TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
Studies on Performance of Pulse Shaped
OFDM Signal
1D. K. Sharma, 2A. Mishra, 3Rajiv Saxena
1Ujjain Engineering College, Ujjain, MP 2Madhav Institute of Technology & Science, Gwalior, MP 3Jaypee Institute of Engineering & Technology, Guna, MP
[email protected], [email protected], [email protected],
Abstract- The Orthogonal Frequency Division Multiplexing
(OFDM) transmission system is one of the optimum versions
of the multi-carrier transmission scheme. The OFDM is
referred in the literature as Multi-carrier, Multi-tone and
Fourier Transform based modulation scheme. The OFDM is
a promising candidate for achieving high data rate
transmission in mobile environment.
In this paper, different power spectral density (PSD)
curves of OFDM signal with various pulse shapes are
presented. The final pulse shaped OFDM waveform is then
analyzed for frequency domain response and the PSD in
each case and it’s also an analyzed on the basis of its
modulation index which equally varies with the used window
function during transmission. The simulation results are
presented in a tabular manner enabling to analyze and
establish the superiority, at a glance, of a specific window
function applied (pulse shaped). The OFDM signals with the
pulse shapes, like Rectangular, Blackman, Gaussian,
Hamming and Hanning are tried. The effect of some of these
time waveforms on the OFDM system performance in terms
of power spectral density (PSD) & modulation index has
been investigated.
Keywords- MI, PSD, FFT, ISI, ICI, OFDM.
I. INTRODUCTION
The concept of using parallel data transmission and
frequency multiplexing was published in the mid of
1960s. After more than thirty years of research and
development, OFDM has been widely implemented in
high speed digital communications. Due to recent
advances of digital signal Processing (DSP) and Very
Large Scale Integrated circuit (VLSI) technologies, the
initial obstacles of OFDM implementation such as
massive complex computation and high speed memory do
not exist anymore [1-3].
The use of Fast Fourier Transform (FFT) algorithms
eliminates arrays of sinusoidal generators and coherent
demodulation required in parallel data systems and makes
the implementation of the technology cost effective [4-5].
The OFDM concept is based on spreading the data to
be transmitted over a large number of carriers, each being
modulated at a low rate. The carriers are made orthogonal
to each other by appropriately choosing the frequency
spacing between them [6-7].
In contrast to conventional Frequency Division
Multiplexing, the spectral overlapping among sub-carriers
are allowed in OFDM since orthogonality will ensure the
sub-carrier separation at the receiver, providing better
spectral efficiency and the use of steep band-pass filter
was eliminated.[8-11]
The orthoganality of sub channels in OFDM can be
maintained and individual sub channels can be completely
separated by the FFT at the receiver when there are no
inter symbol interference (ISI) and inter carrier
interference (ICI) introduced by the transmission channel
distortion.[12-14]
One way to prevent ISI is to create a cyclically
extended guard interval, where each OFDM symbol is
preceded by a periodic extension of the signal itself.
When the guard interval is longer than the channel
impulse response or multi-path delay, the ISI can be
eliminated [15-16].
This paper is organized as follows: in section 2, the
OFDM transmitter is simulated using Matlab. In section 3,
the OFDM transmitter model along with various pulse
shapes are included with their mathematical expressions.
The simulation of various pulse shapes is presented. In
section 4, pulse shaped OFDM waveform is then analyzed
for MI & frequency domain response and the PSD in each
case. In section 5, the simulation results are shown. The
conclusive remarks are given in last section.
II. OFDM TRANSMITTER
A brief description of the model is provided in Figure-
1. The incoming serial data is first converted from serial
to parallel and grouped into x bits, each to form a complex
number. The complex numbers are modulated in a base-
band fashion by the IFFT and converted back to serial
data for transmission [17-18].
Fig.1: OFDM Transmitter.
A guard interval is inserted between symbols to
avoid inter symbol interference (ISI) caused by multi-path
distortion. The discrete symbols are converted to analog
and low-pass filtered for RF up-conversion [19].
