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  • 1. Planning Aspects of WCDMA Mobile Radio Network Deployment YUFEI WU, SAMUEL PIERRE Mobile Computing and Networking Research Laboratory Department of Computer Engineering Ecole Polytechnique de Montreal P.O. Box 6079, Station Centre-ville, Montréal, Que., H3C 3A7, CANADA Abstract: - There are many aspects that have to be considered during planning phase of WCDMA networks. Some of the most important factors are: quality of service (QoS), cost of implementation and provisioning, traffic coverage ratio, and resource utilization. This paper analyzes planning aspects of WCDMA mobile radio network deployment and proposes optimization models which explicitly take into account some important factors such as QoS and power control. It also proposes a tabu search algorithm to solve the overall planning problem considered as NP-hard. Computational experiments with realistic problem sizes are conducted to describe some important aspects of efficient WCDMA deployment, and show both the efficiency and the practicality of the tabu search algorithm. Key-Words: - WCDMA, network planning and optimization, tabu search, NP-hard. 1 Introduction developed. Most of those previous studies have been Every cellular network deployment requires carried out for 2G mobile networks, and have not planning and optimization in order to provide revealed enough information about efficient mobile adequate coverage, capacity, and quality of service network deployment configurations. Planning 3G (QoS). Mobile radio network planning and mobile networks, such as UMTS, is even more optimization is a very complex task, as many sensitive to the planning objective due to the aspects must be taken into account, including the inherent CDMA features [9]. topology, morphology, traffic distribution, existing This paper analyzes planning aspects of 3G infrastructure. Depending on how these and other WCDMA mobile radio network deployment, and factors are incorporated into the planning process, provides some insights into efficient network there can be many possible strategies. When planning and optimization and choosing a good optimization is involved in the planning, each of planning objective by taking into account operators’ these factors can be either part of the objective business demands. function or subject to certain constraints or Section II presents a mobile network planning neglected in the optimization process. Mobile and optimization model. Section III describes the network planning and optimization problem is NP- solution structure and search strategies. Section IV hard [1]. demonstrates experimentally that the model and the A good planning and optimization objective is proposed tabu search algorithm can efficiently find extremely important in selecting an effective good solutions for realistic 3G deployment deployment scenario. In [2][3][4], the models scenarios. proposed are for both microcells and picocells in coverage limited environments. These approaches use an objective function directly related to path loss 2 System Model which is optimized to determine base station In this section, we present the system model for the locations. In [5], authors propose a model which third generation mobile downlink hierarchical cell considers interference limited environments and use planning and optimization problem. We also define an objective function which directly related to QoS. the decision variables, design constraints and In [6], the goal of mobile network planning and objective functions. optimization is to cover the maximum number of subscribers in an effective manner. In [7] a profit maximization model is presented. In [8] a cost 2.1 Working Area and Traffic minimizing planning and optimization model is
  • 2. A working area is the part of a geographical region BS antenna is in configuration w. The decision where the mobile network needs to be deployed. variables are needed for each configuration: Two basic discrete sets of points are identified on it. A set of sites are candidates for the positioning 1 if TP i assigned to BS j base stations, denoted by S = {1,…, m}, where a  xijw =  with configuration w (1) base station (BS) can be installed and that an 0 otherwise  installation and maintenance cost cj is associated with each candidate site j, j∈ S. Each site is defined by its coordinates (x, y), and eventually by z (height 1 if BS with configuration w at site j y jw =  (2) above sea level). 0 otherwise for i∈I, j∈S and w∈L. Once these basic decision l∈L variables have been determined, other dependent j∈S system variables, such as loading factors and SIR for each mobile terminal, etc., can be easily derived from. Fig. 1 illustrates some important parameters. 