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Mathematical Modelling and Comparisons of Four HeuristicOptimization Algorithms for WCDMA Radio Network Planning

Jie Zhang, Jun Yang, Mehmet E. Aydin, Joyce Y. WuCentre for Wireless Network Design (CWIND), Dept. of Computing and Information Systems

University of Luton, Luton, LU1 3JU, UKTel.: +44 1582 743288, Email: jie.zhang@luton.ac.uk

ABSTRACTIn order to obtain accurate and reliable network planning and optimization results. The characteristics ofWCDMA networks such as power control, soft handover (SHO) and the strong couplings between coverage andcapacity have to be modelled accurately. These characteristics lead to unprecedented complexity of WCDMAradio network planning and optimisation that has not been seen in previous cellular networks. In this paper, wewill present mathematical models that consider the characteristics of WCDMA radio networks. We will also

present and compare the performance of four optimisation algorithms based on meta-heuristics that can be usedto find solutions for practical WCDMA radio network planning and optimisation.Keywords: WCDMA, mathematical modelling, radio network planning, optimization algorithms.

1. INTRODUCTION3G (3 rd Generation) cellular networks such as WCDMA are being rapidly deployed/expanded. Without proper

planning, a WCDMA radio network can neither be successfully deployed, nor be successfully expanded. Whilein operation, a WCDMA radio network undergoes frequent optimizations according to changing demands andnew business models, which is similar to planning except that the vast majority of site locations are alreadyfixed. A well planned and optimized WCDMA radio network can provide some 30% extra capacities under thesame infrastructure cost. Hence, network planning and optimization plays a vital role for the deployment andmaintenance of WCDMA radio networks.

Cellular network planning and optimization is not a new topic, but as new technologies emerge, the subjectremains as fresh as before. It has been proved that WCDMA radio network planning is a NP-hard problem [1],therefore, meta-heuristics rather than other exact optimization methods are more suitable for WCDMA networkoptimization.

In this paper, we will present mathematical models that consider the characteristics of WCDMA radio

networks. We will also present and compare the performance of four optimisation algorithms based on meta-heuristics that can be used to find solutions for practical WCDMA radio network planning and optimisation.

2. INTEGER PROGRAMMING MODELS FOR WCDMA RADIO NETWORK PLANNINGOnce the system has been dimensioned, the whole area under consideration can be divided into K regions, andeach region i (i = 1… K ) contains n i candidate sites where base stations (BSs) can be installed. Assume the set of

candidate sites is S = {1, … , p},1

K

ii p n

== ∑ . Only one candidate site to install a BS is allowed to be selected

from each region, and an installation cost ci is associated with each candidate site i, i∈ S . With this simplifiednetwork scenario, the optimization process turns to be more affordable on a personal computer. The service areais represented by a set of mobile station M = {1,…, q}, and the required number of simultaneously activeconnections of Mobile Station (MS) j is denoted by r j , j∈ M .

The problem now is to select one candidate site from each region to install a BS such that the traffic capacityand the number of covered MSs are maximized with the lowest installation cost.

Each candidate site is denoted by a binary variable u i∈ {0, 1}, such that:

1 site is used.

0 elsei

iu i S

⎧= ∈⎨⎩

(1)

The propagation information is also supposed to be known. Let g ↑ij and g ↓ij be the propagation factors of theUL and DL connection between BS i and MS j, respectively. The propagation gain is estimated according to theempirical propagation models such as Hata model or deterministic ray tracing models that are more precise butcomputationally intensive.

We assume that a CPICH (Common Pilot Channel) signal can be detected if and only if the E c /I 0 (energy-per-chip-to-interference-density ratio) is not less than a given threshold γ0. The binary variable t ij is to denote the

CPICH signal detection subject to the following condition:

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( )CPICHc 0 0ij

1 when E /,

0 elseij

I t i S j M

γ ⎧ ≥⎪= ∈ ∈⎨

⎪⎩

(2)

where ( E c /I 0)ijCPICH is the E c /I 0 of CPICH signal from BS i at MS j.

