Wirel. Commun. Mob. Comput. 2003; 3:455– 463 (DOI: 10.1002/wcm.131)
A cell-based location-sensing method for wireless networks
Hung-Chi Chu and Rong-Hong Jan*,†
Department of Computer and Information Science
National Chiao Tung University Hsinchu, 30050
Taiwan
Summary
One of the most important applications for mobile commerce is location-based application and the core technology of location-based applications is the location-determination technology. In this paper, we present a location-sensing method, called cell-based location-sensing method and its positioning accuracy for the wireless networks with hexagonal structure and mesh structure. In addition, the accuracy of the method is optimized by tuning the transmitting power of base stations. In the optimal transmitting power, an accuracy of within 9.1667% (7.2182%) cell area for hexagonal structure (mesh structure) can be achieved by the cell-based location-sensing method. We believe that the results are useful for deploying wireless networks for location-based applications. Copyright 2003 John Wiley & Sons, Ltd. KEY WORDS location sensing location determination location-based applications 1. Introduction
Recently, the wireless networks and the WWW are converging. Mobile commerce is expected to grow at incredible rates as mobile users access the Inter-net. Not only does mobile computing offer conve-nience but it also provides new services and appli-cations. One of the most important new services and applications is location-based service and application.
It allows mobile users to receive services based on their geographic location or position. These services and applications include emergency rescue, resource tracking and management, tour guide [1], location-sensitive billing, points of interest and so on [2,3].
The core technology of location-based services and applications is the location-determination tech-nology. Many papers [4–9] are dedicated to location-determination methods. These methods can be divided
ŁCorrespondence to: Rong-Hong Jan, Department of Computer and Information Science, National Chiao Tung University,
Hsinchu, 30050, Taiwan.
†E-mail: [email protected]
Contract/grant sponsor: Ministry of Education, Taiwan, ROC; contract/grant number: 89-E-FA04-1-4. Contract/grant sponsor: Lee and MTI Center for Networking Research, NCTU, Taiwan.
into two major classes, network-based and handset-based.
The network-based methods collect a handset’s signals and determine its location in a centralized server. Some equipments are used to determine the direction and the time delay of the handset signal and calculate its position. Such solutions do not require any modification to handsets but have low position accuracy and high network cost. Typical network-based methods are Angle of Arrival (AOA) [4], Time Difference of Arrival (TDOA) [4], a combination of AOA and TDOA [4], and so on.
The handset-based methods collect signals from the networks by the mobile device and determine the location by the device itself. Typical handset-based methods are Global Positioning System (GPS) [6,7], Assisted GPS (AGPS) [10,11] and Differential GPS (DGPS) [12,13]. They rely on the 24 satellites that orbit around the earth to transmit precise veloc-ity, latitude, longitude and altitude information to the GPS receiver in the handset. The handset reports its location to the service provider over the wireless net-work. These methods have a higher position accuracy but longer times to first fix (TTFF) and incur cost to handsets.
In addition to the above main classes, there is a cell-based position-determination method. It involves research on coverage problems and power control problems, which has been proposed in some papers [14–16]. In this method, the handset gathers all of the BS signals that it received and transmits the BS identification to the location server. The server then computes the position and forwards it either to the end user or to the location-based service that was requested. The main advantage of the cell-based location-sensing method is the fact that it is available today. As it requires no changes to the existing wireless network architecture, or to the mobile station (MS), it does not substantially increase costs for either network operators or for end users. The cell-based location-sensing technology can be applied to Global System for Mobile Communication (GSM) networks or to IEEE 802.11 wireless LAN. In general, the accuracy of cell-based location sensing increases as the number of cells within range increases, making it more accurate in urban environments for GSM networks.
In this paper, we present an accuracy measure for the cell-based location-sensing method. Two types of cellular networks are considered. One is a cellular network with hexagonal layout and the other is with mesh layout. Next, we optimize the location-sensing
accuracy by tuning the base stations’ (BSs’) transmit-ting power. That is, we find an optimal transmittransmit-ting power for BSs such that the MS can be located at the smallest area in the worst case. The remainder of this paper is organized as follows. In Section 2, we present the cell-based location-sensing method in detail. Sections 3 and 4 give the location-sensing accuracy respectively for the hexagonal wireless net-works and for the mesh wireless netnet-works. Compari-son of the accuracy of hexagonal and mesh structure is given in Section 5. Finally, the conclusion is given in Section 6.
