Reduction of out of band radiation in NonContiguous OFDM based cognitive radio
system using heuristic techniques
Atif Elahi1, Ijaz Mansoor Qureshi2, Fawad Zaman3, Fahad Munir1
Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan.
2
Department of Electrical Engineering, Air University, Islamabad, Pakistan.
3
Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock,
Pakistan.
Email: {atif.phdee40, fahad.munir}@iiu.edu.pk
imqureshi@mail.au.edu.pk
fawad@ciit-attock.edu.pk
1
The purpose of cognitive radio (CR) is to defend the transmission of licensed (primary) user in the
presence of unlicensed (cognitive) users within the same spectral vicinity. Non-contiguous
orthogonal frequency division multiplexing (NC-OFDM) is a favorable and practical methodology
of attaining wireless data transmission which is spectrally dexterous. It portrays an effective
approach for Cognitive users (CU’s) to access patchy spectral openings. One of the major
drawbacks of NC-OFDM is interference to the neighboring wireless channels due to the high
sidelobes. This paper highlights perspective approaches i.e. Genetic algorithm (GA) and
Differential evolution (DE) for the sidelobe power reduction of NC-OFDM signals. The proposed
algorithms estimate the levels of cancellation carriers (CCs) to reduce the out of band radiation
(OOB) emissions. The fitness function is based on linear least square error which requires single
snapshot. The cogency and usefulness of the proposed schemes are verified extensively through
Monte Carlo simulations. The results are compared with the Brandes CC and Ahmed selim
Advance cancellation carrier (ACC), Ahmed selim Advance Subcarrier weighting (ASW)
technique. The proposed scheme produces competitive results and significantly reduces the
sidelobe levels.
Keywords: Cognitive radio, Differential Evolution, Genetic Algorithm, Non-Contiguous OFDM.
1. INTRODUCTION
1
In today’s modern and advanced era, cognitive radio is one of the hot areas of research which has
direct applications in mobile communication [1-3]. The theory of cognitive radio (CR) involves
accessing spectral resources opportunistically and dynamically that might be present at a specific
time and location. These spectral resources are called spectral white spaces [4]. These can be non
– contiguous spectral bands of altered width. The position of these spectral white spaces can
change dynamically with time as the licensed user (Primary users – PU’s) enters or leave from a
given location. A considerable amount of research has been carried out for finding an appropriate
technology, capable of utilizing the vacant spectrums adaptively and to support the secondary user
transmission effectively. The secondary user (SU) must have an ability of molding its transmission
to make the best use of vacant spectrums, while at the same time do not interrupt the primary user
transmission [5, 6]. One of the suitable contenders for the above mentioned performance is Non–
contiguous Orthogonal frequency division multiplexing (NC-OFDM), which is based on the
renowned orthogonal frequency division multiplexing (OFDM) transmission scheme. A prominent
feature of NC-OFDM is its capability of deactivating or nulling subcarriers that are in use of PU’s
for the coexistence with PU’s, whereas idle subcarriers are used by the SU’s. In spite of the above
feature, it has some technical concerns that should be ameliorate to make such type of wireless
transmission a feasible option in Dynamic spectrum access (DSA) environment. One of the
concerns is that such a system experiences out of band radiation (OOB) because of high sidelobes
of the modulated subcarriers. They may result in a detrimental interference to the nearby PUs
frequency band.
In literature several approaches have been investigated for a reduction of sidelobes which can be
categorized into frequency and time domain approaches. Time domain approaches include
adaptive symbol transition [1] and windowing [2], while frequency domain approaches includes
insertion of guard band [1], constellation expansion [3], subcarrier weighting [4], multiple choice
sequence [5], adaptive symbol method [6], insertion of cancellation carriers [7,8], advance
cancellation carriers (ACC) [16] and advance subcarrier weighting (ASW) [17]. Some of these
approaches entail execution of complex optimization for each OFDM symbol, some of them as [3,
5] require the calculation of OOB emissions many times for each OFDM symbol and recently used
approaches [16, 17] uses heuristic approach and involve few computations as compared to the
other approaches for the reduction of OOB emission . The importance of GA and DE in today’s
research is well known. The success, reliability and efficiency of these approaches is beyond doubt
2
for optimization problems. These are a specific class of evolutionary algorithms that use
techniques motivated by the evolutionary biology such as inheritance, mutation, selection and
cross over.
