PERFORMANCE OF MOBILE STATION LOCATION METHODS IN A MANHATTAN MICROCELLULAR ENVIRONMENT Miguel Berg Radio Communication Systems Lab. Dept. of Signals, Sensors and Systems Royal Institute of Technology SE- 44 Stockholm, Sweden Email: miguel.berg@ite.mh.se Abstract Positioning of users in cellular systems is an area attracting large interest and the number of applications for the location information is growing rapidly. Large-scale deployment of such applications will require methods for positioning that are simple enough to be used in mobile phones. In this paper, we evaluate the location accuracy for some different algorithms in a microcellular environment. We propose some simple but quite accurate methods and compare them with commonly known methods. Our results show that in the studied environment, all our proposed algorithms can at least manage the US E9 phase II requirements of positioning emergency calls within 25 m, 67 percent of the time. Introduction The interest for cellular Mobile Station (MS) positioning is growing rapidly and many new location aware services will evolve utilising the position information. One example of an existing location-aware service is to connect the Yellow Pages with a map database giving the user the address to a restaurant or hotel in the vicinity. Another application for the location technology is to alert the user about friends in the vicinity. For the network operator, location information can be used to assist Radio Resource Management (RRM) functions like channel selection and handover []. Perhaps one of the most easily accepted uses of location methods is to automatically locate people making emergency calls from their cellular phone. In the US, beginning October 2, the FCC will require that all emergency calls (9) from cellular phones must be located within 25 m 67% of the time. This is known as phase II of the Enhanced 9 (E9) specification. It is expected that European authorities will follow with similar requirements for 2 calls. In this paper, we propose and evaluate by means of simulation, the location accuracy for a few positioning methods suitable for third generation systems (e.g. UTRA TDD [3]). Our proposed methods are very simple and do not require complicated calculations as opposed to some existing methods. Our performance measure is the cumulative distribution function of the absolute location or and the evaluation is done for a finite Manhattan-like microcellular environment with both outdoor and indoor users. Generally, time based methods [4],[7], achieve higher accuracy than signal-strength based methods [],[2] since the signal strength can vary several orders of magnitude over very short distances. However, in dense urban areas, the accuracy of timing based methods is decreased due to the large possible difference between absolute distance and radio distance for non-line-of-sight paths. Another source of or, for both signal-strength and timing based methods, is multipath propagation. This is not studied in this paper. An overview of radiolocation methods, including some methods to mitigate the NLOS problem, can be found in [6].
Positioning Methods Here, we propose three methods to estimate the position of an MS. The first, PGWC, is based on signal strength, the second, TWC, is based on time, and the third, PGWC+TA, is a hybrid between time and signal-strength methods. We will investigate the accuracy of these methods and compare with three existing ones. The first and simplest of the existing methods is the Cell ID (CID) method where the position estimate is the coordinate of the serving BS. The second of the existing methods is described in [5]; the MS position is calculated as the average (centroid) of the positions of all N BSs whose beacons the MS can decode. We call it UnWeighted Centroid (UWC). The CID method can be regarded as a special case of UWC with N =. Finally, the third benchmark method uses circular multilateration of propagation delays. This is sometimes known as Time-of-Arrival (TOA [6]). In our implementation of TOA, positions are calculated from the MS-BS i propagation delays using a least-squared-or technique. Equal weights are used for the equations. When only two delays can be measured, the solution is ambiguous since two locations are possible. In this case, we select the centroid of those two positions in order to minimise the or. When only one delay can be measured, we revert to the CID method. Signal strength measurements are needed in cellular systems in order to assist handover decisions and sometimes also to assist channel selection and power control. From signal strength, path gain (inverse path loss) can be estimated if transmitter powers are known. Since large-scale path gain decreases with distance in a predictable manner, it seems reasonable to use the path gain in position estimations. A problem here is that shadowing and multipath fading can make the path gain vary several orders of magnitude