Optimal Power Allocation for Green Cognitive Radio using Differential Evolution Approach

Optimal Power Allocation for Green Cognitive Radio using Differential Evolution Approach

K Deepak Raj, Y S S Kaushik, M Siva Kumar

Department of EEE/ENI BITS Pilani K.K Birla Goa Campus

Goa, India

Abstract In this study, the problem of determining the power allocation that maximizes the energy efficiency of cognitive radio network is investigated using differential evolution algorithm with constraint handling technique. The energy-efficient fractional objective is defined in terms of bits per Joule per Hertz. The proposed constrained fractional programming problem is a non-linear non- convex optimization problem. Nature inspired algorithms like Differential Evolution (DE) can describe and resolve complex relationships from intrinsically very simple initial conditions with little or no knowledge of the search space. In simulation results, the effect of different system parameters (interference threshold level, number of primary users and number of secondary users) on the performance of the proposed algorithm is investigated.

2 SYSTEM MODEL AND PROBLEM FORMULATION

We consider a wireless network with a base station (BS), K secondary users (SUs) and M primary users (PUs). M PUs can be either wireless devices or geographic regions in which the strength of the cognitive radio signals must be below a specified interference threshold. Transmissions to each SU takes place on a separate, pre-assigned sub channel; and a central controller decides the power level. We denote total static and leakage circuit power of the transmitter by , pk, denotes the source transmit power to serve kth SU, Im, the interference threshold at the mth PU and hk, the channel from the source to kth SU. So, the channel gain h is modelled as

d

h = h Lo Ko o (1)

Index TermsGreen cognitive radio, power allocation, energy efficiency, differential evolution

1 INTRODUCTION

Energy efficiency plays a key role in designing wireless

communication networks. The energy-efficient wireless networks help in saving the battery life and reduction in

d

where Ko is a constant that depends on the antenna characteristic and average channel attenuation, do is the reference distance for the antenna far field, d is the distance between transmitter and receiver, is the path loss constant and h is the Rayleigh random variable. The parameter

~

o

global warming. Massive growth and demand of high

L 10 Lo 10

is log normal shadowing, where Lo is zero

data rate wireless devices and applications cause significant increase in the greenhouse gas emissions and crowdedness in available frequency spectrum. The main goal of green communication is to develop wireless networks, protocols and devices that jointly maximize the high data rate and minimize the greenhouse gas emissions, that is, minimize the transmit power. The maximum data rate transfer with minimum transmit power is the key of green communication.

Cognitive Radio (CR) is an adaptive, intelligent radio and network technology that can automatically detect available channels in a wireless spectrum and change transmission parameters enabling more communications to run concurrently and improve radio operating behavior. This optimizes the use of available radio- frequency (RF) spectrum while minimizing interference to other users. The main challenge of green cognitive radio is how best a network can allocate power to the wireless devices that can take care of spectrum crowdedness, data rate demand and greenhouse gas emissions.

mean Gaussian with standard deviation . Table 1 presents the summary of notations and symbols used in this paper.

The IEEE WRAN standard consider two schemes to protect PUs from harmful interference. These are spectrum sensing and geo-location-based database schemes. In these schemes, the geographic locations of PUs and SUs are stored in a centralized database. Both PU and SU network have permission to access location database. We assume that the secondary network has both spectrum sensing capability and access privileges to the location database. We also assume that BS can estimate the active PUs channel gains, perhaps via pilot power detection on a regular basis. Fig. 1 shows a typical Cognitive Radio Network. SUs are represented by solid rectangles and PUs by solid triangles. As shown in Fig. 1, each PU has a protected area. Given a distance dm between the BS and the mth PU and the radius Rm of the protected area of the mth

PU, the channel gain from the source to mth PU in kth SU band is given as

~ d

can see that the numerator (p) is a concave function and denominator is an affine function of SUs powers.

Fig. 1. Cognitive radio system model

Unfortunately, the function (p) is not a concave function of SUs power. We cannot apply standard convex optimization techniques to solve (3).

3 DIFFERENTIAL EVOLUTION (DE)

gm,k gm,k Lo Ko o

dm Rm

(2)

Differential evolution (DE) is a population based evolutionary algorithm, capable of handling non-

where gm, k is the small scale fading and is the path loss exponent. For simplicity, throughout this paper and in simulation results we assume that R1 = R2 = ··· = RM. Interference to the PU Im, is defined as the total aggregated interference power level perceived by any primary receiver m. The parameter Im, is the noise floor of the PUs. Any perceived power less than Im will not affect the operations of PUs network.

Our goal is to maximize the EE of the SUs transmissions while meeting the interference constraints because of the PUs. The EE metric we use in this paper is information bits per Joule. We can write the EE maximization problem for cognitive radio as

K log1 p h N

differentiable, non-linear and multi-modal objective functions. A brief description of different steps of DE algorithm is given below:

1. Initialization

   The population is initialized by randomly generating individuals within the boundary constraints,

   ij j j j

   X0 = Xmin + rand × (Xmax Xmin ); i = 1, 2, 3 . . . Np; j = 1, 2, 3 . . . D; (4)

   ij

   where X0 is the initialized jth decision variable of ith population set; rand function generates random values uniformly in the interval [0,1]; Np is the size of the population; D is the number of decision variables. The

   fitness function is evaluated for every individual and Xminj

   max

   p

   k 1 k k o

   K P

   (3)

   and Xmaxj are the lower and upper bound of the jth decision

   o k 1 k

   Subject to

   variable, respectively.

