Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
A Model for Conflict Resolution between Coverage and Cost in Cellular Wireless Networks Roger M. Whitaker, Larry Raisanen∗, Steve Hurley School of Computer Science, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3XF, U.K. Email:
[email protected] Abstract The antenna placement problem, or cell planning problem, involves locating and configuring infrastructure for cellular wireless networks. Many authors have looked at computationally efficient methods to create feasible or optimised cell plans. However in most approaches the tension between conflicting objectives is generally addressed implicitly rather than explicitly. In this paper we present a model for resolving the most fundamental tension, between service coverage and cost of base stations. The model is general in its approach, and its abstract representation means that state-of-theart multiple objective optimisation techniques can readily be applied. We use a synthesised test problem to obtain typical results which demonstrate the tension between objectives and the diminishing return (in terms of service coverage) for additional investment.
1
Introduction
Ubiquitous wireless services are largely provided using cellular systems. Many different types of multimedia services are increasingly being characterised only by bit rate, traffic characteristics of data and user mobility requirements. As new services to support high bit rate multimedia services are imminent, opportunities for mobile E-commerce and business driven applications are set to grow. A fundamental precursor to such service provision is that of infrastructure location and configuration. This applies to every wireless service. From a commercial viewpoint, service providers are under significant pressure to ensure that informed decisions are made with respect to the provision and configuration of infrastructure. Network design can significantly influence ∗ Supported
by a Doctoral Scholarship from EPSRC
the cost base of a provider and also the revenue generated, which is derived, in part, from providing an adequate quality of service. The increased complexity in protocols to support high bit rate services has led to increased complexity in the infrastructure location problem. There are a large number of interdependent factors influencing the location and configuration of transmission infrastructure. For example in cellular systems, these include choice of location, antennae, power control, tilt and azimuth. In this paper we concentrate on the most fundamental conflicting objectives that need to be addressed for every cellular service. These objectives relate to cost of the network and quality of service for subscribers. There is no general foundational theory for cell planning. Therefore we seek to give a framework in which the complex relationships, tensions and dependencies can be explored. We provide a unifying model which abstracts the cell planning problem and characterises solutions in terms of trade-offs between multiple objectives, for frequency division multiple access systems. We show how the model relates to radio engineering factors using an empirical propagation model. Unlike previous methods, the approach we use makes it possible to directly apply any state-of-the-art optimisation technique that characterises solutions in terms of trade-offs between tenuous objectives. Determining globally optimal solutions in a reasonable time frame for this cell planning problem is not feasible due to combinatorial complexity. This is the motivation for application of meta-heuristics. We show the effects of applying one such technique based on evolutionary optimisation.
2
Modeling and Design
From the mobile users viewpoint, the fundamental issues for wide area mobile service provision are based
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
1
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
on: • reception of an adequate received signal strength from at least one source throughout the network; • reception of at least two signals of adequate strength in regions where call handover is required; • mitigation of interference (strong unwanted signals) from multiple sources simultaneously; • adequate quality of service based on call dropping and blocking rates. The first point requires the adequate spatial distribution of transmission infrastructure. From each base station, antennae need to be configured to introduce the signal to the wireless media. The geographical region where adequate signal strength is received from a single antenna is informally called a cell. For an isotropic antenna in a perfect transmission environment across a flat region, each cell constitutes a circle. The second point relates to the overlap of cells across the network. Regions which are contained in multiple cells permit handover, and are necessary for high widearea coverage level since cells do not tessellate, given their theoretical shape. The third issue requires the control on the amount of overlap required for handover. If this is permitted to be too large, the signals received will be particularly strong and in order to maintain an adequate signal to interference ratio, large channel separation will be required at the respective antenna (assuming an FDMA protocol). Additionally large overlap areas will mean an increase in the density of cells in the network. A consequence of this is an increase in network cost. Also, the last issue concerns the multiplexing capability of the network given the demand for services. Each cell has a limited multiplexing capability (also dependent on the protocol) which will determine the extent to which quality of service, in terms of call blocking and dropping, is achieved. In order to give a quality higher quality of service, a high density of small cells is required. To maintain a high cell density and low number of transmission sites, the convention of co-siting multiple directed antennae is used by most operators. Locations at which an antenna or co-sited antennae are located are called base stations. The primary variable, in terms of capital cost, relate to commissioning base stations. Enhancing spatial availability of services will incur a stream of future costs based on site rental and commissioning, and maintenance of infrastructure. This cost stream will vary depending on the location of the base station. For each candidate base station site, we consider the estimated present value of future costs over
a defined time period as a single estimated cost of selecting each potential base station location. These will vary between candidate base station locations dependent on local factors. The problem we address involves selecting and configuring candidate base station locations.
