Energy-Efficient Resource Optimization in Spectrum Sharing Two-Tier Femtocell Networks

Transcription

1 Energy-Efficient Resource Optimization in Spectrum Sharing Two-Tier Femtocell Networks Praneet Bhatia Ayush Yadav Surhud Khare Sanjana Ramachandran 2011A3PS208G 2011A8PS384G 2011A8PS334G 2011A8PS302G Abstract: Power control and sub-channel allocation play a very important role in resource management of wireless networks. By an effective resource allocation scheme, the performance of the system can be improved. In this project we model the sub-channel allocation and power control algorithm using the Artificial Bee Colony Algorithm, where both transmit power and circuit power are considered. We use Shanon s formula and SINR (signal to interference and noise ratio) to generate the utility function of a player (which will also be defined during problem formulation). We will then discuss the use of ABC algorithm to achieve an optimal power control and sub-channel allocation solution for a sample femtocell network. To reduce the complexity while maintaining good performance, we decompose the power control and sub-channel allocation problem into two sub-problems The aim is to then test the algorithm and simulate it and then compare results with classical game theory algorithm.

2 Introduction : Power control and subchannel allocation play a very important role in resource management of wireless networks. By an effective resource allocation scheme, the performance of the system can be improved. As the scarcity of spectrum resource and the demand for high data rate growing exponentially, cellular networks move towards aggressive full frequency reuse scenarios.however, interference and full frequency reuse are seemly perpetual paradox.we focus on interference mitigation by effective subchannel allocation to improve the system throughput. High power transmission always results in serious interference in co-channel deployed femto cells, so power control can not be ignored in wireless resource management. A power control algorithm using ABC(Artificial Bee Colony ) technique is introduced to improve the outage and throughput performance of macro-users with minor impact on femto-users in two-tier Orthogonal Frequency Division Multiple Access (OFDMA) femtocell networks. Power control and subchannel allocation algorithm is investigated to maximize the throughput of OFDMA networks. Most of the existing literatures always focus on throughput maximization of the wireless networks. However, due to the limited battery resources and increasing demand for higher datarate wireless service, energy-efficiency has attracted wide attention recently. Energy-efficiency is measured in bit/joule, and is defined as the number of delivered bits for each energy unit used for transmission. Energy-efficiency is maximized by power control based on non-cooperative game in wireless networks, but subchannel allocation is not considered.traditionally, there are centralized scheduling and distributed scheduling techniques to resolve the general utility maximization. In centralized scheduling, resource allocation

3 decision are generated at a central scheduler. And the scheduler needs to know total channels state information of whole network. Compared with the centralized scheduling,mobile clients have more autonomy in making transmission decisions in distributed manner.in this paper, we investigate the energyefficient powercontrol and subchannel allocation for the uplink of a twotier femtocell networks. We model the power control and subchannel allocation to maximize the energy-efficiency of femtousers, where both the transmit power and circuit power are considered. We decompose the subchannel allocation and power control problem into two sub-problems. A distributed sub-optimal subchannel allocation scheme and a distributed power control scheme are proposed. Simulation results show that the proposed algorithm has a better performance in terms of energy-efficiency. The rest of the paper is organized as follows. We first introduce the system model and problem formulation in Section II. We then discuss the ABC(Artificial Bee Colony) algorithm, decompose the subchannel allocation and power control problem into two steps, and model the power allocation problem as a supermodularity game in Section III. In Section IV, the performance of proposed algorithm is analysed by simulations. Finally, we conclude the paper in Section V.

4 II. SYSTEM MODEL AND PROBLEM FORMULATION A. System Model The scenario we considered consists of a central macrocell which is underlaid with B femtocells, all operating over the same frequency band. It is assumed that, during each signaling slot, the same frequency can be occupied by only one active user in base station, to avoid the intra-cell interference. Let ϕ : [0, 1, 2,...,B] denote the base station set, where, 0 presents the macrocell. ψ : [1, 2, 3,...,B] denotes femtocells in the system, and N = [1, 2,,N] denotes the subchannel set. Ukb (k = 1, 2,,Mb) denotes the kth active user in the bth(b ψ) base station. Because one user may occupy multisubchannels, for describing conveniently in the following, we introduce uk b,n to denote the player, which is equal to user ukb occupying the nth subchannel. Let g(b,uk) b,n denote the channel gain from the player u(k b,n) to the receiving BS b _,b _ ϕ. We define pu(k b,n) as the power of player u(k b,n). The variance of additive white gaussian noise (AWGN) at BS b is σ2. The received signal to interference and noise ratio (SINR) of player u(k b,n) can be expressed as: - (1) where Iu(kb,n) = B_i=0,i_=bpu(ki,n)gb(,uk i,n) +σ2 denotes the interference suffered by player u(k b,n), and B_ i=0,i_=b puk i,ngb,uk

