Communications and Network, 2013, 5, 390-393
http://dx.doi.org/10.4236/cn.2013.53B2071 Published Online September 2013 (http://www.scirp.org/journal/cn)
Performance Comparison between OQAM and
N-continuous OFDM
Guobing Cheng, Huilei Li, Shaoqian Li, Lisha Gong, Binhong Dong, Peng Wei
National Key Laboratory of Science and Technology on Communications,
University of Electronic Science and Technology of China, Chengdu, China
Received August, 2013
ABSTRACT
Orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) and N-continuous OFDM are both improved
multi-carrier modulation (MCM) techniques for the transmission of signals over multipath fading channels. In this pa-
per, we aim to compare these two techniques with respect to out-of-band radiation , bit error ratio (BER) and calcu lation
complexity. Analysis and simulation results show that, compared to the N-continuous OFDM, the OFDM/OQAM has
lower out-of-band radiation, calculation consumption and similar BER performance.
Keywords: OFDM/OQAM; N-continuous OFDM; Out-of-band Radiation
1. Introduction
Orthogonal frequency division multiplexing (OFDM) is
an efficient scheme and it has been some practical appli-
cations. However, the trad itional OFDM has some intrin-
sic drawbacks that the discontinuous phase between ad-
jacent symbols leads to high out-of-band radiations and
its robustness to multi-path propagation effect is acquired
by the insertion of a cyclic prefix (CP). To alleviate these
drawbacks, another MCM schemes such as N-continuous
OFDM and OFDM/offset QAM (OFDM/OQAM) are
proposed in [1,2] respectively. Compared to traditional
CP-OFDM, OFDM/OQAM may provide a higher useful
bit rate since it operates without CP and N-continuous
OFDM has less out-of-band radiation since it has several
continuous order of derivatives at the edge of adjacent
OFDM symbols.
For OFDM/OQAM system, pulse shapes with good
time-frequency localization (TFL) can be introduced.
Among these, a pulse shape named extended Gaussian
functions (EGF) is widely used and its TFL can be ad-
justed by the time and frequency real parameters [3].
Through selecting a suitable parameter, an OFDM/
OQAM signal with very low out-of-band radiation can
be acquired [4]. On the other hand, in the traditional
OFDM system, each OFDM symbol is independently
and the transmitted signals are no t continuous, leading to
high out-of-band radiation. In order to overcome the dis-
continuities between consecutive OFDM symbols, N-
continuous OFDM scheme is proposed at the price of
increasing calculation complexity and/or system per-
formance. Therefore, we have to comprise between these
aspects for practical application.
In this paper, we compare the performance of OFDM/
OQAM and N-continuous OFDM. Firstly, the system
models of them are given in section II. And then we ana-
lyze the out-of-band radiation, bit error ratio (BER) and
calculation complexity of these two schemes in section
III. The simulation results are shown in section IV. Brief
conclusion is given in section V. The analysis and simu-
lation results show that, compared to the N-continuous
OFDM, the OFDM/OQAM system has similar system
performance, lower out-of-band radiation and less calcu-
lation consumption.
2. System Model
2.1. System Model of OFDM/OQAM System
The baseband version of a continuous-time OFDM/
OQAM transmitting signal can be written as [2]


,0
12
,0
0,
mn
Mjjmt
mn
nm
staeegt n



 


 (1)
with M an even number of sub-carriers, ,mn the real-
valued symbol conveyed by the sub-carrier of index m
during the symbol time of index n0
a

the subcarrier
spacing and 0

the time offset between the adjacent real
part and imaginary part of an OFDM/OQAM symbol.
00 0
1 2T1



, with 0 the duration of the complex-
valued symbols. T
,mn

is an additional phase term given
by
C
opyright © 2013 SciRes. CN

G. B. CHENG ET AL. 391

,0()mod
2
mn mn


,

   (2)
where 0

can be arbitrarily chosen.

g
t is the pulse
shape that can be different from the rectangle shape of
conditional OFDM system. The EGF shape is often used
in OFDM/OQAM system and its out-of-band character-
istic can be adjusted by the Gaussian parameter

. In
the following, the adaption and compromise between
BER performance and out-of-band radiation are dis-
cussed.
For a distortion-free channel, perfect reconstruction of
real symbols is obtained owing to the following real or-
thogonal condition

 

*
,,, ,,
|
mnpqmnpqmpnq
gggtgt,

  
 (3)
where is the taking real part operator.