2.1
Cell Plan Model
The model we adopt involves a range of components. The model is completely general in the sense that different assumptions on propagation and optimisation can be incorporated. We define a working area as the region over which transmission is considered. This is characterised by discretized test points. The following sets form the input to our process for finding marginal cost of service coverage: • A set of candidate sites for locating base stations, denoted L = {L1 , . . . , LnBS }. • A list of possible transmission powers p0 , p1 , p2 , . . . , pk in ascending order of magnitude. Zero power is denoted by p0 . • A set of service test points (STP), {s1 , . . . , snstp }, which are geographical locations where a signal must be received above a minimum specified service threshold, Sq , to facilitate wireless communication. • A maximum handover percentage, hmax , used to restrict the size of a the handover region when adding a new cell to the network. • Coverage prediction for omni-directional cell coverage, at each site and power level. We assume that STPs are equally important in terms of coverage, with no differentiation being made, by subscribers, in terms of significance of location. Subscribers are assumed to derive uniform benefit from coverage of individual STPs. Consequently the amount of coverage available to the subscriber is of primary importance. For purposes of commissioning candidate sites, we assume that each base station is operating a single omni-directional antenna with an isotropic radiation pattern. In practice, omni-directional antenna may be replaced by multiple co-sited directed antenna to increase multiplexing capacity, where required. The antenna height is assumed to be fixed at the maximum permitted at the site to enhance potential transmission range. Each base station location Li has a cost $(Li ) associated with commissioning it. Service test points are spaced on a regular grid for test purposes.
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
2
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
2.2
Objectives
We seek to minimise total network cost (based on sum of costs for commissioning the selected base stations) while maximising coverage. This leads to a tension which must be resolved. The optimal trade-off between coverage level and cost, known as the Pareto front, must be estimated. This defines coverage as a function of cost. In order to estimate the Pareto front, we produce a range of so-called Pareto optimal cellular networks. These cellular networks represent a best known trade-off between network cost and service coverage. The following definition is useful in this context. Definition 1 (Pareto optimality) Let o1 , o2 , . . . , on be objective functions which are to be maximised. Let S be the set of all possible solutions. s ∈ S is dominated by t ∈ S (denoted t s) if ∃j, j ∈ {1, . . . , n}, such that oj (t) > oj (s) and ∀i, 1 ≤ i ≤ n, oi (t) ≥ oi (s). A non-dominated solution is said to be Pareto optimal. Our approach is to estimate the Pareto front by finding a wide range of Pareto optimal solutions to the network design problem, using the objectives of coverage and total network cost minimisation. However it is important to note that there are three overarching strategies which can be used to deal with multiple objectives: 1. combine all objectives into a single scalar value, typically as a weighted sum, and optimise the scalar value. 2. solve for the objectives in a hierarchical fashion, optimising for a first objective then, if there is more than one solution, optimise these solution(s) for a second objective, and repeat. 3. Obtain a set of alternative, non-dominated solutions, each of which must be considered equivalent in the absence of further information regarding the relative importance of each of these objectives. Each approach involves exploring the search space of all possible cell plans to find one or more suitable solutions. Approach 1 is by far the most popular approach in the literature (e.g. [3, 20, 4, 24, 21, 12, 22, 1, 2, 9, 8, 23, 16, 17]). The biggest problem though, is setting the relative weights of different components in the cost function, and poor weighting may lead to inappropriate favouring or penalising different single objectives. Approach 2 may be combined with approach 1, as in [13, 15, 25, 19] which may involve changing the objective function at different points in the search in a phased or staged manner. This approach effectively
prioritises different single optimisation objectives a priori. In [18] has a multi-objective search been implemented in the vain of approach 3, where a range of Pareto solutions are approximated. However, unlike [18], our model seeks to provide a general framework where the complex relationships, tensions and dependencies in the cell planning problem. To do this, break down the cell planning problem into its basic components, starting with the issue of coverage and cost of infrastructure. We then apply a proven heuristic optimisation technique which can be easily applied to our general model.
