Coverage Planning Outdoor WLAN

8/3/2019 Coverage Planning Outdoor WLAN

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Coverage Planning for Outdoor Wireless LA N SystemsMax Kamenetskyt and Matthias Unbehaud

ISL, Department of Electrical Engineering, Stanford University, Stanford CA, USA$Departmentof Signals, Sensors and Systems, Royal Institute of Technology (KTH), Stockholm, SwedenAbstract-Wireless LANs (WLANs) are becom ing increasingly pop-

ular for providing high data rate network access to mobile computers.Most of the currently deployed systems operate in the 2.4 GHz unlicensedfrequency hand. However, increasing demand for higher da ta rat es andnetwork capacities has led to new system sta nda rds for the 5 GHz hand.

Unlike traditional cellular telephony systems, WLANs are deployed inan ad-hoc fashion, often based on an educated guess by the person in-stalling the access points (APs). This typically results in coverage gaps orcapacity loss due to misplaced APs. In this paper, we examine methodsfor obtaining a close-to-optimal positioning of WLAN APs and evaluatetheir perform ance in a typical downtownor campus environment.

The system performance is evaluated using an objective functionwhich aims to maximize both the coverage area and the overall signalquality. The optimization algorithms used in this p aper evaluate this oh-jective function over a discrete search space, thereby considerably reduc-ing the inherent complexity of the problem, while at the same time provid-ing a reasonable approximation to the continuous optimization problem.

Numerical results show that random se arch algorithms, such as simu-lated annealing, can yield very good solutions. However, the convergencespeed of simulated annealing strongly depends on the fine-tuning of sim-ulation paramete rs and a good choice of the initial set of trans mitter po-sitions. Successive removal algorithms, such as pruning, though usuallyproducing sub-optimal solutions, converge in polynomial time. We there-fore propose a combination of the two approaches - using pruning forobtaining an initial set of transmit ter positions and refining these by us-ing either neighborhood search or simulated annealing.

Keywords-wireless LAN, coverage planning , outdoor coverage , net-work deployment, simulated annealing, prunin g, neighborhood sear ch

I. INTRODUCTIONHE traditional approach to coverage planning in cellularT etworks aims to achieve optimal placement of the in-frastructure such that the total number of base stations is mini-mized while maintaining a given Quality-of-Service in the en-tire coverage area. Hence, extensive system simulations basedon terrain databases and using statistical propagation predic-tion tools are typically carried out. The costs for such sophis-ticated network optimization are justified by the large savingsit yields, since the installation and operation of large-scale, of-ten nationwide, networks requires substantial investments.Wireless LANs (WLANs) follow a different paradigm.They are designed to provide low cost, best-effort connectiv-ity and are usually deployed in an ad-hoc fashion, i.e. wher-ever coverage is needed and access to a wired backbone is

available. Although certainly beneficial to the overall systemperformance, network planning for WLANs is regarded as toocomplex and too costly. In this paper, we investigate the per-formance improvements that can be obtained by optimizingthe placement of WLAN access points (APs) and study waysto reduce the complexity of the optimization process.Several methods for coverage planning in WLANs can befound in the literature, mostly based on random search [I], gra-dient descent 121 or genetic algorithms [3]. The performance

of these methods strongly depends upon the initial startingconditions and the choice of simulation parameters. Sincethese parameters and a good starting set of APs are usually notknown a priori , the above algorithms often suffer from slowconvergence, and they may, in fact, not converge at all.In this paper, we explore the use of simple heuristic algo-rithms such as pruning and neighborhood search to obtain aclose-to-optimal solution to the AP placement problem. Thesealgorithms do not exhibit the convergence problems describedabove and thus can be used either as standalone optimization

routines or to obtain good starting solutions for use by morecomplex optimization algorithms.The rest of this paper is organized as follows. Section I1provides a brief summary of the WLAN standards consideredin this work. Section I11 discusses the specific problems ofcoverage planning for such networks and introduces suitablepropagation models and performance measures. In section IV ,we review the different optimization approaches and select themost appropriate methods for numerical evaluation. The sim-ulation results are then presented in section V, with specialattention paid to reducing the overall complexity of the opti-mization. Section VI concludes with a summary.

