Genetic Approach with a New Representation for Base Station Placement in Mobile Communications

Jin Kyu Han*, Byoung Seong Park*, Yong Seok Choi**, and Han Kyu Park* * Dept. of Electric and Electronic Engineering, Yonsei University, 134 Shinchon-dong, Seoudaemun-gu, Seoul, Korea, 120-749

** IMT-2000 System Development Division, ETRI, 161 Gajeong-dong, Yusong-Gu, Daejon, Korea, 305-350

{untuchbl, bspark, hkpark}@yonsei.ac.kr, choiys@etri.re.kr

Abstract - In this paper, we find out the best base station placement using genetic approach. A new representation describing base station placement with real number is proposed, and new genetic operators are introduced for it. This new representation can describe not only the locations of base stations but also the number of those. Considering both coverage and economy efficiency, we also suggest a weighted objective function. Our algorithm is applied to an obvious optimization problem and then is verified. Moreover, our approach is tried in inhomogeneous traffic density environment. Simulation result proves that the algorithm enables to find near optimal base station placement and the efficient number of base stations.

I. INTRODUCTION Base station placement is the most important problem to

achieve high cell planning efficiency. It is expected that the third generation wireless systems provide a great variety of services. Thus cell planning should be carried out considering inhomogeneous traffic. How to place base stations depends on traffic density, channel condition, interference scenario, the number of base stations, and the other network planning parameters; at result, it becomes an NP-hard problem. Genetic algorithm is useful to solve this kind of complex problem. This method represents feasible solutions as individuals with genome, and determines which individuals could survive in a certain criterion formulated to maximize (or minimize) a given objective function. In several studies genetic approach has been used to find out the best possible base station placement [ 1,2]. Binary string representation, a classic representation method of genetic algorithm, is applied in [I] , and a hierarchical approach is considered in [2]. However, those approaches have representation limit, and a lot of runs cannot guarantee optimum because the possible base station positions are discrete.

In this paper, we suggest a new representation describing base station placement with real number and introduce new genetic operators for it. Our proposed representation can describe not only the locations of base stations but also the number of those. To consider both coverage and economy efficiency, we establish a simple objective function. Our algorithm is verified through applying it to an obvious optimization problem. In addition, our approach is tried in inhomogeneous traffic density environment.

0-7803-7005-8/01/$10.00 0 2001 IEEE

11. OVERVIEW OF GENETIC ALGORITHM Genetic algorithm is one of the nature-inspired algorithmic

techniques based on the principles of natural evolution [3] and is widely used to solve optimization problem [4]. In genetic algorithm, feasible solutions are modeled as individuals described by genomes. A genome is an arrangement of several chromosomes, which symbolize characteristics of the individual. Population is the total amount of individuals. Some of them can survive and others will die in the next generation by their own fitness and a given selection rule. Fitness is evaluated by a given objective function. Genetic operations such as crossover and mutation are performed to produce new individuals in subsequent generation. The crossover operator defines the procedure generating a child from parent’s genomes. The mutation is carried out chromosome by chromosome, and its exploration and exploitation get the algorithm to avoid local optimum. If current population accepts the given termination condition, new generation is not produced any more. Otherwise, dominant individuals are selected and genetic operators reproduce new individuals from them. The best individual of each generation is transferred over to the next generation if elitism is adopted. Fig. 1 shows the common procedure of the genetic algorithms.

The theoretical basis of genetic algorithm relies on the concept of schema. A schema is defined as the similarity of template describing a subset of genomes with similarities at certain chromosomes. Schemata are available to measure the similarity of individuals. John Holland’s schema theorem and building-block hypothesis [3] have been often used to explain how the genetic algorithm works. According to schema theorem, short, low-order, and above-average schemata receive exponentially increasing trials in subsequent generations. It proves that the individuals with high fitness will have a high survival probability when a suitable representation is applied. The building-block hypothesis suggests that the genetic algorithm will perform well when it is able to identify above-average-fitness and low-order schemata and recombine them to produce higher-order schemata of higher fitness. In sum, individuals with similar characteristics must be represented by similar genotype.