2.3
Abstraction and Creation of the Cell Plan
For coverage estimation, the empirical model due to Hata [10] has been adopted. This is used to find the propagation loss (P L) due to environmental factors in an urban environment. This is defined as: PL =
69.55 + 26.16 log(f ) − 13.82 log(hb ) − a(hm ) −K + (44.9 + 6.55 log(hb )) ∗ log(R)
given particular values for variables such as frequency (f ), base station height (hb ), and mobile receiver height, (hm ). K and a(hm ) are taken to be zero. A particular test point is covered by antenna A if: P − P L ≥ Sq where P is the power of A, P L is the propagation loss between A and the test point, and Sq is the service threshold required by the receiving equipment. The subset of service test points covered by a particular antenna A is the cell served by A, denoted cA . Note that cells served by different antennae are not necessarily disjoint since an STP can potentially be covered by more than one antenna. Such an STP is referred to as a handover STP. For a cell cA , the subset of handover STPs is denoted hA . The handover percentage for cA is defined as |hA | × 100. |cA | Controlling the size and distribution of handover regions is crucial for both operational and financial reasons. Handover regions are a prerequisite for seamless call transfer between cells for mobile users. However, if very large handover regions are permitted, there is a greater potential for interference due to strong signals being received from multiple sources. In frequency division multiple access systems, large handover regions increase the need for large channel separation between adjacent cells in the frequency assignment problem.
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
3
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
Large handover regions may also adversely affect the cost of the network by increasing the total number of base stations required to cover a given area. Under our model, an additional base station cannot be commissioned if it would lead to the new cell having a handover percentage greater than the maximum permitted. In this way, handover is imposed as a constraint and controlled during the creation of a cell plan. The potential base station location Li is referred to as the ith base station. A permutation π, of the potential base station locations, is used to create each cell plan we consider. Under the permutation π, the ith base station location listed is denoted π(i). We introduce a decoder which is a simple method to translate a permutation π into a cell plan. The decoder selects base station locations, stores them in a set L , and allocates a transmission power to each, taking into account constraints concerning handover. This approach mimics the way in which the problem might be attempted manually. The decoder is effectively a greedy, sequential algorithm for creating a cell plan, which is dependent on the order of inspection for commissioning potential sites occurring in π. The decoder adds cells iteratively to create a cell plan L using a few simple steps: • Initially L = ∅. • Potential sites π(1), π(2), . . . , π(n) are inspected (in the order induced by π) for possible selection. • At iteration j (1 ≤ j ≤ n), π(j) is considered for addition to the set L . – Handover between cπ(j) and L is feasible if the hand-over percentage for cπ(j) is less than the maximum permitted. – The largest power setting, denoted pmax , is identified from the list p0 , p1 , p2 , . . . , pk such that handover is feasible between cπ(j) and L . – If pmax = p0 , then π(j) is added to L , and the transmission power of π(j) is recorded as pmax . Otherwise π(j) is not added to L . A number of observations can be made regarding this approach. Firstly, the approach is greedy in the sense that once a base station location is added to L at power pmax , the base station cannot be removed from the cell plan L nor can its transmission power be adjusted. Secondly, for a particular list of potential site locations, characteristics (e.g., cost and coverage) of the
