femtocell paper

0.1. RESOURCES AND SUBCARRIER ALLOCATION IN A TWO-TIER OFDM FEMTOCELL NETWORKWITHQUALITY OF SERVICE GUARANTEE1

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0.1 Resources And Subcarrier Allocation in atwo-tier OFDM Femtocell NetworkWith Qual-ity Of Service Guarantee

0.1.1 1. Abstract

Abstract-In this project, we consider the problem of allocating power and sub-carrier to the femtocell users in a two tier (uplink-downlink) OFDM based net-work. It is a multi-objective optimization problem which aims to maximize thethroughput of all users, simultaneously increasing the power efficiency of femtobase station. Interference to macro users is checked and is kept below a cer-tain tolerable threshold and rate constraint is being imposed on Delay Sensitiveusers. The problem is optimized using NSGA-II algorithm and the results arecompared with the existing scheme. Keywords-OFDM, femtocells, power allo-cation, multi objective optimization, NSGA-II (non-dominanted sorting geneticalgorithm).

0.1.2 2. Introduction

INTRODUCTION

Femtocells are miniature versions of the standard base station. They arelow power base stations designed to facilitate cellular communication in the ar-eas where macrocell base station power received is not adequate to support theactive users or demand for cellular communication is very high and one macrobase station is not adequate to meet the requirements ??. They have a typicalcoverage of 10 meters and are used in small business offices or homes. Spectrumsharing is performed in the region of high number of active users [2]. How-ever, there is a great chance of cross-tier signal interference in such a spectrumsharing system [3]. Hence we allocate resources to enhance the performance ofnetwork and facilitate better cellular communication. In [4], a non-cooperativepower allocation with SINR adaptation is used to alleviate the uplink inter-ference suffered by macrocells; while in [5], a Stackelberg game based powercontrol is formulated to maximize femtocell’s capacity under cross-tier interfer-ence constraints. However, subchannel allocation is not considered. In [6], ajoint subchannel and power allocation algorithm is proposed to maximize totalcapacity in dense femtocell deployments. While in [7], lagrangian approach isused to allocate power in OFDM based femtocell network. In [2], the distributedsubchannel and power allocation for co-channel deployed femtocells is modeledas a non cooperative game, for which a Nash Equilibrium is obtained based on atime-sharing subchannel allocation. However, in these works, joint subchanneland power allocation with users’ QoS and cross-tier interference considerationsis not studied. In [8], a distributed modulation and coding scheme, subchanneland power allocation that supports different throughput constraints per usersis proposed, but it does not consider two tier networks.

Femtocells should be able to support the minimum requirements for delaysensitive users, such as video calling, online multimedia etc. while maximizing

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the capacity of delay tolerant users [9]. Resource allocation not only includesthe power allocation maintaining minimum required SINR, but here we alsoconsider the maximum power utilization of femtocell base station (maximumefficiency). The delay sensitive users have a minimum QoS requirement [10],while delay tolerant users do not. After including the constraints of powerbudget and maximum interference temperature level, we optimize the multi-objective problem formulation using NSGA-II algorithm. The remainder of thepaper is organized into following sections- section 2 provides the modeling of thesystems and the required mathematical model of optimization. In section 3 wediscuss briefly the algorithm used in allocating power and subcarrier to the usersfor two-tier system. In section 4 we have showed the results of simulations andcompared the results of proposed algorithm with existing results. We concludethe paper in section 5.

0.1.3 3. System Model and Optimization

System Model and Optimization

We consider the two-tier femtocell system with total K number of femtocellsin a cellular network, deployed in sub-urban areas. We assume that each fem-tocell comprises of F users and the number of users in macrocell is M. Let thetotal bandwidth allocated to cellular communication in the macrocell be B andthe number of sub-carriers as N. We first calculate the results for uplink caseand extend them to the downlink case. We model the SINR as:

ΥFk,u,n =

pFk,u,ngFk,u,n

pFw,ngFk,w,nM + σ2

(1)