over short distances. Time based methods using propagation delays can give a higher level of accuracy when estimating the position since they do not vary as much as the path gain. However, a disadvantage with time based methods is that, at least in today s GSM systems, they require specific measurements not needed for other purposes. The only useful timing value measured on a regular basis in GSM is the timing advance (TA [7]), which is half the roundtrip delay between the serving BS and the MS. This value is used to advance the mobile station transmit timing in order to keep time slots nonoverlapping in the base station. Circular and hyperbolic multilateration methods (TOA and TDOA [6]) require precise timing measurements on at least three Base Stations (BSs) in order to get a position. We propose an improvement upon UWC, by using a weighting factor w i for each beacon position. This is called Path-Gain Weighted Centroid (PGWC) since the weights are a function of the path gain. For PGWC, the MS position estimate is given as where the weights are N, i i i () N ( x y ) = w ( x, y ) i= w α i = g i. (2) and g i is the path gain from BS i to the MS. A starting point for the choice of weights can be found by looking at the simple case when N = 2 and an MS is located somewhere on a straight line between BS and BS 2. In this case it is easily shown that the optimal weight w i is the inverse of the MS-BS i distance. Assuming that path loss is proportional to the 4th power of the distance, we can use α = 4. Other values of α might give better results since the MS is not always located on a line between the BSs. It would of course be possible to use different α for different MS-BS i links but this is not discussed further here. A disadvantage with PGWC is that a beacon can only pull an MS location estimate closer to itself, not push it away. Thus, we get poor accuracy near the edge of the simulation area since estimates are biased toward the centre of the whole area. If propagation delays are available for more than one MS-BS link, we use these delays to form the weights instead of the path gains. Setting ( c t ) β w, (3) i = i where c is the speed of light and t i is the propagation delay between the MS and BS i, gives us the
Time Weighted Centroid (TWC) method. TWC requires less calculations compared with TOA and does not need any special cases when the number of decodable beacons is less than three. If the only available propagation delay is the TA value ( t ), we construct a hybrid method that we call PGWA+TA. Assuming that (x, y ) is the coordinate of the serving BS, we calculate the estimated position for PGWC+TA as ( x, y) = ( x, y ) ( x, y θ = arg( x, y) R = t c ( x, y ) = ( x + R cosθ, y ) + Rsinθ ), (4) i.e. by first estimating the BS -MS direction with PGWC and then setting the BS -MS distance according to the TA-value t. Models and Performance Measure We study the location performance with models similar to the ones proposed by ETSI for UMTS evaluation [8]. The area consists of 2 by 2 blocks with a total of 72 base stations (BS), see Figure. Street width is 3 m and the minimum distance between two street corners is 23 m. The user distribution is uniform over the whole area except for a variable outer border size µ, where no mobiles are placed. This variable is used when evaluating edge effects on the accuracy of our methods. The area where mobiles are placed is the centre 2 (-2µ ) by 2 (-2µ ) blocks. The uniform distribution yields 25% outdoor and 75% indoor MSs. Mobility is not modelled and we assume that measurement averaging has eliminated ors due to multipath propagation. Base station antennas are placed m above the users but below rooftops. The propagation model is a recursive model [9] where the path loss is calculated as a sum of line-of-sight (LOS) and non-los segments. A dual slope behaviour is included with path loss proportional to d 2 before and d 4 after a breakpoint at 3 m. As in [8], over-the-roof propagation is accounted for by calculating the resulting path loss as the minimum of the recursive model and a rooftop propagation model. For simplicity, outdoor-to-indoor signal propagation is modelled as a turn in a street corner, i.e. with a new path segment, perpendicular to the building wall as shown in Figure 2. An external wall loss of db is also added for indoor users. The resulting path loss for indoor users is comparable with the method in [], at least for small building-penetration depths. Spatially correlated log-normal shadow fading is included with a log-standard deviation of db. The common method of creating spatial correlation using a fixed decorrelation distance is not suitable for a Manhattan environment. Therefore, we propose a model based on ideas by Arnold []. According to Figure. Manhattan environment, 2 by 2 blocks with 72 base stations. Figure 2. Example of Line-Of-Sight (LOS) and Non-Line-Of-Sight (NLOS) propagation paths from a BS to several MSs.
