Using Ray Tracing for Site-Specific Indoor Radio Signal Strength Analysis 1

Transcription

1 Using Ray Tracing for Site-Specific Inoor Raio Signal Strength Analysis 1 Michael Ni, Stephen Mann, an Jay Black Computer Science Department, University of Waterloo, Waterloo, Ontario, NL G1, Canaa Abstract A variation of cone-tracing is use to preict the signal strength in wireless networks. Differences between light an raio waves necessitate certain changes to the basic ray/cone tracing algorithm, as oes the information require of the solution. The new algorithm is compare to a previous algorithm for signal strength preiction, an verifie on some examples. I. Introuction Cellular raio is a victim of its own success. As more uses are foun for the fixe banwith available in the electromagnetic spectrum, the availability of that banwith is ecreasing. The only extensible solution is to ecrease the transmission area use by a single evice, meaning lower power transmissions an smaller cells. When the transmission power is low, it is important to make the most of the available coverage. This means that care must be taken when placing antennas to minimize both the area of poor coverage an the overlap between ifferent antennas regions. In this paper, we present a technique for analyzing signal strength in a room or set of rooms. Raio waves are similar to light waves, just at a much lower frequency. Although the rules for reflection, refraction, an scattering are similar for both types of waves, the longer waves in raio (0cm) are significantly ifferent from light in two important respects. First, the systematic interference cause by the coherence of the transmitte waves an the long wavelengths means that the signal strength oes not fae uniformly along a line of sight from the transmitter. Secon, the interactions between the signal an a surface that is only one or two wavelengths across is no longer the same as for visible light. The first of these ifficulties is aresse by the technique presente in this paper. Dealing properly with the secon problem requires an exact solution, which is more complicate an timeconsuming [10]. In this paper we avoi this secon problem by ealing only with objects having planar surfaces at least two meters on each sie. The strength of the transmitte signal epens on the type of transmitter being use, but more important is the rop in signal that the receiver can etect. Common receivers can resolve signals that are 0.1% of the transmitte intensity. Typically, only 10% of the signal strength remains after reflection or transmission, although these number vary wiely ue to the large variation of materials foun in builings. See the papers by Cox et al. [, ] for a range of examples. Areas of poor coverage are the result of multiple propagation paths existing between the transmitter an a given receiver position. Because these paths have ifferent lengths, the relative 1 This work was supporte in part by the Avance Raioata Research Center of Motorola Canaa Lt. an the Natural Sciences an Engineering Research Council of Canaa phases of the receive carrier waves are not preictable. If they are 180 egrees out of phase, then they completely cancel each other out. This is calle multipath interference. When preicting this interference, the optical istance travele by each component signal must be known to within a fixe tolerance. The ifficulty presente by this restriction is that this tolerance oes not relax at large istances from the transmitter. In the case of 1GHz waves, a 1cm error in istance will cause the phase to be inverte, resulting in estructive interference being preicte where constructive shoul have been observe, an vice versa. Because wavelength is constant, that 1cm error causes the same error in phase angle near the antenna as it oes far from the antenna. Previous work on etermining signal strength for inoor wireless networks falls into two major categories, statistical methos (see [6]) an site-specific methos. Statistical methos essentially average all the objects in the scene, an o not report variations in signal strength aroun any particular object. While this is useful in escribing an average propagation pattern for an antenna (e.g. X has a range of 0 meters, given line-of-sight, in a factory floor environment. ) it oes not help the system planner ecie how to position the antenna for optimal performance. Most of the site-specific techniques have been variations on ray tracing. For example, Seiel an Rappaport [11, 1, 1] use a ray tracing technique to preict the signal strength at a particular location. However, their technique is limite to preicting the signal strength at a single, one pointreceiver. Lecours et al. [] use a similar ray tracing metho that they verifie with physical measurements. A paper by McKown an Hamilton [7] also employs ray tracing, but it uses a very ifferent technique for intersecting rays with objects, an for ynamically ajusting the resolution in areas with a high signal strength graient. The technique closest to that use here has been propose by Sipilä an Heiska [14]. Their metho iffers only in the use of a pre-set maximum number of reflecte rays, rather than the cone moels iscusse below. See [9] for a more complete survey of previous work in signal strength preiction. Ieally, we woul be able to preict the signal strength at all points within the room(s) of interest. However, it shoul be sufficient to preict the signal strength on a single plane in the room (parallel to the floor) because the wireless evices using the network are usually either esktop or hanhel, which we expect to be at a roughly constant istance above the floor. Most of the site-specific techniques only compute the signal strength at a single point, the exceptions being Keenan an Motley [8] an McKown an Hamilton [7]. Keenan an Motley compute the signal strength solely as a function of istance an the number of walls between the source an receiver. McKown an Hamilton calculate the strength at a gri of receiver points, then ynamically increase the resolution of the receiver gri in 1