Where ΥFk,u,n is the SINR at the kε{1, 2, . . . ,K} femtocell base station to its

uε{1, 2, . . . , F} user at the nε{1, 2, . . . , N} subcarrier. Where pFk,u,n is the trans-mission power by the u user belonging to the k femtocell on n subcarrier to thefemtocell base station. gFk,u,n is the channel gain from femto user u to its fem-

tocell base station k on n subcarrier. pFw,n is the macro user’s wε{1, 2, . . . ,M}transmit power on the n sub channel to the macrocell base station. gFk,w,n is the

channel gain on sub channel n of the macro user w to the femtocell k and σ2

is the AWGN (Additive White Gaussian Noise) power. We have assumed theinterference between femtocells to be negligible [11], [12], as they are transmit-ting much lower power [11] than macro base station and separated by a largerdistance to cause any significant interference. Hence we only consider the inter-ference caused by femtocell users on macrocell users. Using Shannon’s capacityformula, we can write:

CFk,u,n = log2(1 + ΥF

k,u,n) (2)

Where CFk,u,n is the Capacity of the femto user u in the k femtocell on the sub

carrier n.


0.1.4 4. Optimization Problem Formulation

Optimization Problem Formulation

Our aim is to maximize the total capacity of all users, satisfying the con-straints of Quality of service. The subcarrier and power allocation will be de-cided by these quality factors. Our objective is to maximize the throughput [10]requirement and to maximize the femtocell power efficiency usage wise:

max

K∑k=1

F∑u=1

N∑n=1

ak,u,nCFk,u,n (3)

minPmax tot −K∑

k=1

N∑n=1

ak,u,npFk,u,n (4)

Subject to:C1 : pFk,u,n ≥ 0,∀k, u, n

C2 : pFk,u,n ≤ Pmax,∀k, u, n

C3 :

N∑n=1

ak,u,nCFk,u,n ≥ Ru,∀k, ∀uεDSk

C4 :

K∑k=1

F∑u=1

ak,u,npFk,u,ng

MFk,w,n ≤ Ithn ,∀n

C5 :

F∑u=1

ak,u,n ≤ 1,∀k, n

C6 : ak,u,nε{0, 1},∀k, u, n

The first objective is to maximize the total throughput capacity of all thefemtocell users [10]. The second objective is the maximum resource/power uti-lization of the femtocell base station. Here ak,u,n is the identifier matrix. Ifak,u,n = 1, means that in k femtocell, the u user is assigned the n sub channel.Otherwise it is zero. It ensures that no two users in a femtocell are allocated thesame sub channel. Pmax is the maximum power that each user can transmit.Pmax tot is the maximum power that all femtocells transmit (in case of down-link, receive) it is equal to Pmax ∗ F ∗K. Here we assume that the maximumpower that a femto base station can transmit is the maximum power that a usercan transmit multiply by total number of femto users.

DSk and DTk are the set of delay sensitive and delay tolerant users in afemtocell k. DSk + DTk = F and DSk ∩ DTk = ∅ [10]. C1 makes sure thatpower transmitted or received (in case of downlink) be greater than zero inthe allocated subcarrier. In C2, we fulfill the QoS requirement of the delaysensitive users. The capacity of delay sensitive users should be more than agiven threshold Ru. In the constraint C3gMF

k,w,n is the channel gain on sub

channel n, from femtocell user u in femtocell k to the macro base station. Ithn is

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the maximum interference temperature level that is tolerated. This constraintimplies that only those sub channels be assigned to the femtocell users whoseinterference temperature level to the macro base station is below this level. C5and C6 implies that no two users, in the same femtocell, is assigned the samesub channel and only one subcarrier is allocated to a user.

0.1.5 5. Subcarrier and Power Allocation Scheme

The above Multi-objective problem is solved using Non Dominated Sorting Ge-netic Algorithm - II (NSGA-II). The algorithm and its benefit over conventionalNSGA is explained in detail in following sub-sections.

5.1 Genetic Algorithm

Genetic Algorithm are a class of evolutionary algorithms use to find solutionfor a multi-objective optimization problem. They provide novel approaches toproblem solving technique inspired by biological evolution. They use operatorslike, Cross-over, Mutation and Selection, who’s functionality is same as theirnatural biological counter parts. This property makes an efficient algorithm insearching solution to the optimization problem from a pool of feasible solution.”Fitness” value of every solution is calculated by the ”fitness function” whichforms the base in deciding how ”fit” the solution is in its population, in otherwords, how well it optimizes the problem.