,1
mp


if and mp,0
mp

 if mp

.
2.2. System model of N-continuous OFDM
System
The baseband equivalent OF DM symbol can be given as
 

0isg i
sts tiTT






(4)
where
s
T is the OFDM symbol duration and
g
T is the
CP length. In order to make the transmitted signal


s
t
and its first N derivatives continuous, the following
equation should be satisfied that
 
1,
gg
nn
itTi tT
nn
dd
sts t
dt dt
 
 (5)
for all and n=0, 1,…, N [1 ,5 ] .
1i
The realization of N-continuous OFDM symbol is to
pre-coder the set of information symbols (taken
from some complex-valued symbol constellation ) in
each OFDM symbol such that

,ki
d


s
t becomes
N-continuous. Concretely, the OFDM symbol


i
s
t can
be expressed as [1]

2
,,
s
k
jt
T
iki g
ks
s
tde TtT





(6)
where and the complex numbers

01 1
,,..., K kk k


,ki
d are the result of pre-coding information symbols
,ki. For OFDM symbols, the characterization (5) be-
comes
d
,,
njk n
ki ki
kk
ke dkd


 


,1
(7)
where 2
g
s
TT

  . An equivalent form of vector is
that
,
ii
Ad Ad
-1
(8)
where


01 1
,, ,
, ,...,,
K
T
ki kiki
dd d


i
d (9)


01
, ,...,,
K
jk jk jk
diag eee


 1 (10)
and
01 1
01 1
11...1
... .
... ......
...
K
NN N
K
kk k
kk k








A (11)
Finally, we can get 1 ()
i

 H
ii
dIPdPΦd, where
. The deducing detail can be
referred to [1].

1
HH 
H PΦAAA AΦ
3. Comparison of the OFDM/OQAM and
N-continuous OFDM System
3.1. Comparison of the Out-of-band Radiation
Because the pulse shape with lower side lobe such as the
EGF shape is used in the OFDM/OQAM system, the
final transmitting signal has very low out-of-band radia-
tion naturally. The EGF shape is defined as [6]

00 0
0
,, ,,
000
,1 ,
00
1
2
cos2
aka
k
l
l
kk
ztdgt gt
t
dl
 
















 



 










(12)
where


g
t

is the Gaussian function defined by
 
2
14
20
t
gte a





.
0

is the frequency paramr, 0 ete

is the time
parameter and 00 12



. For ifferent a, we can get
different transmitting signal and the larger the value of
a is, the lower out-of-band radiation
d
will be.
For N-continuous OFDM system, the out-of-band
radiation is determined by the number of orders that
having continuous derivatives. And the larger is, the
lower out-of-band radiation will be.
N
N
In contrast to OFDM/OQAM, increasing of leads
to not only the decrease of BER performance but also the
rapid increasing of calculation complexity. Therefore, the
compromise should be made between calculation con-
sumption and system performance.
N
3.2. Comparison of the BER Performance
In OFDM/OQAM system, since the pulse shape that
having immunity to the inter-symbol interference (ISI) is
introduced, the CP is not necessary. Then it can provide
higher bit rate or equivalently higher bit energy.
While for the N-continuous OFDM, the using of CP
cannot be avoided. Furthermore, since the maximum-
likelihood detector of N-continuous is prohibitively

G. B. CHENG ET AL.
392
complex, suboptimal iterative detector is usually used
and there is a certain performance loss when the iterative
time is less than 4.
3.3. Comparison of the Calculation Complexity
In the OFDM/OQAM system, the complex data sources
are divided into real and image part and carried out FFT
calculation respectively. Then a pulse shape with the
duration of 0c is met. Finally these two paths
signals are added and we get the transmitting OFDM/
OQAM signal [4]. Therefore the OFDM/OQAM system
calculation consumption comprises of
TmT
2
2log 4
M
MmM