11. WIRELESS ANsMost of todays WLAN systems operate in the unlicensed2.4 GHz band and follow the IEEE 802.1 b standard, whichis a wireless extension of the Ethernet standard and allowsdata rates up to 11Mbps. A new generation, using the 5 GHzband and delivering up to 54 Mbps, is expected to appear onthe consumer market soon. These systems are based on twoharmonized standards developed by ETSI [4] and IEEE [ 5 ] .Both use advanced radio resource management schemes, suchas link adaptation and dynamic channel allocation, for fine-tuning the network parameters. Although these algorithms en-sure the best possible performance for a given network struc-ture, they do not improve the topology itself, i.e. they cannotcompensate for misplaced APs or fix coverage gaps.In order to analyze the performance improvement achieved

by optimizing AP locations, we need to consider a non-trivialnetwork deployment, i.e. an environment where the propaga-tion is difficult to estimate and hence an educated guess clearlyresults in suboptimal performance. An example of a trivialcase is a completely symmetric environment,e.g. an open fieldwithout trees, houses or any other obstacles, or an empty room.In realistic situations it is usually not possible to guess (e.g. us-ing geometric considerations) the local propagation situation.Typical usage scenarios for WLANs are offices, campus

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environments, manufacturing or storage facilities, shoppingmalls, conference venues, or other locations where networkaccess for portable computers or other devices is required. Anumber of representative environments are proposed in [6],and it was found that typical campus or downtown locationsare the most difficult to cover. Hence, we will use the campusexample for examining the performance of the network plan-ning algorithms.

111. COVERAGEP TIM IZATIONA. Wireless Campus Network

The campus environment has a typical urban layout withstreets, small squares and complex building structures. Thetotal area is approximately 100,000m2, however only the out-door part of 45,000 m2 should be considered as service areafor network planning. Coverage from outdoor APs into thebuildings is neglected, and only the streets and squares areused for estimating wireless coverage. All buildings are con-structed with reinforced, 50 cm-thick concrete walls. APs areinstalled using masts or utilizing existing lamp poles, whereavailable. The height of the APs is assumed to be 5m abovestreet level.The possible AP sites, from which the optimization algo-rithm should select a set that provides the best coverage, arelimited to a grid. We discuss this approach in detail in sec-tion 111-B and choose a suitable grid size in section V-A. Anillustration of the campus environment and the A P placementgrid is shown in Fig. 7.The received power is sampled at M = 450 measurementpoints, regularly dispersed in the considered service area at10 m intervals. Ray-tracing is used to obtain the propagationdata, since it is a very accurate tool for modeling propagationin highly complex environments such as the one we are consid-ering. Such detailed modeling is needed to accurately evaluatethe impact of differentAP locations on system coverage.B. Grid-based Approach

The main disadvantage of ray-tracing is its computationalcomplexity, which depends on the number of sample pointsMand AP locations N and is approximately of order 0 (MN ) .However, coverage optimization algorithms are also highlycomplex and combining both will most likely render the entireproblem unsolvable. We therefore separate the two problemsand perform propagation prediction and coverage optimizationas independent, consecutive steps:1. We define a finite set of possible AP installation sitesA = { A I , . A N } nd the propagation data are then ob-tained for all sites in A. Hence, the inherently infinite

search space is reduced to a finite set of size N .2. The optimization algorithm identifies the subset of Ksites that provide the best coverage.The fundamental tradeoff is now between selecting an appro-priate number of grid points, N , such that the overall complex-ity is manageable and providing a sufficiently fine granularityfor the coverage optimization to converge to a point close tothe global optimum in the continuous search space. In orderto find a reasonable grid size, we first need to introduce ap-

propriate performance measures and then select suitable opti-mization schemes.C. Objective Function