2.3 Design Constraints i∈I Constraints (3) make sure that each TP i is assigned to at most one BS. Note that by restricting the µi assignment variables xijw to take binary values, it is SIRtar , Ptar , Pi required that in every feasible solution all active Fig. 1. Simplified system model connections must be assigned to a single BS. A set of traffic test points (TPs) I = {1,…, n} are ∑∑x ijw ≤1 (3) illustrated in Fig. 1. Each TP i∈ I can be considered j∈S w∈L as a centroid where a given amount of traffic di is requested and where a certain level of service If the left terms of constraints (3) were forced to (measured in terms of SIR) must be guaranteed [11]. be equal to one, that is, each TP must connect to a The required number of simultaneously active BS, the results would too demanding for network connections for TP i, denoted by ui, turns out to be a resources. In some cases, a feasible solution would function of the traffic, i.e., ui = φ(di). The mobile not be found. Therefore, constraints (3) are relaxed terminals are located on TPs, where the network and intentionally allow some TPs not to be assigned. must overcome a signal quality threshold SIRmin, to The constraints (4) are called minimum service ensure a given quality of service (QoS). The value requirements, which ensure that service is available of the threshold depends on the service type. To in the working area that have at least a proportion β check the signal quality threshold on each TP, the of all traffic demand nodes. field strength has to be computed on each point. ∑∑∑ µ x j∈S w∈L i∈I i ijw ≥ β .∑ µ i i∈ I (4) 2.2 Decision Variables In general, a BS antenna can be in one out of q In our model, the cost of a BS involves the cost different configurations, denoted by set L = {1,…, of site installation and cost of the configuration: q}. A configuration represents a sextuplet BS = (location, type, height, tilt, azimuth, power). This C j ( yjw) = C S + C L (5) j j accounts, for instance, for a variable tilt selected out of a set of possible angles with respect to the vertical axis, and for a variable height selected from The overall cost of a radio access network in the a finite set of values with respect to the ground predefined working area, C(y), is the sum of the S level. Since propagation gains depend on the BS non-configuration cost of each BS antenna C j , and w antenna configuration, we denote by g ij the L its associated configuration cost C j , i.e., C(y) = propagation gain from TP i to potential site j if the
  • 3. ∑∑ y w∈L j∈S jw .C j ( y jw ) . Cost is an extremely important Ptar xijw ≥ SIRmin xijw (10) I int er + I int ra factor for choosing an adequate network configuration. Denote Cmax an externally given ceiling cost, or a budgetary limit in total monetary Equation (11) represents the total interference investment. In most cases, it is practical to consider incurred in the same cell, whereas Equation (12) the budget constraints (6). describes the interference from all the other BSs, measured at mobile unit i in the service area. ∑∑ y jw .C j ( y jw ) ≤ C max (6)   w∈L j∈S  w g ij Ptar  Iintra = α  ∑ u k w xkjw − Ptar  (11)  g ij Pmax  w  k∈I σj ijw g kj     x =1  xijw ≤ min 1,  y jw (7)  kjw    Ptar   v g il Ptar Constraints (7) correspond to the most stringent Iinter = ∑∑∑ v∈L l∈S k∈I lσ ilv uk v g kl xklv (12) constraints among the coherence constraint l ≠ j xkl =1 xijw ≤ y jw , which ensures that TP i is only assigned to site j if a BS with configuration w is installed in j, where for any site l ∈ S, w ∈ L, the index set I l ilw σ and the power limit on a single connection from BS denotes the set of all TPs in I that fall within the j to TP i: sector σilw of the BS with configuration w and location l, which contains TP i. Ptar w xijw ≤ Pmax y jw (8) g ij 2.4 Problem Formulation where Pmax is the maximum emission power for the Our aim is to formulate the 3G cell downlink w planning problem as an optimization problem. The connection from site j to TP i and Ptar/ g ij available cell sites (S), the traffic demand nodes (I) corresponds to the emission power required by BS j with capacity requirements (µ), configuration set (L) to guarantee the target received power Ptar at TP i. are fixed input parameters. We will introduce three For each pair of site j ∈ S and TP i ∈ I, constraints formulations of the cell planning problem. In all (8), which are active only if TP i is assigned to BS j cases, the following variables are the basic decision (i.e., xijw = 1), correspond to the signal quality variables. Based on these basic decision variables, requirement. Finally, constraints (9) impose an most of radio access network parameters can be upper limit Ptot on the total emission power of every derived from. BS.  The number of selected base stations and their P configuration, denoted by multi-dimensional ∑ gtar xijw ≤ Ptot y jw i∈I w (9) vector y, ij  The capacity assignment matrix, x,  The power assignment vector (mobile transmitter In addition to the constraints (8) and (9), the quality participation), p. of service constraints should be emphasized. Since w in a power-based power control mechanism Ptar/ g ij is the power that needs to be emitted from a BS with 2.4.1 Minimal Cost Planning configuration w in site j to guarantee a received A practical objective deals with the price of the power of Ptar at TP i. For each connection between a solution in terms of installation and provision costs. BS installed in j and a TP i falling in a sector of this In this formulation, the goal of the planning is to BS, the SIR constraints can be expressed as follows achieve as low cost as possible. Instead of [12]: optimizing the technical performance, such as coverage outage, which would potentially lead to a network with unnecessary high resource usage, we