5 i,n is the interference caused by co-channel players in other base stations. According to the Shannon s capacity formula, the maximum achievable data rate of player uk b,n can be expressed as: -(2) where, w is the bandwidth of each subchannel, and r(uk b,n) is given by (1). In this paper, we consider the energy-efficiency of the two tier femto cell networks, and the utility function of player u(kb,n) is defined as, -( 3) where pc is the circuit power of mobile devices, including the energy consumption of mixers, filters, and digital-to-analog converters [11]. A. Problem Formulation Here we assume that, there are B femtocells overlaid on a central macrocell, and N subchannels shared by each base station. The energy-efficiency of overall femtocells can be formulated as:

6 where we have pukb,n> 0, if the nth subchannel is allocated to uk b,n, else puk b,n = 0. Pmax is the maximum total transmit power of a femto-user. Moreover, we assume that the subchannel allocation and power control can be operated indepently for each subchannel,the problem formulation can be simplified as: where, pmax is maximum power allocation on subchannel occupied by player uk b,n, which satisfies pmax = Pmax/î, and î is the number of subchannels allocated to the user ukb

7 Proposed Algorithm: Artificial Bee Colony The artificial bee colony algorithm (ABC) is an optimization algorithm based on the intelligent foraging behaviour of honey bee swarm, proposed by Karaboga in The minimal model of swarm intelligent forage selection in a honey bee swarm consists of three kinds of bees: employed bees, onlooker bees, and scout bees. Employed bees are responsible for exploiting the nectar sources explored before and they give information to the other waiting bees in the hive about the quality of the food source which they are exploiting. Onlooker bees wait in the hive and establish food source to exploit deping on the information shared by the employed bees. Scouts search environment in order to find a new food source deping on an internal motivation or external clues or randomly. The position of a food source represents a possible solution to the optimization problem and the nectar amount of a food source corresponds to the quality (fitness) of the associated solution. The number of the employed bees is equal to the number of solutions in the population. In our model the correspondence between ABC terminology and programs is as follows. Food Source: - A combined matrix which contains user allocation and power allocation in a network. Employed Bee:- A program which calculates the fitness of the objective function of the existing matrix. Onlooker Bee: - A program which chooses the optimum objective function value based on the data provided by the Employed Bee.

8 Scout Bee: - A program which randomly allocates values of power and user in the food matrix. It is assumed that there is only one artificial employed bee for each food source. In other words, the number of employed bees in the colony is equal to the number of food sources around the hive. Employed bees go to their food source and come back to hive and dance on this area. The employed bee whose food source has been abandoned becomes a scout and starts to search for finding a new food source. Onlookers watch the dances of employed bees and choose food sources deping on dances. The main steps of the algorithm are given below: Initial food sources are produced for all employed bees. Repeat o Each employed bee goes to a food source in her memory and determines a neighbour source, then evaluates its nectar amount and dances in the hive. o Each onlooker watches the dance of employed bees and chooses one of their sources deping on the dances, and then goes to that source. After choosing a neighbour around that, she evaluates its nectar amount. o Abandoned food sources are determined and are replaced with the new food sources discovered by scouts. o The best food source found so far is registered. Until (requirements are met). In ABC, a population based algorithm, the position of a food source represents a possible solution to the optimization problem and the nectar amount of a food source corresponds to the quality (fitness) of the associated solution. The number of the employed bees is equal to the number of solutions in the population.

9 Since most of the optimization algorithms have been primarily designed to address unconstrained optimization problems, constraint handling techniques are usually incorporated in the algorithms in order to direct the search towards the feasible regions of the search space. Methods dealing with the constraints were grouped into four categories: (i) Methods based on preserving feasibility of solutions by transforming infeasible solutions to feasible ones with some operators (ii) Methods based on penalty functions which introduce a penalty term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one. (iii) Methods that make a clear distinction between feasible and infeasible solutions (iv) Other hybrid methods combining evolutionary computation techniques with deterministic procedures for numerical optimization. Because initialization with feasible solutions is very time consuming process and in some cases it is impossible to produce a feasible solution randomly, ABC algorithm does not consider the initial population to be feasible. In initialization phase, random values between the lower and the upper boundaries of the parameters are assigned for the parameters of solutions. ABC algorithm is exted by replacing the selection mechanism of the simple ABC algorithm with Deb s selection mechanism in order to cope with the constraints and introducing a probabilistic selection scheme that assigns probability values to feasible solutions based on their fitness values and to infeasible individuals based on their violations.