Coverage planning typically comprises two objectives: im-proving the average signal quality in the entire service area andminimizing the areas with poor signal quality. The two objec-tives are not always compatible and hence a suitable tradeoffmust be found. We use an approach proposed in [2], a combi-nation of a minisuni and a minimax objective function.The first objective is achieved by evaluating and minimizingthe average pathloss, expressed by the function

i= l

over the entire service area. Here, M is the total number ofmeasurement points in the service area and gZ() is the pathlossfrom the i-th point to AP IC . Each point is assigned to the APfrom which it measures the minimum pathloss, i.e.

The term gmax efines the maximum tolerable pathloss, whichcauses a penalty term of p gik)- max) to be added if thethreshold of gmaxs exceeded. By minimizing (l), we obtaina minisunz objective function.In order to mitigate the worst-case situation, we considerthe measurement point with the maximum pathloss and try tominimize its contribution, obtaining a minimax objective func-tion:

(

(3)Finally, the total objective function (OF) is a convex com-bination of (1) and (3), controlled by a balancing parameter

11, E [0,1] hat defines the relative contributions of (1 ) and (3):(4)

The optimal location for only one AP can be obtained by eval-uating (4) or all possible AP locations and picking the onethat achieves the minimum OF. Since the number of OF evalu-ations grows linearly with the number of possible AP sites, N ,the global optimal solution in this case can be easily obtainedvia exhaustive search.The problem of placing K APs out of N possible sites is acombinatorial problem of order 0(6)hus makingexhaustive search algorithms appropriate only for cases whereK and N are small. Since A is usually limited to a smallrange bounded by coverage (minimum number of APs to coverthe area) and economic (maximum number of APs allowed bybudget) constraints, one may be tempted to decrease N in or-der to make exhaustive search feasible. However, a small Nis equivalent to a sparse quantization of the continuous searchspace, which increases the likelihood that none of the quan-tized grid points is sufficiently close to the global optimum inthe continuous search space.

F = $fl + (1 - I f 2

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Unfortunately, there is no known polynomial t ime algorithmthat can provide an exact solution to the above problem. Con-sequently, for realistic problems with a reasonably large N ,heuristic-based and other locally optimal algorithms need tobe explored.IV. OPTIMIZATIONLGORITHMSDifferent approaches to coverage optimization for wirelesssystems can be found in the literature. Prior work has mostlyfocused on gradient descent [2], random search [11and geneticalgorithms [3]. Gradient descent is an attractive approach be-cause of existing convergence proofs that can guarantee con-vergence under a specific set of conditions (usually constraintson the step size in the negative direction of the gradient). Un-fortunately, gradient descent depends upon knowledge of theOF surface or gradient estimate. Thus, it is restricted to caseswhere the OF is smooth, which is certainly not the case for thedifficult propagation situation in the campus environment.Random search and genetic algorithms do not requireknowledge of the gradient. However, they lack strong conver-gence proofs, are highly dependent upon starting conditionsand algorithm parameters, and lack a clear termination con-dition. Therefore, we propose a new pruning algorithm thatis guaranteed to converge, does not require knowledge of thegradient, is independent of starting conditions, and can be used

to provide a solution that can serve as a starting point for morecomplex search algorithms.We first define a reference structure, which serves as a per-formance benchmark, and then outline the heuristic algorithmsused in this paper.A . Reference Installation

The simplest possible heuristic solution is a uniform, or reg-ular placement. In this scheme, the environment is subdividedinto K equal regions R k , k = 1,. ,K . Then, for each k, APA k is placed in the Euclidean center of R k .This algorithm is clearly suboptimal. However. it is sim-ple to implement, and it is reasonable to expect that a simi-lar method will be employed in installations by users with noknowledge of the environment other than its general geometry.As such, it is a useful metric and can serve as a reference pointfor other more computationally expensive algorithms. Finally,it is important to point out that regular placement will be glob-ally optimal in a completely symmetric environment.B. Pruning