If one or more CPICH signals are detected, the best server is chosen to be the BS whose CPICH is received by the MS with the highest level. That is denoted by

1 BS is the best server of MS,

0 elseij

i jb i S j M

⎧= ∈ ∈⎨⎩

(3)

For simplicity, only CPICH channel and dedicated physical data channel (DPDCH) are considered in thedownlink. Consider a 2-way soft handover, i.e., one MS connects to two BSs (SHO scenarios with more than 2connections can be analysed in a similar way). Define sijk as

1 MS is in SHO with BS and BS , BS is the best server , , .

0 elseijk

j i k i s i k S j M

⎧= ∈ ∈⎨⎩

(4)

and also define s j as

1 MS is in SHO.

0 else j

j s j M

⎧= ∈⎨

⎩

(5)

Four kinds of SHO gains are taken into account: SHO gains over the received power in uplink, SHO gainsover the APR (Average Power Rise) in uplink, SHO gains over the power control headroom in uplink, and SHOgains over the transmission power in downlink. All SHO gains are functions of MS speed and the received

power level difference between radio links with BS i and BS k , these functions are obtained from link-levelsimulations. For practical WCDMA radio network planning and optimisation, some constraints should beconsidered in the optimisation, such as:1. To be severed by the network, the MS should receive at least one CPICH signal with an E c/ I 0 that exceeds the

threshold value of CPICH signal detection.2. An MS severed by the network must have one and only one best sever, whose CPICH signal is received with

the highest E c/ I 0 at the MS (without consideration of call admission control — CAC).3. In downlink, the relative CPICH power is used to determine the SHO server. Therefore, for an MS that is in

the SHO state, at least one CPICH signal from a BS rather than its best sever should be received by the MSwith a power that differs from its best server by no more than a threshold value . This BS will be added intothe active set of the MS and selected as one SHO server.

With the consideration of installation costs, system coverage and traffic capacity, the cost function can beformulated as:

cov1 2 3min 1 1

i ii S ered severed

i total i S

c un T

c q T λ λ λ ∈

∈

⎧ ⎫⎛ ⎞⎛ ⎞⎪ ⎪

+ − + −⎨ ⎬⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎪ ⎪

⎩ ⎭

∑∑ (6)

where ncovered is the number of MSs that severed by the network, T total is total required traffic, and T severed is thetraffic supported by the network. λ1, λ2, and λ3 are associated weighting factors for the normalized installationcost, the percentage of uncovered MSs, and the percentage of unsupported traffic. Other performance indicators,such as uplink and downlink loading factors, pilot power, quality of received signal and SHO area etc., can also

be taken into account in the cost function with proper weighting factors, and this framework stands extendable ifone wants to work out with more variables.

To find a set of candidate sites, with which the cost function achieves the minimum, is the task ofoptimization algorithms. WCDMA radio network planning a multi-objective optimization problem, which can besolved as a single-objective problem by assigning different weighting factors to different objective terms, asshown in (6), or can be solved by using the method of Pareto front.

3. OPTIMISATION STRATEGIES AND HEURISTIC OPTIMIZATION ALGORITHMSThe problem discussed in the above section turns to be a p-median problem when only BS location is consideredas the decision variable. Moreover, we implement a particular reductionism that result in a significant shrinkingof the search space. The p-median problem constitutes seeking p number of locations each time regardless ofhow distant the sites are, while we divide the whole region under consideration into p ( K in this case as denoted

in Section II) segments. Every time one candidate site is selected from each segment. That makes the searcheasier and more affordable on a personal computer.The solutions are altered within their neighborhood via the neighborhood structures , which are very effective

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on the performance of exploration with search methods. In this study, we identified a neighborhood structureworking based on a totally random selection which is proved to be robust for different problem instances and canavoid the limitations with some directed exploration heuristics. Therefore, the main neighbourhood structureoffers moving to a neighboring state by simply and randomly switching to another candidate site.

In this paper, we have examined and used one simple hill climbing local search algorithm (Greedy) and threewell-known meta-heuristics: namely Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS).

Throughout the study, we worked out the critical parameters to fine tune the implementations. The SA has beenimplemented with a recently proposed approach, which is called evolutionary SA (ESA) [3], while GA and TSalgorithms are kept rather standard.

The greedy algorithm implemented in this work is used to benchmark the performance of other heuristicalgorithms. It does a simple hill climbing local search with the neighbourhood structure used across the wholestudy. The idea is to look for a better state of solution, if the state altered is better than the original one, the moveis adopted; otherwise, it is rejected and go to another neighbouring state. Using such a simple algorithm, we testthe minimum level of achievable optimization, which will benchmark other heuristic algorithms, and thehardness of the problem instances. If a heuristics algorithm cannot outperform the greedy algorithm, then it hasa serious correctness problem.

