Comparison of traffic performance of QPSK and 16-QAM modulation techniques for OFDM system

Abstract

Orthogonal frequency division multiplexing (OFDM) provides better spectral efficiency than frequency division multiplexing (FDM), while maintaining orthogonal relation between carriers; hence traffic is better carried by OFDM than FDM within the same spectrum. This paper reveals a comparison of spectral efficiency, performance of communication system in context of bit error rate (BER) for the same information rate and peak to average power ratio (PAPR) of quadrature amplitude shift keying (QPSK) and 16-quadrature amplitude modulation (16-QAM) technique.

Full text

Regular paper Comparison of traffic
performance of QPSK and 16-QAM
modulation techniques for OFDM system
Imdadul Islam and Siddique Hossain
Abstract— Orthogonal frequency division multiplexing
(OFDM) provides better spectral efficiency than frequency
division multiplexing (FDM), while maintaining orthogonal
relation between carriers; hence traffic is better carried by
OFDM than FDM within the same spectrum. This paper
reveals a comparison of spectral efficiency, performance of
communication system in context of bit error rate (BER) for
the same information rate and peak to average power ratio
(PAPR) of quadrature amplitude shift keying (QPSK) and
16-quadrature amplitude modulation (16-QAM) technique.
Keywords— OFDM, QPSK, 16-QAM, IFFT, frequency spec-
trum, PAPR, BER.
1. Introduction
Today major challenge in telecommunication is to con-
vey as much information as possible through limited spec-
tral width. Orthogonal frequency division multiplexing
(OFDM) introduces the concept of allocating more traf-
fic channels within limited bandwidth of physical channel.
Here the available bandwidth is split into several narrow
band channels for simultaneous transmission. In frequency
division multiplexing (FDM) a guard band is provided be-
tween individual channels, which separates the spectrum
of different channels, and enables a practical band pass fil-
ter to detect individual channel. But the situation is com-
pletely different in OFDM where spectrums of adjacent
channels are overlapped which resembles adjacent channel
interference, but interference is avoided by maintaining or-
thogonal relation between sub-carriers. First of all high
speed serial data is converted to low speed parallel data, as
shown in Fig. 1 based on [1, 2]. Therefore transmitted sig-
nal is a vector addition of orthogonal modulated carriers,
makes large peak to average power ratio, therefore dynamic
range of devices should be large enough, as summarized
in [3–5].
Output of each parallel line is modulated; here two dif-
ferent types of modulation quadrature amplitude shift
keying (QPSK) and 16-quadrature amplitude modulation
(16-QAM) are selected for this paper, whose constellations
are shown in Fig. 2. QPSK waves have constant peaked si-
nusoidal wave but phase angle is different for four different
combinations of 2 bits. In 16-QAM both amplitude and
phase of the wave varies according to 16 different combi-
nation of 4 bits. In this paper 7 parallel lines are used,
hence 7 different carrier frequencies are used for simula-
tion. Parallel waves are again converted to an instantaneous
serial waves prior to transmission. This phenomenon re-
sembles inverse first Fourier transform (IFFT) mentioned
in [3, 6–8]. At receiving end signals are detected by co-
herent or envelope detection but this paper considers only
coherent detection. In Section 2 complete analysis of trans-
mitted signal in both time and frequency domain is done
explicitly along with carrier waves (both before and af-
ter modulation) using constellation vectors of QPSK and
16-QAM. All the equations needed to detect signal at re-
ceiving end along with evaluation of peak to average power
ratio (PAPR) [9, 10] are also summarized in this section.
Section 3 deals with simulation of OFDM in additive white
Gaussian noise (AWGN) environment to evaluate the per-
formance of both modulation techniques in context of bit
error rate (BER) and PAPR. Finally a comparison of both
modulation techniques is given in a nutshell in Section 4
based on complete analysis previous sections.
2. Methodology
Typical FFT-based OFDM communication system is shown
in Fig. 1. Modulator part of the figure will use only QPSK
and 16-QAM technique whose constellation is shown in
Fig. 2. In OFDM each sub-carrier is modulated indepen-
dently with complex modulation symbol vector and added
for simultaneous transmission; it is expressed like [6, 8]:
v(t) = ˜v(t)ej2
π
fct.(1)
Complex envelope ˜v(t)of above equation is summarized
succinctly in [1–3, 6] given by
˜v(t) = Ac
N−1
∑
n=0
ω
n
φ
n(t); 0 >t>T,(2a)
where Acis the peak carrier amplitude and
ω
nis the N-ele-
ment parallel vector.
For orthogonal relation the sub-carrier frequencies are re-
lated as
φ
n=ej2
π
fntand fn=1
Tn−N−1
2.(2b)
Figure 3a shows the OFDM signal, i.e., summation of sub-
carriers prior to modulation and Fig. 3b depicts the same
signal after QPSK modulation. Before modulation, the
waves have the same starting and ending point since each
147