Pruning is a simple algorithm for combinatorial optimiza-tion. The pseudocode for this algorithm is shown in Table I.In the initialization stage, the algorithm starts with N APs,one for each available AP site. Then, each AP is iterativelyremoved, the OF is re-evaluated without the removed AP, andthe removed AP is re-seeded. This proceeds until the algo-rithm has calculated the OF for every possible AP removal.The AP whose removal achieved the lowest OF is then perma-nently removed and the algorithm repeats for the remainingN - 1APs. This continues until there are only K APs left.Pruning is greedy in the sense that it tries to minimize theOF at each step, without looking ahead to how that move may

TABLE IPRUNINGL G O R I T H M

I seed each of all N vailable APs with an APset number-of-placedAPs := Nwhile number-of-placedAPs > Kset k :=1while k 5 number-of-placedAPsremove AP A Levaluate OF for the remaining APs, store it as J Ere-seed AP Aleset k := C + 1end I* inner loop *Iset I :=argmin,, J Lremove AP AA.*set number-of-placedAPs := number-of-placed-APs - 1end I* outer loop ' I

affect the OF at future steps [ 7 ] . As such, it is suboptimalbecause it may remove an AP that, though not necessary in theearly stages of pruning, may actually be part of the globallyoptimal solution.However, several observations are in order. First, pruning isclearly optimal for the case where K =N - 1. Second, prun-ing is significantly less complex than exhaustive search. Ingeneral, pruning requires O(KN )OF evaluations compared

to the 0(6)F evaluations for exhaustive search.Third, pruning exhibits computational complexity behaviorthat is, in essence, the opposite of exhaustive search. Thatis, for a fixed N , exhaustive search becomes more complexas K grows while pruning at the same time becomes simpler.As such, pruning provides a very attractive solution methodfor cases where K is very large. Fourth, pruning has a natu-ral termination condition in that the algorithm is finished whenexactly K APs remain and no further pruning is possible. Andfinally, pruning may be used to provide a good starting solu-tion to other heuristic search algorithms, such as neighborhoodsearch and simulated annealing, described below.C. Neighborhood Search

Neighborhood search (NS) is a simple heuristic for findinga local optimum of the OF [8]. In general terms, for some ini-tial solution So, the algorithm searches the neighborhood ofSo, N(So),or a solution SI hat achieves a lower objectivefunction. If such a solution is found, the algorithm moves to itand repeats the search. Otherwise, the algorithm is terminatedwith the last found solution. In practice, NS is commonly com-bined with steepest descent, whereby in the search step, the al-gorithm evaluates all the solutions in the neighborhood of thecurrent solution and picks one that achieves the lowest OF.

Table I1 shows the pseudocode for one possible implemen-tation of NS for the AP placement problem. In this imple-mentation, the algorithm starts ou t with an initial solution, ob-tained either randomly, by pruning, or by some other algo-rithm. Then, for every AP, NS performs a local search in theneighborhood of that AP for a better AP site, where the neigh-borhood of AP number k in a solution s, N k ( S ) , is definedas the set of p grid points that are closest (in Euclidean dis-tance) to AP Ak. If the algorithm finds more than one AP that

