Optimizing UMTS radio coverage via base station configuration

OPTIMIZING UMTS RADIO COVERAGE VIA BASE STATION CONFIGURATION Edoardo Amaldi, Antonio Capone and Federico Malucelli DEI, Politecnico di Milano Piazza L. da Vinci 32, 20133 Milano, Italy {amaldi, capone, malucell}@elet.polimi.it Abstract— Due to the W-CDMA radio interface, the area covered by a set of UMTS base stations depends on the signal quality requirements, the power control mechanism as well as on the traffic distribution. In previous work we have proposed discrete optimization models and algorithms for locating base stations in UMTS networks. In this paper we address the general problem of optimizing base station locations as well as their configurations, such as antenna height, tilt, and sector orientation. The proposed model, which can also be used to only optimize the base station configurations, accounts for the power control mechanism typical of W-CDMA an considers the Signal-to-Interference Ratio (SIR) as quality measure. To find good approximate solutions of this NP-hard problem, we develop a Tabu Search algorithm which takes into account traffic coverage and installation costs. Experimental results showing the effect of considering base station configurations in the planning process are reported. I. Introduction In recent years mobile service providers have afforded huge investments to develop network infrastructures using second generation systems technologies. Due to the high costs and the scarcity of radio resources, an accurate and efficient mobile network planning appears of outmost importance. With the advent of third generation systems, such as UMTS (Universal Mobile Telecommunication System), this need is now even more acute due to the increased complexity of the system and the number of parameters that must be considered [4]. In second generation systems the planning problem is usually subdivided into a coverage problem (in which base stations are located and configured so as to guarantee a high enough signal level in the service area) and a frequency assignment problem (in which channels are assigned to each base station taking into account traffic requirements and service quality), see e.g. [14], [12], [9]. Such a two-phase approach is no longer appropriate for UMTS networks because the bandwidth is shared in W-CDMA (Wideband Code Division Multiple Access) systems and there is no actual frequency assignment. Moreover, the area actually covered by a base station (BS) also depends on the signal quality constraints, usually expressed in terms of SIR, and on the traffic distribution. Since SIR values depend on emission powers, the This work has been supported by “Progetto Cofinanziato MURST 2001, Optimization Models and Methods for Telecommunications Network Design and Management”

0-7803-7589-0/02/$17.00 ©2002 IEEE

specific power control mechanism and the power limitations must be taken into account. Based on these observations we have recently proposed [1], [2], [3] new discrete optimization models and algorithms to help deciding where to install new BSs so as to cover the traffic in a given service area as well as possible. As in previous work [5], [11], [6], [8], our models take as input the following three types of information related to the service area: i) a set of candidate sites (CSs) where BSs can be installed, ii) the traffic distribution estimated by using empirical prediction models and iii) the propagation description based on approximate radio channel models or ray tracing techniques. Selecting the sites where to install the BSs while taking into account costs and service coverage is an important planning issue. However, optimizing BS configurations can be even more critical for service providers. This is, for instance, the case when the number of CSs is very limited or when an existing network needs to face a substantial change in traffic demand. In this paper we propose an enhanced model which aims at optimizing BS locations as well as their configurations, such as antenna height, tilt, and sector orientation. To find good approximate solutions in a reasonable amount of time, we develop a Tabu Search algorithm which takes into account traffic coverage and installation costs. For a matter of space, the focus here is on the uplink (mobile to base station) direction but the model and algorithm have been adapted to also account for the downlink direction. In Section II we briefly discuss the main issues of BS location and configuration. In Section III the model that we proposed and investigated in [1], [2], [3] for the case with omnidirectional BSs is first extended to the case with directional BSs and then to that with configurations. Some experimental results obtained with our Tabu Search heuristic for medium-size realistic instances generated using classical propagation models are reported in Section IV. Section V contains some concluding remarks. II. Base station location and configuration In W-CDMA cellular systems like UMTS, the amount of traffic that can be served by each BS is not limited a priori by a fixed channel assignment as in TDMA (Time Division Multiple Access) systems, but it is just limited by the SIR constraints. This allows a flexible use of radio resources depending on interference and propagation conditions, but it makes the problem of radio network planning and of traffic control (call admission control procedures) more complex. Signal power and interference levels are functions of the emitted powers which, due to the power control (PC) mechanism, depend on the mobile station posi-