Initially random ”population”, a set of random solutions, is created. Thefitness of each member of the population is tested. Based on their fitness value,they are mated to give offspring that have different or mixed characteristics,in other words, fragments of different solutions are used to make new solution.This new set of solution contains mixed traits from their parent population.This process is called ”cross-over”.” Mutation” is performed to search for newvariety of solutions, more than what is available in the initial population. Eachset of solution (also known as a ”Chromosome”) goes through all the steps toform more fit ”generation”.

Many times in a multi-objective optimization problem, there are conflictingobjectives. Hence there is not a single non-dominating solution but a set ofnon-dominating solution. Parito fronts are plotted and the best solution (non-dominating) is selected (choice of selection may vary from person to personother system specification).

5.2 NSGA-II

Genetic Algorithm, even though delivered exceptional results, suffered fromvarious drawbacks. One of them being their computational complexity. Theyhave the computational complexity of the order of O(MN3). Where M is thenumber of objectives and N is the Population size. They lacked elitism too.Even better solutions had the tendency of being modified. It also required asharing parameter in order to obtain a wide variety of equivalent solutions.

The initial population in the NSGA-II algorithm is first sorted into fronts.Where the members of first front are non dominated by any other member.The members of second front are dominated by the members of first front onlyand so on. A solution is said to dominate the other solution if its fitness value,


for all objective function, is better than the other. The individuals in the rth

front are assigned a value of r. Crowding distance is a parameter that is use todescribe how close an individual is to its neighbor. It is a measure of diversityin population.

Each individual chromosome is coded as a two dimensional matrix with Frows and K columns. Each element of the chromosome matrix is composed oftwo parts, the left hand side (dimensionless quantity) denotes the nth subcar-rier that is assigned to the femto user in that particular Femtocell. We assumethat only one subcarrier is assigned to each femto user. The right hand sidedenotes his uplink/downlink power on that subcarrier. Keeping in mind thatpower allocated to each user is less than Pmax, satisfies constraint 1 and 2. andonly one subcarrier is assigned to each user satisfies constraint C5 and C6. Thefigure below shows the structure of a chromosome (where we have assumed thatthere are only two femto users). The last row depicts how chromosomes wouldbe considered for crossover and mutation.

Users/Femtocells FC1 FC2 ————— FCKF1 12 17dbm 36 14dbm ————— 15 16dbmF2 21 19dbm 42 18dbm 02 17dbm

Used as string 12172119 361442218 ————— 15160217

The standard NSGA-II algorithm is as follows:i) Generation- Initially the population is randomly generated.

ii) Fitness Check -The fitness of each individual is evaluated through all the ob-jective functions.iii) Ranking-Rank the population using Non Dominant Sorting Algorithm de-scribed in section 5.2.3.iv) Crowding Distance- Calculate the crowding distance by using the crowdingdistance algorithm described in 5.2.3.v) Generating new generation- This is done by following described operations:

• Selection- Select two chromosomes based on crowding selection operator.which is described in section 5.2.4.

• Crossover-With a crossover probability cross over the parents to form newoffspring (children). If no crossover was performed, offspring is the exactcopy of parents. The single point crossover is explained in section 5.2.5.

• Mutation-With the probability of mutation, mutate new offspring at eachlocus (position in chromosome). Mutation is explained in section 5.2.5.

• Acceptance- Place new offspring in the new population.

• Replace- Use new generation for the further run of algorithm.

• Test-If the end condition is satisfied (e.g. when reaches a constant numberof generation for which the algorithm is run), stop and return the bestsolution in current population.

• Loop- Go back to fitness again.

The following sub sections provide detailed description of steps involved inresource allocation using NSGA-II algorithm.

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5.2.1 Population initializationNumber of population and number of generation are fixed at the very begin-ning of simulation/algorithm. Let the number of population be P and letthe number of generations be G. Hence the dimension of population will beP × (F ×K × 4). Each individual is created by generating a single digit ran-dom number.

5.2.2 Evaluate Objective FunctionThe fitness of each individual chromosome is evaluated with respect to eachobjective function.

