
digital filtering technique. The estimated channel response for data subcarriers m,

nLs  m  n  1 Ls is given as [4],
ˆ
ˆ
H m  H nLs  i 

(7)

The second order interpolation is implemented by a linear time-invariant FIR filter. The estimated
channel response is expressed by [4],

ˆ
ˆ
H m  H nLs  i 
ˆ
ˆ
ˆ
 D1H pi n  1  D0 H pi n  D1H pi n  1
where

D1 

   1
2

, D0    1  1, D1 

(8)

   1
2

,  i N .

5. SIMULATION RESULTS AND DISCUSSION
The simulation of OFDM system in Fig. 1 has been performed using Matlab 7.5 programming
language. The parameters used for the simulation are listed in Table 1. The graphical
representation of simulation results are shown in Figures 3 to 7. The Doppler frequency and
number of channel taps are considered as 80 Hz and 20, respectively.
Table 1. Simulation Parameters

Parameter
Number of Sub-carrier
Pilot Ratio
Pilot-to-Data Power Ratio
IFFT, FFT Size
Guard Type
Cyclic Prefix (C.P.) Length
Constellation
Channel Model
Number of Channel Taps
Doppler Frequency

Specification
256
1/8
2
256
Cyclic Extension
32
BPSK, QPSK, 4QAM, 16QAM, 64QAM
Rayleigh, Racian
20
80 Hz

The BER performance of the simulated wireless OFDM system over Rayleigh multipath fading
channel without and with the employment of comb type pilot-based channel estimation (LS and
MMSE) is shown in Fig. 3. The input binary data were BPSK modulated and the channel
49


estimation at data subcarriers was obtained by low-pass interpolation. It is seen that without using
any channel estimation algorithm, the bit error rate at the receiver is very high. However, with the
employment of MMSE channel estimation, the OFDM system performance has greatly improved
which results from the decrease of the amplitude and phase distortion of the transmitted signal
because of multipath fading. In Fig. 3, comb pilot-based, low complexity, LS channel estimation
is also incorporated for the comparison. It is clear that the MMSE channel estimator gives better
BER performance than the LS estimator in data transmission over the Rayleigh channel. Similar
results were observed in [12, 14] in studying the performance of channel estimation methods for
SISO and MIMO OFDM system.

0

10

-1

BER

10

-2

10

No Channel Estimation
With LS
With MMSE
-3

10

0

4

8

12

16

20

SNR(dB)

Fig. 3 BER performance of OFDM system without and with comb
pilot-based channel estimation (LS and MMSE).
0

10

Low-Pass
Second Order
Linear
-1

BER

10

-2

10

-3

10

0

4

8

12

16

20

SNR(dB)

Fig.4 Performance of different interpolation techniques used in Comb
pilot-based channel estimation of OFDM system

Fig. 4 depicts the impact of various channel interpolation techniques on the performance of
OFDM system. The simulation is performed under BPSK signal mapping over Rayleigh fading
50


channel. The performance of different interpolation techniques used in comb pilot-based MMSE
channel estimation follows the sequence of best to the worst as low-pass, second order and linear.
This result is consistent with earlier studies [9, 13].
The BER comparison of OFDM system with MMSE-interpolation-based comb type channel
estimation for different number of channel taps is shown in Fig. 5. Low-pass interpolation and
BPSK modulation were used for the system simulation over Rayleigh fading channel. The result
shows that the system performance is increased when we choose the number of channel taps per
multipath less than the CP length, whereas the performance getting worse if the number of
channel taps exceed the CP length. As we increase the number of taps, the transmitted signal go
under high degradation because of the increase of the number of times it would be reflected by
the multipath channel taps and, thus, the system performance degrades [15].
Fig. 6 demonstrates the BER performance of OFDM system with comb pilot-based MMSE
channel estimation over Rayleigh fading channel for BPSK, QPSK, 4QAM, 16QAM and 64QAM
signal mapping. Low-pass interpolation was used to estimate channel frequency response (CFR)
at data frequencies. Number of channel taps was chosen as 20. As seen the OFDM system
outperforms at BPSK modulation [10, 11] and the performance degrades with increasing the order
of the modulation over Rayleigh channel. The worst performance is observed at 64QAM
modulation. For a typical SNR of 8 dB, the BER values for BPSK and 64-QAM modulations are
0.032 and 1.141, respectively. Accordingly, the system performance is improved by 15.5 dB with
the use of BPSK modulation.

0

10

Taps: 10
Taps: 20
Taps: 40
Taps: 60
-1

BER

10

-2

10

-3

10

0

4

8

12

16

20

SNR(dB)
Fig.5 BER comparison of OFDM system with MMSE-interpolation-based
channel estimation for different number of channel taps.

The BER performance of OFDM system with comb pilot-based MMSE channel estimation over
Rician fading channel for BPSK, QPSK, 4QAM, 16QAM and 64QAM digital modulations are
shown in Fig. 7. Channel taps was selected as 20 per multipath and low-pass interpolation was
used for the estimation of channel at data frequencies. It is evident that the system provides better
error rate performance with BPSK [10] than other modulations used over Rician channel. The
OFDM system performance with BPSK is improved by 6.9 dB as compared to 64QAM at the
SNR of 8 dB.
51


0

10

-1

BER

10

-2

BPSK
QPSK
4QAM
16QAM
64QAM

10

-3

10

0

4

8

12

16

20

SNR(dB)

Fig.6 Performance of OFDM system with comb pilot-based channel estimation
for different signal mapping over Rayleigh fading channel.

0

10

-1

BER

10

-2

10

BPSK
QPSK
4QAM
16QAM
64QAM

-3

10

0

4

8

12

16

20

SNR(dB)
Fig. 7 Performance of OFDM system with comb pilot-based channel estimation
for different signal mapping over Rician fading channel.

Comparing the BER performance of OFDM system with comb pilot-based MMSE channel
estimation over Rayleigh and Rician multipath fading channels in Figs. 6 and 7, respectively, it is
observable that the system performance over Rician channel is somewhat better than that over the
Rayleigh channel environment [16]. For a typical SNR of 10 dB, the BER values for BPSK
modulation over Rayleigh and Rician channels are 0.032 and 0.0165, respectively, which
indicates that the system performance in Racian fading channel is improved by 2.88 dB.

52


6. CONCLUSIONS
In this paper, the BER performance of wireless OFDM system with the implementation of comb
pilot-based channel estimation is examined for different signal mapping over multi-path Rayleigh
and Rician fading channels. In channel estimation, the MMSE method is used for the estimation
of channel at pilot subcarriers while different interpolation techniques are employed to estimate
the channel at data subcarriers. From the present simulation based comparative study it can be
concluded that the deployment of BPSK modulated OFDM system with MMSE and low-pass
interpolation-based comb type channel estimation achieves good error rate performance in data
transmission over all multipath fading environments involved.

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A COMPARATIVE PERFORMANCE STUDY OF OFDM SYSTEM WITH THE IMPLEMENTATION OF COMB PILOT-BASED MMSE CHANNEL ESTIMATION

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