2. Cell-based Location-sensing Method
Consider a physical layout of the wireless network as shown in Figure 1. The area covered by the BS is called a cell. Each cell has the shape of a circle. The signal coverage of the BSs may overlap. The MS can receive a radio signal containing a cell number from the BS, if it is in the signal coverage of that BS. Note that an MS may receive more than one cell number when it is in the signal-overlapping area. For example, as shown in Figure 1, an MS in area A can receive the signals from BSs 0, 1, and 6, and in area B can receive the signals from BSs 0 and 2. Thus, the signal coverage can be used to determine the MS’s location. Suppose that we have a location server maintaining the signal coverage data. The MS sends the list of every BS that is within range back to the location server upon receipt of the signal. The server
0 1 2 3 4 5 6 C R S T U V M I J K L B A
then computes the position for the MS. In this way, we can determine the MS’s location. This method is known as the cell-based location-sensing method.
Next, we will discuss the accuracy for the cell-based location-sensing method. Consider the wireless network as shown in Figure 1. When an MS reports to the location server that it can receive the signals of BSs 0 and 2, the location server determines that the MS is in area B. This means that we can claim an accuracy of within area B for the MS. Formally, we define a distinguishable area as the area in which every MS receives a unique set of BSs’ signals. Then, the accuracy of cell-based location-sensing method can be defined as the size of the distinguishable area. The maximum of all distinguishable areas is the location-sensing accuracy of the given network deployment.
3. Location Sensing for the Network with Hexagonal Structure
In this section, we consider a wireless network in which the BSs are deployed as a hexagon and each BS has the same coverage area with a radius R as shown in Figure 2. For simplicity, assume that the distance between two adjacent BSs is one unit; the accuracy of the location-sensing method in border cells is not considered in this section.
Since the structure of the network is symmetric, without loss of generality, we consider the circle covered by the signal of BS 0 as shown in Figure 1.
0 1 2 3 4 5 6
Fig. 2. A wireless network with hexagonal structure.
The circle can be partitioned into 13 distinguishable areas. These areas can be classified into three types: 1. Type 1 area: The mobile station within the area
can listen to three BSs’ signals. There are six distinguishable areas in the circle that belong to type 1, that is, areas A, R, S, T, U, and V. 2. Type 2 area: The MS within the area can listen
to two BSs’ signals. There are six distinguishable areas in the circle that belong to type 2, that is, areas B, I, J, K, L, and M.
3. Type 3 area: The MS within the area can only listen to the signal of BS 0. It is at the central region of the circle, that is, area C.
Note that the radius R of the circle is assumed to be bounded within [1/p3,p3/2]. This is because (i) if R < 1/p3, then there exist some areas that are not covered by any signal (see Figure 3a); (ii) if R >p3/2, then the type 2 area, for example area B, will be separated into two subareas (see Figure 3b).
The accuracy of cell-based location-sensing method depends on the size of the distinguishable areas. A smaller area means more positioning accuracy. In the following text we will find the size for each distin-guishable area. Let 6 abc denote the angle of a, b, c
and a,b,c denote the triangle of a, b, c. Let sX
denote the area of X, for example, sa,b,cdenotes
the area of triangle a,b,c. Thus, the area of the shaded
region of A, as shown in Figure 4, can be deter-mined by
1 21R
2s i,j,0
where R is the radius of the circle, 1D6 i0j. The
si,j,0can be obtained by
si,j,0 D 1 2 2R sin 1 2 Rcos 1 2 DR2sin 1 2 cos 1 2
Thus, the area of A is sA D3 1 21R 2s i,j,0 Csi,j,k 1
where si,j,kcan be computed by
si,j,k D p 3 4 2R sin 1 2 2 D p 3R2sin2 1 2
−2 −1 0 1 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1 0 1 2 (b) r = 3 2 (a) r = 1 3
Fig. 3. Hexagonal layout with R D 1/p3 and R Dp3/2.
0 i j k 1 2 m a a q1
Fig. 4. A type 1 area for hexagonal structure.
Then, replace si,j,0and si,j,kin Equation (1).
We have sA D3 1 21R 2R2sin 1 2 cos 1 2 Cp3R2sin2 1 2 DR2 3 21C p 3 sin2 1 2 3 sin 1 2 cos 1 2
Note that 1, can be rewritten as a function of R
as follows.
Consider the triangle 0im. The lengths of line seg-ments 0i and 0m are R and 1/2, respectively. Thus,
cos1C˛ D 1 2R 1C˛ Dcos1 1 2R 2 Note that 6 102 D /3. Then,
1C2˛ D
3 3
From Equations (2) and (3), we have 1D2 cos1 1 2R 3 4
Replace 1in Equation (1) by 1 D2[cos11/2R]
/3. Thus, the area of A can be rewritten as a function of R (denoted as fAR) as follows: sA D fAR D R2 3 21C p 3 sin2 1 2 3 sin 1 2 cos 1 2 where 1 D2[cos11/2R] /3.