PIMRC 2002

tions. Since the power available for transmission is limited, mobile stations that are far away from the BS may not reach the minimum SIR when the interference level is too high. Therefore, the area actually covered by each BS is heavily affected by the traffic distribution and its size can vary when the interference level changes (this is the so-called cell breathing effect). Since the interference levels depend both on the connections within a given cell and on those in neighboring cells, the SIR values and the capacity are highly affected by the traffic distribution in the whole area. When designing a new network or expanding an existing network to serve increased traffic, one must decide where to install new BSs. This decision process may aim at the best trade-off between maximizing the amount of traffic served and minimizing the total installation costs. In real system planning, however, optimizing BS configuration can often be more critical than BS location since service providers may have a very limited set of candidate sites due to authority constraints on new antenna installation and on electromagnetic pollution in urban areas. So they are very interested in maximizing the coverage achieved with a given set of BSs by modifying their configurations, adding new BSs only when they are strictly needed. It is worth emphasizing that not only BS location but also antenna configuration has a strong impact on the traffic covered and the connection quality. For example, when considering three-sector antennas, the interference in each sector depends on its horizontal orientation which can be optimized taking into account traffic distribution. Since the vertical radiation diagram is not uniform, also the vertical orientation (tilt) of the antenna affects the SIR values. Smaller tilt angles tend to increase not only the coverage ray but also the captured interference, while larger angles yield the opposite effect. The abovementioned parameters as well as antenna height can thus be tuned in order to maximize traffic coverage. By simultaneously optimizing antenna configuration and base station location, one may also try to reduce the number of BSs (the cost of the network) needed to cover a given traffic. Due to the many issues that affect system performance, the network designer’s task is quite complex and software planning tools based on optimization models and algorithms can make a substantial difference.

link between TP i, 1 ≤ i ≤ n, and a CS j, 1 ≤ j ≤ m. The propagation information is thus summarized by the gain matrix G = [gij ]1≤i≤n,1≤j≤m . In the W-CDMA UMTS base station location and configuration problem one wishes to select a subset of candidate sites within the set S where to install BSs as well as their configurations, and to assign the TPs to the available BSs so as to maximize the traffic covered and/or minimize the installation costs while taking into account the signal quality requirements in terms of SIR and the power limits on the mobile stations. As in [1], [2], [3] we assume a power-based PC mechanism in which the power received Preceived at BS j from each mobile station in a TP assigned to it is equal to Ptar and consider the SIR as signal quality measure. In the uplink direction, the signal quality constraint for each connection amounts to Preceived /(Iin + Iout ) ≥ SIRmin , where SIRmin is the minimum SIR before de-spreading and the thermal noise is omitted as in the other works considering a power-based PC(see e.g. [16]). Refer to [3] for a model assuming a SIR-based PC mechanism. Let us define the two classes of decision variables: ½ 1 if a BS is installed in j yj = 0 otherwise

III. Optimization models

where Ptar is by definition the power received from each assigned TP. It is not difficult to verify that constraint (1) enforces that, if a BS is installed in site j ∈ S (i.e., yj = 1), the SIR value in each sector σ must exceed the given SIRmin . For any single connection assigned to sector σ of the BS located in site j, the numerator of the left-hand-side term is the power of the relevant signal received in j while the denominator amounts to the total interference due to all other connections within sector σ. Indeed, the double summation term expresses the total power received at site j from all TPs h in Ijσ , i.e. all TPs falling within sector σ, from which the received power Ptar of the relevant signal is subtracted. More specifically, for any TP h within sector σ the quantity Ptar /ght amounts to the emission power required at TP h to guarantee P a received power value of Ptar at site t. Note that, m since t=1 xht = 1, the only term of the inner summation (over index t) that is nonzero corresponds to the

As in [1], [2], [3] we assume that a set of candidate sites S = {1, . . . , m} where a BS can be installed, is given and that an installation cost cj is associated with each candidate site j, j ∈ S. A set of test points (TPs) I = {1, . . . , n} is also given. Each TP i ∈ I can be considered as a centroid where a given amount of traffic di (in Erlang) is requested and where a certain level of service (measured in terms of SIR) must be guaranteed [15]. The required number of simultaneously active connections for TP i, denoted by ui , turns out to be a function of the traffic demand, i.e., ui = φ(di ). The propagation information is also supposed to be known, either computed by using prediction tools (e.g. Hata’s models or ray tracing [13]) or obtained by actual measurements. In the case of omnidirectional BSs or of directive BSs with an omnidirectional horizontal diagram let gij , 0 < gij ≤ 1, be the propagation factor of the radio