real multiplications and

2
2log4 1
M
MmM real
additions.
For N-continuous OFDM, the system calculation con-
sumption comprises of 2 8
M
real multiplications and
2
82
M
M real additions. Because both multiplications
and additions calculation are directional proportional to
the square of the number of subcarriers M. Therefore the
calculation consumption increases rapidly for a large M.
Taking the number of subcarriers and the
length the of pulse shape is four times of the length of
OFDM symbol, i.e., , for example, the numerical
comparison of calculation complexity is listed in Table 1.
It is shown that the calculation complexity of N-con-
tinuous OFDM is far more than that of the OFDM/
OQAM system.
256M
4m
4. Simulation Results
In this section, it aims to compare the out-of-band radia-
tion and BER performance of OFDM/OQAM with the
N-continuous system. Unless other wise stated, the
simulation parameters are: the number of subcarriers is
M = 512, sampling time Ts = 1/15 ms, CP length Tg =
144Tsamp, the data is modulated by 16QAM. A 3GPP
EVA fading channel is combined without carrier fre-
quency offset and synchronization errors. The power
spectrum is estimated by Welch’s averaged periodogram
method with sampling duration Tsamp, a 4096-sample
Hanning window and 512-sampleoverlap. And the simu-
lation results are shown in Figure 1 and Figure 2.
Figure 1 shows the results of BER performance of N-
continuous OFDM and OFDM/OQAM, and the results of
original OFDM are also given. It can be seen that N-
continuous OFDM has poorer performance than original
Table 1. Numerical comparison of calculation complexity.
scheme real multiplication addition real
OQAM/OFDM 8192 7168
N-continuou
Figure 1. Comparison of BER performance of N-continuous
OFDM and OFDM/OQAM.
Figure 2. Comparison of out-of-band radiation of N-con-
tinuous OFDM and OFDM/OQAM.
OFDM and the situation is more serious when the N is up
to 10. On the other hand, for OFDM/OQAM system, it
has similar performance with origin OFDM, and the per-
formance loss is negligible even for 2

.
In Figure 2, it sh ows the power spectral density of N-
continuous OFDM and OFDM/OQAM, together with the
results of original OFDM. The results imply that the N-
continuous OFDM has lower out-of-band radiation than
original OFDM. And the larger N is, the lower out-of-
band radiation will be. While for OFDM/OQAM system,
it has a sharp decay at the edge of the main lobe, which is
better for transmission in means of avoiding adjacent
interference. And the parameter

has a certain effect
on the out-of-band radiation. When N = 10, N-continu-
ous OFDM is a little better than that of OFDM/OQAM
with 0.5


. But at same time, the calculation con-
sumption is very large.
5. Conclusions
524288
OFDM 523776
In this paper, the performance of OFDM/OQAM and

G. B. CHENG ET AL.
393
N-continuous OFDM are compared with respect to out-
of-band radiation, BER performance and calculation
complexity with different system parameters. We show
that N-continuous OFDM is only designed to suppress
the out-of-band radiation, but this benefit is acquired
with large calculation consumption increase. The advan-
tages of OFDM/OQAM lie in that it has not only the na-
ture advantage of low out-of-band radiation, but also the
strong immunity to ISI and inter-carrier interference si-
multaneously. When the length of pulse shape is suitable
selected, while with moderate complexity increase. In
whole, OFDM/OQAM system outperforms the N-con-
tinuous OFDM system.
6. Acknowledgements
This work is supported in part by the National Science
Foundation of China under Grant number 61101101,
National Grand Special Science and Technology Project
of China under Grant No. 2010ZX03006-002-02,, Pro-
gram for New Century Excellent Talents in University of
China ((NCET110058), the Foundation Project of Na-
tional Key Laboratory of Science and Technology on
Communications under Grant 9140C020404120C0201,
and Key Laboratory of Universal Wireless Communica-
tions, Beijing university of Posts and Telecommunica-
tions, Ministry of Education, P.R.China (No. KFKT-
2012102).
REFERENCES
[1] J. van de Beek and F. Berggren, “N-continuous OFDM,”
IEEE Communications Letters, Vol. 13, No. 1, 2009, pp.
1-3. doi:10.1109/LCOMM.2009.081446
[2] B. Le Floch, M. Alard and C. Berrou, “Coded Orthogonal
Frequency Division Multiplex,” Proceedings of IEEE,
Vol. 83, 1995, pp. 982-996. doi:10.1109/5.387096
[3] P. Siohan and C. Roche. “Cosine-Modulated Filter-
banks Based on Extended Gaussian Function,” IEEE
Transactions on Signal Processing, Vol. 48, No. 11, 2000,
pp. 3052-3061. doi:10.1109/78.875463
[4] J. F. Du, S. Signell, “Time Frequency Localization of
Pulse Shaping Filters in OFD/OQAM Systems,” 6th In-
ternational Conference on Information, Communications
& Signal Processing, Dec. 2007.
[5] J. van de Beek and F. Berggren, “Out-of-band Power
Suppression in OFDM,” IEEE Communications Letters,
Vol. 12, No. 9, 2008, pp. 609-611.
doi:10.1109/LCOMM.2008.080587
[6] C. Roche and P. Siohan, “A Family of E xtende d Gaussia n
Functions with An Early Optimal Localization Property,”
First International Workshop Multi-Carrier
Spread-Spectrum, 1997, pp. 179-186.
doi:10.1007/978-1-4615-6231-3_21