  • 4. choose the objective for minimizing the network  Evaluation methods for gains in objective values. cost. The planning objective is defined as follows: Minimize ∑∑ y w∈L j∈S jw .C j ( y jw ) (13) 3.1 Solution Structure and Neighborhood Decision variables are the BS locations, their powers, their antenna heights, etc. Given these decision variables, a radio access network 2.4.2 Maximum Capacity Planning configuration can be defined as a set of vectors [(p1, A more real-life formulation of the cell planning h1, …), …, (pm, hm, …)], which can be represented problem is to aim for maximizing the satisfied abstractly by the network configuration vector y. In capacity demands. The optimization problem can be practice, configuration parameters can take values written as: from a certain range. After y is decided, every traffic demand node TP Maximize ∑∑∑ µ x w∈L j∈S i∈I i ijw (14) i ∈ I is assigned to a serving BS using a capacity assignment algorithm, described later in this section, that is, to determine the capacity assignment pattern, The objective function is the sum of the served denoted by vector x. capacity demands. The constraints for this Each feasible search space point, denoted by J(x, optimization scenario are the same as in the y), is a particular set of locations, powers, heights, previous formulation. and other configurations for each BS, and a particular assignment pattern of traffic demand nodes to each selected BS satisfying the various 2.4.3 Maximum Profit Planning constraints. To generate a new neighbor, two sets of This model explicitly considers the trade-off neighborhood generating operators are required, one between the revenue potential of each BS site with that moves the locations and configurations of BSs its cost of installation and configuration. This trade- and another that changes the capacity assignment off is subject to QoS constraints in terms of pattern for each BS. The first set of operators are sufficient SIR ratios (constraints (10)). The objective defined as follows: of the model is to maximize the total annual profit generated by the cellular network operator, which is  on-off: a BS site is chosen randomly. If there is a equal to the total annual revenue minus the annual BS at the site, it is removed. If there is no BS at costs. Mathematically we have: the site yet, a new BS is placed at the site.  local move: one of the decision variables (power, [θ ∑∑∑ εµ i xijw - height, or other configuration parameters) of a w∈L j∈S i∈I randomly chosen BS is appointed randomly, and Maximize (15) the new neighbor is generated by taking its value ∑∑ y w∈L j∈S jw .C j ( y jw ) ] one size above or one size below its current value. ε denotes the annual revenue ($) generated by each 3.2 Capacity Assignment Algorithm channel utilized in the working area. θ is a The second set of operators is the capacity weighting factor. Relation (15) represents the assignment algorithm. Given the locations of BSs, maximum profit optimization when θ = 1. their powers, heights and other configurations, All three formulations (13), (14) and (15) are demand nodes I should be assigned first to the subject to constraints (3) – (12). available BS that has the largest signal attenuation factor before establishing connections to other BSs [11]. The algorithm works like this: 3 Solution Procedure In order to apply tabu search to the planning Step 0: Start with a given radio access network problem, we must define: configuration y. Step 1: For each i ∈ I, calculate minimum power  An initial feasible solution, w Ptar / g ij w  Representations for feasible solutions, according to propagation matrix G = [ g ij  Neighborhoods for feasible solutions, ]; assign demand node i to its closest BS j, requiring  Search techniques for neighborhoods, and