[], shadow fading consists of two parts: one contribution from the signal path and one from the area around the mobile. In our implementation, we cover the simulation area with a regular grid with resolution d = 5 m. We then create two maps M p and M l with the same size as the grid. Each element in the two maps contains an independent random value from N(,). Along the signal path from BS to MS, we take a number of equally spaced samples from M p. These samples are then weighted and summed to form the path-dependent fading part, S p. The weights are exponentially decaying with the distance from the MS and scaled so that the sum of their squares equals one, resulting in a variance of one. The location dependent part S l is formed by first filtering M l with an exponential filter kernel to get correlated values and then sampling the filtered map at the MS position. The filter kernel corresponds to a decorrelation distance of approximately m. The sampled value of S l is also scaled in the same way as S p. Finally, S l and S p are added to form the total shadow fading, S, and scaled to get the wanted total standard deviation of db. The result has similar behaviour as the measurements in [2] regarding correlation on both LOS and NLOS streets. Our performance measure is the cumulative probability distribution function (CDF) of the absolute position or in meters. The path loss measurement or for a mobile is assumed to follow a normal distribution and have a standard deviation of 2 db. All the timing values are assumed to be accurate to within ± one half WCDMA [3] chip, i.e. we add a uniform random time or corresponding to a maximum distance or of about ± 39 m. Unless otherwise noted, the maximum number of decodable beacons, N max, is set to six in our simulations. There is also a Signal-to-Noise-Ratio (SNR) limit, which means that beacons can not be decoded and used if their SNR is too low. This mainly affects some of the indoor users. We assume that the locations of all the base stations are perfectly known through the use of e.g. differential GPS. Numerical Results overall results. Further, unless otherwise stated, the border µ is zero, i.e. mobiles over the whole area. We start by evaluating PGWC for both 2 and 8-dB standard deviation of path-gain measurement or. For comparison, the performance for CID and UWC is also included. The result is shown in Figure 3 and we see that even with 8-dB standard deviation of the measurement or, PGWC is superior to CID and UWC. It might seem strange that UWC performs worse than CID but this is due to border effects. Near the centre of the simulation area, UWC improves. If path gain can be measured with an or of 2 db or less, PGWC will manage the 25 m, 67 % of the time requirement (two dashed lines in the figure)..8.6 =6, µ=., α=2,.4 PGWC, G =2. db PGWC, G =8. db.2 CID, G =2. db UWC, G =2. db 2 3 4 5 Absolute position or [m] Figure 3. Position or for PGWC (2, 8 db), CID, and UWC methods. Our time based method TWC and the hybrid method PGWC+TA are compared against the TOA method in Figure 4. The time measurement or is indicated as the corresponding distance or, D. TWC performs similar to TOA, which seems reasonable since they use the same time measurements, while PGWC+TA lags behind since it relies more on the path gains. The next result is Figure 5, which shows what happens if the time or is eight times larger, i.e. closer to the situation with existing cellular systems. When the or in the time measurements correspond to a distance or of 33 m, none of the methods can achieve the E9 phase II requirements. In the following results, the parameter α used in (2) is set to 2 instead of 4 since this gives slightly better
=6, µ=., D =39 m, α=2, β=2 =6, µ=.42, α=2, β=2.8.8.6.4.2 TWC TOA PGWC+TA.6 2 3 4 5 Absolute position or [m].4 TWC PGWC+TA.2 TOA PGWC 2 3 4 5 Absolute position or [m] Figure 4. Position or for TWC, TOA, and PGWC+TA when D = 39 m..8.6.4 =6, µ=., D =33 m, α=2, β=2 TWC.2 PGWC+TA TOA 2 3 4 5 Absolute position or [m] Figure 5. Position or for TWC, TOA, and PGWC+TA when D = 33 m. Our final result is regarding the edge effects for some of our methods. As stated earlier, PGWC (and TWC) should have poor accuracy close to the edge of the simulation area. We have performed a set of simulations in order to test this assumption. As mentioned earlier, the parameter µ can be seen as the size of a border where there are no MSs. For instance, µ = 5/2 (.42) means that the border size is 5 blocks and mobiles are only placed in the middle 2 by 2 blocks. The result in Figure 6 shows, as expected, that the location or is smaller near the centre of the simulation area. The or for TWC is less than 6 m 67 % of the time while the or for PGWC is less than 9 m 67 % of the time. This clearly shows that we could gain a lot of accuracy if the edge effects can be controlled. Figure 6. Position or for TWC, PGWC+TA, TOA, and PGWC when mobiles are only placed in the centre 2 by 2 blocks (µ =.42). Conclusions Our three proposed methods, PGWA, PGWA+TA, and TWC can fulfil the E9 phase II requirements in the studied environment if measurement ors can be kept small enough. TWC beats all the other tested methods including TOA. When looking at mobiles in cells near the centre of the simulation area, even the hybrid solution beats TOA. We believe that even further improvements are possible while still keeping the algorithms simple. To be fair, the TOA implementation used as benchmark could be improved by using weighted least square and NLOS mitigation techniques but that would lead to increased computational complexity. Future work will include studies regarding possible cellular traffic capacity improvements by using location information in RRM algorithms. Suggestions in the literature include using location information in handover decisions and channel setup. References [] M. Hata, T. Nagatsu, Mobile Location Using Signal Strength Measurements in a Cellular System, IEEE Trans. on Vehicular Tech., Vol. VT-29, No.2, May 98, pp. 245-25. [2] H.-L. Song, Automatic Vehicle Location in Cellular Communication Systems, IEEE Trans. on Vehicular Tech., Vol. 43, Nov 994, pp. 92-98.
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