III. FFT IMPLEMENTATION
The selection of FFT also plays an important role in
design of an OFDM system because of the size of the FFT
is to be taken as balance between the protection against
Doppler shift, multipath and design complexity. The
610
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
OFDM spectrum is centered on cf , i.e., sub-carrier 1 is
7.61/2 MHz to the left of the carrier and sub-carrier 1,705
is 7.61/2 MHz to the right. One simple way to achieve the
centering is to use a 2N-IFFT and T/2 as the elementary
period. The OFDM symbol duration, U , is specified
considering a 2,048-IFFT (N=2,048); therefore, we shall
use a 4,096-IFFT. A block diagram of the generation of
one OFDM symbol is as shown in Figure-2, where the
variables indicated are used in the source code. The next
task to consider is the appropriate simulation period. T is
defined as the elementary period for a base-band signal,
but since we are simulating a band-pass signal, we have to
relate it to a time-period, ,/1 sR that considers at least
twice the carrier frequency. For simplicity, we use an
integer relation, sR =40/T. This relation gives a carrier
frequency close to 90 MHz, which is in the range of a
VHF channel five, a common TV channel in any city [20].
Fig.2: Simulation of OFDM Transmitter.
The complex envelope of the OFDM signal,
consisting of N carriers is given [22] by,
)1.....(..1
0
2
,
k
N
n
tT
jn
kntotal ekttgaS
Where g(t) is rectangular pulse of duration T and T is
OFDM symbol duration.
A. Pulse shaping
There are two effects caused by frequency offset; (I)
reduction of signal amplitude in the output of the filters
matched to each of the carriers and (II) introduction of ICI
from the other carriers which are now no longer
orthogonal to the filter. The time-domain pulse shaping
method can also reduce ICI through multiplying the
transmitted time-domain signals by a well-designed pulse
shaping function proposed a pulse shaping method to
reduce ICI by cyclically extending by v samples the time
domain signal associated with each symbol [23-24]. The
whole of the resulting signal is then shaped with the pulse
function. It is important to note that DFT transform in the
receiver is N point whereas that in the transmitter is N/2
point. If v< N/2, then the signal corresponding to each
symbol is zero padded at the receiver to give length N [25,
26, 27].
The simplest way to reduce the Peal to Average Power
Ration (PAPR) is to clip the signal, but this significantly
increases the out of band radiation. A different approach
is to multiply large signal peak with a Gaussian pulse
shaped proposed. But, in fact any pulse shaping function
can be used, provided it has good spectral properties.
Since the OFDM signal is multiplied with several of these
pulse functions the resulting spectrum is a convolution of
the original OFDM spectrum with the spectrum of the
applied pulse function. So, ideally the pulse should be as
narrow band as possible. On the other hand, the pulse
function should not be too long in the time domain,
because that implies that many signal samples are
affected, which increases the bit error ratio. Examples of
suitable pulse functions are the Cosine, Kaiser and
Hamming window [28-29].
B. Methodology
Among the existing methods, Pulse shaping exhibits
good properties such as very simple to implement,
independent of number of carriers, no affect in coding rate
and large reduction in PAPR. Then, we propose a method
to be used with pulse shaping to reduce the PAPR further.
OFDM signal is multiplied by the pulse shaping function
when the signal peak exceeds the clipping level. Unlike
the clipping, the OFDM signal within the pulse width is
modified. This results in a smoothed OFDM signal.
Consider the OFDM system shown in Figure-2, IFFT
output, exhibit PAPR and is multiplied by a pulse shaping
function to reduce PAPR. This will cause signal distortion
[30-31].
Let, the modulated data be nx where n=0, 1, 2, …., N-1.
OFDM signal can be expressed as,
)3.......(
)2(..........
0
2
N
k
N
nkj
kn
nn
ex
IFFTx
The OFDM signal after multiplication by pulse shaping
function can be evaluated as,
.2/,...1,0;_
)4.......(..........,
2/
Mjlevelclipxif
otherwisex
gxz
n
n
JMjn
n
C Mathematical Model of OFDM:
The expression for an OFDM symbol at
t = ts is given as:
)5.......(..........,0)(
,5.0
2exp2
2
2/Re)(
Tsttsttts
Tsttsts
ttT
ic
fj
sN
sN
is
Nidts
Where, id = complex modulation symbols, S =
number of sub carriers, T = symbol duration, cf = carrier
frequency.