Imdadul Islam and Siddique Hossain
Fig. 1. OFDM communication system.
Fig. 2. Constellation vector (a) of QPSK and (b) of 16-QAM. Fig. 3. Sub-carriers (a) befor and (b) after modulation.
148

Comparison of traffic performance of QPSK and 16-QAM modulation techniques for OFDM system
Fig. 4. Real and imaginary part of complex envelope of OFDM
(a) of QPSK in time domain and (b) of 16-QAM in time domain.
carrier has an integer number of cycles over a symbol pe-
riod to maintain orthogonal relation but after modulation
start and end points are shifted due to multiplication of
constellation vectors. For Fig. 3b constellation vectors for
QPSK and 16-QAM are taken as
WQPSK =












ej
π
/2
ej3
π
/2
ej
π
ej
π
/2
ej
π
ej
π
/2
ej0












W16-QAM =












1+j
3+j
3−3j
−1+j
−3−3j
3−i
3+3i












Real and imaginary part of complex envelope of 7 simul-
taneously transmitted signal is shown in Fig. 4 for both
16-QAM and QPSK. Signals have very wide dynamic
ranges for both cases.
Frequency spectrum of complex envelope [16] is given by
Ψ(f) = C
N−1
∑
n=0|sinc(f−fn)T|2.(3)
Spectrum of QPSK and 16-QAM signals is depicted in
Fig. 5 for a symbol period of T=1.2and 2.4 units
Fig. 5. Frequency spectrum of complex envelope (a) of QPSK
and (b) of 16-QAM.
for QPSK modulation and T=2.4and 4.8 units for that
of 16-QAM. Symbol period of 16-QAM is taken twice
compare to that of QPSK, since each modulation sym-
bol of 16-QAM holds 4 bits but that of QPSK holds only
two bits.
If there is Ndifferent users, i.e., Nsub-carriers OFDM
system, nth signal block [7, 8, 11] is represented as
Sn(t) = 1
√N
N−1
∑
k=0
Sn,kgk(t−nT ).(4a)
Entire continuous time signal:
S(t) = 1
√N
∞
∑
n=0
N−1
∑
k=0
Sn,kgk(t−nT ).(4b)
Where the constellation vector Sn,kof kth sub-carrier is
recovered using cross correlation of following equation:
Sn,k=√N
TSDSn(t),gk(t−nT )E,(5)
where
gk,gl=Zgk(t)gl(t)dt .
149

Imdadul Islam and Siddique Hossain
At receiving end, the constellation vector becomes [4]:
Rn,k=√N
TSDrn(t),gk(t−nT )E,(6)
where rn(t) = Sn(t) + n(t);n(t)is AWGN of environment.
A maximum likelihood sequence estimator would have
to choose one out of all possibly transmitted symbol se-
quence
µ
. The sequence estimator determines an estimated
<Sn,k>according to the following criterion:
hˆ
Sn,ki=min ∑
k
Rn,k−Hn,kSn,k(
µ
)

2,(7)
where
µ
is the types of possible modulation symbols and
Hn,kis the transfer function of channel [12].
Finally peak to average power ratio is evaluated as
PAPR =maxh|s(t)|2i
meanh|s(t)|2i.(8)
3. Simulation and results
A simulation work is done based on Eqs. (1)–(8) by the
authors using MATLAB-6.5 in their own way to evaluate
Fig. 6. Comparison of performance (a) of 16-QAM and
(b) of QPSK under AWGM.
Fig. 7. Comparison of PAPR (a) of 16-QAM and (b) of QPSK.
Fig. 8. Difference between PAPR of QPSK and 16-QAM for
same throughput.
150