4. EXPERIMENTAL STUDIES A. Simulation configurationBased on the above-mentioned mathematical models, we developed a static simulator for WCDMA network toevaluate the performance of different heuristic optimisation algorithms. An example area for setting upa WCDMA network is shown in Figure 1. We consider a rectangular service area of 18km×16km containing

K = 19 base stations with 3-sector antennas, i.e. 57 cells in total. All 3-sector antennas are installed with theazimuth being 0 o offset from north and 0 o down tilt. For each BS, ni = n = 5 candidate sites are kept available,from which only one site will be selected to install a BS. q = 3600 traffic nodes (TN) are uniformly distributed inthis area, and all TNs have a traffic activity factor of 1.0.

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

Y - c o o r d

i n a

t e [ m ]

X-coordinate[m]

Candidate Site

Figure 1. The example area to be considered for a WCDMA network.

Network parameters used in the simulation are listed in Table 1.

Table 1. Network parameters used in the simulation.

Traffic 12.2 kbps voice Chip rate 3.84 McpsMax. BS Tx power 43 dBm Max. BS Tx power per link 40 dBmCPICH power 30 dBm Max. MS Tx power 24 dBmThreshold of CPICH E c/I0 -18 dB Noise power density -174 dBm/HzUL E b/N0 requirement 4.0 dB DL E b/N0 requirement 11.0 dBDL orthogonality 0.7 Traffic activity factor 1.0

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B. Configuring the Heuristic AlgorithmsThe parameter settings of the heuristic optimization algorithms used in this work are shown in Table 2.

Table 2. Parameter settings of heuristic optimization algorithms.GA population size 20GA crossover probability 0.1

GA generation number 200GA mutation probability 0.9GA crossover probability 0.1ESA population size 1Iteration number for each SA operator in ESA 200

Number of inner iterations for ESA 15TS Tabu list size/Neighbourhood list size 13

C. Experimental resultsFigure 2 shows the results obtained from them with 6000 iterations ( n s=6000), which is normally a very smallnumber of iterations for heuristic search algorithms to offer a reasonable solution. This corresponds to a “quick”search. Each experiment was repeated 100 times with the same conditions. Thus there are 100 optimizationresults obtained with each algorithm for a particular network instance. All the results were sorted in ascending

order for a better display. Thus, the best results come first, the others thereafter, and all unwanted results remainin late part of the figure.

0 10 20 30 40 50 60 70 80 90 100

0.26

0.27

0.28

0.29

0.30

0.31

R e s u

l t i n g

C o s

t

Index of results

Greedy GA ESA TS

Figure 2. Results of heuristic algorithms; sorted in ascending order (n s = 6000).

Obviously, the best results obtained are with TS as Figure 2 shows that TS hits the best solution (0.255) for25 times out of 100 runs, while ESA hits it 19 times, i.e. 6% less than TS, Greedy does 8 times, and GA hits it

with an even smaller number (4 times).For TS, only 1 result is slightly bigger than 0.265, it shows that TS has a very strong ability to “hit” the

optimum or near-optimum solutions even with a small number of searches. Although it is reported that SAconverges to the global optimal with probability 1.0 [2], that does not mean any SA implementation would reachthe optimum in the earlier stage of the search. As a well studied SA implementation, ESA provides veryimpressive but not as good as TS does. It has 6 results that are bigger than 0.265 while TS produced only 1 overthat value. This performance reveals that ESA needs further iterations and further investigations for better one.

5. CONCLUSIONSIn this paper, we proposed an integer programming model for WCDMA radio network planning andoptimization. Four heuristic algorithms, namely tabu search, simulated annealing, genetic algorithm and hillclimbing local search, are used to find optimized network configurations. The experiments show that TS

achieved the best performance and outperformed the other heuristics, while the worst performance appeared withGreedy algorithm, which was expected. ESA did slightly worse than TS, but GA was strongly significantlyworse, even with a delicate search.

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ACKNOWLEDGEMENTThe work is supported by the EPSRC under grant number GR/S69429/01, and The Nuffield Foundation underthe grant number NAL/00717/G.

REFERENCES

[1] E. Amaldi, A. Capone, and F. Malucelli, “Planning UMTS Base Station Location: Optimization ModelsWith Power Control and Algorithms”, IEEE Trans. Wireless Communications , vol. 2, no. 5, pp. 939-952,Sep. 2003.

[2] V. Laarhoven, P.J.M. and E.H. Aarts. “ Simulate Annealing: Theory and Applications ”. Dordrecht, Holland:D. Reidel, 1987.

[3] M.E. Aydin and T.C. Fogarty, “A Distributed Evolutionary Simulated Annealing for CombinatorialOptimization Problems”, Journal of Heuristics , vol. 10, no. 3., pp. 269-292, 2004.