This paper addresses the reduction of sidelobe power in NC-OFDM signals using GA and DE.
These are the searching techniques that are employed for finding the best result from large solution
spaces. For the reduction of the OOB emissions of an NC-OFDM transmission, the amplitude of
cancellation carriers (CCs) is to be determined with the help of GA and DE. These signals do not
carry any data and are planned to minimize the OOB radiation when added to the original
transmitted signal. Though, with this approach, there is a small loss in signal to noise ratio (SNR),
and slightly increased peak to mean power ratio (PMPR) which is caused by the fact that a
specified amount of transmission power is lost. In this work, the Performance of the proposed GA
and DE techniques are compared with the already existing Traditional method have been presented
via simulations.
The rest of the paper is organized as follows: Section 2 describes data model about the concept of
cancellation carriers, Section 3 discusses the proposed methodology, Section 4 and 5 are dedicated
for Simulations results and conclusion respectively.
2. DATA MODEL
Let us consider an NC – OFDM system having a total of Ns subcarriers, out of which N subcarriers
are used by Nc Cognitive users carrying input data that are modulated with Quadrature amplitude
modulation (QAM) or Phase shift keying (PSK) cn  c  [c1, c2 ,..., cN ]T while Ns – N subcarriers
that are leftover are not used for data transmission, but acting as a guard carriers. As an alternative
of guard carriers is to insert some CC’s on the either sides of each cognitive user as shown in fig.1
[3]. These carriers are not used for data transmission, but carries complex weights (amplitudes of
main lobe of cancellation carriers) a j  a  [a1 , a2 ,..., aM ]T and these weights are so adjusted that
the sidelobes of CC’s cancels the sidelobes of the original transmitted signal Tx In specific defined
region called as optimization range.
Finally the transmitted signal Ts consists of N data carriers and M CC’s given as [7, 8].
3
s  P[w1, w2 ,..., wM , c1, c2 ,..., cN , wM ,..., wM ]
2
2
(1)
1
Where √𝑃 The normalization factor0 < 𝑃 ≤ 1 is introduced to keep the power level of the
transmitted signal Ts with CC’s same as it was without the CC’s.
i.e. s
2
2
 c is given as.
P
c
2
2
c  w
2
1
(2)
Fig 1.Concept of CCs: Insertion of CCs at both sides of the used spectrum.
The transmitted signal Ts of each cognitive radio is then modulated with N + M ≤ Ns subcarriers
using inverse fast Fourier transformation (IFFT) following parallel to serial conversion, resulting
in time domain signal protracted by guard interval in the form of cyclic prefix exceeding the delay
spread of the multipath channel. In order to perform the sidelobe suppression each CC is
multiplied by some specific complex weighting factor wm, m = 1,2,…,M that are determined such
that the amplitude of sidelobe of the weighted CCs equals to the amplitude of the sidelobe of the
original transmitted signal Tx when added results in suppression of sidelobes of the transmitted
signal. Such an optimization can be formulated as a linear least squares problem [7, 8].
4
2
min  Su  Dw subject to w  
2
(3)
w
Where D  [d1 , d 2 ,..., d M ] is a matrix of dimension K × M, where K is the number of samples on
the either side of the data subcarriers, dm contains the samples of spectrum of the mth CC in the
optimization range, w contains weights of the CCs that have to be optimized, S  [s1 , s 2 ,..., s N ] is
also a matrix of dimension 𝐾 × 𝑁 with sn contains the samples of spectrum of the nth data carrier
in the optimization range and 𝒖is a vector contains the weights of each data carrier. The constraint
given in the above equation bounds the power of the CC’s to β such that CC’s do not affect the
power of the transmitted signal too much. Solution to such linear least square problem with
quadratic inequalities can be found in [14, 15].
The spectrum of the original transmitted signal and CC’s have to be calculated for optimization
and we are exploiting the fact that the rectangular shaping filter is applied implicitly in time
domain. The spectral shape of the transmitted signal is obtained by Fourier transform of the time
domain rectangular window which is equal to the sinc function defined as sin c(x) 
sin x
. The
x
spectrum W(f) of the nth subcarrier is a sinc pulse modulated with data symbol cn and is shifted to
the respected subcarrier frequency fn.