Similarly, as shown in Figure 5, the area of B can be obtained by fBR D2 1 22R 2s s,t,0 2fAR
0 s t 1 2 n 6 q2
Fig. 5. A type 2 area for hexagonal structure.
where ss,t,0 D1/2R sin2/2 and 2D6 s0t D
2 cos11/2R.
Finally, area of C can be found by fCR D R26fAR 6fBR
Note that the accuracy of cell-based location sens-ing is the maximal size of distsens-inguishable area in the system. That is, the accuracy e D maxffAR, fBR,
fCRg. We can claim an accuracy of within area e
for the hexagon wireless network with radius R. If the transmitting power of BS can be adjusted, then the coverage of BS will vary. Let us con-sider how to arrange the coverage of BS such that the accuracy is optimized. This problem is equivalent to finding a radius R such that e D maxffAR, fBR, fCRgis minimized. That is,
z D min 1 p 3R p 3 2 e D min 1 p 3R p 3 2 maxffAR, fBR, fCRg 5
Figure 6 shows the functions fAR, fBR, and
fCR, for 1/
p
3 R p3/2. The function fAR
is an increasing function and the function fCR is
a decreasing function where 1/p3 R p3/2. Let RŁ be the radius such that fARŁ D fCRŁ. Thus,
maxffAR, fBR, fCRg D fCR if 1p 3 R R Ł fAR if RŁ R p 3 2 0.550 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.1 0.2 0.3 0.4 0.5 0.6 Radius Area 0.7791 0.1748 C A B 1 3 2 3
Fig. 6. Accuracy of the network with hexagonal structure.
and the minimum of maxffAR, fBR, fCRg
occurs at fAR D fCR. By numerical method, we
find R D 0.7791 such that fAR ³ fCR. In the
optimal layout, areas of A, B and C are fAR,
fBR, fCR ³ 0.1748, 0.1138, 0.1748). The area
of a cell in the optimal layout is ð RŁ2D1.9069.
Thus, we can claim an accuracy of within 0.1748/ 1.9069 D 9.1667% cell area for the optimal layout.
4. Location Sensing for the Network with Mesh Structure
Next, we consider a wireless network in which the BSs are deployed as a mesh shape. Assume that each BS has the same coverage area with a radius R, the distance between two adjacent BSs is one unit and the accuracy location sensing in border cells is not considered in this section. In addition, we assume that the radius R of the circle is bounded within [p2/2, 1]. This is because (i) if R <p2/2, then there exist some areas that are not covered by any signal; (ii) if R > 1, then the cell-based location-sensing method will fail. Similarly, the circle covered by the signal of BS 0 can be partitioned into 21 distinguishable areas as shown in Figure 7. These areas can be classified into four types:
1. Type 1 area: The MS within the area can listen to four BSs’ signals, for example area D. There are four distinguishable areas in the circle, belonging to type 1.
2. Type 2 area: The MS within the area can listen to three BSs’ signals, for example area E. There are
0 1 2 3 4 5 6 7 8 G F E D
Fig. 7. A wireless network with mesh structure.
12 distinguishable areas in the circle, belonging to type 2.
3. Type 3 area: The MS within the area can listen to two BSs’ signals, for example area F. There are four distinguishable areas in the circle, belonging to type 3.
4. Type 4 area: The MS within the area can only listen to the signal of BS 0. It is at the central region of the circle, that is, area G.
The area of D, as shown in Figure 8, can be determined as fDR D4 1 21R 2s i,j,0 Csi,j,k,l 6
where 1D2 cos11/2R /2, si,j,0 D
R2sin1/2 cos1/2, and si,j,k,ldenotes the area
of square i, j, k, l and si,j,k,l D4R2sin21/2.
The area of E, as shown in Figure 9, can be determined as fER D 1 2 2 1 22R 2s s,t,0 fDR 7 where ss,t,0 D p 2/2R sin2/2 and 2D6 s0t D
2 cos1p2/2R. The area of F, as shown in
Figure 10, can be determined as fFR D2 1 23R 2s u,v,0 2fDR 4fER 8 0 1 a a 2 3 i j m k l q1
Fig. 8. Area D for mesh structure.
0 1 2 3 s t m n q2
Fig. 9. Area E for mesh structure.
where su,v,0 D1/2R sin3/2 and 3D6 u0v D
2 cos11/2R. Finally, the area of G is
fGR D R24fDR 12fER 4fFR 9
Thus, the accuracy for mesh structure is e D maxffDR, fER, fFR, fGRg. Next, we
con-sider how to arrange the coverage of BS for mesh structure such that the accuracy is optimized. The problem is to find a radius R such that e D maxffDR, fER, fFR, fGRg is minimized.