The above equation (5) can also be expressed as:
)6....()(.Re)(0
67
0
,,,,
2max
min
m l
klm
k
kk
klm
tfjtCets c
W
here
611
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
SS
mLk
j
klm mltml
otherwise
etSS
U
16868;
7..................;0
{68
'2
,,
Where: k = carrier number; l = OFDM symbol number; m
= transmission frame number; K = number of transmitted
carriers; S = symbol duration; U = inverse of the
carrier spacing; Δ = duration of the guard interval; cf =
central frequency of the radio frequency (RF) signal; k′ =
carrier index relative to the center frequency,
2/minmax
' and kimC ,, = complex
symbol for the carrier K of the data symbol frame from
number 0, 1, 2, 3….67 in frame number m.
D. OFDM Pulse Shaping
The ISI can be reduced by increasing the symbol
duration or by introducing the guard interval between the
OFDM symbols, the expected multipath delay spread can
be taken care of by increasing the guard interval and in
this way the ISI can be completely eliminated but addition
of guard interval to an OFDM system accounts for a
decrease in bandwidth efficiency and an increase power
requirement which are not the desirable features for
spectrally efficient wireless communication system [32-
33].
One way to solve this problem is to adopt a
proper prototype pulse shape function well localized in
time and frequency domain so that the combined ISI / ICI
can be combated efficiently without utilizing any cyclic
prefix [34-35].
At the stage of modulating the OFDM signal by
applying the pulse g(t) an exhaustive analysis has been
done by varying the pulse shape g(n) as follows:
Case1: Rectangular Pulse
g(n) = 1, for n = 0,1,2,3...,M.
0 , otherwise.
Case2: Blackman pulse
1/4cos0801/2cos50420 nn
Case3: Gaussian pulse
g(n) = 2
0,/22
1exp
2
nforn
Case 4: Hamming pulse
g(n) = 1/2cos460540 n
Case5: Hanning pulse
g(n) = 1/2cos12
1n
The above mentioned five pulse shapes have been
simulated and representing in time and frequency domain
as shown in Figure-3 and Figure-4.
10 20 30 40 50 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Samples
Am
plit
ude
Time domain
w indow #1
w indow #2
w indow #3
w indow #4
w indow #5
Fig.3: Various pulse shapes in time domain.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-140
-120
-100
-80
-60
-40
-20
0
20
40
Normalized Frequency ( rad/sample)
Magnitu
de (
dB
)
Representation of Different pulse shapes in frequency domain
rectw in#1
blackman#2
gaussw in#3
hamming#4
hanning#5
Fig.4: Various pulse shapes in frequency domain.
IV. PULSE SHAPED OFDM SIGNAL
In OFDM systems, the information bit stream (bit rate
bR =
b
1) is first modulated in base band signal using
M-ary quadrature amplitude modulation (M-QAM) with
symbol duration being defined as S = 2logb , and is
then divided into N parallel symbol streams which are
then multiplied by pulse shape function g(t) or g(n) [2, 8,
28].
The transmitted signal in the analytic form can be
represented as
)()( ,, tgatSn
nmnm
(8)
Where )1......,2,1,0,(, Nmna nm represents
the base band modulated information symbol conveyed
with the sub-carrier of index m during the symbol time of
index n, and )(, tg nm represent the pulse shape of index
(m, n) in the synthesis basis which is derived by the time-
frequency translated version of the pulse shaped function
g(t) as
,)( 2
, nTtgetg mFtj
nm
Where, nm, (9)
612
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
Where ,1j F represents the inter-carrier
frequency spacing and T is the OFDM symbol duration,
hence )(, tg nm forms an infinite set of pulse spaced at
multiples of T and frequency shifted by multiple of F.
Consequently the density of OFDM lattice is TF/1 .