Wn ( f )  cn sin c( ( f  f n )To )
(4)
Where f denote the frequency, fn is the center frequency of the nth subcarrier, To is the OFDM
symbol duration and (f – fn) denotes the normalized center frequency of the nth subcarrier. In this
paper our goal is to estimate weights (amplitudes of the main lobe of cancellation carriers)
a j  a  [a1 , a2 ,..., aM ]T by using GA, and DE and its comparison with the Brandes CC technique,
Ahmed selim ACC technique and Ahmed selim ASW techniques.
3. PROPOSED METHODOLOGIES
This section comprises of a brief introduction, flow diagram and parameters settings that have been
used for the estimation of the weights of CC’s for GA and DE [9 – 12].
5
(a) GA: GA is a feature selection algorithms devised on the process of natural genetics and natural
selection. This approach randomly hunts for the finest characteristics from the search space
provided to it, which is done on the basis of fitness function, used to discover the best fit, within
the search space. This function is assessed at each distinct search point in the population over a
number of generations until a configuration is found that meets the desired objective. Although
GA is comparatively slow as compared to the other recursive and deterministic methods such as
LMS, RLS etc but GA has inherently high stochastic nature due to which it can handle effectively
very difficult optimization problem with rough surfaces. It is considered as the most reliable,
efficient search algorithm and simple too. Fig 2 [9 – 12] shows the cycle of GA, the procedural
steps of GA are as follows.
Step I: (Initialization) Generate N number of candidate solutions (Chromosomes) randomly, each
candidate solution has M number of genes. Where each gene represents the weights (amplitude)
of each cancellation carrier that we are using on the left and right side of data subcarriers.
Mathematically the jth candidate solution is given as:
a  [a1 , a2 ,..., aM ]
(5)
Here aj ϵ R: Lb ≤ aj ≤ Ub, Where Lb denotes the lower bound and Ub denotes the upper bound of
the weights (amplitudes) of the cancellation carrier and for all j= 1,2,3,…, M.
Step II: (Fitness Evaluation) Determine the fitness of each individual (Chromosome) in the
current population, sort these individuals in the descending order of their fitness, (the one with the
highest fitness at the top and the one with the lowest fitness at the bottom).Our fitness function
derived from equation (3) for the jth Chromosome is given as:
E j  EDj  ECj
E
1
K 1
K
j 0
 Ej
(6)
(7)
Where K is the total number of sample points taken on the left and right side of the data
subcarriers.
N 1
EDj   ED (i , j )
i 0
6
(8)
M
2
1
M 1
(9)
ECj   EC (i , j ) ai   EC (i , j ) ai
i 0
i
M
2
Equation (8) shows the sum of the amplitudes of ith data carrier at jth sample point and in equation
(9) EC(i,j) shows the amplitudes of ith left and ith right cancellation carriers at jth sample point and 𝑎𝑖
shows the amplitudes of main lobe of ith left and ith right cancellation carrier.
Step III: (Selection of parents and production of offspring) Those chromosomes that are sorted
in descending order are parents to the next generation, they will be produced with a probability
proportional to their fitness. This production is via cross over (single point cross over, multiple
point cross over). The parents with the higher fitness could produce more children and the one
with lower fitness could produce lesser number of children. In this there could be two approaches.
1. Select the parents with a probability indirect proportion to their fitness value and let them
produce.
2. Use roulette wheel method, the angle of sector is directly proportional to the fitness. The
sector with a bigger angle has more chance to win as preferential parent.
Step IV: (Populating the new generation) New population is generated by using three methods
Generational replacement, Elitism and but the suggested method is survival of the fitness approach.
Step V: (Mutation) If there is no improvement in fitness in the new generation or the problem is
converging very fast or steady state is reached very early, then mutation is one solution to this
problem. Mutation is done for a gene in chromosome. Probability of mutation is very low, could
be as low as in one thousand for any particular gene.
Step VI: (Stoppage/Termination criteria) Program for GA will stop, if the total numbers of
iteration/flights are executed for the algorithm or the pre-defined value of MSE is achieved
whichever is earlier set to be 1000 and 10-7 respectively.
