Communications and Network, 2013, 5, 327-332
http://dx.doi.org/10.4236/cn.2013.53B2060 Published Online September 2013 (http://www.scirp.org/journal/cn)
Sidelobe Suppression in CR-OFDM system by Adding
Extended Data Carriers
Tianwei Wen, Yafeng Wang
Wireless Theory & Technology lab (WT&T), Beijing University of Posts and Telecommunications, Beijing, China
Received July, 2013
ABSTRACT
Out-band radiation is a severe problem for Cognitive Radio with OFDM system (CR-OFDM) which is caused by the
sidelobe of OFDM signals. Lots of studies have been done on suppressing the sidelobe power and numerous methods
have been proposed. In this paper, we propose a novel method to minimize the sidelobe by adding extended data carrier
so called EDC to the original data carriers so as to protect primary user (PU) spectrum. Unlik e the methods before, the
EDCs are deployed within the secondary user (SU) data frequency spectrum to fully use the spectrum. Moreover, we
derive the linear least squares problem to get the optimal weighting factors of EDCs to minimize the sidelobe power
which is subject to an original data in terference constraint. By simulation, we find that EDC is more capable in sidelobe
suppression than method of Cancellation Carrier (CC) while EDC has only a small loss in BER performance.
Keywords: Cognitive Radio; Extended Data Carrier; OFDM; Sidelobe Suppression; Linear Least Square
1. Introduction
The wireless spectrum has been a scarce resource with
the development of wireless communication. However,
there are lots of spectrum holes in time-domain and
frequency-domain which means the licensed users’
utilization of spectrum is still very low according to the
reports by the Spectrum Policy Task Force (SPT) [1].
Recently Cognitive Radio (CR) has attracted more and
more attention in improving the utilization of spectrum.
CR system based on OFDM divides the whole spectrum
into many small spectral bands which have equal interval
between each other. The licensed users or primary users
(PUs) will use one or more bands to transmit its services.
And the temporarily unused bands which are called white
holes can be detected and used by the unlicensed users or
secondary users (SUs). That’s the reason why CR can
use the spectral resources more effectively [2]. However
the OFDM signal has a drawback in high out-of-band
sidelobe power which can bring a great interference to
PUs and then cause PU’s performance degradation. So
we have to suppress SU’s sidelobe sufficiently.
Several techniques have been proposed to suppress the
sidelobe of OFDM symbols. Generally we will turn off
some subcarriers at both ends of SU’s spectral bands to
create a Guard Band to protect PU’s transmission from
SU’s sidelobe interference [3]. However this method
does not fully use the spectrum resources and its ability
of sidelobe suppression is so limited. Windowing the
transmitted signals in time-domain [4] and multiplying
the signals with a shaping filter in frequency-domain [5]
may bring huge complexity. Multiplying signals with a
shaping filter equals to a convolution in time-domain
which brings the interference between OFDM symbols.
Furthermore, some techniques which do not use the
symbol processing are proposed such as additive signals
(AS) [6] and subcarriers weighting (SW) [7]. They are
useful in reducing the sidelobe power. However, SW
cannot be applied to the OFDM system with QAM
modulation because the demodulation of QAM is
sensitive to the amplitude of received signals which can
be seriously affected by the weighted factors.
The cancellation carrier method so called CC is
mentioned in [8,9]. Key point of CC is to insert some
subcarriers to the Guard Band located at both ends of the
used OFDM spectrum. They are not designed to transmit
data but used to carry complex weighted factors to offset
the sidelobe power of transmitted data signals which will
create a clean and clear spectrum notch at the PU’s
spectrum.
CC might be a useful method but we are embarrassed
by the quantity and accuracy of CCs. Because the Guard
Band is always too narrow and CCs are only a few
subcarriers located within the Guard Band and their
interval is same to OFDM system’s subcarrier interval.
So the effect of sidelobe suppression will be very limited
and that will not be sufficient. Based on the considerations
mentioned above, we propose a novel method which is
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T. W. WEN, Y. F. WANG
328
called extended data carrier (EDC) to suppress the
sidelobe sufficiently.
With the EDC method, we will deploy the extended
data carriers over the whole used OFDM spectrum and
also over the Guard Band. When EDC’s interval is equal
to OFDM system’s interval, it’s possible to cause a
severe interference to the original data carriers. On
account of this, we will use the EDC with different
intervals. Then there will be a relatively large number of
cancellation carriers and they can change their own
weighted factors to minimize the sidelobe more precisely
so as to get a better suppression effect.
Because of the different intervals, we cannot calculate
the interference using the CC method mentioned in [8,9].
The weighted subcarriers of EDCs should be transformed
into additive signals in time-domain using the way
mentioned in [10-11].
This paper is organized as follows: Section 2 describes
the principle of extended data carriers. Section 3 shows
the optimal problem in deriving the weighted factors.
Section 4 gives simulation and results. Finally conclud-
ing remarks are made in Section 5.
2. Principle of Extended Data Carrier
As mentioned above, EDC signals will be transformed
into time-domain form because there are no closer fre-
quency points in frequency-domain for CR-OFDM sys-
tem. So we cannot operate in the way mentioned in [8,9]
to get a superposition of each subcarrier’s spectrum. The
detailed process is shown in Figure 1.
Binary data will be generated and experience Digital
Modulation such as QPSK, 8PSK, 16QAM to get a string
of complex data . By S/P conversion, the serial
data will be converted into parallel data of N indexes
where N is the size of Fourier transform. Then EDC
module will use each set of N points called an OFDM
symbol to calculate an optimal value of EDCs’ weighted
factors.
()Dn
Calculation of optimal EDCs’ weigh ted factors will be
under the principle of minimizing the sidelobe power of
SU and not causing severe transmission performance
degradation. Then the weighted factors will be used to
generate the time-domain cancellation signals .
IFFT will transform into N length time-domain
signals which are then converted into serial data
()cn
()dn
()Dn
Figure 1. Illustration of CR-OFDM system with EDC.
by P/S conversion. So the finally transmitted data
will be the sum of original Tx signals and cancel-
lation signals . ’s sidelobe power spectrum
density is wished to be low enough to protect the PU
spectrum.
()tn
()dn
()cn ()tn
3. The Optimal Extended Data Carrier with
Original Data Interference Constraint
Unlike the CCs mentioned in [8,9] which are just em-
ployed at both ends of data carriers, the extended data
carriers are illustrated in Figure 2. EDCs are employed
over the whole data spectrum band and the Guard Band
and they do not occupy PU’s frequency when the latter is
in the name of Optimization range here.
3.1. Sidelobes of Data Carriers
The frequencies of data signals consisting of K subcarri-
ers are donated by 01 1 ,,..
K
x
xx
. is data symbol
modulated on subcarrier k. Then in a CR-OFDM system,
symbols can be expressed in discrete-time as
()Dk
1
( )( )exp( 2)
12
()exp(),0,.. 1
kS s
kS
n
dnDkjk f
Nf
jkn
Dkn N
NN