for j ∈ S and xij =

½

1 0

TP i is assigned to BS j otherwise

for i ∈ I and j ∈ S. Suppose we consider directive BSs with three identical 120 degree sectors and with an omnidirectional antenna diagram along the horizontal axis. Let the index set Ijσ ⊆ I denote the set of all TPs i that fall within the sector σ of the BS installed in CS j. Obviously, for each j, Ij1 ∪ Ij2 ∪ Ij3 = I and the index sets Ijσ with σ = 1, 2, 3 are disjoint. Since connections within a given sector of a BS are only affected by TPs that fall within that sector, for each CS j ∈ S and each sector σ we have a different SIR constraint that can be expressed as follows: P

h∈Ijσ

uh ghj

Ptar Pm

Ptar t=1 ght

xht − Ptar

≥ SIRmin yj , (1)

site to which TP h is actually assigned. Thus, if this site is denoted Pn by t(h), the outer summation can be rewritten as h=1 uh ghj (Ptar /ght(h) ) where ghj (Ptar /ght(h) ) is the power received at site j from TP h and uh is the number of connections required from TP h. Clearly, the contribution to the outer summation of any TP h assigned to site j amounts to uh Ptar since ghj = ght(h) . Finally note that, since we consider directive BSs with omnidirectional antennas diagram along the horizontal axis, the propagation gains gij do only depend on the distance between TP i and CS j and not on the sector σ in which TP i falls. Thus, assuming a power-based PC mechanism, the integer programming model for the case with three sectors amounts to Pn Pm Pm max (2) i=1 j=1 ui xij − λ j=1 cj yj s.t. Pm i∈I (3) j=1 xij ≤ 1 gij Pmax Ptar }yj

xij ≤ min{1, ³P Pm yj h∈I σ t=1 uh j

xij , yj ∈ {0, 1}

ghj ght

i ∈ I, j ∈ S (4) ´ xht − 1 ≤ SIR1min (5) j ∈ S, σ ∈ Σ i ∈ I, j ∈ S. (6)

The first term in the objective function (2) corresponds to the total traffic covered to be maximized and the second one to the total installation cost to be minimized. λ ≥ 0 is a trade-off parameter between these two contrasting objectives. Constraints (3) make sure that each TP i is assigned to at most a BS. Note that by restricting the assignment variables xij to take binary values, it is required that in every feasible solution all active connections must be assigned to a single BS. For each pair of TP i in I and CS j in S, constraints (4) correspond to the most stringent constraint among the coherence constraint xij ≤ yj , which ensures that TP i is only assigned to site j if a BS is installed in j, and the power limit on the user terminal: Ptar xij ≤ Pmax yj (7) gij where Pmax is the maximum emission power and Ptar /gij corresponds to the emission power required by a mobile station in TP i to guarantee the target received power Ptar at site j. The bilinear SIR constraints (5) are obtained by multiplying both sides of the inequality (1) by the denominator of its left hand side and by dividing the left and right members by Ptar · SIRmin . We now turn to the general setting in which each BS can be in one out of l different configurations. This 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 out of a finite set of values with respect to the ground level. Since propagation gains depend on the BS configuration, we denote k by ghj the propagation gain from TP h to CS j if the BS is in configuration k. To extend the model (2)-(6) to the general case, different variables are needed for each configuration: ½ 1 if a BS with configuration k is installed in j yjk = 0 otherwise

for j ∈ S and ½ 1 TP i is assigned to BS j with configuration k xijk = 0 otherwise for i ∈ I and j ∈ S. Then, for each triple of candidate site j, configuration k and sector σ, we have the following SIR constraint: P

σ h∈Ijk

k uh ghj

Ptar P m Pl t=1

Ptar s s=1 ght

xhts − Ptar

≥ SIRmin yjk ,

(8) σ denotes the set of all TPs that fall within sector where Ijk σ of a BS in site j if this BS has a configuration k. Thus the general integer programming model for optimizing BS location as well as configuration amounts to: n X m X l X

max

ui xijk − λ

i=1 j=1 k=1

m X l X

cjk yjk

(9)

j=1 k=1

s.t. l m X X

xijk ≤ 1

i∈I

(10)

j=1 k=1

xijk ≤ min{1,

k gij Pmax }yjk Ptar

l X

yjk ≤ 1

i ∈ I, j ∈ S, k ∈ K (11) j∈S

(12)

k=1



yjk 

 k ghj 1 uh s xhts − 1 ≤ g SIR min ht t=1 s=1

l m X X X

σ h∈Ijk

xijk , yjk ∈ {0, 1}

(13)

j ∈ S, σ ∈ Σ, k ∈ K

i ∈ I, j ∈ S, k ∈ K

(14)