Comparison of traffic performance of QPSK and 16-QAM modulation techniques for OFDM system
performance of QPSK and 16-QAM for OFDM in AWGM
environment in context of spectral width, BER and PAPR
shown in Figs. 5–7. Spectrum of narrower time slot be-
comes wider in frequency domain, visualized by solid lines
of Fig. 5. Each symbol of QPSK convey 2 bits but that of
16-QAM is 4 bits/symbol therefore in time domain equiv-
alent symbol period of 16-QAM is twice as long.
In this paper 10 000 random bits are generated to detect
channel performance in AWGN environment. Rising cosine
filter is used to emulate transmission medium and SNR is
varied from 0 to 18 dB depicted in Fig. 6. One of the
major problems in OFDM is the peak to average power
ratio of un-coded signals. Here no coding technique is
used to improve PAPR like [5, 13] since our aim is to
compare performance of modulation technique in severe
environment. Here PAPR is evaluated for 200 samples for
both modulation techniques depicted in Fig. 7. Variation of
PAPR lies between 5 to 15 units in Fig. 7 also verified in
Fig. 8 where difference between PAPR of two modulation
technique is measured shows the same difference. PAPR
of QPSK and 16-QAM appear identical and it is really
difficult to make command about improvement of PAPR
but performance of both could be improved using coding
technique summarized in [5, 13, 14].
4. Conclusion
It is obvious from Fig. 5 that spectral width of 16-QAM
is narrower than that of QPSK for same information rate.
Each symbol of QPSK conveys 2 bits but that of 16-QAM
is 4 bits/symbol therefore in time domain equivalent sym-
bol period of 16-QAM is twice as long. This phenomenon
is verified from the simulation program. In context of BER,
QPSK yields better performance than that of 16-QAM,
shown in Fig. 6. Finally it could be concluded that BER
performance of QPSK is better than that of 16-QAM at
the expense of spectral width. Therefore 16-QAM can
carry more traffic than QPSK at the expense of BER which
is obvious in context of digital modulation technique
hence analysis of the paper yield logical results in context
of OFDM. PAPR solely depends on coding technique not
on modulation technique, which is also verified from the
simulation.
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Imdadul Islam has received
his B.Sc. in electrical and elec-
tronic engineering from Ban-
gladesh University of Engineer-
ing and Technology, Dhaka, in
1993 and the M.Sc. from the
same institute in 1998. Now he
is perusing Ph.D. at the depart-
ment of EEE, BUET, Dhaka,
in the field of teletraffic engi-
neering. He worked as an As-
sistant Engineer in Sheba Telecom (Pvt.) Ltd. (a joint
venture company between Bangladesh and Malaysia, for
mobile cellular and WLL), from Sept’94 to July’96. He
has very good field experiences in installation of radio
base station and switching center for WLL. He is now
working as an Associate Professor, at the Department of
Electronics and Computer Science, Jahangirnagar Univer-
sity, Savar, Dhaka, Bangladesh. His research field is net-
work traffic, OFDMA, WCDMA and array antenna sys-
tems. He has published more than 20 papers in national
and international journal and conference proceedings.
e-mail: imdad22000@yahoo.com
Department of Electronic and Computer Science
Jahangirnagar University, Savar, Dhaka
Bangladesh
151

Imdadul Islam and Siddique Hossain
Siddique Hossain is the most
senior Professor of Department
of Electrical and Electronic
Engineering, Bangladesh Uni-
versity of Engineering and
Technology, Dhaka. He has
more than 32 years of teaching,
research and administrative
experience both at home and
abroad. Worked as the Head,
EEE Dept., Head, CSE Dept.,
Dean, EEE Faculty and Director, BUET Computer Centre.
He worked as a visiting faculty member of more than ten
universities. He is a Senior Member of IEEE and was
engaged as Chief of IEEE in Bangladesh in 1997–1998.
Dr. Siddique Hossain is interested in the field of computers
and communication engineering, 3G mobile communica-
tion, WCDMA for UMTS, etc. He has more than 30 pub-
lications in national, international journals and conference
proceedings.
e-mail: sdq@eee.buet.ac.bd
Department of Electrical and Electronic Engineering
Bangladesh University of Engineering and Technology
Dhaka-1000, Bangladesh
152