Transmitter Model
We consider an OFDM system with a total of N
orthogonal sub-carriers. Each sub-carrier is modulated
with a low rate sequence of symbols and uses a pulse
shape of the same duration as the OFDM symbol duration
T [27]. The transmitter block diagram is shown in Figure-
5.
Fig.5: Block diagram of the OFDM scheme using time-
limited waveforms.
The equivalent low-pass representation of the
transmitted signal is given
by
1
0
2
, .1,)(m
tfj
km tetpSt m
………. (10)
where kkkoK sssS ,1,1, ,.....,,
uncorrelated complex base-band modulated signals related
to the used modulation scheme and
m
fm ,
m=0,1,2,……N-1 is the carrier frequency of sub-carrier
m.
)(tpm is a pulse shape of duration T used at sub-carrier
m with .)(2dttpm
This pulse is defined according to [10] to be
t
sm
itptwwhere
mtmtwtp
.)(
)11_(__________.1......,
......2,1,0,2/)(
is a
periodic function with a period T and p(t) is a time limited
waveform of duration T and
.2/2/,1
.,0
t
otherwiset
S =T/N; is the symbol duration of the base-band
modulation signal. We assume that the total number of
harmonics for the pulse )(tpm shape is L+U+1. Using
(11), the pulse shape of sub-carrier m becomes
,2/)(22
teectpU
L
T
tij
N
mij
im
L, U<N, M= 0, 1, 2….., N-1…(12)
The discrete representation of this set of time waveforms
is given in [28-30] and is written in a vector form as:
mp [ N
mLj
Lec2
, ,.....,
)1(2
1N
Lmj
L ec
N
Umj
U ec
)1(2
1
, N
mUj
U ec2
, 0, ……, 0]
m = 0, 1, 2,….., N-1…(13)
Where
)(1
)(1
0
2
,
ipdtetpc m
T
tij
mim
is the exponential Fourier series coefficient with
1
2
,
imc And )( fPm is the Fourier transform
of )(tpm .
If we replace )(tpm by its expression in (10), the
equivalent low pass of the OFDM signal becomes in a
matrix form
KKUNKLKLk
kk
SsssS
sPS
,~,......,~,~~)14.......(
~
,1,1,
is as defined previously, and
)15.....(...........
.
1
1
2
2
1
0
PD
PD
DP
P
P
is an )( UL shaping matrix, and m
i PD is
the ith cyclic shift of the vector mp .
The definition of the matrix P indicates that each sub-
carrier pulse of the OFDM scheme has a different shape
and all these pulse shapes are derived by cyclic shifts of
613
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
the same pulse. This will also reduce the PAPR of the
OFDM transmitted signal since the peak amplitude of the
different pulse shapes will never occur at the same time
instant unless p (t) is a rectangular pulse [32].
As shown in Figure-6, the OFDM transmitter
system with pulse shaping can be equivalently represented
by a discrete shaping matrix P followed by a regular
OFDM scheme. The OFDM transmitted signal with pulse
shaping is generated as follows. The information is first
passed through a shaping processor, which consists of
multiplying the input sequence, S by the transpose of
the shaping matrix P. The output is then modulated using
a regular OFDM scheme with L+N+U sub-carriers giving
the signal x (t) as defined in (10). The entities of the
shaping matrix are directly obtained from the selected set
of time waveforms that reduce the PAPR of OFDM
signals [3, 34].
Fig.6: Discrete representation of OFDM modulation
schemes with time-limited waveforms.
The ISI and ICI within an OFDM block are
avoided by adding a cyclic prefix (CP). The cyclic prefix
is simply a copy of the M last symbols of the N samples
and is added to the front of the OFDM block, making the
signal to appear periodic in the receiver as shown in
Figure-7.
Fig.
7: Adding the cyclic prefix, CP.
There is a trade off between bit rate and low ISI
and the optimum length of the cyclic prefix depends on
the delay spread of the channel. The length of cyclic
prefix is chosen larger than expected delay spread of the
channel.
The purpose of this paper is to look at designing
an optimum set of waveforms for the OFDM scheme by
varying the related parameter of p(t). The OFDM system
with pulse shaping was introduced and the system
performance was evaluated assuming that each sub-carrier
uses the same pulse shape. In our model the system
performance based on choosing the set of pulses that give
performance of OFDM system in terms of PSD and MI.
