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Adaptive Step Size and Weighting Factor Based Power Allocation in
Cognitive Radio Networks
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V. Jagadesh Chandra Prasad, 2M.Nageswariah
M.tech student, ECE Department, SITE College,Tirupati, India,jagadeshvanneti@gmail.com
2
Associate professor, ECE Department, SITE College, Tirupati, India, mnagesh427@gmail.com
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Abstract--The gradient-based method is used for power
spectrum, which is allocated to licensed PU without
allocation in ofdm-based cognitive radio networks. Their
effecting interference to PUs.The technique for the spectrum
arise
management and interface cancellation in CR networks are
resource
allocation
problem.
For
mutual
interference constraint is considered. We use gradient
discussed.
decent approach for power allocation to subcarrier in
The power allocation in OFDM and its optimal solution
CR network. The proposed gradient based for power
is compared with the water filling technique, which is going
allocation method to a defined step size easily
to used for the maximization of capacity with power
approximate the solution by a few iterations, By the
constraint. These technique is employed for single user CR
derived equation the step size is small for power
systems. The SUs can access the band which is unoccupied
allotment in time varying channels. This paper presents
by Pus frequency.
the selecting the step size for understanding purpose, a
This paper focuses on the power allocation
greedy power allocation method is unstable and is used
problem in OFDM based CR networks with multiple
for power alloction. Both the methods have complexity
interference.Usaully these interference depends upon the
to calculate. But the proposed gradient based method is
transmit power, channel conditions, and the spectral
some who less. The result shows that proposed method is
distance between the PUs and SUs.They are of two kinds of
easy to achieve to a near optimal solution with less
inferences in CR networks. The first one is introduced by
iterations and low computing complexity of O(n).
Pus and SUs,which brings signal-to-noise ratio loss in CR
networks. The second most one is introduced by SUs to
Index Terms— cognitive radio networks, gradient descent,
power
allocation
and
orthogonal
frequency
division
multiplexing OFDM .
PUs.
We are going to present the gradient descent based
method for solving the power allocation problem. This
technique is used for finding the local minimum function
I.
INTRODUCTION
The commission of Federal Communication states that
spectrum in licensed band is partially used. By that user
going to use the required licensed spectrum difficult. So that
wireless communications systems becomes difficult to
wider range for wider use. The Cognitive Radio based on
software defined ratio is represented to solve the problem
that reduce the spectrum scarcity. These can be reduced by
secondary users(SUs) to communicate with spectrum for
frequencies bands which is assigned to primary users(PSs)
should not all (SUs) at a time.
So that OFDM is suggested as a required technique in CR
networks. If unlicensed SU is allowed to access the
and also for solving the power allocation problem of
multicarrier systems. This gradient descent technique is
employed in cross layer optimization of multipath routing
and power allocation for ad hoc networks. For the different
objectives these gradient descent approach is applied in
multiple-I/P-multiple-O/P broadcast channels. By which
convergences to a stationary point.
By the gradient based method we are going to solve the
power allocation problem related to interference constraint
OFDM based in CR networks. The technique of
optimization constraint is a considerable problem, by
therefore the method of steepest descent is cannot employed
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directly. The solution obtained by these has to be in feasible
introduced to the PU bands below.The capacity of CR users
region. The power allocation we are going to allocate should
is defined as follows:
be positive. The constraint considered to be satisfied. By
that the projected gradient method can be apply. The
Euclidean projection technique is used to perform projection
of power allocation on constraint set by the way resource
can be fully used and the constraint can be satisfied.
The major issues is to find the step size. That step size
determines the accuracy of the approximation and the
iteration number. The gradient based method with adaptive
Figure 1: PUs and SUs/CR users Spectrum distribution in
the frequency domain representation
step size can get the approximation solution within three
iterations. For the analysis of the step size, the value and
Where N denotes the total numbers of OFDM
selection should be approximately determined to achieve a
subcarriers; denotes the channel gain,p is a vector whose
good performance.
nth element is pn.
The defined gradient based method is depend on
algorithm of gradient projection with in the Euclidean
projection technique for solving of interference has a less
complexity of o(n).These method can be applicable for
multiple SUs and multiple Pus is determined for each CR
users, which is because equation derived by the power
allocation problem in an adaptive manner, the proposed
technique is feasible for allocation of power allocation of
power in case of time varying channels also.
The overall view of this paper is: The problem formulation
III. GRADIENT BASED POWER ALLOCATION
is mentioned in section 2.The proposed gradient based
METHOD
method is developed in section 3.In section 4 the analysis of
selection of step size and weighting factor. The proposed
greedy power loading method for optimal solution in section
5.Simulation results for the proposed gradient based method
in section 6.finally the conclusion in section 7.