  • 5. the minimal transmit power; calculate x. In this step, relation (13), (14) or (15). The set of taboo and constraints (7) are automatically satisfied. aspirant moves is initialized, i.e., T(l) = ∅, and Step 2: If x from Step 1 and y satisfy constraints A(l) = ∅. A candidate list M(l) is initialized. (9), go to Step 3; otherwise repeat the process: Step 1: If the stop criterion is satisfied, randomly select and disconnect a demand node i belonging to the overcrowded BS j, which will the procedure ends and a transition to Step 9 is reduce its transmit power accordingly, until performed. constraints (9) are satisfied. Step 2: The set of move operators M is applied Step 3: If x from Step 2 and y satisfy constraints to solution Jl, and hence, a new set of candidate (10), go to Step 4; randomly select and disconnect a solution list M(l) is produced. Each move demand node i belonging to the overcrowded BS j, produces a new neighbor of the current search which will reduce its transmit power accordingly, space point. until constraints (10) are satisfied. Step 3: The M(l) set is examined to satisfy the Step 4: Output final capacity assignment vector x. constraints (8), (9), and (10) forms the new set of solutions N(l) that are neighbouring to solution Jl. 3.3 Initial Solution Generation Step 4: The set of solution, C(l), that are An initial network configuration is generated by intuitively (randomly) placing BSs at potential candidate for obtaining the best solution status, locations with a uniform distribution, in such a way and therefore, for replacing solution Jl in the that the number of initial locations is approximately next algorithm iteration, is formed through the half the total number of possible locations in our relation C(l) = N(l) – T(l). Moreover, solution Jl implementation, and assigning their powers, antenna is appended in the C(l) set. heights, and other configuration parameters within Step 5: The A(l) set is formed. More the respective feasible ranges. Then every traffic specifically, the objective function value that is demand node TP i is assigned to a closest serving scored by the solutions in the T(l) set is BS using the demand assignment algorithm, computed. Those solutions that improve the described earlier in this section. objective function by more than a given level The next step is the optimization process. The are removed from the T(l) set and placed in the heuristic algorithm receives as input the initial network configuration, finds better configurations A(l) set. by improving the measure of performance in Step 6: The set of solutions C(l) is enhanced successive iterations and returns a final good quality through the relation C(l) = C(l) ∪ A(l). network configuration and traffic assignment Step 7: The solution of the C(l) set that is the pattern. best in improving the objective function becomes the best solution that will be used in the next algorithm iteration. 3.4 Tabu Search Step 8: l ← l + 1. The next algorithm iteration is The tabu search implementation for the cell prepared. Therefore, the set of tabu moves that planning and optimization problem may be will be used in the next algorithm iteration is described as follows [13]: updated through the relation T(l + 1) = T(l) ∪ Step 0: l ← 0. The counter of the M(l). Moreover, solutions that have stayed in algorithm iterations, l, is initialized. An initial the taboo set for more than a given number of solution Jo(x, y) is chosen randomly in such a algorithm iterations are removed form the T(l + way that the number of BSs is equal to half the 1) set. Finally, A(l + 1) = ∅ and C(l) = ∅. A total potential locations, and that the power, the transition to Step 1 is performed. height and other configuration parameters of a Step 9: End. selected BS are chosen randomly from an element of the corresponding feasible set. Then, the capacity assignment algorithm is applied to 4 EXPERIMENTAL RESULTS Numerical experiments are made for 3G downlink generate the capacity assignment pattern. cell planning and optimization. The system Calculate the objective function, f(Jo) from performance evaluations are based on 3G WCDMA
  • 6. system specification. The optimization strategies Max transmit power BS antenna height used in these experiments are also applicable to Permitted Cost Permitted Cost other systems (e.g., TD-SCDMA, CDMA 2000). values (unit $K) values (unit $K) (watts) (m) We will present in detail a realistic planning 20 100 10 10 scenario in this section. 40 150 20 20 In pure capacity maximization planning, the 80 200 30 30 network cost is not included in the optimization Table 2. Feasible values for antenna power, height process, which may result in network configurations with their respective cost. with unnecessarily high cost. In pure cost minimization planning, the capacity is not included From Table 2, intuitively, BS antenna height in the optimization process, which may result in configuration costs are not significant when network configurations with unacceptable low compared to other cost components. This means that capacity. Our purpose with the following the antenna heights are not important in cost quantitative examples is to illustrate the tradeoff optimization, but important in capacity between capacity and cost. Table 1 contains optimization, because antenna heights are a important planning input data. dominating factor in determining coverage area and received power strengths at traffic demand node Parameters Values points. We apply tabu search to solve the above Mobile antenna height 1.8 m planning problem, but using alternative objective Frequency 2 GHz functions, according to the following three Mobile antenna gain 0 db scenarios: BS antenna gain 14 db SIRmin 0.009789 Eb/Io 7 db Processing gain 512 Mobile receiver sensitivity -110 dBm WCDMA orthogonality 0.7 Thermal noise density -130 dBm/Hz Annual revenue per channel $10,000 Table 1. 