5.2.3.1 Non Dominated Sorting Algorithm

• For each individual p in the main population P do the following:

– Initialize Sp = φ. This set would contain all the individuals that aredominated by p.

– Initialize np = 0. This is the number of individuals that dominate p.

– For each individual q in p:

∗ If p dominates q then add q to the set Sp i.e. Sp = Sp ∪ {q}.∗ Else if q dominates p then increment the domination counter forp i.e. np = np + 1.

– If np = 0 i.e., no individuals dominate p then p belongs to the firstfront. Set rank of individual p to 1 i.e., prank = 1. Update the firstfront set by adding p to front one i.e., F1 = F1 ∪ {p}.

• This is carried out for all the individuals in main population P .

• Initialize the front counter to one i.e., i = 1.

• Following is carried out while the ith front is nonempty i.e., Fi 6= ∅:

– Q 6= ∅ The set for storing the individuals for (i+ 1)th front.

– For each individual p in front Fi.

∗ for each individual q in Sp (Sp is the set of individuals dominatedby p).

· nq = nq − 1, decrement the domination count for individualq.

· If nq = 0 then none of the individuals in the subsequentfronts would dominate q. Hence set qrank = i + 1. Updatethe set Q with individual q i.e., Q = Q ∪ {q}.· Increment the front counter by one i.e., i = i+ 1.

· Now the set Q is the next front and hence Fi = Q.

Here we are also keeping record for each individual, the number of individ-uals that dominate it and also those individual that are dominated by it. Thisunique feature makes NSGA-II more attractive than NSGA.

5.2.3.2 Crowding Distance CalculationCrowding Distance is a measure of diversity amongst the individuals. This is


calculated for all the individuals of a front. The crowding distance is comparedbetween the individuals belonging to the same front only. The algorithm ofcalculating crowding distance is described below:

• For each front Fi we do the following:

– Take any objective function (say m) to begin with, and for eachobjective function do the following:

∗ Calculate the ”Fitness” (value) of each individual front with re-spect to the above objective function only.

∗ Store them in the ascending order in a set I, i.e. I = sort(Fi,m).

∗ Assign infinite distance to the first (one with minimum valueof crowding distance) and the last (one with maximum valueof crowding distance) solution points. These form the boundarypoints for this generation, i.e. I(d1) =∞ and I(dl) =∞. Wherel is the total number of individuals in front Fi.

∗ Re calculate the value of other points with respect to theseboundary point value. Let j be the jth individual in front Fi.

∗ For j = 2 to l − 1:

· I(dj) = I(dj)+I(j + 1).m− I(j − 1).m

fmaxm − fmin

m

where I(j).m is the

value of mth objective function for jth individual in frontFi. f

maxm and fmin

m are the maximum and minimum value ofobjective function m.

Crowding distance is the distance between individual solutions when plottedin an m dimensional space. The boundary points always optimize an objectivefunction. Hence they are given infinite value so that they are always selected.

5.2.4 Tournament selectionTill this stage we have grouped individuals of the population in Fronts andassigned crowding distance to each of them. The next step is to select the indi-viduals for mating to produce a new generation. Hence it is called Tournamentselection. The selection is done using a crowding-comparison- operator (≺n).Every individual in a population has two major attributes, its rank (prank) andits crowding distance Fi(dj) (It is the crowding distance of jth individual infront i). We define partial order as:

• p ≺ q if prank < qrank.

• If they belong to the same front Fi than Fi(dp) > Fi(dq).

In other words, for selection purpose, we choose the individual with the lowerrank, and if they belong to the same front, we choose the one with lower crowd-ing distance. The mating pool is prepared based on this selection whose size is P .