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initialize population

select individuals for mating

mate individuals to provide offspring

mutate offspring

I . . . k . . . / . . . K

insert offspring into population

are stopping criteria satisfied?

fi finish

Fig. 1. Brief flow chart for genetic algorithms

111. PROPOSED ALGORITHM FOR BASE STATION PLACEMENT We propose a genetic algorithm working well on base

station placement problem. The main particulars considered for developing algorithm are:

(Pl) One genome must represent all of the base station locations, and genotype can describe the number of base stations as well as base station position.

(P2) A chromosome expresses one base station position. (P3) The number of possible base station locations must be

unlimited; therefore, there are infinite candidates of the base station locations.

(P4) Similar genotypes represent the genomes of the closely located base stations.

An algorithm satisfying above factors is consistent with the building-block hypothesis and schema theorem.

Three things we must establish to solve a problem through a genetic algorithm is following:

o Define a representation o Define the genetic operators o Define the objective function

How to define a representation, genetic operators, and objective function determines the algorithms. We should design the genetic algorithm as considering (Pl-P4). Followings explain our proposed algorithm in detail.

A. Representation Fig. 2 illustrates how to represent genomes. A genome i s

denoted as a vector g =(cI,-..,cn) where c, = ( x , , y , ) is the chromosome for k-th base station position. This method fulfills (Pl) and (P2). K is the maximum number of base stations, and all of them can be located in x-range [-Xmx, Xmx] and y-range [-Y,, , YmX] with origin (0,O) .

.... -U,,* i (0.0)

Kth BS

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genetic algorithm. The easiest scheme is termination upon generation. When the number of current generation is larger than the specified number of generation, the algorithm is finished. Termination upon convergence compares the previous best-of-generation to the current best-of-generation. If the current convergence is less than the requested convergence, reproduction procedure is ceased. Termination upon population convergence compares the population average to the score of the best individual in the population.

In our application, we use one child crossover operator. A single child c;Md is born from dad and mom, CY and c,""" . Fig. 3 shows the procedure of one child crossover operation in our algorithm. If one of parents is NULL, the child receives the other parent's attribution. Otherwise, the child is generated by

I Dad

1 Mom

l child ~ 1

a are not NULL

Fig. 3. One child crossover operation

Individual m ' 1 2

NULL P=Pn

NULL

P=P"

where oc is the parameter of crossover operation. I Xkd"d - x;"" I and I y,"" - y;"" I can be used as a measure of closeness. This method is based on the fact that if the attribution of both parents is similar, child's is also similar to parents ' .

Mutation is performed chromosome by chromosome with probability P",, . Fig. 4 shows the procedure of mutation operation in our algorithm. Mutation is very close to the initialization scheme with user defined base station position. If c,, =NULL, redefine c,,,, = NULL with probability or c,, = ( u , , ~ , ) with probability 1-% . If c,, f NULL, redefine c,", = (x",, + xI, Y , , ~ -t x,) with probability P, or c",~ =NULL with probability 1 - P, , where xI and xz are Gaussian distributed random variables with zero mean and variance o,:,. <$",and a,: are the parameters of mutation operation.

Roulette wheel method is applied for the selection scheme. This selection method picks an individual based on the magnitude of the fitness score relative to the rest of the population. The higher the score is, the more selective an individual will be. Any individual has a probability p of the choice where p is equal to the fitness of the individual divided by the sum of the fitness of each individual in the population. Therefore, the individual with high fitness can survive with high probability.

C. Fitness Evaluation Fig. 5 illustrates the fitness evaluation procedure composed

of evaluator and objective function. Evaluator calculates the covered traffic and n(g) for a given g using propagation model, traffic map, and map for path loss prediction. Cell area covered by the base stations of g is evaluated, and then the covered traffic by g is obtained. Considering coverage and economy efficiency, we define the objective function as

f ( g > = w , * f ; (g>+wc. . t . (g)

trafficmap map

cover e d g evaluator

propagation model weghts

Fig. 4. Mutation operation

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Fig. 5. Fitness evaluation

where f, and f, are the objective functions for coverage and economy respectively and these are defined as

P"

p . = p , c.,

covered traffic K - n(g) and f,(d = -. '(') = total offered traffic K

0.1 xm. = y , 7.5 km

0.5 p.' - 0.2 - 3826.5m c c 0.51m

As the covered traffic area widens corresponding to g , ' ( g ) is increasing. On the other hand, f,(g) increases when the less base stations are placed. Total fitness is calculated with w, and we subject to w, +we = 1 . The weights are determined by user's preference. If the coverage is more important, one may choose large w,. Otherwise, large w, may be chosen to be more desirable using less base stations.