The modulation index (M.I.) of pulse shaped
OFDM signal is calculated by expression [28] as
)16..(..........100..minmax
minmax
VV
VVIM
Where minmax &VV are the maximum and minimum
amplitude of pulse shaped OFDM transmitted signal. We
evaluated various minmax &VV for above said pulse
shapes and presented in Table-1. The pulse shaped OFDM
waveforms are plotted in Figure-8 to Figure-12.
2 4 6 8 10 12 14
x 10-7
-150
-100
-50
0
50
100
150
Time(sec)
Am
plit
ude
Fig-9-Time response of signal s(t)
data 1
Fig.8: Time Response of OFDM signal for Rectangular pulse
2 4 6 8 10 12 14
x 10-7
-50
-40
-30
-20
-10
0
10
20
30
40
50
Time(sec)
Am
plit
ude
Fig-9-Time response of signal s(t)
data 1
Fig.9: Time Response of OFDM signal for Blackman pulse
2 4 6 8 10 12 14
x 10-7
-60
-40
-20
0
20
40
60
Time(sec)
Am
plit
ude
Fig-9-Time response of signal s(t)
data 1
Fig.10: Time Response of OFDM signal for Gaussian pulse
2 4 6 8 10 12 14
x 10-7
-60
-40
-20
0
20
40
60
Time(sec)
Am
plit
ude
Fig-9-Time response of signal s(t)
data 1
Fig.11: Time Response of OFDM signal for Hamming pulse
614
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
2 4 6 8 10 12 14
x 10-7
-80
-60
-40
-20
0
20
40
60
80
Time(sec)
Am
plit
ude
Fig-9-Time response of signal s(t)
data 1
Fig.12: Time Response of OFDM signal for Hanning pulse
The pulse shaped OFDM waveforms is then analyzed
for frequency domain response and the PSD in each case
as mentioned above are plotted in Figure-13 to Figure-17.
The PSD of each carrier at frequency defined by the
expression as:
17.....2 SincfPk
where
)20....(;2/'
)19........(
);18.......(
maxminminmax
'
kkkkkkk
andk
ff
ff
u
ck
sk
0 0.5 1 1.5 2 2.5 3 3.5 4
x 108
0
5
10
15
20
25
Frequency(Hz)
Magnitude
Fig-10-s(t) FFT
0 20 40 60 80 100 120 140 160 180-120
-100
-80
-60
-40
-20
Frequency (MHz)
Pow
er/
frequency (
dB
/Hz)
Welch Power Spectral Density Estimate
Fig.13: Frequency Response & PSD of signal for Rectangular pulse.
0 0.5 1 1.5 2 2.5 3 3.5 4
x 108
0
2
4
6
8
10
Frequency(Hz)
Magnitude
Fig-10-s(t) FFT
0 20 40 60 80 100 120 140 160 180-140
-120
-100
-80
-60
-40
Frequency (MHz)
Pow
er/
frequency (
dB
/Hz)
Fig-10-s(t) FFT
data 1
data 2
Fig.14: Frequency Response & PSD of signal for Blackman pulse.
0 0.5 1 1.5 2 2.5 3 3.5 4
x 108
0
2
4
6
8
10
Frequency(Hz)
Magnitude
Fig-10-s(t) FFT
0 20 40 60 80 100 120 140 160 180-140
-120
-100
-80
-60
-40
Frequency (MHz)
Pow
er/
frequency (
dB
/Hz)
Welch Power Spectral Density Estimate
data 1
data 2
Fig.15: Frequency Response & PSD of signal for Gaussian pulse.
0 0.5 1 1.5 2 2.5 3 3.5 4
x 108
0
2
4
6
8
10
12
Frequency(Hz)
Magnitude
Fig-10-s(t) FFT
0 20 40 60 80 100 120 140 160 180-140
-120
-100
-80
-60
-40
Frequency (MHz)
Pow
er/
frequency (
dB
/Hz)
Welch Power Spectral Density Estimate
data 1
data 2
Fig.16: Frequency Response & PSD of signal for Hamming pulse.