II. PROBLEM FORMULATION
The frequency domain spectrum is distributed to Pus
This gives overall view of sloving the power allocation
in
gradient
based
method
with
the
interference
constraint.Becuase of the constarint,these method need to
project the gradient vector on the cconstraint vector in oder
to obtain the feasible direction.In oder to obtain these the
subcarriers is going to assaign the zero power.In the sence
the subcarrier is not considered.To,maximization the
and SUs of CR users. frequency bands of bandwidth ,is
channel
going to be censored by the CR systems, as shown in
eculidean projection operation is performed.So the proposed
fig.1,Lbands have been used by Pus. The unoccupied bands
gradient
are allocated to CR users, that are going to have N OFDM
subcomponents,i.e,,the gradient descent approach and the
subcarriers. The subcarriers of bandwidth are Hz.
eculidean projection.
Suppose that L pu are active while one CR user is
transmitting in frequency bands.Our aim is to maximaze the
capacity of the CR users while maintaining the interference
capacity
based
while
satisfying
method
A.Gradient Descent Approach
the
consist
constraint,the
of
two
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Usually the gradient depends upon the pratial derivative
of
technique is going to be used to perform the power
allocation onto the set of constraint .Thenonly the
The gradient with respect to power vector is
interference constraint can be staisfied.The subcarriers of
nonnegitive power assignment are used to perform the
projection.The euclidean projection is given as
Since p is a vector p=(p1,p2,,,pn).The orthogonal projection
Projected power Pn(t+1) is obtained and it satisfy the
of any vector on to null space of K invloves multiplication
constraint.Here we introduce the weighting function
by the matrix J,
composed of projection power Pn(t+1)and its expression is
given as;
Where (0,1) is a weighting factor.The interference
Where t is the iteration index,alfa is positive step size,
The sum of caused interference is less than or equal to
interference constraint Ith,the next step is calculate the
capacity improvement,
constraint is going to be updated powerPn(t+1).After
weighting factor is approximately set,the capacity C can be
calculated.By the achievable capacity is improved ,then only
gradient based method is continued to update the power
term.
The procedure for power allocation is shown in figure 2.
This process terminates if capacity improvement becomes
negative.Which indicates that capacity is going to
decrease.The goal of this technique is to find the amount of
power
allocated
for
each
subcarriers
directly.The
complexity of the gradient-based method is o(n) in each
iteration.
A simple strategy to find adaptive step size and
weighting factor is to give fixed values in advance for this
method.The value that we are going to assign that can be
calculate.We will give improtance to the performance
comparison for the proposed method with different fixed
step size and weighting factor also should be
size.The analysis is derived based on the
under consideration.
Figure 2: Flowchart of gradient based power allocation.
B.Euclidean Projection
If the sum of caused interference KnPn exceeds
interference
constarint
Ith,the
euclidean
projection
fixed in
performance
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The anlysis of the weighting factor can be made by the
following procedure and the step size can be found by the
previous scetion.
Through this procedure the adaptive step size and
weighting factor can be found easily and the obtained
solution is near optimal with extremely small number of
iterations.
V. MODIFIED GREEDY POWER-LOADING
METHOD
This modified power loading method is a optimization
technique to obtain optimal sloution for the specified user if
Table 1: Comparison of techniques
the parametrs are well definied.The user specified
parameters may include
IV. ANALYSIS FOR THE SELECTION OF THE
barrier method,the Newton
method,line search method.There is a trade off between
STEP SIZE AND THE WEIGHTING FACTOR
The selection of the step size and the weighting factor
accuracy and of iterations.More over in the initial stage it
should determine the functioning of the suggestted gradient
must obey the feasible starting point.The barrier function is
based power allocation method
responible
to
determine
the
accuracy
and
the
approximation.There should be computational complexity
.
for finding the inverse hessian matrix for fast algorithm is
It working should be more efficient when we do more
iterations unless the value taken should be small.In the
consider.To make the iteration procedure suitable we are
going to modify the optimization problem.
otherside if we take large value the fast rate is achieved but
perforamance is near optimal.
VI SIMULATION RESULT
The selection of step size and weighting factor is
presented.
A.Selection of the step size
For the analysis,power vector is written as
Where
Power update for subcarrier is rewritten as
For
allocating
nonnegitive
power
Figure 3:Input signal
to
all
the
subcarriers,step size on a per subacrriers is as,
B.Selection of the weighting factor
The power allocated for design of the proposed gradient
based method is going to multiplied by the interference
factor and that should be equal to interference constraint.If
not we should perform the euclidean projection.