(b)DE. DE is a heuristic approach that is based on GA or Particle swarm optimization (PSO)
algorithms. The flow chart of DE is shown in Fig 3, while the steps of algorithm are given as [13]:
Step 1: (initialization) The first step of DE is the initialization of randomly generated population
of N vectors.
7
snd,G  L  rand (H L)
(10)
Where 1 ≤ n ≤ N, 1 ≤ d ≤ D
Here n = Chromosome number, d = Gene number, G = Generation number, H = Upper
limit, L = Lower limit.
Step 2: Upgrade all the chromosomes of the current generation “G”. Let us choose nth chromosome
snd,G .
I). Mutation: Select three numbers (r1, r2, r3) from the population having constraint that they are
all distinct and also not equal to n.
und,G  sr ,G  F (sr ,G  sr ,G )
1
2
3
Fig 2. Flow chart for Genetic Algorithm
8
(11)
Where F is called as mutation factor, it is problem dependent and it should be smartly placed
keeping the value of genes between L and H. and u nd ,G is called as mutant vector.
II). Cross over: Here the mutant vector and the current generation members are allowed to cross
over to create another population as:
n ,G

u
w nd,G   nd,G

 sd
if
rand ()  Cr (or) J  J rand
(12)
Otherwise
Where Cr = cross over rate is normally taken near to 0.5 either above or below.
III). Selection Operation:
 w n ,G
s n,G 1   n,G
s
if
f (w
n ,G
)  f (s
n ,G
)
(13)
Otherwise
Step 3:
If f (s n,G 1 )  E
then Stop
else if the required number of generation has reached
Stop
else Go to Step 2.
9
(14)
Start
Initialize
Population
Update the Generation
Calculate the next
Generation
Mutation
No
Cross Over
Stop
Selection
Best Individual
Yes
Termination Criteria
Fig 3. Flow diagram of Differential Evolution
4. SIMULATIONS AND RESULTS
In this section the accuracy and reliability of GA and DE are discussed for the calculation of
weights (amplitudes) of main lobe of CC’s and comparing these results with the Brandes CC and
Ahmed selim CC, Ahmed selim ASW techniques . Equal number of CC’s are used on both sides
of the cognitive radio in order to suppress the sidelobes in the optimization range. Several cases
are discussed on the basis of number of spectral white spaces, its band width and band width
between these spectral white spaces. A MATLAB built-in toolbox “optimization of population"
based algorithm is used having the setting shown in Table 1 and a MATLAB version R2012b
(8.0.0.783).
10
4.1 Case I
In this case we are considering interference suppression spectrum sharing scenario in NC – OFDM
having equal bandwidth between the spectral white spaces II, IV, VI and VIII i.e. locations I, III,
V, VII and IX have equal bandwidth while locations II, IV, VI and VIII are also have equal
bandwidth having 32 subcarriers each. In order to not to interfere with the PU’s two CC’s on the
either side of the locations II, IV, VI and VIII are inserted. So 𝑁 = 32 data subcarriers and 𝑀 = 4
cancellation carriers are there in each location II, IV, VI and VIII.
Table 1. Parameter setting for GA.
GA
Parameters
Settings
Population size
240
No. of generations
1000
Migration direction
Both way
Cross over fraction
0.2
Cross over
Heuristic
Function tolerance
1e-6
Initial range
[0,1]
Scaling function
Rank
Selection
Stochastic uniform
Elite count
2
Mutation function
Adaptive feasible
The Optimization range for the calculation of weights spans the sidelobes in the locations I, III, V,
VII and IX, here we have taken 10 samples per sidelobes to keep the computational complexity
low. Fig 4 and Fig 5 shows the normalized power spectral density of the NC – OFDM signal
modulated with symbol cn = 1 on all data subcarriers. The weights that are optimized according to
Brandes CC, Ahmed selim technique, according to GA and DE without constraints are given in
Table 2.