0 0.5 1 1.5 2 2.5 3 3.5 4
x 108
0
2
4
6
8
10
12
Frequency(Hz)
Magnitude
Fig-10-s(t) FFT
0 20 40 60 80 100 120 140 160 180-140
-120
-100
-80
-60
-40
Frequency (MHz)
Pow
er/
frequency (
dB
/Hz)
Welch Power Spectral Density Estimate
data 1
data 3
Fig.17: Frequency Response & PSD of signal for Hanning pulse.
V. RESULTS AND DISCUSSION
The modulation index after getting the OFDM for
applied five different pulses shape i.e. rectangular,
Blackman, Gaussian, Hamming and Hanning pulse has
been investigated and reported in Table-1.
The modulation index of OFDM for Rectangular
pulse is lower but the modulation index of OFDM signal
for Gaussian pulse is higher.
Various parameters of Magnitude Spectrum and
Power Spectral Density of OFDM transmitted signal for
different pulse shapes are tabulated in Table-2 and Table-
3 respectively.
Table-1: Simulation result of: Max and Min. Values &
modulation index of OFDM signal.
Sr.
No.
Types of
Pulse maxV minV M. I.
(%)
1 Rectangular
Pulse
113.1370 8.483 86.05
2 Blackman
Pulse
45.8639 3.263 86.72
3 Gaussian
Pulse
54.2013 3.076 89.26
4 Hamming
Pulse
59.2022 4.249 86.61
5 Hanning
Pulse
60.0577 4.353 86.48
VI. CONCLUSION
A study on pulse shaped OFDM signal is made and
the power spectral density (PSD) and MI of different
pulse shaped OFDM signal is presented in this paper. The
OFDM waveform is then analyzed for MI & frequency
domain response and the PSD in each case.
It is also possible to design a set of time domain
waveforms that will reduce the PAPR of the OFDM
615
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
transmitted signal and improve its power spectrum
simultaneously. The effect of some of these sets of time
waveform on the OFDM system performance in terms of
MI & power spectral density (PSD) is investigated and the
data is tabulated to analyze and establish the superiority of
a specific pulse shape over the other depending on the
application or requirement.
In this paper, envelope of pulse shaped OFDM signal
are shown and the variations in modulation index with
respect to pulse shape or window function used are
tabulated. The results are enabling to analyze and
establish the superiority at a glance of a specific window
function applied.
This study definitely looks forward and it reveals that
this will act as the stepping stone especially in the designs
of 4G Mobile Communication System.
REFERENCES [1] A. V. Oppenheim and R. W. Schafer, “Discrete-Time Signal
Processing,” Englewood Cliffs, NJ: Prentice Hall, 1989.
[2] J. Armstrong, “OFDM,” John Wiley and Sons Ltd., ISBN: 0470015667, January 2007.
[3] H. Schulze and C. Lueders, “Theory and Applications of OFDM and CDMA: Wideband Wireless Communications,” John Wiley & Sons, ISBN: 0470850698, September 2005.
[4] J. K. Gautam, A. Kumar and Rajiv Saxena, “On the Modified Bartlett-Hanning Windows (Family),” IEEE Transaction on Signal Processing, vol. 44, no. 8, pp. 2098-2102, August 1996.
[5] A. Mishra, R. Saxena and Y. M. Gupta, “Digital Modulation Techniques,” Indian Journal of Telecommunications, vol. 53, no. 5, pp. 34-47, Sept.-Oct. 2003.
[6] J. Heiskala and J. Terry, “OFDM Wireless LANs: A Theoretical and Practical Guide,” Sams, December 2001.
[7] P. Banelli and S. Cacopardi, “Theoretical Analysis and Performance of OFDM Signals in Nonlinear AWGN Channels,” IEEE Transaction on Communications, vol. 48, no. 3, pp. 430-438, March 2000.
[8] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Transaction on Communications, vol. 42, pp. 2908-2914, Oct. 1994.
