Sidelobe Suppression in CR-OFDM system by Adding Extended Data Carriers

doi:10.4236/cn.2013.53B2060

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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

Email: [email protected].cn, [email protected]

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

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

,,..

. is data symbol

modulated on subcarrier k. Then in a CR-OFDM system,

symbols can be expressed in discrete-time as

()Dk

( )( )exp( 2)

()exp(),0,.. 1

kS s

dnDkjk f

jkn

Dkn N













(1)

where N is the size of inverse fast Fourier transform and

S is the set consisting of indexes of the data subcarriers.



is the frequency interval between system subcarriers

and

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

ff f



()( )exp(),0,...,1

dns

jnf

Em dnmM













 (2)

Combini ng (1 ) and (2), we ge t

()[( )exp()]exp()

0,..., 1

dnkS s

jnf

jkn

Em Dk













 f

(3)





-2



Figure 2. Illustration of the frequency domain representa-

tion of EDCs.

T. W. WEN, Y. F. WANG 329

For simplicity,

EPD (4)

where and [(0),(1),...( 1)]

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

ff f



)(cn

()()exp(),0,.. 1

jnf

cnCln N







 (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

()()exp(),0,...,1

cns

jnf

Em cnmM















(6)

Combini n g (5) and (6), we get

()[( )exp()]exp()

0,..., 1

NL l

cnl ss

jnf jnf

Em Cl













 t



(7)

For simplicity,

EPC (8)

where and

[(0),(1),...( 1)]

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

()exp(),

()

0, ,

jnk

cnk S

Ik N



















 (9)

Combini n g (5) and (9), we get



 (10)

where and

[(0), (1),..., (1)]T

cc cc

II IIN

[(0),CC



(1),..., (1)]T

CCL.

()

k is zero for kS



3.4. Optimization Problem with Constraint

()Cl should weight the EDC carriers to minimize the

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:





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

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/

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



, the improvement will be significant that

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

 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

 and its gain is

only -40dB which is worse than the 1

 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



interval is a little worse

than it. However, EDC with 1



interval experiences a

significant BER performance degradation at a high SNR.

At last, we find that the BER performance of EDC with

1/5

 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

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

-5

-4

-3

-2

-1

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

Normali z ed F requency

Norm alized P ower Spec trum Density(dB )

Tu r nin g Off

EDC

Figure 5. Comparison of normalized power spectrum den-

sity of the CR-OFDM signals with different sidelobe sup-

pression methods.

T. W. WEN, Y. F. WANG 331

0246810 12

-5

-4

-3

-2

-1

Eb/N0

BER

Tu r n in g Off

EDC

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

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

-4

-3

-2

-1

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.

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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