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T A B L E I1N E I G H B O R H O O DE A R C H N S )

start with initial solution S = { A I .A z , . . AKevaluate OF, store it as Joldset Jnew := Joldwhile TRUEset k :=1while k 5 Kevaluate OF for all solutions in N k (S )

store the minimum value as Jkif J k < Jnewmove to new solution S that achieves OF J kset Jnew :=J kendifset k := k + 1end I* inner loop * Iif Jnew = Joldelseendif

break I* outer loop *Iset Jold := Jnew

end I* outer loop *I

achieves a lower OF, it updates the solution with the locationof the best AP. NS then iterates over all APs in the solutionuntil it can no longer improve the OF.N S is not guaranteed to achieve a globally optimal solution,though it is guaranteed that the solution it achieves will be atleast locally optimal. Initial solutions that are "far away" fromthe global optimum are unlikely to converge to it. In fact, onlysolutions whose neighborhood includes the global optimumcan be assured of convergence to it. Therefore, picking a goodinitial solution for NS is extremely important for achieving alow OF. For that reason, one of the main benefits of NS lies inits use as the last step for refining solutions obtained by reg-ular placement, pruning, or other more complex optimizationalgorithms that can achieve good, though not necessarily lo-

cally optimal, solutions.D. Simulated A nnealing

Simulated annealing (SA) is a random search algorithmwhich slowly decreases the degree of randomness until it con-verges to a local optimum. A good example of how SA canbe applied to cellular network planning is found in [11and wewill adopt the proposed approach for our purposes.The algorithm starts with an initial solution SOand evalu-ates the OF for that solution. The AP positions are then ran-domly altered, resulting in a new system state SI . If the newplacement results in an improvement, i.e. OF(S1) OF(&,), the system moves to the new state SI withan acceptance probability

where y is an attenuation coefficient for limiting P,(T) withina suitable range and the parameter T is called the system tem-perature (TO eing the starting temperature). The algorithmthen repeats.

Initial APpositionNeighbors TO

Fig. 1.necessarily drawn to scale.

Cooling strategy for simulated annealing. Th e circle radii are not

T is a measure for the intensity of the random alterationsto the system state S. To improve convergence, SA usesa cooling strategy, where the randomness is gradually re-duced as the simulation progresses. Hence, SA tends to set-tle close to points with a low OF. The cooling strategy usedfor the AP placement problem is shown in Fig. 1. Dur-ing the first phase, corresponding to start temperature TO,the position of an A P can be changed over a large radiusTO . Since we assume a grid of available sites, an AP canmove to any of the no adjacent sites within the circle deter-mined by TO . A s the temperature is lowered, the circle be-comes smaller and hence the number of available neighborsdecreases. In the simulations, we use five temperature lev-els T = { f i R g r i d , & Rg ri d , 2 R gr id , f i R g r i d , R g r i d } , wheref i g r i d is the distance between two adjacent grid points. Ona regular grid, these temperature levels correspond to n ={24,20,12,8,4}neighbors.

The gradual decrease of the temperature T permits a largesearch space in the early phases of the algorithm and restrictsit as the algorithm progresses and is likely close to finding anoptimum. The acceptance probability P, (7') should preventthe algorithm from becoming trapped in a local optimum. Itneeds to be carefully tuned by adjusting y uch that typically0 5 P,(T) 5 0.1 to ensure convergence while permitting suf-ficient inertia to eventually escape a bad local optimum. Theconvergence speed of SA also strongly depends on the initialsolution SO,which can be obtained either randomly, by regularplacement, or by pruning.Due to the random nature of SA and the rough OF surface, i tis difficult to determine convergence and decide when to stopthe simulation. Therefore, we ran SA for a fixed number ofiterations at each of the five temperature levels. Out of all theAP constellations which were evaluated at one temperature,the one resulting in the lowest OF was used as the start set forthe next temperature level (or as the final solution when thesimulation reached T4).

Finally, it has been shown that in order to guarantee con-vergence to the global optimum, SA will in general requiremore iterations than exhaustive search [9]. Thus, like the otherheuristic algorithms described above, it is only practical to useSA to attempt to find a good local optimum.