(1)
where N is the size of inverse fast Fourier transform and
S is the set consisting of indexes of the data subcarriers.
f

is the frequency interval between system subcarriers
and
s
f
is the sample frequency of data. Thus is
zero forkS ()Dk

.
What we want to observe is the sidelobe power on the
optimization range. If we take M frequency points
01 1
as the sample points at optimization
range band, the sum of the sidelobe’s sampled energy is
{ ,,...,}
tt t
M
ff f

1
0
2
()( )exp(),0,...,1
t
Nm
dns
jnf
Em dnmM
f






 (2)
Combini ng (1 ) and (2), we ge t
1
0
2 12
()[( )exp()]exp()
0,..., 1
t
Nm
dnkS s
jnf jkn
Em Dk
NN
mM
 





 f
(3)
0t
f
t
m
f
1
t
m
f

1
t
M
f

0c
f
1c
f
-2
c
L
f
1
c
L
f

0
x
1
x
1K
x

2K
x

Figure 2. Illustration of the frequency domain representa-
tion of EDCs.

T. W. WEN, Y. F. WANG 329
For simplicity,
dd
EPD (4)
where and [(0),(1),...( 1)]
T
dd dd
EE EEM[(0),DD

. (1),.., (1)]T DDN
3.2. Sidelobes of Extended Data Carriers
For EDCs, is their weighted factor and their L
frequency points are donated by 011 . The
sidelobe suppression signals is expres sed as
()Cl { ,,...,}
ccc
L
ff f

)(cn
1
0
2 1
()()exp(),0,.. 1
c
Ll
ls
jnf
cnCln N
Nf




 (5)
Then the transmit ted signals at the sending end will be
. To calculate , should be
derived firstly. Similarly, we will observe extended data
signals’ sidelobe power in optimization range and the
sum of ’s sampled energy in optimization range is
()() ()tndn cn
()cn
()cn ()Cl
1
0
2
()()exp(),0,...,1
t
Nm
cns
jnf
Em cnmM
f