resultant cell plan L is entirely dependent on the order (i.e., permutation π) in which the base stations are considered for selection. Thirdly, only the cell being added is checked for permissible overlap, and only at the time that it is added. This permits the decoder to operate quickly but at the expense of approximation. Finally, handover between cells is imposed as a constraint rather than an objective. This means that there is no guarantee of a specific minimum handover region between cells. However, the greedy nature of the decoder means that in practice, cells will be commissioned with the largest power possible, subject to not violating the handover constraint, up until commissioning of additional cells becomes impossible. Consequently, for a given candidate site ordering, cells are sequentially packed as densely as possible, subject to the maximum permitted handover percentage. This means that handover regions for call transfer are provided, dependent on hmax . We also note that the maximum permitted handover percentage parameter hmax will directly affect the quality of service experienced by subscribers in terms of call dropping under mobility. At each value of hmax , an individual marginal revenue curve will exist, as will an individual marginal cost curve. Consequently we use a range of values for hmax in experimentation. The representation we use is unique in its use of permutations to select and configure base stations. This abstracts the cell planning problem and allows optimisation effort to focus on finding orderings of candidate base station locations which decode to give Pareto optimal cell plans. It is important to note that many different decoders could be imposed to translate the sequencing of base station candidate sites into a cell plan. This is the basis of ongoing experimentation.
2.4
Extension to Real World Planning
In order to perform real world cell planning, which is the primary interest of many authors, it is important to note how the abstracted model relates to real world considerations including 3D-models, terrain and sectorization of traffic. Note that cells are defined as sets of reception test points. This means that there is no assumption that the cells are shaped in any particular way, although in idealised propagation scenarios with a flat terrain, cells will be circular. Additionally, there are no assumptions that the model is 2-dimensional, since we are considering discretized test points. The only requirement is that we know (either by estimation, modeling or data from the field) the received signal strength from potential candidate site locations,
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
4
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
when an omni-transmitter is in operation, for a range of different power levels. This allows us to define the coverage of potential cells. Omni-directional transmission is considered in the model because reception is the fundamental prerequisite for service. Therefore it is sensible to assume transmitters have the widest potential coverage beam for purposes of minimising the number of sites required. However, in capacitated networks, it will be important to consider traffic and sectorization. This constitutes a further optimisation step where the commissioned sites (assuming omni-directional transmission) are reconfigured with directed antennae, required to increase multiplexing capacity. For cells in very busy areas, it may also be necessary to cap the maximum power value used, so that not too much sectorization is required in each cell.
3
100 Pareto optimal front
final population
mid-way progress
Maximize Cover initial population
0 0
800 Minimize Cost
Figure 1. Progress towards Pareto front of cost and coverage.