[9] S. Kumar and Rajiv Saxena, “MC-CDMA for Mobile Communication,” Telecommunications, vol. 52, no. 3, pp. 28-36, May-June 2002.
[10] S. N. Sharma, S. C. Saxena and Rajiv Saxena, “Design of FIR Filter Using Variable Window Families: A Comparative Study,” Journal of the Indian Institute of Science, vol. 84, no. 5, pp. 155-161, Sep.-Oct. 2004.
[11] C. Esli and H. Delic, “Coded OFDM with Transmitter Diversity for Digital Television Terrestrial Broadcosting,” IEEE Transaction on Broadcasting, vol. 52, no. 4, pp. 586-596, December 2006.
[12] C. W. Chow, C. H. Yeh, C. H. Wang, C. L. Wu, S. Chi and C. Lin, “Studies of OFDM Signal for Broadband Optical Access Networks,” IEEE Journal on Selected Areas in Communications, vol. 28, no. 6, pp. 800-807, August 2010.
[13] ETS 300 744, “Digital broadcasting systems for television, sound and data services; framing structure, channel coding, and modulation for digital terrestrial television,” European Telecommunication Standard, Doc. 300 744, 1997.
[14] H. G. Ryu, Y. Li and J. S. Park, “An Improved ICI Reduction Method in OFDM Communication System,” IEEE Transactions on Broadcasting, vol. 51, no. 3, pp. 395-400, September 2005.
[15] J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Transaction on Communications, vol. 47, pp. 365-369, Mar. 1999.
[16] J. Zhang, L. L. Yang, X. Liu and L. Hanzo, “Inter-Carrier Interference Analysis of OFDM System Communicating over
Rapidly-Fading Nakagami-m Channels,” IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications, pp. 79-83, 2006.
[17] K. Fazel and S. Kaiser, “Multi-Carrier and Spread Spectrum System,” John Wiley & Sons, Inc., 2003.
[18] J. Gross, M. Emmelmann, O. Punal and A. Wolisz, “Enhancing IEEE 802.11a/n with dynamic single-user OFDM adaptation,” Elsevier Journal on Performance Evaluation, vol. 66, pp. 240-257, 2009.
[19] K. N. Le, “Insights on ICI and its effects on performance of OFDM systems,” Elsevier Journal on Digital Signal Processing, vol. 18, pp. 876-884, 2008.
[20] K. Singh, R. Khanna and Rajiv Saxena, “Fractional Fourier Transform Based Beam-forming for Next Generation Wireless Communication Systems,” IETE Technical Review, vol. 21, no. 5, pp. 357-366, Sep.-Oct. 2004.
[21] Rajiv Saxena and K. Singh, “Fractional Fourier Transform: A Novel Tool For Signal Processing,” Journal of the Indian Institute of Science, vol. 85, no. 1, pp. 11-26, Jan.-Feb. 2005.
[22] E. Saberinia, J. Tang, A. H. Tewfik and K. K. Parhi, “Pulsed-OFDM Modulation for Ultrawideband Communications,” IEEE Transactions on Vehicular Technology, vol. 58, no. 2, pp. 720-726, February 2009.
[23] N. C. Beaulieu and P. Tan, “On the Effects of Receiver Windowing on OFDM Performance in the Presence of Carrier Frequency Offset,” IEEE Transactions on Wireless Communications, vol. 6, no. 1, pp. 202-209, January 2007.
[24] M. Russell and G. L. Stiiuber, “Interchannel interference analysis of OFDM in a mobile environment,” in Proc. IEEE 45th Vehicular Technology Conference, vol. 2, pp. 820-824, 1995.
[25] J. K. Gautam, A. Kumar and Rajiv Saxena, “WINDOWS: A Tool in Signal Processing,” IETE Technical Review, vol. 12, no. 3, pp. 217-226, May-June 1995.
[26] T. Fusco, A. Petrella and M. Tanda, “Non-data-aided carrier-frequency offset estimation for pulse-shaping OFDM/OQAM systems,” Elsevier Journal on Signal Processing, vol. 88, pp.1958-1970, 2008.