Table 2. Weights of left and right cancellation carriers estimated via TM, GA and DE
11
Technique
Technique
Ahmed selim
DE
GA
Brandes
Weights of left and right cancellation carriers
g1
g2
g3
g4
Region II
0.097389646
0.565982392
0.563872468
0.09577352
Region IV
0.101642877
0.572094857
0.571412847
0.101117628
Region VI
0.096936313
0.565667338
0.566257592
0.097435632
Region VIII
0.099804045
0.569352285
0.562955386
0.094859683
Region II
0.138865777
0.630490598
0.630490598
0.138865777
Region IV
0.138865777
0.630490598
0.630490598
0.138865777
Region VI
0.138865777
0.630490598
0.630490598
0.138865777
Region VIII
0.138865777
0.630490598
0.630490598
0.138865777
Region II
0.137106473
0.629719568
0.629719568
0.137106473
Region IV
0.137677839
0.629686074
0.629686074
0.137677839
Region VI
0.137677839
0.629686074
0.629686074
0.137677839
Region VIII
0.137106473
0.629719568
0.629719568
0.137106473
Region II
0.329931554
0.024064869
0.326312669
0.025179360
Region IV
0.335296926
0.022352001
0.334408187
0.022640844
Region VI
0.327343628
0.024865137
0.328947328
0.024371174
Region VIII
0.332960730
0.023106880
0.384316408
0.056289423
Suppression of side lobe powers levels at locations I, III, V, VII and IX with and without CC’s
Brandes technique, CC’s Ahmed selim technique, ASW’s Ahmed selim technique, GA and DE
are given in Table 3, which shows that significant reduction of sidelobe power levels is achieved
by GA and DE.
12
20
Normalized power spectral density (dB)
0
I
II
III
IV
V
VI
VII
IX
VIII
-20
-40
-60
-80
-100
original
2 CC B technique
2 CC GA
2 CC DE
-120
-140
0
100
200
300
Normalized frequency (Hz)
400
500
Fig 4. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 32 data
subcarriers and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII, cn=1,
n =1, 2… N.
20
Normalized power spectral density (dB)
0
I
II
III
V
IV
VI
VII
VIII
IX
-20
-40
-60
-80
-100
original
2 CC AS technique
ASW AS technique
2 CC GA
2 CC DE
-120
-140
0
100
200
300
Normalized frequency (Hz)
400
500
Fig. 5 Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 32 data
subcarriers and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII, cn=1,
n =1, 2… N.
13
Table 3. Sidelobe power suppression with different techniques
Sidelobe power in Locations
I
III
V
VII
IX
W / O CCs
-33dB
-28dB
-28dB
-28dB
-33dB
WCCs Brandes Technique
-47dB
-42dB
-42dB
-42dB
-47dB
WCCs GA
-59dB
-57dB
-57dB
-57dB
-59dB
WCCs DE
-80dB
-70dB
-70dB
-70dB
-80dB
WCC’s Ahmed selim Technique
-38dB
-33dB
-33dB
-33dB
-44dB
WSW Ahmed selim Technique
-45dB
-38dB
-38dB
-38dB
-45dB
4.2 Case II
In this case we are considering interference suppression spectrum sharing scenario in NC – OFDM
having unequal bandwidth between the spectral white spaces II, IV, VI and VIII are un equal i.e.
locations I, III, V, VII and IX have an un-equal bandwidth while locations II, IV, VI and VIII are
have equal bandwidth having 32 subcarriers each. In order to not to interfere with the PU’s two
CC’s on either side of the location II, IV, VI and VIII are inserted. So 𝑁 = 32 data subcarriers and
𝑀 = 4 CC’s are there in each location II, IV, VI and VIII. The Optimization range for the
calculation of weights spans the sidelobes in the location I, III, V, VII and IX, here we have taken
10 samples per sidelobes to keep the computational complexity low. Fig 6 and Fig 7 shows the
normalized power spectral density of the NC – OFDM signal modulated with symbol cn = 1 on all
data subcarriers. The weights that are optimized according to the Brandes technique, Ahmed selim
technique, GA and DE without constraints are given in Table 4.