7 8 1 0 u p v 2 3 q3
Fig. 10. Area F for mesh structure.
That is, z Dpmin 2 2 R 1 maxffDR, fER, fFR, fGRg 10 Figure 11 shows the functions fDR, fER, fFR
and fGR, for
p
2/2 R 1. Let R1and R2be the
radiuses such that fGR1 D fFR1 and fFR2 D
fDR2, respectively. Thus, maxffDR, fER, fFR, fGRg D fGR if p 2 2 R R1 fFR if R1 R R2 fDR if R2 R 1
and the minimum of maxffDR, fER, fFR,
fGRgoccurs at R2. By numerical method, we find
R2 D0.9389 such that fFR2 ³ fDR2. In the
opti-mal layout, areas of D, E, F, and G are fDR2,
fER2, fFR2, fGR2 ³ 0.1999, 0.0963, 0.1999,
0.0153). The area of a cell in the optimal layout is ð R22D2.7694. Thus, we can claim an accuracy
of within 0.1999/2.7694 D 7.2182% cell area for the optimal layout.
5. Comparing the Accuracy of Hexagonal and Mesh Structures
In the previous sections, we found that an MS can be accurately located within 9.1667% (7.2182%) cell area in the optimal hexagonal (mesh) structure. This is under the assumption that the distance between two adjacent BSs is one unit. In this section, we consider that given a fixed number of BSs, which structure gives better accuracy.
At first, we construct two networks with hexag-onal structure and mesh structure whose coverage areas are equal. As shown in Figure 12, the dis-tance between two adjacent BSs is fixed to one unit for mesh structure. Then, we adjust the distance between two adjacent BSs for hexagonal structure such that the area of quadrangle e, f, g, h equals the area of square a, b, c, d (see Figure 12). That is, the distances of ef, fg, gh and eh are set to
0.7 0.75 0.8 0.85 0.9 0.95 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Radius Area 0.9389 0.1999 D E F G 2 2 0.3227 0.7384
a b d e h f (a) (b) c g
Fig. 12. The fixed coverage for the mesh and hexagonal structures.
be
2/p3. Thus, the area of the shaded region in Figure 12(a) is equal to the area of the shaded region in Figure 12(b) and the BS numbers for the two struc-tures are the same.
By applying the same approaches in Sections 3 and 4, we find that the maximal distinguishable areas are 0.2019 (i.e. z D 0.2019) for the hexagonal ture and 0.1999 (i.e. z D 0.1999) for the mesh struc-ture in the optimal layout. This means that the mesh structure is a little better than the hexago-nal structure.
6. Conclusions
In this paper, we have presented a cell-based location-sensing method for wireless networks. The main advantage of the cell-based location method is that it requires no changes to the existing wireless net-work architecture, or to the MS, and it does not substantially increase costs for either network oper-ators or end users. We also find the optimal lay-out for wireless networks with hexagonal structure as well as mesh structure. In the optimal hexag-onal (mesh) structure where the distance between two adjacent BSs is one unit, an MS can be accu-rately located within 9.1667% (7.2182%) cell area. In addition, on the basis of a fixed number of BSs and a fixed coverage area, the mesh struc-ture gives a little better accuracy compared to the hexagonal structure in the optimal layout. We believe that these results are useful for deploying wireless networks for location-based applications. The fol-lowing directions might be interesting for possible future work:
1. Find the accuracy of cell-based location-sensing method for networks with irregular structure and unequal transmitting power of BSs.
2. Find an optimal layout for irregular structure by tuning BSs’ transmitting power.
Acknowledgments
This work was supported in part by the Ministry of Education, Taiwan, ROC under grant 89-E-FA04-1-4, and the Lee and MTI Center for Networking Research, NCTU, Taiwan.
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Authors’ Biographies
Hung-Chi Chu received the B.S.
and M.S. degrees in computer sci-ence and engineering from Tatung University, Taiwan, in 1995 and 1997 respectively. Since 2001, he has been working toward the Ph.D. degree in Computer and Informa-tion Science at NaInforma-tional Chiao Tung University, Taiwan. His research interests include wireless networks and artificial intelligence.
Rong-Hong Jan received the B.S.
and M.S. degrees in industrial engineering, and the Ph.D. degree in computer science from National Tsing Hua University, Taiwan, in 1979, 1983, and 1987, respectively. He joined the Department of Computer and Information Science, National Chiao Tung University, in 1987, where he is currently a professor. During 1991–1992, he was a visiting associate professor in the Department of Computer Science, University of Maryland, College Park, Maryland. His research interests include wireless networks, mobile computing, distributed systems, network reliability and operations research.