5.2.5 Single Point CrossoverMating between the selected individuals is done by the mechanism of cross-over. Fragments of individuals that were selected are exchanged to produce offsprings with new or mixed characteristics. Our chromosomes is basically an

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array of integers. Single point crossover is performed to swap some portion ofone parent chromosome with another to produce two new (child) chromosomes.An example is shown below where all the integers after | are exchanged to formnew individuals:parent 1: 17491311|1814 parent 2: 13251822|1234offspring 1: 17491311|1234 offspring 2:13251822|1814

5.2.6 MutationMutation is performed in order to maintain diversity in population. It is ana-logues to biological mutation. Here we alter some digits of our chromosomes.This is done by assigning a random variable to the digits of chromosomes whichgives the information regarding alteration of that digit. The probability of mu-tation, Pm is usually kept 100 times lower than the probability of crossover, Pc.The purpose of mutation is to avoid generation of local maxima/minima by pre-venting the chromosomes to become too similar to each other. Thus preventingor slowing evolution. An example of mutation is shown below, where the bolddigit is being mutated: parent: 18271-9441214offspring: 18271-5441214

5.2.7 Generation of new populationWe have with us a pool of individuals from the original population and off-springs. The new population is formed, based on the non-dominant sortingand crowding distance operator. Steps 5.2.4, 5.2.5 and 5.2.6 are repeated for Gnumber of times.

In [12] elitism was assured by using Largest Weighted Delay First, LWDF.Here since all the best individuals from the current and previous populationsare added to the new population, elitism is guaranteed. The best individualchromosome from the final population gives the desired allocation of subcarriersand bits per subcarrier.

0.1.6 6.Simulation Results and Discussion

Simulation results, given in this section are compared with the “Existing So-lutions” [10]. The femtocells are randomly placed over the cell. The coverageradius of macro cell is 500 m while femtocell is 10 m. Macro cell and femtocellusers can transmit a maximum of 23dbm power. The carrier frequency is 2Ghz, bandwidthB = 10 Mhz, N = 50, M = 50, σ2 = B

NN0 where N0 = −174dBm/Hz is AWGN (Additive White Gaussian Noise) power spectral density.The path loss models for indoor femto users and outdoor macro users are basedon [15] and block fading channel gains are modeled as i.i.d. unit exponentiallydistributed random variables. Standard deviation of shadow fading between theMBS and user is 8dB, while that between an FBS and user is 10dB. The “Ex-isting algorithm” included in the simulation for comparison is the sub channelallocation scheme proposed in [10] in conjunction with optimal power allocationproposed in this paper.

Figure 1 to 5 shows the parito front for uplink network i.e. the total ca-pacity of all users versus power difference per femtocell (power difference is thedifference between the total power that is being transmitted and the maximumpower budget of femto base station). The parameters used in generating theplots are: F = 2, Ru = 9 bps/Hz, Pmax = 23dbm (uplink), Pmax = 20dBm


(downlink) and threshold interference level Ithn = 7.5x10−14w (-101.2 dBm).The total transmitted power cannot be greater than the total power budget,

hence we get negative values on the Y-axis. As NSGA-II algorithm works onminimization of objective function, we multiply the objective function in (3) by-1 and plot the result. Hence on both the axis we get negative values. The bestpoints (non dominated points) in all the parito fronts are chosen and plottedin figure 8. From the figures 1 to 5 we observe that the power difference perfemtocell remains almost constant, averaging to 0.0365 Watts.

Figure 6 shows the total capacity of all delay sensitive users versus numberof femtocells, the parameters set are same as above. From the figure we seethat the capacity obtained by proposed algorithm is much higher than that ofexisting algorithm. We can clearly see from the figure that it also satisfies theconstraint of minimum capacity for DS users. Similar result is observed fordownlink network.

Figure 7 shows the total capacity of Delay tolerant users versus total numberof femtocells. From the figure we see that the capacity of delay tolerant usersover the femtocell range, is almost same as that of delay sensitive users. This isbecause we are maximizing the capacity of both the type of users giving equalweights to them. It is however less than the existing scheme. Similar result isobserved for downlink network.

Figure 8 shows the total capacity of all users over number of femtocells. Weobserve that the total capacity (capacity of DS users + capacity of DT users) isslightly greater than the existing algorithm. Averaging over all femtocells, thetotal capacity is greater by 4.5 than existing scheme. Same is true for downlinkcase.