3G cell planning and optimization data Let us assume that the task is to design 3G downlink radio access network (cell deployment pattern) to provide conversational service over a predefined urban working area 1.5 km × 1.5 km. There are 500 demand nodes (n) uniformly distributed, and for the sake of simplicity, each demand node channel requirement µi takes one Fig. 2. Resulting overall traffic coverage ratios and value from the set {1, 2, 3} for each i ∈ I. There are total cost histograms for three different capacity 100 potential candidate BS locations (m) which are weighting factors, θ = 0.1, 1 and 10. randomly generated with an uniformly distribution. Assume that annual site non-configuration cost is Capacity optimization (CO): cost is completely $100K for each potential site. BS antennas are disregarded during the optimization, the objective assumed to be omnidirectional at every site. For the function is formulated in relation (14) to maximize sake of presentation clarity, we define the feasible the served traffic in the working area (or minimize power- and antenna height sets for all sites the number of unserved traffic points where some uniformly. The three power and height values, as constraints are not satisfied (outage). For simplicity, well as their associated configuration costs, are we call this scenario pure capacity optimization. shown in Table 2. For simplicity, we assume the Cost optimization (COST): capacity factor is power-based power control mechanism is adopted, completely ignored during the optimization, the because it requires much less computational effect. objective function is formulated in relation (13) to COST 231 Hata urban propagation model [14] is minimize the total cost and hopefully find the w used to generate configuration gain matrix G = [ g ij cheapest feasible network configuration during the ]. optimization process.
  • 7. Combined cost and capacity optimization optimization case yields considerable cost reduction (COM): cost is part of the objective function, when at least 40% traffic demand must be satisfied. according to relation (15). The weighing factor θ It is believed that pure cost optimization case would allows us to give priority to either minimizing cost not select any BS if we did not specify a minimum or maximizing capacity. To find an appropriate traffic satisfaction requirement. Likewise, pure value for θ, a number of alternative values have capacity optimization yields considerable cost been applied, and the results are subject to increase. Here we assume that the budgetary comparisons based on a large number of constraint allows no more than 20 BS sites installed. independent tabu search executions. Fig. 2 The combined cost and capacity optimization case summaries the results of four representative values, lies somewhere between two extreme cases, striking θ = 0.1, 1.0 and 10. a meaningful tradeoff. For explanation we can look Low θ value results in low success in terms of at Table 3, which contains that statistical results of finding high capacity feasible network 100 resulted network configurations found by tabu configurations, which can be attributed to the search for each objective (CO, COST, COM). The possibility to sacrifice one or more traffic demand resource utilization of the networks is measured by nodes to obtain a cheaper network configuration. the average number of BS transmitters in the This phenomenon is demonstrated by the low traffic networks, average total power, average height of service ratio (capacity) as well as by the apparently antennas in the networks and by the average cost. low total cost figures, as it is exemplified by the θ = Besides the average values over the 100 runs, we 0.1 case in Fig. 2. The θ = 1 case already represents indicate the parameters of the best found network in a situation where network configurations have on terms of cost. average a higher capacity and cost than feasible Comparing the statistical values, the total power usage of these three cases are very similar. In pure configurations with low network cost. The θ = 10 capacity optimization, the results favor networks case makes solutions cluster than θ =1. Increasing θ with a larger number of lower BSs. In contrast to further does not lead to additional capacity that, networks of the pure cost optimization contain improvement (not shown here). fewer BSs with higher structural antenna. COM (θ = Optimization case COST CO 1) mean mean mean best best best No. of BS 12 14.78 5 6.60 8 10.71 Total power 56.81 57.29 53.98 55.46 55.05 56.17 Average power 46.02 45.59 46.99 47.27 46.23 45.87 Average height 17.05 16.08 22.00 22.12 17.50 17.48 Total cost 3060 3745 