[27] P. Tan and N. C. Beaulieu, “Reduced ICI in OFDM systems using the “better than” raised-cosine pulse,” IEEE Communication Letters, vol. 8, pp. 135-137, Mar. 2004.
[28] D. K. Sharma, A. Mishra and Rajiv Saxena, “Analysis of Modulation Index of OFDM Signal with Different Pulse Shapes,” Engineering and Environmental Sciences Journal, vol. 3, no. 2, pp. 56-64, December 2007.
[29] V. Kumbasar and O. Kucur, “ICI reduction in OFDM systems by using improved sinc power pulse,” Elsevier Journal on Digital Signal Processing, vol. 17, pp. 997-1006, 2007.
[30] D. K. Sharma, A. Mishra and Rajiv Saxena, “BER Based Performance Evaluation by Pulse Shaping in OFDM,” Proceeding of IEEE Computer Society of International Conference on Computational Intelligence and Communication Network (CICN-2010) at RGPV Bhopal, pp. 482-487, 26th to 28th Nov. 2010.
[31] H. Zhang and Y. Li, “Optimum frequency-domain partial response encoding in OFDM system,” IEEE Transaction on Communications, vol. 51, pp. 1064-1068, July 2003.
[32] N. D. Alexandru and A. L. Onofrei, “Improved Nyquist filter with an ideal piece-wise rectangular characteristic,” International Journal of Electronics and Communications (AEU), vol. 64, pp. 766–773, 2010.
[33] R. Mohseni, A. Sheikhi and M. A. M. Shirazi, “Multicarrier constant envelope OFDM signal design for radar applications,” International Journal of Electronics and Communications (AEU), no. 64, pp. 999–1008, 2010.
[34] S. L. Jansen, B. Spinnler, I. Morita, S. Randel and H. Tanaka, “100GBE: QPSK versus OFDM,” Elsevier Journal on Optical Fiber Technology, vol. 15, pp. 407-413, 2009.
[35] D. K. Sharma, A. Mishra and Rajiv Saxena, “The Modulation Index of Various Pulse Shapes in OFDM,” presented in National Conference on Wireless Communication & VLSI Design (NCWCVD-2010), Technically Supported by IEEE MP Subsection, Gwalior, March 27th & 28th, 2010.
616
TECHNIA – International Journal of Computing Science and Communication Technologies, VOL. 3, NO. 2, Jan. 2011. (ISSN 0974-3375)
Table-2: The Parameters of Magnitude Spectrum of OFDM Transmitted Signal With Different Pulse Shapes
Para. Time (Sec.) Rect. Blackman Hanning Gaussian Hamming
Min: 8.9286310 8.3295
510 3.1005510 8.2062
510 1.1100410 9.1606
510
Max: 3.6571810 20.7719 8.3305 10.9302 9.8474 10.7639
Mean 1.8286810 0.3850 0.1563 0.2049 0.1844 0.2017
Median 1.8286810 0.0025 0.0010 0.0013 0.0012 0.0013
Mode: 8.9286810 8.3295
510 3.1005510 8.2062
510 1.1100410 9.1606
510
Std 1.0557810 1.9815 0.8034 1.0534 0.9483 1.0370
Range 3.6571810 20.7719 8.3305 10.9301 9.8473 10.7638
Table-3: The Parameters of Power Spectral Density of OFDM Transmitted Signal With Different Pulse Shapes
Para. Time(sec.) Rect. Blackman Hanning Gaussian Hamming
Min: 0 -116.5818 -124.3722 -122.0185 -122.9310 -122.1541
Max: 182.8571 -35.1984 -43.1080 -40.7408 -41.6560 -40.8792
Mean 91.4286 -105.1980 -112.9823 -110.6529 -111.5612 -110.7903
Median 91.4286 -110.1268 -117.9741 -115.6195 -116.5291 -115.7503
Mode: 0 -116.5818 -124.3722 -122.0185 -122.9310 -122.1541
Std 52.7911 15.7749 15.7621 15.7525 15.7516 15.7482
Range 182.8571 81.3834 81.2642 81.2777 81.2750 81.2749
617