Evolutionary Optimisation
To perform optimisation of the sequencing of candidate sites for the simple decoder proposed, we apply a state-of-the-art multi-objective optimisation. The aim is to approximate the Pareto front, by establishing cell plans which exhibit high performance in two dimensions, total network cost and coverage level. Only over the last decade have genetic algorithms (GAs) been successfully adapted to solve multiple objective problems. An excellent overview of this area is given in [5]. The general principle is to breed a new population of solutions through a process of selection and recombination. This occurs over a number of generations to try to improve the performance of the population, as shown in Figure 1. The expectation is that desirable characteristics in solutions from one generation will combine to produce better solutions for the next generation. Introduced by Holland [11], GAs are supported by theory which identifies the conditions under which solutions converge to a high performing set of solutions. GAs which approximate the Pareto front seek to find, ideally, a diverse set of solutions spread evenly over the entire range of the Pareto optimal front. In this paper we apply a technique known as NSGAII (non-dominated sorting genetic algorithm version II). NSGA-II was introduced in [6], and has been well studied (e.g., [7, 14]). We apply it to orderings of candidate base station sites. Therefore each solution (equivalently individual in GA nomenclature) constitutes a permutation. Solutions are compared by decoding them and considering their performance in terms of domination. At each generation t, NSGA-II maintains two populations, the archive or parent population Pt , which stores the most fit individuals in each
generation, and a child population Ct . The child population Ct is formed from Pt by performing selection, crossover and mutation. A simple binary tournament with replacement is used to find parents. In the binary tournament, two population members, i and j, are chosen at random (uniformly) from Pt . Member i wins the tournament if i dominates j, and i becomes a parent. A second parent is selected similarly and both are put forward for crossover and mutation to create an offspring for Ct . This is repeated until Ct is size n. Note that each population Pt and Ct remains fixed at size n. The algorithm proceeds with the multi-set union Pt ∪ Ct , denoted Ut . Then, n members are selected from Ut to form the new parent population for the next generation Pt+1 . Before this occurs, Ut is partitioned into a number of sets called fronts, which are constructed iteratively. Front 1, F1 , consists of the non-dominated members from Ut . Front 2, F2 , consists of the non-dominated members from the set Ut − F1 . In general, front i, Fi , consists of the non-dominated members from the set Ut − (F1 ∪ F2 ∪ · · · ∪ Fi−1 ). Fronts are constructed in this manner until Ut is empty. The authors of NSGAII describe an efficient algorithm (fast non-dominated sort) to partition Ut into fronts (see [6]). Fronts are then used to form Pt+1 . If |F1 | = n, then the new parent population, Pt+1 , is set to contain the members of F1 . Otherwise, F1 , F2 , . . . are added to Pt+1 in order (front one followed by front two and so on). The process stops with front Fj being added to Pt+1 when F1 ∪ F2 ∪ · · · ∪ Fj ≤ n and F1 ∪ F2 ∪ · · · ∪ Fj ∪ Fj+1 > n. If |F1 ∪ F2 ∪ · · · ∪ Fj | < n then solutions have to be chosen from Fj+1 for inclu-
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
5
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
Generate initial population P0 of size n Rank and sort P0 based on non-domination level Apply selection, recombination and mutation to create a child population C0 of size n set t = 0, T = of generations (ngen ) while t < T do Ut = Pt ∪ Ct Partition Ut into fronts F1 , F2 , . . . Set Pt+1 = ∅, i = 1. while |Pt+1 | ≤ n do Calculate crowding distance in Fi if |Fi | + |Pt+1 | ≤ n then Pt+1 = Pt+1 ∪ Fi else if |Fi | + |Pt+1 | > n then Decreasing sort of Fi members by crowding distance Pt+1 = Pt+1 + the first (n − |Pt+1 |)) elements of Fi . end if end if i=i+1 end while Calculate crowded comparison operator ∀ i ∈ Pt+1 Create Ct+1 of size n by applying recombination and mutation to parents selected via binary tournaments on Pt+1 . t = t + 1; end while
sion in Pt+1 to ensure that population Pt+1 is size n. For each solution i in Fj+1 , a crowding distance cdik is calculated based on each of the multiple objectives, ok . The solutions in Fj+1 are ordered with respect to ascending magnitude of their value in ok . The first and last members from the front are assigned infinity as their crowding distance with respect to ok . For all other members of the front, cdik is calculated as the sum of the absolute difference between the objective function values of i and its adjacent solutions in the front. The overall crowding distance for a solution i, CrwDi , is defined as: CrwDi =
cdik
∀ok
The greater the crowding distance the greater the isolation of that particular solution in objective space. Solutions with the highest crowding values are added to Pt+1 until |Pt+1 | = n. At this point, the procedures described are re-iterated until a termination condition has been satisfied. We summarise the pseudo-code in Figure 2. Throughout, the well-known cycle crossover has been used as the recombination operator and the mutation operator involves the simple transposition of candidate base station locations in a randomly selected pair of positions. This was governed by a mutation rate (set to 1%) to restrict the frequency of mutation.