2. Mutation

   C1: K

   k 1

   pk g

   m,k

   Im

   ,m

   As a step of generating offspring, the operations of

   C2: pk 0,k 1,2,…k

   i

   X

   a

   In (3), the constraint C1 assures that interference to PUs is less than a specified threshold. For notational simplicity, we denote throughout this paper SE as

   mutation are applied. Mutation occupies quite a key role in the reproduction cycle. The mutation operation creates mutant vectors Xk by perturbing a randomly selected vector k with the difference of two other randomly selected vectors Xk and Xk at kth iteration as per following equation.

   p K log1 p h N

   b

   c

   i a b c

   k 1

   k k o

   and EE as

   Xk = Xk + F x (Xk Xk ); i = 1, 2, ……Np (5)

   p p o

   K

   k 1

   Pk . From the EEexpression, (p) we

   i

   a b

   where Xk is the newly generated ith population set after performing mutation operation at kth iteration; Xk , Xk and

   X

   c

   k are randomly chosen vectors at kth iteration [i=1, 2,

   3, . . .Np] and a b c i. Xk , Xk and Xk are selected for

   a b c

   each parent vectors and F [0,2] is known as scaling factor used to control the amount of perturbation in the mutation process and improve convergence. Many schemes of creation of a candidate are possible here but strategy 1 has been mentioned in the algorithm.

3. Crossover

   Crossover represents a typical case of a genes exchange. The parent vector is mixed with the mutated vector to create a trial vector, according to the following equation:

   ij

   Xk = {

   k if rand j < Cr or j = q

   (18)

   X

   X

   ij

   ij

   k otherwise (6)

   where i=1, 2, 3, . . ., Np; j=1, . . ., D. Xk , Xk , and Xk are

   ij ij ij

   the jth individual of ith target vector, mutant vector, and trial vector at kth iteration, respectively. q is a randomly chosen index (j = 1, 2, . . ., D) that guarantees that the trial vector gets at least one parameter from the mutant vector even if Cr

   = 0. Cr [0,1] is the Crossover constant that controls the diversity of the population and aids the algorithm to escape from local optima.

4. Selection

   Selection procedure is used among the set of trial vector and the updated target vector to choose the best. Each solution in the population has the same chance of being selected as parents. Selection is realized by comparing the objective function values of target vector and trial vector. For minimization problem, if the trial vector has better value of the objective function, then it replaces the updated one as per (7).

   Fig. 2. 3D plot of the objective function with p = 1 and p = 2.5

1. SIMULATION RESULTS AND DISCUSSION

   In this section, we present the simulation results to demonstrate the performance and convergence of the proposed algorithm. The impact of network parameters is also investigated. In all the results, for the SUs channel h, we set do = 20 m, Ko = 50 and = 3. For PUs channel g, we set do = 1m, Ko = 1 and = 3. The PUs protected distance Rm is set to 10 m. We also assume that distance d is greater than do. The SUs and PUs are uniformly distributed and the maximum coverage distance of BS is set to 1000 m. The static and leakage circuit power is set to 10 6 W and for shadowing, we set = 10 db.

   i

   Xk+1 = {

   X_k if f (X_k ) f (Xk )

   i i i

   Xk i otherwise i = 1, 2, . . . Np (7)

   i

   where Xk+1 is the ith population set obtained after selection operation at the end of kth iteration, to be used as parent population set (in ith row of population matrix) in next iteration (k + 1th).

   Fig. 3. EE against number of SU plot, M= {1, 11} The interference threshold of each PU is set to 10 W

   Fig. 3 and 4 presents EE and SE against number of SUs with different number of PUs a satisfy the worst PU. Note that main aim of the objective function is to maximize the EE. We also observe that EE decreases with the increase in number of PUs. In both figures, the parameters are set to M= {1, 11}, Im = 10W, No=1 W/Hz. The optimal EE does not always mean minimum power usage. Owing to the structure of the EE optimization objective, a slight increase or decrease in the power will change EE many folds. The results of Fig. 5 confirm these explanations.

   Fig. 4. SE against number of SU plot, M= {1, 11} The interference threshold of each PU is set to 10 W

   Figs. 5 and 6 present the performance of the proposed differential algorithm with number of iterations for different number of SUs, PUs and interference thresholds.

   Fig. 5. Performance with number of iterations

   In Figs. 5 and 6 the simulations parameters are set to {K, M, Im,} = {25, 1, 1 W} and {5, 20, 10 W}, respectively. We can observe that the EE becomes stable in less number of iterations with low interference threshold. We also see that the differential evolution algorithm converges to the optimal solution within ten iterations, for all the different scenarios

   (different SUs, PUs etc.). From Fig 7, we can observe that transmission power decreases with the number of SUs and the EE increases with the number of SUs.

   Fig. 6. Performance with number of iterations

   Fig. 6. Performance with number of iterations

   Fig. 6. Performance with number of iterations

   This is because with more SUs, there is more freedom in power allocation. We also observe that the EE decreases with the increase in the number of PUs, because the optimization problem has more number of constraints to satisfy.

   Fig. 7. EE and total transmission power against number of SU plot, M= {1, 11}. The interference threshold of each PU is set to 10

   W

2. CONCLUSIONS

In this paper, an algorithm that employs Differential Evolution (a meta-heuristic search technique), is used to determine the power allocated to each secondary user that maximizes the energy efficiency of the cognitive radio network. The energy-efficient fractional objective is defined in terms of bits per Joule per Hertz. The main advantage of this proposed method is that it systematically decides the

power allocation to realize the optimum energy efficiency. The effect of different system parameters (interference threshold level, number of primary users and number of secondary users) on the performance of the proposed algorithm is investigated.

ACKNOWLEDGMENT

We express our deep gratitude to Assistant Prof. Nitin Sharma for his support and guidance during the project which motivated us to pursue in-depth research in this field. It also gave us an insight into the opportunities in the field of Wireless Communications.

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