V. SIMULATIONESULTSA. Simulation Parameters and Grid Size Selection

The objective function in (4) is based on the pathloss, thuslimiting the number of relevant system parameters to a fewfundamental link layer constants, which are summarized in Ta-

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T A B L E 111S I M U L A T I O NA R A M E T E R S

Target frequencyChannel bandwidthNoise floorNoise figureTransmission powerMin. required signal qualityMax. pathlossOutage probab ilityBalancing parameterPenalty factorAttenuation coefficient

fo 5 GH zB 20 MHzNoB -101 dBmNF 9 dBEIRP 20 dBmSNRmtm 15 dBgmax 97 dBP r { S N R < SNR,,,,,} 4 0%

0.6fi 2iY 100

Fi g . 2. SNR for different grid sizes. The dashed l ine denotes the maximumallowed outage probability.

ble 111. The balancing parameter 1c, is set to a rather low valuewithin the range of 1c, E [0.5,1] ecommended in [2]. This rep-resents an almost even tradeoff between (1) and (3), with aslight emphasis on (1).As discussed in section III-B, we first need to identify a

suitable grid point density to be used in the optimization algo-rithms. The results shown in Fig. 2 are obtained by restrictingthe service area to a subset that is sufficiently small so as toallow exhaustive search.We notice that a 50 m quantization of the search space is toocoarse. The grid points are likely too far from the global opti-mum in the continuous search space and hence system perfor-mance suffers considerably compared to a finer quantization,such as 20 m. However, refining the grid further to 10 m or

5 m yields no substantial performance improvement, particu-larly when considering the 10% outage limit. Therefore, weselect the 20 m grid as the best tradeoff between complexityand accuracy of the obtained solution.B. Fair Comparison of the Algorithms

For comparing the convergence behavior of different algo-rithms, a reasonable metric is required. All of the algorithmswere implemented using the same math library functions inMATLAB 6 and hence the total simulation time should be areasonably reliable indicator for the convergence speed of thedifferent algorithms. All simulations were run on a 700 M HzPentium processor using Linux.Furthermore, it is important to provide the same starting

I109 -

10 ' 100 10, 1d 102SlrmlaWn ime 151Fi g . 3 . Conver gence of the optimization algori thms for6 A P s .

conditions for all approaches. Pruning differs considerably inthat respect from random search algorithms (e.g. SA). It startsby evaluating the OF for all grid points, whereas SA proceedsfrom a set of starting points which have been chosen accordingto certain criteria. Selecting appropriate starting conditions forSA requires some knowledge about the underlying system ge-ometry. For a fair comparison between pruning and SA, weneed to start both with the same information about the system,that is: no prior knowledge. Therefore, SA will be initializedwith a randomly selected set of starting points and we willuse the ensemble average over a number of independent real-izations for evaluating convergence and the resulting systemperformance.C. Convergence Speed and System Perjorma ncelowing algorithms:We can now compare the convergence behavior of the fol-

PruningSA (100, 1000 and 10000 iterations at each temperature)8 Pruning followed by NSPruning and SA (500 iterations at each temperature)

Figs. 3and 4 show convergence and system performance for 6APs. All algorithms achieve considerable improvement com-pared to the reference installation and converge in a rathershort time, however none reaches the performance target of15 dB (SNR,i, in Table 111) in 90% of the service area. Notethat pruning has no convergence behavior; instead, it producesone single solution after removing all excess APs and henceappears as a straight line in the figures.Figs. 5 and 6 show that in the 8 AP case, most algorithmsachieve adequate coverage. Pruning produces a solution inabout the same time as for 6 APs. Additional NS after prun-ing yields a further 8% performance improvement (shown asan asterisk in Fig. 5) with virtually no extra computation time(additional 260 ms). An illustration of the optimization resultsis given in Fig. 7, where the AP positions obtained from prun-ing followed byN S are shown as bold points (e).By comparison, SA requires about 25 times longer thanpruning to converge. If the number of iterations for SA is ad-justed such that it uses approximately the same time as pruningwith NS (= 60 s), it was found that SA produces an equallygood or better solution with only a 30% probability. Using SA

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Fig. 4. SNR achieved by the optimization algorithms for 6 APs.