Table 4. Weights of left and right cancellation carriers estimated via TM, GA and DE
Technique
Brandes
Weights of left and right sided cancellation carriers
g1
g2
g3
g4
Region II
0.09768205
0.566598076
0.565423456
0.096746511
Region IV
0.095833433
0.564201615
0.567176241
0.098212031
Region VI
0.099911314
0.569491578
0.562817426
0.094754733
Region VIII
0.096812768
0.56537614
0.565712937
0.097058616
14
GA
Technique
DE
Ahmed selim
Region II
0.138865777
0.630490598
0.138865777
0.630490598
Region IV
0.138865777
0.630490598
0.138865777
0.630490598
Region VI
0.138865777
0.630490598
0.138865777
0.630490598
Region VIII
0.138865777
0.630490598
0.138865777
0.630490598
Region II
0.137106473
0.629719568
0.629719568
0.137106473
Region IV
0.137106473
0.629719568
0.629719568
0.137106473
Region VI
0.137106473
0.629719568
0.629719568
0.137106473
Region VIII
0.137106473
0.629719568
0.629719568
0.137106473
Region II
0.329344490
0.024247861
0.326932041
0.024990894
Region IV
0.325046670
0.025561691
0.331093421
0.023700165
Region VI
0.333149752
0.023046327
0.322665432
0.026270394
Region VIII
0.327948797
0.024679480
0.328352857
0.024555019
Suppression of side lobe powers levels at locations I, III, V, VII and IX with and without CC’s
Brandes technique, CC’s Ahmed selim technique, SW’s Brandes technique, ASW Ahmed selim
technique, GA and DE are given in Table 5, which shows that significant reduction of sidelobe
power levels is achieved by GA and DE.
20
Normalized power spectral density (dB)
0
I
III
II
V
IV
VI
VII
VIII
-20
-40
-60
-80
-100
original
2 CC B Technique
2 CC GA
2 CC DE
-120
-140
0
100
200
300
Normalized frequency (Hz)
15
400
500
IX
Fig 6. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 32 data
subcarriers and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII, cn=1,
n =1, 2… N.
20
Normalized power spectral density (dB)
0
I
II
III
IV
V
VI
VII
VIII
IX
-20
-40
-60
-80
-100
original
2 CC AS tehcnique
ASW AS technique
2 CC GA
2 CC DE
-120
-140
0
100
200
300
Normalized frequency (Hz)
400
500
Fig 7. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 32 data
subcarriers and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII, cn=1,
n =1, 2… N.
Table 5. Sidelobe power suppression with different techniques
Sidelobe power in Locations
I
III
V
VII
IX
W / O CCs
-31dB
-30dB
-28dB
-30dB
-30dB
WCCs Brandes Technique
-45dB
-43dB
-42dB
-44dB
-43dB
WCCs GA
-57dB
-57dB
-57dB
-57dB
-57dB
WCCs DE
-82dB
-63dB
-60dB
-70dB
-65dB
WCC Ahmed selim Technique
-36dB
-34dB
-34dB
-35dB
-34dB
ASW Ahmed selim Technique
-42dB
-40dB
-39dB
-41dB
-40dB
16
4.3 Case III
In this case we are considering interference suppression spectrum sharing scenario in NC – OFDM
having equal bandwidth between the spectral white spaces II, IV, VI and VIII i.e. region I, III, V,
VII and IX have equal bandwidth while locations II, IV, VI and VIII are have an un-equal
bandwidth comprising 16, 32, 64 and 128 subcarriers. In order to not to interfere with the PU’s
two CC’s on either side of the location II, IV, VI and VIII are inserted. So 𝑁 = 16 data subcarriers
and 𝑀 = 4 CC’s are there in each location II, 𝑁 = 32 data subcarriers and 𝑀 = 4 CC’s are there in
location IV, 𝑁 = 64 data carriers and 𝑀 = 4 CC’s are there in location VI and 𝑁 = 128 data carriers
and 𝑀 = 4 CC’s are there in location VIII. The Optimization range for the calculation of weights
spans the sidelobes in the location I, III, V, VII and IX, here we have taken 10 samples per
sidelobes to keep the computational complexity low. Fig 8 and Fig 9 shows the normalized power
spectral density of the NC – OFDM signal modulated with symbol cn = 1 on all data subcarriers.
The weights that are optimized according to traditional method given by equation (3), GA and DE
without constraints are given in Table 6.
The side lobe powers of each location I, III, V, VII and IX with and without CC’s are given in
table XI, and the suppression of these sidelobes with traditional method, GA and DE are given in
Table 7, which shows that significant reduction of sidelobe power levels is achieved by GA and
DE.