10 Results of Simulations Number of Base Stations Number of Subchannels Number of users/femtocell ObjVal ObjVal/N

11 References : 1. Energy-Efficient Resource Optimization in Spectrum Sharing Two-Tier Femtocell Networks. Zhicai Zhang, Haijun Zhang, Hui Liu, Wenpeng Jing, Xiangming Wen 2. A modified Artificial Bee Colony (ABC) algorithm for constrained optimization problems. Dervis Karaboga., Bahriye Akay

12 Appix : Main Module %/* ABC algorithm coded using MATLAB language */ %/* Artificial Bee Colony (ABC) is one of the most recently defined algorithms by Dervis Karaboga in 2005, motivated by the intelligent behavior of honey bees. */ %/* Referance Papers*/ %/*D. Karaboga, AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION,TECHNICAL REPORT-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department 2005.*/ %/*D. Karaboga, B. Basturk, A powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm, Journal of Global Optimization, Volume:39, Issue:3,pp: , November 2007,ISSN: , doi: /s x */ %/*D. Karaboga, B. Basturk, On The Performance Of Artificial Bee Colony (ABC) Algorithm, Applied Soft Computing,Volume 8, Issue 1, January 2008, Pages */ %/*D. Karaboga, B. Akay, A Comparative Study of Artificial Bee Colony Algorithm, Applied Mathematics and Computation, 214, , */ %/*Copyright ï ½ 2009 Erciyes University, Intelligent Systems Research Group, The Dept. of Computer Engineering*/ %/*Contact: %Dervis Karaboga (karaboga@erciyes.edu.tr ) %Bahriye Basturk Akay (bahriye@erciyes.edu.tr) %*/ clear all close all clc global B; global K; global N; B=30; K=8; N=50; global h;

13 for Base=1:B for k=1:k for n=1:n h(((base-1).*(k.*n)) + (k-1).*n + n)=abs(randn) %/* Control Parameters of ABC algorithm*/ NP=30; %/* The number of colony size (Foods bees+onlooker bees)*/ FoodNumber=NP/2; %/*The number of food sources equals the half of the colony size*/ maxcycle=2; %/*The number of cycles for foraging {a stopping criteria}*/ tol=0.01; %/* Problem specific variables*/ objfun='tension'; %cost function to be optimized constraint='constraint'; D=2.*B.*N; %/*The number of parameters of the problem to be optimized*/ limit=np*d; %/*A food source which could not be improved through "limit" trials is abandoned by its Foods bee*/ ub1=ones(1,d/2)*k; %/*lower bounds of the parameters. */ ub2=ones(1,d/2)*17; %/*lower bounds of the parameters. */ ub=[ub1 ub2]; lb1=ones(1,d/2)*(1);%/*upper bound of the parameters.*/ lb2=ones(1,d/2)*1; %/*lower bounds of the parameters. */ lb=[lb1 lb2]; minf=0; bestviolation=1e40; bestmaxim=tol; runtime=1;%/*algorithm can be run many times in order to see its robustness*/ %Foods [FoodNumber][D]; /*Foods is the population of food sources. Each row of Foods matrix is a vector holding D parameters to be optimized. The number of rows of Foods matrix equals to the FoodNumber*/ %ObjVal[FoodNumber]; /*f is a vector holding objective function values associated with food sources */ %Fitness[FoodNumber]; /*fitness is a vector holding fitness (quality) values associated with food sources*/ %trial[foodnumber]; /*trial is a vector holding trial numbers through which solutions can not be improved*/ %prob[foodnumber]; /*prob is a vector holding probabilities of food sources (solutions) to be chosen*/ %solution [D]; /*New solution (neighbour) produced by v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij}) j is a randomly chosen parameter and k is a randomlu chosen solution different from i*/ %ObjValSol; /*Objective function value of new solution*/ %FitnessSol; /*Fitness value of new solution*/ %neighbour, param2change; /*param2change corrresponds to j, neighbour corresponds to k in equation v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij})*/ %GlobalMin; /*Optimum solution obtained by ABC algorithm*/