10 10 1dSINIaba tm[*I100

,-IO-

Fig. 5. Convergence of the optimization algorithms for 8 APs.

to refine the pruning solution improves performance in onlyabout 10%of the cases.Since SA typically does not produce unique solutions, themajor difficulty in using SA by itself lies in the uncertaintyof deciding whether it found a reasonably good solution orwas trapped in a bad local minimum. Hence, SA needs to berepeated a number of times if a relatively reliable outcome isrequired. (Note that the results for SA in Figs. 3-6 are obtainedfrom ensemble averages over 10 independent realizations.)

The trends observed for 6 (8) AP s are emphasized whenusing fewer (more) APs. Using the reference installation, ade-

x x0 - I X

0 so 100 1% 2w 2% 300 1Fig. 7. Campus environment with the AP positions obtained by pruning andNS ( 0 ) . The crosses (x) represent the grid of possible AP installation sites,based on a 20 m grid spacing.

quate coverage could not be achieved with fewer than 12 APs.Hence, using even relatively simple optimization schemes,such as pruning together with NS , translates into a 33 % in-frastructure cost saving. On the other hand, for the same caseof 12 APs, SA alone cannot produce a reliable performanceimprovement even for 10000 iterations per temperature level.

V I. SUMMARYIn this paper, we discussed different approaches to coverageplanning for WLAN systems. A new optimization scheme,pruning, has been proposed, which is easy to implement, doesnot depend on a good starting solution, and requires no fine-tuning of simulation parameters. When combined with a com-parably simple neighborhood search, it outperforms simulatedannealing for realistic network sizes. Numerical simulations ina typical campus environment showed that 1/3 of the infras-tructure costs (ie.number of APs) could be saved comparedto a regular dispersed network, where the AP positions are se-

lected uniformly within the environment.REFERENCES

H. Anderson and J . McGeehan, Optimizing microcell base station lo-cations using simulated annealing techniques, in Proceedings of WC.Stockholm, Sweden, June 1994, vol. 2 , pp. 858-862.H. D. Sherali, C. M. Pendyala, and T. S. Rappaport , Optimal locationof transmitters for micro-cellular radio communication system design,IEEE Journal on Selected Areas in Coininunications, vol. 14, no. 4, pp.6 6 2 - 6 7 3 , May 1996.K . Lieska, E. Laitinen, and J. Liihteenmiki, Radio coverage optimiza-tion with genetic algorithms, in Proceedings ojPIMRC, Boston, MA,September 1998, vol. 1, pp. 3 1 8 -3 2 2 .ETSI, Broadband radio access network (BRAN); HIPERLAN type 2technical specification; physical (PHY) layer, Tech. Rep., ETSI, 1999.IEEE Standard 802.1 la , Part 11, Wireless LAN medium access con-trol (MAC) and physical layer (PHY) specifications: High speed physicallayer in the 5 GHz band, Tech. Rep., IEEE, 1999.M. Unbehaun, A feasibility study of wireless networks for 17 and60 GHz and the impact of deployment strategies on the system perfor-mance, Licentiate thesis, KTH, Stockholm, Sweden, March 2 0 0 1 .W. J. Cook, W. H . Cunningham, W. R. Pulleyblank. and A. Schrijver,Coinbinutorial Optirnizarion, John Wiley, New York, NY, 1998.S. M. Sait and H. Youssef, Iterative C oinputer Algorithms with Appli-cations in Engineering: Solving Coinbinatorial Optimization Problems.LEEE Computer Society, Los Alamitos, CA, 1999.V. Rayward-Smith, I. Osman, C . Reeves, and G. mith, Eds., ModernHeurisric Search Methods, John Wiley, Chichester, UK, 1996.

Fig. 6. SNR achieved by the optimization algorithms for 8 APs.

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Coverage Planning Outdoor WLAN