Table 6. Weights of left and right cancellation carriers estimated via TM, GA and DE
GA
Technique
Brandes
Weights of left and right sided cancellation carriers
g1
g2
g3
g4
Region II
0.091784075
0.554019705
0.559322087
0.095982099
Region IV
0.096174094
0.564686156
0.567600684
0.098409395
Region VI
0.101217371
0.573564032
0.571245149
0.099533696
Region VIII
0.106350221
0.583279189
0.578188267
0.102846381
Region II
0.127273160
0.611152805
0.611152805
0.127273160
Region IV
0.138865777
0.630490598
0.630490598
0.138865777
Region VI
0.142475021
0.637210197
0.637210197
0.142475021
Region VIII
0.147859645
0.646063755
0.646063755
0.147859645
17
Technique
DE
Ahmed selim
Region II
0.130092496
0.615282174
0.615282174
0.130092496
Region IV
0.138865777
0.630490598
0.630490598
0.138865777
Region VI
0.143698876
0.638229424
0.638229424
0.143698876
Region VIII
0.149016646
0.647713894
0.647713894
0.149016646
Region II
0.307934971
0.018695719
0.315496912
0.015717667
Region IV
0.325688297
0.025368404
0.330510828
0.023883461
Region VI
0.341243928
0.027763878
0.338440157
0.028529542
Region VIII
0.360485741
0.034152791
0.355359900
0.035268311
20
Normalized power spectral density (dB)
0
I
II
III
IV
V
VI
VII
IX
VIII
-20
-40
-60
-80
-100
original
2 CC B technique
2 CC GA
2 CC DE
-120
-140
0
100
200
300
Normalized frequency (Hz)
400
500
Fig 8. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 16 data
subcarriers in location II, 𝑵 = 32 in location IV, 𝑵 = 64 in location VI and 𝑵 =128 in
location VIII and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII,
cn=1, n =1, 2… N.
18
20
Normalized power spectral density (dB)
0
II
I
III
IV
V
VI
VII
VIII
IX
-20
-40
-60
-80
original
2 CC AS technique
ASW AS technique
2 CC GA
2 CC DE
-100
-120
-140
0
100
200
300
Normalized frequency (Hz)
400
500
Fig 9. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 16 data
subcarriers in location II, 𝑵 = 32 in location IV, 𝑵 = 64 in location VI and 𝑵 =128 in
location VIII and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII,
cn=1, n =1, 2… N.
Table 7. Sidelobe power suppression with different techniques
Sidelobe power in Locations
I
III
V
VII
IX
W / O CCs
-33dB
-27dB
-26dB
-24dB
-25dB
WCCs Brandes Technique
-46dB
-42dB
-40dB
-38dB
-38dB
WCCs GA
-59dB
-58dB
-40dB
-52dB
-54dB
WCCs DE
-64dB
-68dB
-66dB
-56dB
-58dB
WCC’s Ahmed selim Technique
-37dB
-32dB
-30dB
-28dB
-30dB
ASW’s Ahmed selim Technique
-44dB
-38dB
-34dB
-30dB
-35dB
4.4 Case IV
In this case we are considering interference suppression spectrum sharing scenario in NC – OFDM
having unequal bandwidth between the spectral white spaces II, IV, VI and VIII i.e. location I, III,
V, VII and IX have un-equal bandwidth while location II, IV, VI and VIII are also having an un19
equal bandwidth comprising 16, 32, 64 and 128 subcarriers. In order to not to interfere with the
PU’s two CC’s on either side of the location II, IV, VI and VIII are inserted. So 𝑁 = 16 data
subcarriers and 𝑀 = 4 CC’s are there in location II, 𝑁 = 32 data subcarriers and 𝑀 = 4 CC’s are
there in location IV, 𝑁 = 64 data carriers and 𝑀 = 4 CC’s are there in location VI and 𝑁 = 128
data carriers and 𝑀 = 4 CC’s are there in location VIII. The Optimization range for the calculation
of weights spans the sidelobes in the location I, III, V, VII and IX, here we have taken 10 samples
per sidelobes to keep the computational complexity low. Fig 10 and Fig 11 shows the normalized
power spectral density of the NC – OFDM signal modulated with symbol cn = 1 on all data
subcarriers. The weights that are optimized according to traditional method given by equation (3)
without constraints, according to GA and DE are given in Table 8.