 (6)
Combini n g (5) and (6), we get
11
00
22 1
()[( )exp()]exp()
0,..., 1
c
NL l
cnl ss
jnf jnf
Em Cl
Nf
mM






 t
m
f

(7)
For simplicity,
cc
EPC (8)
where and
[(0),(1),...( 1)]
T
cc cc
EE EEM
[(0),CC(1),..., (1)]T CCL.
3.3. Interference to Original Data Carriers
Unlike the sidelobe interference to data carriers by CCs
who are deployed out of the data spectrum band, EDCs
are just deployed within it and their interference to
original data carriers will be direct and severe. Especially,
when EDCs’ interval is same to that of OFDM system,
the EDC will directly change the magnitude of data
carriers and lead to severe performance degradation. So
we have to take this interference into account and we will
minimize the interference while minimizing the data
carriers’ sidelobe power.
Based on the assumptions mentioned in section 3.1
and 3.2, we derive the expression of interference that
EDCs impose on the data carriers as
1
0
2
()exp(),
()
0, ,
N
n
c
jnk
cnk S
Ik N
kS



 




 (9)
Combini n g (5) and (9), we get
ci
I
PC

 (10)
where and [(0), (1),..., (1)]T
cc cc
II IIN
[(0),CC

(1),..., (1)]T CCL.
()
c
I
k is zero for kS

.
3.4. Optimization Problem with Constraint
()Cl should weight the EDC carriers to minimize the
2
dc
EE so as to suppress the sidelobe in the optimi-
zation range sufficiently. Meanwhile EDCs’ interference
should be constrained to protect the original data trans-
mission. Then the optimization can be formulated as a
linear least square problem with a constraint:


22
min dc c
CEE I
  (11)
The constraint

indicates the emphasis on the
protection of original data and it’s actually a tradeoff
between the sidelobe power and the interference caused
by EDCs. Solutions to the linear least square problem
can be found in [12,13].
To solve the formula (11), we have to combine (4) and
(8). For each CR-OFDM symbol, data will gen-
erate d and it’s easy to get a solution to the weighted
factors of EDCs when , and is calculated in
advance.
()Dk
E
d
Pc Pi P
4. Simulation and Results
In our simulation, we assume a secondary user of
CR-OFDM system with NS=10 subcarriers and a N=64
FFT applied for OFDM modulation. To observe the
sidelobe distinctly, SU’s normalized frequency points are
located in the middle of system frequency points and
they are [28:37] respectively. Considering the narrow
Guard Band, here we assume EDCs’ range is [26:39],
and the interval b etween EDCs will be 1/
K
where K is
integer and we assume K = 1,3,5. The optimization range
will be the zone out of the EDC’s range and we set the
sample point interval asof system normalized
frequency point which is 1 actually.
1/10
For the OFDM system, we generate 1000000 bits data
source to experience a QPSK modulation and then go
through an AWGN channel.
Figure 3 exhibits the normalized power spectrum of
transmitted signals using different subcarrier intervals of
EDC while using the curve line of Turning Off the sub-
carriers at PU spectrum range as a baseline.
It’s obvious that simply turning off the subcarriers
which are out of SU’s band will cause an average
sidelobe of -20dB at the optimization range and that’s a
considerable interference to the PU. That is far from
satisfactory of protection of PU. When the interval of
EDCs is 1
f

, the improvement will be significant that
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T. W. WEN, Y. F. WANG
330
the sidelobe power is suppressed by about 45 dB. The
interference is reduced greatly, which ensures a protection
to PU to some degree. Much greater improvement is
gained by EDCs when their interval is much closer such
as 1/3
f
 and the gains are -52 dB. To some degree,
with the number of inserted carriers increasing, there will
be much more choice for their weighted factors from the
process of solving the optimal linear least square problem.
However, the sidelobe suppression effect worsens
dramatically when the interval is 1/5
f
 and its gain is
only -40dB which is worse than the 1
f
 interval. It’s
also easy to understand that phenomenon because with
the subcarriers interval decreasing and the number of
subcarriers increasing, the interference to the data
carriers will be harder and harder to eliminate.
BER performance is an important evaluation indicator
for a method’s value. Figure 4 shows the difference of
BER performance using different subcarrier intervals of
EDC while using the curve line of Turning Off the sub-
carriers at PU spectrum range as a baseline.
Apparently, the BER performance of Turning off is the
best and that of EDC with 1/3
f