Figure 9 shows the variation in capacity versus variation in InterferenceTemperature Level for both the uplink and downlink case. The value of Pmax

used is 23 dbm for uplink and 20 dbm for downlink for K=10. Curve is plottedfor F=2 and F=4 with Ru = 9 bps/Hz. From the graph we observe that thesum capacity increases as we decrease the interference tolerance temperaturelevel because we are increasing the allowable tolerance with macro users. Aswe increase femto users from 2 to 4 we get a rise of almost 20% in the totalcapacity in both the uplink and downlink network. Also increasing the Pmax

from 20 dbm to 23dbm we get to see a rise of almost 20% in the total capacity.

0.1.7 9. Conclusion

In this paper we considered the problem of subcarrier allocation and powerallocation to the femtocell users considering the constraints of Quality of Servicefor delay sensitive users. The proposed algorithm has properly allocated all theresources and from the simulation we can see that it provides more efficientresults than the existing algorithm.

0.1.8 References

[1] D. Lopez-Perez, A. Valcarce, G. de la Roche, and J. Zhang, “Ofdma fem-tocells: A roadmap on interference avoidance,” IEEE Commun. Mag., vol.47, no. 9, pp. 41–48, 2009. [2] J.-H. Yun and K. G. Shin, “Adaptive inter-ference management of ofdma femtocells for co-channel deployment,” IEEE J.Sel. Areas in Commun., vol. 29, no. 6, pp. 1225–1241, 2011. [3] K. Son,

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S. Lee, Y. Yi, and S. Chong, “Refim: A practical interference management inheterogeneous wireless access networks,” IEEE J. Sel. Areas in Commun., vol.29, no. 6, pp. 1260–1272, 2011. [4] V. Chandrasekhar, J. G. Andrews, T.Muharemovic, Z. Shen, and A. Gatherer, “Power control in two-tier femtocellnetworks,” IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4316–4328,2009. [5] X. Kang, R. Zhang, and M. Motani, “Price-based resource alloca-tion for spectrum-sharing femtocell networks: a stackelberg game approach,”IEEE J. Sel. Areas in Commun., 2012. [6] J. Kim and D.-H. Cho, “A jointpower and subchannel allocation scheme maximizing system capacity in indoordense mobile communication systems,” IEEE Trans. Veh. Technol., vol. 59,no. 9, pp. 4340–4353, 2010. [7] Wei-Chen Pao • Yung-Fang Chen • Chia-Yen Chan, “Power allocation schemes in OFDM-Based Femtocell Networks”in Wireless Personal Communication, DOI 10.1007/s11277-012-0626-2 [8] D.Lopez-Perez, A. Ladanyi, A. Juttner, H. Rivano, and J. Zhang, “Optimizationmethod for the joint allocation of modulation schemes, coding rates, resourceblocks and power in self-organizing lte networks,” in INFOCOM, 2011 Proceed-ings IEEE, april 2011, pp. 111–115. [9] M. Tao, Y.-C. Liang, and F. Zhang,“Resource allocation for delay differentiated traffic in multiuser ofdm systems,”IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2190–2201, June 2008.[10] Haijun Zhang, Wei Zheng, Xiaoli Chu, Xiangming Wen, Meixia Tao, A.Nallanathan, David Lopez-Perez, “Joint Subchannel and Power Allocation inInterference-Limited OFDMA Femtocells with Heterogeneous QoS Guarantee,”in Globecom 2012-Wireless communication symposium. [11] V. Chandrasekharand J. G. Andrews, “Femtocell networks: A survey,” IEEE Commun. Mag.,vol. 46, no. 9, pp. 59–67, 2008. [12] H.-S. Jo, C. Mun, J. Moon, and J.-G.Yook, “Interference mitigation using uplink power control for two-tier femtocellnetworks,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 4906–4910,Oct. 2009. [13] Nitin Sharma , K. R. Anupama, “On the use of NSGA-II formulti-objective resource allocation in MIMO-OFDMA systems”, Wireless Netw(2011) 17:1191–1201, DOI 10.1007/s11276-011-0340-0 [14] Kalyanmoy Deb, As-sociate Member, IEEE, Amrit Pratap, Sameer Agarwal, and T. Meyarivan, “AFast and Elitist Multiobjective Genetic Algorithm: NSGA-II”, IEEE TRANS-ACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO. 2, APRIL2002 [15] Further Advancements for E-UTRA, Physical Layer Aspects, 3GPPStd. TR 36.814 v9.0.0, 2010.

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