14 %GlobalParams[D]; /*Parameters of the optimum solution*/ %GlobalMins[runtime]; /*GlobalMins holds the GlobalMin of each run in multiple runs*/ MR=0.8; SPP=0.5*NP*D; scout_counter=0; GlobalMins=zeros(1,runtime); for r=1:runtime % /*All food sources are initialized */ %/*Variables are initialized in the range [lb,ub]. If each parameter has different range, use arrays lb[j], ub[j] instead of lb and ub */ Range1 = repmat((ub1-lb1),[foodnumber 1]); Lower1 = repmat(lb1, [FoodNumber 1]); Foods1 = round(rand(foodnumber,d/2).* Range1 + Lower1); Range2 = repmat((ub2-lb2),[foodnumber 1]); Lower2 = repmat(lb2, [FoodNumber 1]); Foods2 = (rand(foodnumber,d/2).* Range2 + Lower2); Foods=[Foods1 Foods2]; ObjVal=feval(objfun,Foods); Fitness=calculateFitness(ObjVal); Violation=feval(constraint,Foods); %reset trial counters trial=zeros(1,foodnumber); %/*The best food source is memorized*/ BestInd=find(ObjVal==min(ObjVal)); BestInd=BestInd(); GlobalMin=ObjVal(BestInd); GlobalParams=Foods(BestInd,:); iter=1; while ((iter <= maxcycle)), c=0; %%%%%%%%% Foods BEE PHASE %%%%%%%%%%%%%%%%%%%%%%%% for i=1:(foodnumber) %/*The parameter to be changed is determined randomly*/ Param2Change=fix(rand*D)+1;

15 %/*A randomly chosen solution is used in producing a mutant solution of the solution i*/ neighbour=fix(rand*(foodnumber))+1; %/*Randomly selected solution must be different from the solution i*/ while(neighbour==i) neighbour=fix(rand*(foodnumber))+1; sol=foods(i,:); for z=1:d if (rand<mr) %when random number(0,1) is less than MR change a food source according to the following equation if (z>(d/2)) sol(z)=foods(i,z)+(foods(i,z)-foods(neighbour,z))*(rand- 0.5)*2; else sol(z)=foods(i,z)+(foods(i,z)- Foods(neighbour,z))*round((rand-0.5)*2); c=1; %to check whether a food source has been changed else sol(z)=foods(i,z); %else dont make any changes if(c==0) % /*v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij}) */ if (z>(d/2)) sol(param2change)=foods(i,param2change)+(foods(i,param2change)- Foods(neighbour,Param2Change))*(rand-0.5)*2; else sol(param2change)=foods(i,param2change)+(foods(i,param2change)- Foods(neighbour,Param2Change))*round((rand-0.5)*2); % /*if generated parameter value is out of boundaries, it is shifted onto the boundaries*/ ind=find(sol<lb); sol(ind)=lb(ind); ind=find(sol>ub); sol(ind)=ub(ind); %evaluate new solution ObjValSol=feval(objfun,sol); FitnessSol=calculateFitness(ObjValSol); ViolationSol=feval(constraint,sol) % /*a Deb selection is applied between the current solution i and its mutant*/ if( (ViolationSol<=tol) && (Violation(i)<=tol) )

16 if (FitnessSol>Fitness(i)) %/*If the mutant solution is better than the current solution i, replace the solution with the mutant and reset the trial counter of solution i*/ Foods(i,:)=sol; Fitness(i)=FitnessSol; ObjVal(i)=ObjValSol; Violation(i)=ViolationSol; trial(i)=0; else trial(i)=trial(i)+1; %/*if the solution i can not be improved, increase its trial counter*/ elseif( (ViolationSol<=tol) && (Violation(i)>=tol) ) Foods(i,:)=sol; Fitness(i)=FitnessSol; ObjVal(i)=ObjValSol; Violation(i)=ViolationSol; trial(i)=0; else trial(i)=trial(i)+1; %/*if the solution i can not be improved, increase its trial counter*/ if(violation(i)<=tol) prob(i)=(0.9.*fitness(i)/sum(fitness))+0.1; else prob(i)=(1-violation(i)/sum(violation))*0.1; %%%%%%%%%%%%%%%%%%%%%%%% CalculateProbabilities %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %/* A food source is chosen with the probability which is proportioal to its quality*/ %/*Different schemes can be used to calculate the probability values*/ %/*For example prob(i)=fitness(i)/sum(fitness)*/ %/*or in a way used in the metot below prob(i)=a*fitness(i)/max(fitness)+b*/ %/*probability values are calculated by using fitness values and normalized by dividing maximum fitness value*/ %%%%%%%%%%%%%%%%%%%%%%%% ONLOOKER BEE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% i=1; t=0; while(t<foodnumber) if(rand<prob(i)) t=t+1; %/*The parameter to be changed is determined randomly*/ Param2Change=fix(rand*D)+1; %/*A randomly chosen solution is used in producing a mutant solution of the solution i*/