interval is a little worse
than it. However, EDC with 1
f

interval experiences a
significant BER performance degradation at a high SNR.
At last, we find that the BER performance of EDC with
1/5
f
 interval is so terrible that the system almost
cannot work normally. The reasons explaining the result
of sidelobe suppression can also be used to explain the
BER result.
From the results mentioned above, we can obtain that
lessening the interval of EDCs properly can significantly
improve both the sidelobe suppression performance and
BER performance. That benefits from the increasing of
quantity of subcarriers and accuracy of operations which
010 20 30 4050 60
-70
-60
-50
-40
-30
-20
-10
0
10
Normal i ze d Frequ enc y
Norm alized P ower S pect rum Dens ity (dB)
Turning Off
EDC-1
EDC-1/3
EDC-1/5
Figure 3. Comparison of normalized power spectrum den-
sity of the CR-OFDM signals with EDC of different inter-
vals.
means more fine and smooth operations on eliminating
the interference both to data carriers and to the PU spec-
trum. However, neither too large interval nor too small
interval will get a high system performance.
Then we would like to compare the performance of
CR-OFDM with different methods of sidelobe suppres-
sion. When we compare the performance of EDC with
CC method, we can see from Figure 5 that the former’s
sidelobe suppression ability is much stronger than that of
latter with about 10dB gain.
Furthermore, both their BER performance are
acceptable although the EDC has a little disadvantage in
BER performance than CC which is shown in Figure 6.
Because of the narrow Guard Band, the CCs’ location
range will be very limited and that may explain the
weaker ability of sidelobe suppression.
0246810 1
2
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/N0
BER
Turning Off
EDC-1
EDC-1/3
EDC-1/5
Figure 4. Comparison of BER performance of CR-OFDM
system with EDC of different intervals.
010 20 30 40 50 60
-60
-50
-40
-30
-20
-10
0
Normali z ed F requency
Norm alized P ower Spec trum Density(dB )
Tu r nin g Off
EDC
CC
Figure 5. Comparison of normalized power spectrum den-
sity of the CR-OFDM signals with different sidelobe sup-
pression methods.
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T. W. WEN, Y. F. WANG 331
0246810 12
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Eb/N0
BER
Tu r n in g Off
EDC
CC
Figure 6. Comparison of BER performance of CR-OFDM
system with different sidelobe suppression methods.
Next we research the effect of constraint variable

in the linear least square problem where

is used to
constrain EDCs’ interfe rence to the original data.
As we can expect, the result is shown in Figure 7.
With the d ecreme nt of

, effect of sidelobe suppression
is becoming better. And the best of them has an almost
-90dB gain at the optimization range which is so terrific
and exciting.
Lager

means a more strict constraint on their
transmission power and data carrier amplitudes. So the
suppression effect will be constrained to a large extent
which brings the decrement on the suppression perform-
ance.
On the other hand, the difference between their BER
performances is also apparent while the followed rule is
just opposite to the former which is shown in Figure 8.
With the decremen t of

, BER performance gets worse
and worse. What the BER performance of 0.0000005


can tell is that the interference to the original data under
this constraint is so serious that its excellent sidelobe
suppression ability is already meaningless. That will be a
bad choice for CR-OF DM sys tem.
5. Conclusions
Inspired by the method of Cancellation Carriers for
sidelobe suppression, we propose an improved method
called Extended Data Carriers which are deployed in the
SU spectrum. We analyze the interference of original
transmitted data signals and the interference of EDCs’ in
the optimization range. Also we analyze the EDCs’
interference to the original transmitted data. Then we
derive the formulation of each kind of interference using
the matrix form.
010 20 30 40 50 60
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Normal ized Frequency
Normal ize d P ower Spec t rum De nsi ty (dB )
u=0 .000 0005
u=0 .000 5
u=0 .5
Figure 7. Comparison of normalized power spectrum den-
sity of CR-OFDM signals with EDC under different

con-
straints.
012 345678910
10
-4
10
-3
10
-2
10
-1
10
0
Eb/N0
BER
u=0 .00000 05
u=0 ,0005
u=0 .5
Figure 8. Comparison of BER performance of CR-OFDM
signals with EDC under different

constraints.
Combining them, we get the sum of interference what
SUs act on PUs. To derive the weighted factors of EDCs,
we describe the summation as a linear least square
problem which is subject to an original data interference
constraint and solve it.
Then we investigate the difference in normalized
power spectrum density and BER for different sidelobe
suppression methods. We can say that EDCs with a proper
narrow interval can suppress sidelobe more significantly
than just turning off carriers or CC. Furthermore, different
carrier intervals will have different impa cts on t he s yste m
performance. Neither too loose nor too close will give
sufficient sidelobe suppression effect. Moreover, for the
original data interference we emphasize, the higher its
proportion in our formula is, the better system’s BER
performance we will get while the weaker its sidelobe
suppression ability will be.
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T. W. WEN, Y. F. WANG
332
In the next, we will combine some mature methods
such as windowing in time-domain and filtering in fre-
quency-domain with our EDC methods and wish to reach
a more excellent system performance.
6. Acknowledgements
This paper is supported by National Key Technology
R&D Program of China (Research on Cognitive Radio in
TD-LTE System) under grant No. 2012Z X 03003006.
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