where cjk is the cost for installing a BS in configuration k in site j and constraints (12) make sure that for each site j at most one BS configuration is selected. IV. Some computational results The UMTS base station location and configuration problem is NP-hard since it includes as a special case the standard facility location problem. To find good approximate solutions in a reasonable amount of time, we have extended the heuristics presented in [1], [2], [3] for the location models. In particular we propose a Tabu Search, which is a meta-heuristic based on local search. Starting from an initial solution, provided by means of a randomized greedy algorithm, the solution space is explored by performing a sequence of ’moves’. The moves we consider are: removing a BS, installing a new BS, removing a BS and installing a new one, and changing the configuration of a given BS. Each time a move requires the installation

of a new BS, the best configuration in terms of the objective function is selected. At each step, a new current solution is obtained by carrying out the best available move even though it may worsen the objective function value. To prevent cycles and try to escape from local optima, some moves are forbidden for a certain number of steps (they are put in a Tabu list). The best solution found during the iterations is stored and returned after a predefined maximum number of steps. To evaluate the performance of our algorithm we have considered synthetic but realistic uplink instances. Each instance is specified by a square service area D × D, by m CSs in which to locate three-sector antennas and by n TPs. The position of TPs and CSs is randomly selected as follows. Subdivide the area into d × d smaller square regions by using a regular grid. Each region can contain a high (H) , medium (M) or low (L) number of TPs, or even no TP at all. The number of regions with H, L, M TPs is set to nH , nL , nM respectively, so that H · nH + M · nM + L · nL = n. Using a pseudo-random number generator we first select which regions contain a number H TPs. To each region i is associated a weight wi initially set to 1. Regions are iteratively picked with P a probability Pi = wi /( i wi ). After each iteration the weight wi of the selected region is set to zero, and the weights of the neighboring regions are increased by 1. Once all nH TPs with high traffic have been selected, the nM TPs with medium traffic and the nL TPs with low traffic are selected according to the same procedure. This mechanism produces realistic instances characterized by clusters with high traffic surrounded by areas with lower traffic as usually observed in cities and their suburban areas. The position of CSs is also randomly selected in the set of crossing points of the regular grid. The procedure adopted is similar to the previous one: to each grid point is assigned a weight equal to the number of TPs in the four adjacent regions. After each iteration the weight of the selected point is set to zero and the weights of its neighboring points is increased by 1. The propagation matrix G is obtained by using classical Hata’s formulas [10] which give the attenuation A (loss) in dB due to signal propagation as a function of the distance between transmitter and receiver, the transmission frequency, and the base and mobile stations heights (see[1], [2], [3]). Moreover, we take into account the antenna tilt by considering a realistic vertical radiation diagram with a main lobe 30 degrees wide and a gain (in dB) which decreases linearly outside the main lobe. To evaluate the effect of optimizing BS configuration on the traffic coverage and the total installation cost, we have considered the following configurations: BS antenna height (which has an impact on G through Hata’s formula), antenna tilt (whose impact on G is due to the translation of the vertical antenna radiation diagram), and sector orientation (which changes the sets Ijσ ). More specifically, we consider 0, 30, 60 or 90 degree rotations, 10, 20, 30 or 40 degree tilts with respect to the vertical axis and 5, 10, 20, 30 meters above ground level. We now report some typical results obtained for randomly generated instances with n = 881 TPs and a 1005 × 1005 meter service area which is subdivided into 225 square regions of size 67 × 67. The number of regions with respectively high, medium and low traffic are: nH = 45, nM = nL = 68, and the corresponding number of TPs per region are: H = 9, M = 5, and L = 2.

Table I shows the results obtained with the Tabu Search algorithm considering either fixed sector orientations or configurable ones (while tilts and heights are fixed). All ten instances contain m = 100 CSs. Notice that in all cases optimizing the sector orientation yields a higher traffic coverage and/or a lower number of BSs installed. Table II reports the results obtained considering either fixed or configurable antenna tilts (while sector orientations and heights are fixed). All ten instances contain m = 55 CSs. Also in this case we observe that when the optimization algorithm is allowed to configure the antenna tilts it leads to a higher traffic coverage and/or a lower number of BSs installed. Finally, Table III shows a comparison between three scenarios: in the first one only sector orientations can be configured, in the second one only antenna tilts can be tuned while in the third one both set of parameters are optimized. V. Concluding remarks We have proposed an integer programming model and a Tabu Search algorithm for optimizing BS location and configuration, which are aimed at helping service providers to plan UMTS networks in an efficient and cost effective way. Experimental results show that taking configurations into account can lead to significant improvements in terms of solution quality. Our model and algorithm, which can also be used to only optimize the configuration of a given set of BSs, have already been extended to the downlink direction, and the case with soft hand-over is currently under consideration. Although more detailed planning aspects can be included in the model (see e.g. [7]), the resulting instances tend to be beyond the reach of state-of-the-art optimization software. It is thus important to find a good trade-off between an accurate description of the network planning problem and a computationally solvable model. References [1]