Figure 4:Minimum power
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Figure (5) It is the minimum power to the generated
carrier of the OFDM. In the generated carrier of the
cognitive radio networks the users are going to be attain the
stable strength to generated the desired signal from long
distance without any inter connection of the destination.
This would be possible through the software defined radio.
It is also varies from x-axis’s (0-1000) and similarly YFigure 5: Minimum power1
axis’s (0-8). The obtained waveform is a increasing signal
from origin.
Figure (6) It is the power allocation to the users in the Pus
and the SUs in the defined bands. There we going to be get
the noise component. In the obtained flowchart blue color
one is noise component and where as the red color is the
allocated power. The X-axis’s is the number of channels in
Figure 6:Power allocation in ofdm
the Pus and the SUs. The Y-axis’s is the noise and power
components. There would we clearly understand that the
noise is more when compared with the allocated power
through the OFDM technique. By using the cognitive radio
networks we are going to prove that the power going to
allocate is less than the OFDM technique.
Figure (7) it is the performance analysis between the
cognitive radio networks to the OFDM technique. For
Figure 7: Performance Analysis
simple understanding purpose we are going to consider the
Figure (3) In This power allocation technique we are
two user only in the performance analysis purpose. In this
going to give input first. There is a number of users out of
power allocate is more in OFDM when compared to the
which there is power is going to varies between the x-axis’s
cognitive radio networks. The power allocation in the
from (0-1000) and similarly Y-axis’s from (0-11).This input
cognitive radio networks represented (M=2,4) is less when
signal is decreasing signal and slowly it get strength from
compared to the OFDM technique.
VII. CONCLUSION
allocated power through the input.
Figure (4) it is the carrier generation. After allocating the
input signal, we are going to give the minimum power to the
users in the primary and the secondary bands. By this the
users in the allocated power can able to convey the message
through the cognitive radios somehow distance long
compared to the users in outside band. This minimum power
allocation waveform also varies from x-axis’s (0-1000) and
the Y-axis’s from (0-11).This curve is also decreasing first
after allocating minimum power their it would get
strengthen and their it starts going to increase.
The overall powe allocation power can be resloved by
the by suggested gardient based power allocation with the
Euclidaen projection and the adapitve step size can be found
by the analysis made in this paper.The iteration procedure
can be made easily by the setting small values at the initial
stage itself to obtain the near optimal values which can be
obtained by the greedy power loading method.Performance
can be achieved by the help of suggested greedy power
loading technique.
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VIII. REFERENCES
[1] ”Report of spectrum efficiency working group”
Fed.commun. commision, spectrum policy Task Force,
Washington DC, USA, Nov.2002.
[2]J.Mitola and G.Q.Maguire,”cognitive radio: making
software
radios
more
personal,”IEEE
pers.commun.,
vol.6,no.4,pp.13-18,Aug.1999.
[3]
S.Haykin,”Cognitive
wireless
radio:
Brain-empowered
communications”,IEEE
J.sel.Area
University in the Discipline of VLSI. He has been actively involved in
teaching and he is working as Assoc Professor, in the Dept of ECE,
SHREE College Of Engineering, Tirupati. AP, India studied BTECH in
commun.,vol.23,no.2,pp.201-22-,Feb 2005.
[4]D.G.Luenberger and Y.Ye,Linear and Nonlinear
Electronics and Communication Engineering JNTUA-HYD (2005)..His
current Research interest in individually-image processing, could
programming,3rd
ed.Newyork,NY,USA:Springer-
verlag,2008
computing, VLSI, stygnography. He has done three international journals,
two national journals, four international conferences.
[5]Y.R.Zheng and C.Xiao,”Improved models for the
generation of multiple uncorrelated Rayleigh fading
waveforms,”IEEE
commun.Lett.,
vol.6,no.6,pp.256-
258,jun.2002.
[6]P.Pedregal,Introductionto
optimization
newyork,NY,USA:Springer-Verlag,2003.
[7]Technical specification group GSM/EDGE Radio
Access
2. M.Nageswariah has received his Master’s Degree from JNTUA
Network;
Radio
transmission
and
reception,valbone,france.
[8]D.P.Bertseka Nonlinear programming .Belmont, MA,
USA: Athena scientific,1995.
[9]E.K.P.Chongand S.H.Zak, An
Introduction to
optimization. Hoboken, J, USA:Wiley,2001.
AUTHORS:
1.V.Jagadesh Chandra Prasad has received his B.Tech from JNTU
Anantapur with Electronics & Communications Engineering Specialization
and present he is pursuing M.Tech from JNTU Anantapur University,
(AP)India in the area of digital electronics and communication systems .He
has actively involving in college level activities and technical symposiums.