1410 1866 2040 2727 Fig. 3. Resulting total cost values for pure capacity Table 3. Summary of allocated resources for optimization, pure cost optimization, combined cost scenarios CO, COST, COM. Measurement unit: and capacity optimization (θ = 1). power [dBm], height [m], and cost [× $K]. Comparing the best achievable results of CO and Fig. 3 summaries the results of the three COM, the total power usage (i.e., CO, 56.81 dBm optimization cases CO, COST, COM in terms of the and COM, 55.05 dBm) and the average antenna total cost of the obtained network configurations. height (CO, 17.05 m and COM, 17.50 m) are The histograms are generated from the results of approximately the same for both objectives, but the 100 independent tabu search runs for each of the number of BSs is decreased from 12 (CO) to 8 three cases. We use the same parameters and test (COM). This result indicates that the network cases as above for CO, COST, and COM, and apply remains “over-provisioned” under CO, that is, the θ =1 for COM. It can be seen that pure cost optimization does not attempt to remove
  • 8. unnecessary BSs, neither to cut back excessive for Indoor Wireless Networks, IEEE J. power. Selected Areas in Communications, Vol. 14, No. 4, May 1996, pp. 651-661. [5] K. W. Cheung, and R. D. Murch, Optimising 4 Conclusion Indoor Base Station Locations in Coverage and This paper analyzes planning aspects of WCDMA Interference Limited Indoor Environments, mobile radio network deployment and proposes Proceedings of IEE Communications, Dec. optimization models which explicitly take into 1998, pp. 445-450. account some important factors such as QoS and [6] R. K. Rawnsley, and S. Hurley, Towards power control. It also proposes a tabu search Automatic Cell Planning, Proceedings of the algorithm to solve the overall planning problem 11th IEEE International Symposium on considered as NP-hard. Personal, Indoor, and Mobile Radio The main contributions of our model are four- Communications, Sept. 2000, pp. 1583-1588. fold: firstly, instead of just minimizing the cost as [7] J. Kalvenes, J. Kennington, and E. Olinick, most previous works do, we consider alternative Hierarchical Cellular Network Design with objectives, which better reflect the dynamics of the Channel Allocation, Technical Report 01- various requirements of potential mobile operators. EMIS-08, Southern Methodist University, Secondly, the decision variables and traffic capacity 2001. can be embedded in the objective function and are [8] A. Dutta and V. Hsu, Cellular Network Design optimized in a single integrated step. This can result Site Selection and Frequency Planning,” in the tradeoff between the cost reduction and the Annals of Operations Research, Vol. 106, capacity improvement, compared with approaches 2001, pp. 287–306. where they are considered separately. Thirdly, the [9] C. Y. Samuel, CDMA RF System Engineering, model represents three-tier hierarchical cell Artech House, 1998. structure that contains macrocell, microcell and [10] E. Amaldi, A. Capone, and F. Malucelli, picocell, because at each selected base station Discrete Models and Algorithms for the location, the network can use different equipment Capacitated Location Problem Arising in types to generate coverage areas corresponding to UMTS Network Planning, Proceedings of different cell sizes. Finally, the model accurately ACM Dial-M, 2001, pp. 1-8. incorporates the important mobile radio network [11] K. Tutschku and P. Tran-Gia, Spatial Traffic planning issues, such as the radio propagation, Estimation and Characterization for Mobile interference, QoS, and traffic. Communication Network Design, IEEE J. Future work should focus on developing better Selected Areas in Communications, Vol. 16, algorithms and models which incorporate multi- No. 5, 1998, pp. 804-811. traffic scenarios, existing network expansion, and [12] E. Amaldi, A. Capone, and F. Malucelli, Base time factors. Station Configuration and Location Problems in UMTS Networks, Proceedings of the 9th References: Conference on Telecommunication Systems, [1] M. R. Garey and D. S. Johnson. Computers Modeling and Analysis, 2001. and Intractability: a guide to the theory of NP- [13] F. Glover, E. Taillard and D. de Werra, A completeness, W. H. Freeman and Company, user’s guide to tabu search, Annals of 1979. Operations Research, Vol. 41, 1993, pp. 3-28. [2] H. R. Anderson and J. P. McGeehan, [14] COST 231 Final Report, Digital Mobile Radio: Optimizing Microcell Base Station Locations COST 231 View on the Evolution Towards 3rd Using Simulated Annealing Techniques, Generation System, 1999. Proceedings of IEEE Vehi. Tech. Conf., Vol. 2, June 1994, pp. 858-862. [3] H. D. Sherali, C. M. Pendyala, and T. S. Rappaport, Optimal Location of Transmitters for Microcellular Radio Communication System design, IEEE J. Selected Areas in Communications, Vol. 14, No. 4, May 1996, pp. 662-673. [4] D. Stamatelos and A. Ephremides, Spectral Efficiency and Optimal Base Station Placement