Allocating Channels to a Temporary Base Station

XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP Allocating Channels to a Temporary Base Station J. N. Portela and M. S. Alencar the signal-to-interference ratio (SIR). As the SIR value falls below an accepted threshold, the quality of a link may cause outage [2]. The signal power decreases with distance, thus, the cochannel interference is a function of distance as well as the path loss of the interfering signal. The channel allocation system must guarantee a minimum SIR value to the TBS. That is, the allocated group of channels should not be used concurrently by neighbor BSs, except by distant ones, outside the reach of the TBS signal. This paper shows a solution to the channel allocation problem by using Voronoi diagrams in searching the nearest Keywords— Land mobile radio cellular systems, Predicand the farthest neighbor BS [3]. tion methods, Voronoi diagrams. Abstract— This paper presents the allocation of cells of a mobile cellular network as a dynamic ordered orderk multiplicatively weighted Voronoi diagram. The farthest neighbor search is applied to the channel allocation scheme of a temporary base station. Whenever a temporary base station is deployed, its power, antenna height, group of channels and other features are to be configured. The nearest and the farthest point search are applied to the problem of finding the nearest and the farthest base station surrounding the temporary station, in order to identify the group of channels to be allocated. Proximity relations are acquired from the Voronoi diagram and used in solving the problem of allocating channels with a minimum cochannel interference. I. I NTRODUCTION II. T HE N EAREST AND THE FARTHEST N EIGHBOR S EARCH Temporary base stations (TBS)1 are deployed in a cellular network when large amounts of people move to a certain area, or when a new cell is to be added to the existing service area [1]. An occasional populational concentration may overload a base station (BS), augmenting unusually the call blocking. To support the traffic of the overloaded BS, a TBS is usually deployed. Proximity between base stations thus becomes the key parameter to determine the cochannel interference and which group of channels should be allocated to the TBS. Neighbor BSs are related to traffic operations as handoff and blocking while the farthest one is related to interference phenomena as outage, frequency reuse and channel allocation. Interference is important to assess the performance of the cellular network, since cells are intended to be intersecting zones with minimum interference. Proximity between them may affect The nearest neighbor search is used in communication systems and signal processing in the optimum receiver design, constellation diagrams, bit error probability estimation, pattern recognition and vector quantizing. The farthest neighbor search is used in scientific and engineering applications to detect the minimum influence of a point in a certain area or similarities in a given data [4]. These methods can be applied to identify the cochannel BS in a cluster, whose interference intensity is inversely related to distance. The inclusion of a TBS in a service area modifies coverage and handoff processing of the surrounding cells. The cells proximity relations are closely related to the cochannel interference and the channel allocation scheme. The farthest neighbor search provides a way to allocate channels to a TBS. J. N. Portela, Centro Federal de Educação Tecnológica do Ceará, Fortaleza, CE, Brasil, phone: +55 83 33101391, E-mail:portela@dee.ufcg.edu.br. M. S. Alencar, Institute for Advanced Studies in Communications, Department of Electrical Engineering, Universidade Federal de Campina Grande (UFCG), Campina Grande, PB, Brasil, phone: +55 83 33101410, E-mail:malencar@dee.ufcg.edu.br. This work is supported by the National Council for Scientific and Technological Development (CNPq). 1 A TBS may be portable or fixed. 