17 neighbour=fix(rand*(foodnumber))+1; %/*Randomly selected solution must be different from the solution i*/ while(neighbour==i) neighbour=fix(rand*(foodnumber))+1; sol=foods(i,:); for z=1:d if (rand<mr) %when random number(0,1) is less than MR change a food source according to the following equation if (z>(d/2)) sol(z)=foods(i,z)+(foods(i,z)-foods(neighbour,z))*(rand- 0.5)*2; else sol(z)=foods(i,z)+(foods(i,z)- Foods(neighbour,z))*round((rand-0.5)*2); c=1; %to check whether a food source has been changed else sol(z)=foods(i,z); %else dont make any changes if(c==0) % /*v_{ij}=x_{ij}+\phi_{ij}*(x_{kj}-x_{ij}) */ if (z>(d/2)) sol(param2change)=foods(i,param2change)+(foods(i,param2change)- Foods(neighbour,Param2Change))*(rand-0.5)*2; else sol(param2change)=foods(i,param2change)+(foods(i,param2change)- Foods(neighbour,Param2Change))*round((rand-0.5)*2); % /*if generated parameter value is out of boundaries, it is shifted onto the boundaries*/ ind=find(sol<lb); sol(ind)=lb(ind); ind=find(sol>ub); sol(ind)=ub(ind); %evaluate new solution ObjValSol=feval(objfun,sol); FitnessSol=calculateFitness(ObjValSol); ViolationSol=feval(constraint,sol); % /*a Deb selection is applied between the current solution i and its mutant*/ if( (ViolationSol<=tol) && (Violation(i)<=tol) ) if (FitnessSol>Fitness(i)) %/*If the mutant solution is better than the current solution i, replace the solution with the mutant and reset the trial counter of solution i*/ Foods(i,:)=sol;

18 Fitness(i)=FitnessSol; ObjVal(i)=ObjValSol; Violation(i)=ViolationSol; trial(i)=0; else trial(i)=trial(i)+1; %/*if the solution i can not be improved, increase its trial counter*/ elseif( (ViolationSol<=tol) && (Violation(i)>tol) ) Foods(i,:)=sol; Fitness(i)=FitnessSol; ObjVal(i)=ObjValSol; Violation(i)=ViolationSol; trial(i)=0; elseif (ViolationSol>tol) && (Violation(i)>tol) trial(i)=trial(i)+1; if (ViolationSol<Violation(i)) Violation(i)=ViolationSol; Fitness(i)=FitnessSol; ObjVal(i)=ObjValSol; Foods(i,:)=sol; i=i+1; if (i==(foodnumber)+1) i=1; %/*The best food source is memorized*/ ind=find(objval==min(objval)); ind=ind(); if (ObjVal(ind)<GlobalMin) GlobalMin=ObjVal(ind); GlobalParams=Foods(ind,:); %%%%%%%%%%%% SCOUT BEE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %/*determine the food sources whose trial counter exceeds the "limit" value. %In Basic ABC, only one scout is allowed to occur in each cycle*/ scout_counter=scout_counter+1; ind=find(trial==max(trial)); ind=ind(); if ((trial(ind)>limit)&& (scout_counter>=spp))

19 trial(ind)=0; sol=(ub-lb).*rand(1,d)+lb; ObjValSol=feval(objfun,sol); FitnessSol=calculateFitness(ObjValSol); ViolationSol=feval(constraint,sol); Foods(ind,:)=sol; Fitness(ind)=FitnessSol; ObjVal(ind)=ObjValSol; Violation(ind)=ViolationSol; fprintf('iter=%d ObjVal=%g\n',iter,GlobalMin); iter=iter+1; % End of ABC GlobalMins(r)=GlobalMin; % of runs save all

20 Objective Function module function out=tension(colony) colony global B; global K; global N; global h; for i=1:size(colony,1) OB=0; for b=1:b for k=1:k for n=1:n y=colony(i,(b.*n)+((b-1)*n)+n).*(((b-1).*(k.*n))+((k-1).*n)+n); x=0; for j=1:b if (colony(i,((j-1)*n)+n)==colony(i,((b-1)*n)+n)) x=x+((colony(i,(b.*n)+((j-1)*n)+n)).*(((b- 1).*(K.*N))+((k-1).*N)+n)); z=y./(x-y); z_final=10.*(log10(1+z)); z_superfinal=z_final./(colony(i,(b.*n)+((b-1)*n)+n)) OB=OB+z_superfinal; if OB==Inf OB=0 out(i)=-ob;

21 Constraints module function out=constraint(colony) global B; global K; global N; global h; for i=1:size(colony,1) out(i)=0; for b=1:b x=0; for n=1:n x=x+colony(i,(b.*n)+((b-1)*n)+n); if x>20 out(i)=out(i)+ x - 20;

22