[2] [3]

[4]

[5] [6]

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E. Amaldi, A. Capone, and F. Malucelli. Discrete models and algorithms for the capacitated location problem arising in UMTS network planning. In Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M), pages 1– 8. ACM, 2001. E. Amaldi, A. Capone, and F. Malucelli. Improved models and algorithms for UMTS radio planning. In Proceedings of IEEE VTC Fall 2001, 2001. E. Amaldi, A. Capone, and F. Malucelli. Planning UMTS base station location: Optimization models with power control and algorithms. IEEE Transactions on Wireless Communications, 2002. E. Berruto, M. Gudmundson, R. Menolascino, W. Mohr, and M. Pizarroso. Research activities on UMTS radio interface, network architectures, and planning. IEEE Communications Magazine, pages 82–95, February 1998. P. Cal´ egari, F. Guidec, P. Kuonen, and D. Wagner. Genetic approach to radio network oprimization for mobile systems. In Proceedings of IEEE VTC 97, pages 755–759, 1997. B. Chamaret, S. Josselin, P. Kuonen, M. Pizarroso, B. SalasManzanedo, S. Ubeda, and D. Wagner. Radio network optimization with maximum independent set search. In Proceedings of IEEE VTC 97, pages 770–774, 1997. A. Eisenblatter, A. Fugenschuh, T. Koch, A. Koster, A. Martin, T. Pfender, O. Wegel, and R. Wessaly. Modelling feasible network configurations for UMTS. Technical Report 02-16, Konrad-Zuse-Zentrum fur Informationstechnik (ZIB), Berlin, Germany, 2002.

Served TPs best sol. 873/881 881/881 881/881 880/881 881/881 881/881 878/881 881/881 867/881 881/881

fixed orientation # of BSs Served TPs best sol. average 19 873/881 16 881/881 18 881/881 19 880/881 16 881/881 17 881/881 18 878/881 16 881/881 19 867/881 18 881/881

# of BSs average 19.8 16.4 18.3 19.9 16.8 17.8 18.6 16.8 19.6 19.3

Served TPs best sol. 881/881 881/881 881/881 881/881 881/881 881/881 881/881 881/881 880/881 881/881

configurable orientation # of BSs Served TPs best sol. best sol. 18 881/881 16 881/881 16 881/881 17 881/881 15 881/881 15 881/881 16 881/881 15 881/881 18 880/881 16 881/881

# of BSs average 18.3 16.6 17.3 17.6 16.1 16.5 16.9 16.1 18.6 17.7

TABLE I Results obtained with fixed and configurable sector orientations: n = 881, m = 100.

Served TPs best sol. 855/881 867/881 881/881 881/881 851/881 842/881 832/881 875/881 803/881 855/881

fixed tilt # of BSs Served TPs best sol. average 19 854.2/881 23 867/881 19 881/881 18 881/881 21 851/881 21 842/881 18 832/881 20 875/881 15 803/881 19 855/881

# of BSs average 18.9 23 19.1 18 21 21 18 20 15.4 19

Served TPs best sol. 866/881 879/881 881/881 881/881 855/881 847/881 847/881 881/881 817/881 869/881

configurable tilt # of BSs Served TPs best sol. average 20 861.9/881 20 877/881 18 881/881 16 881/881 19 853/881 17 847/881 18 845.9/881 19 880/881 20 815/881 19 867.2/881

# of BSs average 20.1 21.4 18.6 17.5 19.9 18.4 18.9 19.5 16.8 19.4

TABLE II Results obtained with fixed and configurable antenna tilt: n = 881, m = 55. configurable orientation Served TPs # of BSs 881/881 17 867/881 18 851/881 21 859/881 18 873/881 19

configurable tilt Served TPs # of BSs 881/881 16 855/881 19 847/881 17 847/881 18 880/881 21

configurable orientation and tilt Served TPs # of BSs 881/881 16 872/881 18 867/881 19 873/881 20 881/881 18

TABLE III Best solutions obtained with configurable orientations, configurable tilts, and configurable orientations and tilts: n = 881, m = 55.

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