4
Results
Our results focus on a case study for planning across a particular region. We document the parameter settings used in the model and algorithm in Tables 1 and 2. These have been selected for demonstration purposes only and we emphasise that many other settings could have equally been adopted. A period of 500 generations has been selected, since experiments suggest that generational increase in fitness has degraded by this point. The service threshold is realistic for current European GSM services, based on the requirements for 8 Watt equipment in an outdoor environment. We use a randomly generated test problem, specifying candidate size locations, to demonstrate the feasibility of our cell planning model and optimisation approach. The particular instance involves a 30km by 30km working region with 108 sites available for selection. This gives a candidate site density of 0.12 sites per km2 . The dispersion of candidate sites are represented by the black points in Figure 4. The output from the optimisation process is displayed in Figure 3. The optimisation process has been applied five times, using different random
Figure 2. The NSGA-II procedure. seeds, to find a range of solutions. From these solutions, the non-dominated ones are displayed. The costs of the candidates sites has been allocated randomly, in the range 1 to 2 units. This means that some base stations can be up to twice as expensive as others. The interesting observation concerns the progressive diminishing return, in terms of extra service coverage, for additional cost. For example, the cost change due to increasing coverage from 92% to 94% is approximately 1 unit. However increasing coverage from 96% to 98% leads to a 3 unit increase in cost. This demonstrates that it becomes increasingly more difficult to cover the last remaining test points without inducing significant overhead from increasing overlap. For inspection purposes, in Figure 4 we give an example of a cell plan produced during the creation the Pareto front, with 96% coverage.
5
Conclusions
In this paper we have presented and explained a multiple objective modelling approach for cell planning, which addresses the fundamental tensions relating to
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
6
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
Parameter f hb hm a(hm ), K hmax ngen n Sq
Description frequency base station height receiver height propagation parameters maximum handover % number of generations population size Service threshold
Setting 800 Mhz 31 metres 1.5 metres 0 30 500 100 -90 dBm
Table 1. Settings for Propagation Model and NGSA-II.
Power Setting p1 p2 p3 p4 p5
dBW 30 27 24 21 18
Watts 1000 501 251 125 63
Figure 4. A cell plan solution at the 96% cover level.
Table 2. Specification of power settings.
higher coverage levels.
24
23
References
22
[1] E. Amaldi, A. Capone, and F. Malucelli. Improved models and algorithms for UMTS radio planning. In Proceedings 54th IEEE Conference on Vehicular Technology, volume 2, pages 920–924, 2001.
21
20
19
[2] E. Amaldi, A. Capone, and F. Malucelli. Optimizing base station siting in UMTS networks. In Proceedings 53th IEEE Conference on Vehicular Technology, volume 4, pages 2828–2832, 2001.
18
17
16
15 86
88
90
92
94
96
98
Figure 3. The Pareto front for the test problem considered ( y-axis cost and x-axis coverage %).