605 III. T HE C ELL R ADIUS P REDICTION The cells are not well defined but have fuzzy boundaries because of the statistical fluctuations in radio path losses. However, it is possible to establish a mean boundary using path loss prediction models [5]. These models associate the path loss with distance and makes it possible to predict the cell XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP radius. When the downlink received power reaches a minimum acceptable value (received power threshold), the mobile receiver blocks the reception and determines a limit to the cell. In an isotropic propagation environment, the maximum path, determined by the receiver blocking, corresponds to the radius of a circle. The received power Pr is given by Pr = Pt + Gt + Gr − L, (1) The cell radius can also be estimated by statistical method in which the signal envelope is considered to follow the Rayleigh, Lognormal and Suzuki distributions [7]. IV. T HE M OBILE C ELLULAR N ETWORK AS A DYNAMIC O RDERED O RDER -k M ULTIPLICATIVELY W EIGHTED VORONOI D IAGRAM where Pt is the transmission power, Gt and Gr are the antenna gains and L is the predicted path loss. When Pr reaches the received power threshold Z, the signal radio suffers the maximum path loss. As the path loss depends on distance, it is possible to express the distance corresponding to the minimum received power by means of the path loss expression [6] The Voronoi diagram is a partition set, generated by site points. This geometric structure assumes the nearest neighbor rule in associating a point, in the Rn space, to a site point nearest to it. Each resulting partition is named Voronoi region [8]. Let x be a point in the Rn space, ci the i-th site point and Vi the Voronoi region generated by ci . The association x ∈ Vi occurs according to the nearest neighbor rule L = a + b log(d), If D(x, ci ) ≤ D(x, cj ), ∀j 6= i, then x ∈ Vi . (2) where a and b are parameters dependent on the path loss prediction model. For example, the COST-Hata model gives the path loss by L = 46.3 + 33.9 log(f ) − 13.82 log(hb )− A(hm ) + (44.9 − 6.55 log(hb )) log(d), (3) A(hm ) = (1.1 log(f ) − 0.7)hm − (1.56 log(f ) − 0.8), Else x ∈ Vj . The proximity metric D is a function of distance. In a multiplicatively weighted Voronoi diagram, D = d/w, where d is the Euclidean distance from x to ci and w is the weight of the site point. The nearest neighbor rule is thus defined as If for medium sized cities and medium trees density, where hb and hm are, respectively, the base station and the mobile antenna heights and f is the carrier frequency. By comparing (2) to (3) d(x, cj ) d(x, ci ) ≤ , ∀j 6= i, then x ∈ Vi . wi wj Else x ∈ Vj . 6 (5) 4 P Inserting (2) in (1) 2 r 0 r Pr = Pt + Gt + Gr − a − b log(d). (6) Solving for d, yields y(km) r1 d = 10 (10) Consider the proximity model with two adjacent site points (c1 , c2 ) illustrated in Figure 1. The distance a = 46.3+33.9 log(f )−13.82 log(hb )−A(hm ); (4) b = 44.9 − 6.55 log(hb ). (9) 0 . (7) As the propagation environment is assumed to be isotropic, for Pr = Z, the path loss is omnidirectional and the distance in (7) corresponds to the cell radius Pt +Gt +Gr −Z−a b r = 10 . (8) 606 c2 c1 (x0 ,y0) d2 d −2 Pt +Gt +Gr −Pr −a b 2 1 −4 −6 −6 −4 −2 0 2 4 6 8 x(km) Fig. 1. Two adjacent site points model. The locus of the distance ratio d1 /d2 corresponds to the circumference of the Apollonius circle, shown in thick line. XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP 1.1461 y(km) 0 BS1 −1 BS 2 −2 −3 0.8725 643 0.6 57 50 0. 2 4 6 74 0 54 −2 97 −5 (13) 1.313 6.3021 0.1587 1 1.50 (w12 ) y2 − y1 , (w12 )2 − 1 1.7 25 4 2 1. y0 = 63 26 2. 