IV. SIMULATION RESULTS To demonstrate our algorithm, we consider the 1-tier

hexagonal cellular environment, where traffic is distributed uniformly in each hexagon cell whose radius is 2.5 km. In this case, the optimum position of base station is the center of hexagon and the optimum number of base stations is 7 obviously. The simulation parameters are listed in table 1. Path loss prediction is carried out using the following equation.

L = Lo x (d /d0Y

where Lo = 140 dB and do = 2.5 km. Because the largest path loss in coverage is assumed 140 dB, a base station can cover on hexagon cell. Fig. 6 shows the results. In fig. 6 (a), there is the initiation of simulation with five base stations. As the generation increases, the base stations tend to be placed to the optimum and the number of base stations is also converged automatically. After 700th generation, we can find out base station placement that guarantees 97.8% coverage.

TABLE 1. Simulation Parameters

elitism I used I initialization I random

termination I upon generation I M I 30

stations are obtained after 700 generation. Those base stations cover 88.1% offered traffic. These results verify that our proposed algorithm can provide appropriate base station locations and proper number of base stations, and user can control tendency by deciding preference weights. For example, if one prefers 90% coverage with 7 base stations rather than 100% coverage with 10 base stations, the weights can be determined by the following equation.

1 . 0 ~ w, + ~ ( 1 - ~ , ) < 0 . 9 x w , +-(1-w,) 10-7 10 10

Left side of above equation is the fitness of 100% coverage with 10 base stations, and right side is the fitness of 90% coverage hith 7 base stations. The condition of 'w, < 0.75 is recommended in this case.

(a) initial generation (b) after 2nd generation

(c) after 400th generation (d) after 700th generation

Fig. 6. Base station placement on generation (k: = 7, w, = 1)

.I I (a) initial generation (b) after 700th generation

Fig. 7. Base station placement ( K = lO,w,? = 0.3)

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I I

(a) initial generation (b) after 700th generation

Fig. 8. Base station placement ( K = 10, y = 0.27)

5

4 5

4

3 5

3

2 5

2

1 5

I

0 5

60

50

40

30

20

10

(a) traffic density (b) altitude

(c) initial generation (d) after 1000th generation

Fig. 9. Base station placement in inhomogeneous traffic

Fig. 9 is an example of simulation result considering inhomogeneous traffic distribution. Given traffic density is shown in fig. 9(a). Hata model [5] is applied for propagation model and altitude is shown in fig. 9(b). We take w, =0.8 and K=12 for this simulation, and 99% coverage is achieved after 1000th generation.

V. CONCLUSION In this paper, we proposed a genetic approach with a new

representation for base station placement and verified it. We also define genetic operators to utilize the representation with real number, and establish the objective function in consideration of coverage and economy efficiency. The proposed algorithm can be used to locate the base stations with more coverage and less base stations. Simulation result proves that we can find near optimal solution by the algorithm.

Measured traffic density and realistic altitude map will be taken into account in further study. The representation scheme can be expanded to optimize other cell planning parameters such as antenna configuration, transmit power, polarization, and so on. The genetic algorithm can also be modified to obtain the base station placement considering not only traffic density but also various service types.

REFERENCES [I ] Calegari P., Cuidec F., Kuonen P., and Wagner D.,

“Genetic Approach to Radio Network Optimization for Mobile Systems,” Proc. IEEE VTC 1997, vol. 2, pp.755- 759,1997. X. Huang, U. Nehr, and W. Wiesbeck, “Automatic Base Station Placement and Dimensioning for Mobile Network Planning,” Proc. IEEE VTC 2000 Fall, vol. 4, pp. 1544- 1549,2000. Holland J.H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975. Goldberg, David E, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989.

[SI Hata M., “Empirical Formula for Propagation for Propagation Loss in Land Mobile Radio Services,’’ IEEE Trans. on Vehicular Technology, vol. 29, pp. 317-325, Aug., 1980.

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