coverage and cost of the network. An evolutionary approach to optimisation has been applied, and this has resulted in an approximate optimal trade-off between coverage and cost. The model is general in the sense that different radio engineering factors, such as propagation modelling, can be incorporated, as can alternative models for optimisation. The results of our case study quantify the non-linear cost increase required for
[3] H.R. Anderson and J.P. McGeehan. Optimizing microcell base station locations using simulated annealing techniques. In Proceedings 44th IEEE Conference on Vehicular Technology, pages 858– 862, 1994. [4] P. Calegari, F. Guidec, P. Kuonen, and D. Wagner. Genetic approach to radio network optimizations for mobile systems. In Proceedings 47th IEEE Conference on Vehicular Technology, volume 2, pages 755–759, 1997. [5] K. Deb. Multi-Objective Optimization using Evolutionary Algorithms. John Wiley and Sons, 2001. [6] K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast elitist non-dominated sorting genetic
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
7
Proceedings of the 37th Hawaii International Conference on System Sciences - 2004
algorithm for multi-objective optimization: Nsgaii. In Lecture Notes in Computer Science, volume 1917, pages 848–849, 2000. [7] K. Deb, M. Mohan, and S. Mishra. A fast multiobjective evolutionary algorithm for finding wellspread pareto-optimal solutions. KanGAL Report No. 2003002, 2003. [8] M. Galota, C. Glasser, S. Reith, and H. Vollmer. A polynomial-time approximation scheme for base station positioning in UMTS networks. In Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Rome, Italy, pages 52–59, July 2001. [9] J.K. Han, B.S. Park, Y.S. Choi, and Park H.K. Genetic approach with a new representation base station placement in mobile communications. In Proceedings 54th IEEE Conference on Vehicular Technology, volume 4, pages 2703–2707, 2001.
[18] H. Meunier, E. Talbi, and P. Reininger. A multiobjective genetic algorithm for radio network optimization. In Proceedings of the 2000 Congress on Evolutionary Computation, volume 1, pages 317– 324, 2000. [19] P. Reininger, S. Iksal, A. Caminada, and J.J. Korczak. Multi-stage optimization for mobile radio network planning. In Proceedings of the IEEE VTC’99 Conference, volume 3, pages 2034–2038, 1999. [20] H.D. Sherali, C.H. Pendyala, and T.S. Rappaport. Optimal location of transmitters for microcellular radio communication system design. IEEE Journal on Selected Areas in Communications, 14(4):662–673, May 1996. [21] K. Tutschku. Interference minimization using automatic design of cellular communication networks. In Proceedings of the IEEE VTC’98 Conference, pages 634–638, 1998.
[10] M. Hata. Empirical formula for propogation loss in land mobile radio services. IEEE Transactions on Vehicular Technology, 29(3):317–325, August 1980.
[22] M. Vasquez and J-K. Hao. A heuristic approach for antenna positioning in cellular networks. Journal of Heuristics, 7:443–472, 2001.
[11] J.H. Holland, editor. Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor, 1975.
[23] J.K.L. Wong, M.J. Neve, and K.W. Sowerby. Optimisation strategy for wireless communications system planning using linear programming. IEE Electronics Letters, 37(17):1086–1087, 2001.
[12] I. Howitt and S-Y. Ham. Base station location optimization. In Proceedings of the IEEE VTC’99 Conference, volume 4, pages 2067–2071, 1999. [13] S Hurley. Planning effective cellular mobile radio networks. IEEE Transactions on Vehicular Technology, 51(2):243–253, March 2002. [14] V. Khare, X. Yao, and K. Deb. Performance scaling of multi-objective evolutionary algorithms. KanGAL Report No. 20020029, 2002.
[24] M.H. Wright. Optimization methods for base station placement in wireless systems. In Proceedings of the IEEE VTC’98 Conference, pages 387–391, 1998. [25] J. Zimmermann, R. Hons, and H. Muhlenbein. ENCON: evolutionary algorithm for the antenna placement problem. Computers and Industrial Engineering, 44:209–226, 2003.
[15] C.Y. Lee and H.G. Kang. Cell planning with capacity expansion in mobile communications: A tabu search approach. IEEE Transactions on Vehicular Technology, 49(5):1678–1691, March 2000. [16] R.M. Mathar and M. Schmeink. Optimal base station positioning and channel assignment for 3G mobile networks by integer programming. Annals of Operations Research, 107:225–236, 2001. [17] R.M. Mathar and M. Schmeink. Integrated optimal cell site selection and frequency allocation for cellular radio networks. Telecommunication Systems, 21:339–347, 2002.
0-7695-2056-1/04 $17.00 (C) 2004 IEEE
8