3 −4 2 5 0.7613 4 12 (12) 44 (w12 )2 x2 − x1 ; (w12 )2 − 1 5 6 79 0.5 x0 = w12=1 0. ratio w12 = d1 /d2 is constant along the circumference shown in thick line, whose radius r0 and center hx0 , y0 i are given by ¯ ¯ ¯ d12 w12 ¯ ¯; ¯ r0 = ¯ (11) (w12 )2 − 1 ¯ 8 10 12 x(km) where hxi , yi i is the site points location and d12 is the distance c1 c2 . The circumferences with radii r1 and r2 intersect at point P and gives Fig. 2. Edges of two adjacent BSs in terms of the distance ratio (w12 = r1 /r2 ). r1 d1 = . d2 r2 (14) d1 d2 = , r1 r2 (15) The order-k diagram is obtained from the order(k − 1) diagram according to the following procedure [9]: 1. Remove a site point ci obtaining new edges for the N − 1 site points diagram. The effect of removing ci is the elimination of the edges determined by ci and the extension of the neighbor edges to the interior of Vi ; 2. Place the previous removed site point ci back into its location and remove another site point; 3. Repeat for all the site points. Expressing (14) as yields the definition of the nearest neighbor rule in (10). If the site points represent base stations, the weights in (15) correspond to the cells radii wi = ri (16) and the distance ratio is ri wij = . rj B. The ordered order-k Voronoi diagram (17) The proximity relations between cells are represented by the multiplicatively weighted Voronoi diagram, since the link mobile-BS is established according on a proximity rule expressed as a function of the received power. A BS works as a site point determining a Voronoi region by means of its radio signal. Figure 2 shows the edges between two BSs in terms of the distance ratio. A. The order-k Voronoi diagram Let C = {c1 , ..., cN }, |C| = N , be the site points set, X a subset of C, |X| = k, X = C − X. The order-k Voronoi region is defined as The ordered order-k multiplicatively weighted Voronoi diagram is an order-k diagram where the proximity relations are ordered in sequence of proximity. It is obtained from the superposition of the order-k, k−1, ..., 1 diagrams [10]. A Voronoi region, depicted as O(X), X = {i, j, ..., q}, is the locus of all the points closest to the site point ci . If ci is removed, the site point cj becomes the closest to O and cq is the farthest one. The edges E(i, j) of the diagram define the Voronoi regions. Each edge is a bisector, it divides the plane into half-planes (ξ) (ξ) πi , πj , where ξ indicates the order of the edge. Each Voronoi region O is the intersection of the half-planes \ O(X) = πn(ξ) , (19) n∈X,ξ∈[1,k] V (X) = {x : D(x, ci ) ≤ D(x, cj ), ∀ci ∈ X, ∀cj ∈ X}, (18) where x is a point in Rn , D is a function of distance, k ∈ Z+ and k ∈ [1, N − 1]. 607 For instance, see the region (1) (2) (3) O(3, 2, 1) = π3 ∩ π2 ∩ π1 illustrated in Figure 3. XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP order−1 order−2 order−3 (3) E(1,4) π4 (1) π2 (3) π1 (1) E(2,3) π3 O(3,2,1) (2) π2 (2) π1 Fig. 3. E(1,2) Limits of an ordered order-3 Voronoi region in the plane. This gives spatial information to plan frequency reuse and channel allocation, since cochannel interference is a function of proximity. V. A LLOCATING C HANNELS TO A T EMPORARY BASE S TATION An example of the method to allocate temporary channels is described below. The data of the BSs is given in Table I, the Voronoi edges are described in Table II. Four groups of channels are assigned to the BSs: BS1 → group A, BS2 → group B, BS3 → group C and BS4 → group D. The data of TBS is: antenna height=5.7 m, gain=6 dB, power=36 dBm. The TBS cell radius predicted by Equation (8) is 1.2 km. The carrier frequency is 1800 MHz, the mobile antenna gain is assumed to be 3 dB, the mobile antenna height 3 m, the received power threshold -100 dBm. The COST-Hata model is adopted to predict the path loss. The algorithm for the Voronoi diagram construction in R2 is now summarized. The input data is: the order of the diagram k, BS locations hxi , yi i and cells radii ri . The output is the collection of circular arcs E(i, j) described by the center coordinates hx0 , y0 i and radius r0 . INPUT: k, hxi , yi i, ri . OUTPUT: E(i, j) ≡ (hx0 , y0 i, r0 ). Step 1. Initialization: order= 1. Step 2. Compute E(i, j), taking BSs pairwise, using Equations (11), (12) and (13). Step 3. Determine the intersections of bisectors. Step 4. IF order= k, EXIT. Step 5. ELSE order→order+1. Extend bisectors to reach an end point. GO TO 4. % An end point is an intersection between edges. The outer edges have no end point and must be truncated. Figure 4 shows the resulting ordered order-3 Voronoi diagram. The regions are depicted as O(i, j, p). This means that the region O is nearest to 608 BSi and