Suppression of side lobe powers at locations I, III, V, VII and IX with and without CC’s with
traditional method, GA and DE are given in Table 9, which shows that significant reduction of
sidelobe power levels is achieved by GA and DE.
Table 8. Weights of left and right cancellation carriers estimated via TM, GA and DE
g1
g2
g3
g4
Region II
0.095719544
0.558989434
0.55435298
0.092043824
Region IV
0.096568283
0.565040743
0.566044218
0.097300772
Region VI
0.103201112
0.576131613
0.569503633
0.098140022
Region VIII
0.105760982
0.580571509
0.574429211
0.101148034
Region II
0.127273160
0.611152805
0.611152805
0.127273160
Region IV
0.138865777
0.630490598
0.630490598
0.138865777
Region VI
0.143698876
0.638229424
0.638229424
0.143698876
Region VIII
Region II
0.149016646
0.130092496
0.647713894
0.615282174
0.647713894
0.615282174
0.149016646
0.130092496
Region IV
0.138865777
0.630490598
0.630490598
0.138865777
Region VI
0.143698876
0.638229424
0.638229424
0.143698876
Region VIII
0.147859645
0.646063755
0.646063755
0.147859645
Region II
0.315067921
0.015894472
0.308452906
0.018500532
Region IV
0.327546029
0.024803143
0.328749912
0.024432323
Ahm
ed
selim
Tech
nique
DE
GA
Brandes
Technique
Weights of left and right sided cancellation carriers
20
Region VI
0.344732857
0.026792434
0.334593657
0.029558146
Region VIII
0.352394520
0.028485124
0.344396760
0.030548890
20
Normalized power spectral density (dB)
0
I II
III
IV
V
VIII
VII
VI
IX
-20
-40
-60
-80
original
2 CC B technique
2 CC GA
2 CC DE
-100
-120
-140
0
100
200
300
400
Normalized frequency (Hz)
500
600
Fig 10. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 16 data
subcarriers in location II, 𝑵 = 32 in location IV, 𝑵 = 64 in location VI and 𝑵 =128 in
location VIII and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII,
cn=1, n =1, 2… N.
21
20
Normalized power spectral density (dB)
0
I
II
III
IV
V
VI
VII
VIII
IX
-20
-40
-60
-80
original
2 CC AS technique
ASW AS technique
2 CC GA
2 CC DE
-100
-120
-140
0
100
200
300
400
Normalized frequency (Hz)
500
600
Fig 11. Power spectrum of NC – OFDM signals with and without CC’s; 𝑵 = 16 data
subcarriers in location II, 𝑵 = 32 in location IV, 𝑵 = 64 in location VI and 𝑵 =128 in
location VIII and 𝑴 = 4 cancellation carriers in each of the location II, IV, VI and VIII,
cn=1, n =1, 2… N.
Table 9. Sidelobe power suppression with different techniques
Sidelobe power in Locations
I
III
V
VII
IX
W / O CCs
-30dB
-29dB
-20dB
-27dB
-32dB
WCCs Brandes Technique
-45dB
-42dB
-35dB
-41dB
-46dB
WCCs GA
-56dB
-62dB
-42dB
-52dB
-62dB
WCCs DE
-70dB
-68dB
-42dB
-66dB
-68dB
WCCs Ahmed selim Technique
-35dB
-34dB
-26dB
-32dB
-38dB
WASW Ahmed selim Technique
-40dB
-40dB
-28dB
-36dB
-42dB
5. CONCLUSION AND FUTURE WORK
In this paper we proposed GA and DE for estimating the weights of the CC’s to suppress the
sidelobes in NC – OFDM based cognitive radio and compare the results of the GA and DE with
the already exiting approaches. Simulation results show that considerable reduction of sidelobes
22
is achieved while using GA and DE and specially DE shows overall better results as compared to
the GA as well as to the existing method. In future we can use these techniques in joint estimation
of amplitude, direction, angle, frequency and range of near and far field sources.
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