farthest to BSq such that q 6∈ {i, j, p}. Figure 4 shows arbitrary locations marked as λ, ϕ, β, Φ and ∆, where a TBS is to be located. The group of channel allocated to TBS is taken from the farthest BS as shown in Table III. The λ-location case is shown as an example in Figure 5, where E(2,λ) is a closed arc, thus it generates no order-k (k > 1) edges, because higher order edges are extensions of the lower ones. The same case occurs for Φ-location. At locations β and ϕ, the edges of BS2 and BS3 are simultaneously modified and new order-k Voronoi regions are generated. The case of β-location is shown in Figure 6 where the regions O(β, 1) and O(β, 3) are the overlapping area between cells of BS2 , BS3 and β-TBS. The ∆-location, similarly to the β case, modifies the edges between BS1 and BS3 but does not alter the remaining edges. TABLE I BASE STATION DATA . BS Channels Location Power (dBm) Antenna Height (m) Cell Radius (km) COST-Hata parameters 1 A h1,1i 40 41.56 2 B h3,10i 40 50.89 3 C h5,6i 34 73.55 4 D h9,12i 43 48.86 4.0 3.6 3.2 4.8 a1 =129.8 b1 =34.3 a2 =128.7 b2 =33.7 a3 =126.5 b3 =32.7 a4 =128.9 b4 =33.8 TABLE II VORONOI EDGES DATA AND DISTANCE RATIO . E(1,2) E(1,3) E(1,4) E(2,3) E(2,4) E(3,4) Center h-7.5,-37.6i h20,24.8i h-9.3,-13.1i h8.6,-1.1i h-10.6,5.5i h1.8,1.2i Radius (km) 43.869 27.131 23.318 9.962 17.205 8.655 Distance ratio 0.9 1.12 0.75 1.24 0.833 0.666 VI. C ONCLUSIONS The ordered order-k multiplicatively weighted Voronoi diagram represents the coverage of the cells as a space tessellation. It provides proximity relations useful in searching the farthest BS from a given area, in order to allocate channels to a TBS. It is an efficient tool for space and proximity XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP order−1 E(1,3) 16 order−2 order−3 O(2,4,3) O(4,2,3) 14 12 E(1,4) 10 BS4 BS2 λ O(2,3,4) O(2 8 ϕ ,3,1 O(2,1,3) ) E(3,4) O(3 BS E(2,3) 3 ,2,1 Φ O(3,1 ,2) 4 0 BS1 β ) ,1 ,4 (3 O(1,3,2) O 2 O(4,3,2) ,2) O(1,2,3) ) 3,4 O( 6 ) ,2,4 O(3 O (3 ,1 ,4 ) O(4,3,1) ∆ E(1,2) O(1,4,3) E(2,4) −2 −5 0 5 10 15 Fig. 4. A cluster of four cells represented by an ordered order-3 multiplicatively weighted Voronoi diagram. Each Voronoi region is defined by three circular arcs as shown in Figure 3. Temporary BSs are arbitrarily located at λ, ϕ, β, Φ and ∆. 16 16 order−1 order−2 E(2,4) E(2,4) 14 12 14 12 E(λ,2) 2 10 λ −TBS 6 ) 2,3 E( y(km) y(km) 10 8 BS4 BS2 BS4 BS E(1,2) E(1,4) 8 6 BS3 E(1,2) O(β,3) BS 3 4 4 E(3,4) 2 BS1 2 β −TBS E(1,3) BS1 0 0 E(2,3) E(1,4) −2 −5 0 5 x(km) 10 O(β,1) E(1,4) −2 15 −5 Fig. 5. A TBS deployed at λ-location modifies the coverage of BS2 only. The order-1 edge E(λ, 2) is a closed arc, it can not extend to generate an edge of order higher than 1. 609 0 5 x(km) 10 15 Fig. 6. A TBS deployed at β-location modifies the coverage of BS1 and BS3 . Order-2 edges of Voronoi regions are generated. The coverage of BS2 and BS4 are not altered. XXII SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇÕES - SBrT’05, 04-08 DE SETEMBRO DE 2005, CAMPINAS, SP TABLE III TBS LOCATION AND ITS VORONOI REGIONS . NEAREST AND FARTHEST BS , ALLOCATED GROUP OF CHANNELS CORRESPONDING TO THE FARTHEST BS . TBS location λ ϕ β Φ ∆ Voronoi region O(2,4,3) O(2,3,4) O(3,1,2) O(3,4,2) O(4,3,1) Nearest BS BS2 BS2 BS3 BS3 BS4 Farthest BS BS1 BS1 BS4 BS1 BS2 Group of Channels A A D A B relations analysis. The space information on the proximity between cells can be used in planning traffic operations as handoff, frequency reuse and channel allocation. R EFERENCES [1] A. M. Monk and L. B. Milstein, “A CDMA cellular system in a mobile base station environment”, IEEE Global Telecommunications Conference, GLOBECOM’93, vol.4, pp. 65 - 69, 29 Nov.-2 Dec. 1993. [2] J. N. Portela and M. S. Alencar, “Outage contour using a Voronoi diagram”, Proceedings of the IEEE Wireless Communication and Networking Conference, WCNC’04, Atlanta, GA, 21-26 Mar. 2004. [3] M. I. Shamos and D. Hoey, “Closest-point problems”, Proceedings of the Annual IEEE Foundations of Computer Science, pp. 151-162, Oct. 1975. [4] M. 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