2 areas of high variability. Their technique is expensive because for each receiver point they reflect in every possible surface to etermine all paths to the transmitter. In this paper, we escribe a metho for using ray tracing techniques for signal strength preiction. In computer graphics, stanar ray tracing [4, p.701] reners a scene by casting rays from the esire viewing location through an imagine vieo isplay. This technique requires the eye-point, isplay location, resolution, an orientation to be efine a priori, thereby etermining the initial rays. The color of the pixel through which each ray passes is etermine by casting rays from the nearest intersecte surface to all light sources. In a room-size environment, the physical properties of visible frequency raiation are fairly simple. However, several important ifferences are encountere when translating this style approach to a raiofrequency environment. First, we are intereste in the signal strength at a particular plane in the room. Although similar to the projection plane of ray tracing, for signal strength analysis we are intereste in all signals passing through this plane, regarless of the irection of propagation. Secon, we are intereste in the phase of the waves at each point, as there will be both constructive an estructive interference of these waves. These two ifferences require us to trace all signals emitte from the source until their strength has attenuate below a given tolerance. The solution we propose gives an approximation of signal strength for a particular altitue throughout a room. The plane for which the signal is approximate is a collection of iscrete squares, which we call the signal intensity gri. The approximation technique first ivies the raiate signal into a collection of cones with triangular cross-sections that originate from a single common point, an completely span three-space without overlap. These cones are trace through the room, an reflecte off an transmitte through surfaces. We then recor the phase an strength of these cones as they pass through the signal intensity gri. Ientifying similarly behave volumes allows the effect of incient signals to be more efficiently recore within these areas. If rays are use, care must be taken to avoi having two rays that represent the same optical path from being ae to the same iscrete area. It is similarly important to avoi having rays strale a particular area. Using soli cones instea of a ense collections of rays avois the ifficulty of ensuring that each optical path to a iscrete portion of a surface is consiere exactly once. II. Cone Tracing Cone tracing has been use in computer graphics as an antialiasing technique for ray tracing [1]. Instea of casting rays, cones are cast into the scene. If the cone partially hits an object, this partial coverage is use to weight the color compute for that cone. Our use of cones for signal strength preiction iffers in that we use the cones to trace the wavefront emitting from a transmitter in all irections. The initial approximation ivies the raiate signal into a collection of cones with triangular crosssection that originate from the transmitter, an completely span three-space without overlap. Figure 1: Cone Tracing. Gri squares in both the signal intensity gri an the various wall panels are fille in arker in areas of stronger raiate intensity (from a single emitte cone). Each of these cones can be completely escribe by three bounary rays an an origin. Each cone is examine to fin the closest object intersecte by part of the cone. If the entire cone oes not strike that object, then the cone is subivie on the bounaries of the object. Cones that strike exactly one object are use to generate aughter cones corresponing to reflecte an transmitte signals. Furthermore, once a cone is seen to be well behave, (i.e. it strikes only one wall) its intersection with the signal intensity gri is foun, an its effect on this gri is recore. Fig. 1 gives two ifferent perspective views of this process for a single cone. A. Phase Calculation Once a well-behave cone has been foun that intersects exactly one wall, it must be reflecte an transmitte. An image of the source (also referre to as a virtual source ) is associate with each cone. The initial location of the virtual source is the actual transmission antenna. Each time the cone is reflecte, the source location is also reflecte in the plane of the wall (to a point on the other sie of the wall having the same perpenicular istance). Thus the straight-line istance to the virtual source is the same as the optical istance to the true source. If a cone passes through the signal strength intensity gri, its effect on each iscrete section of this gri must be foun. Both signal strength an phase must be accounte for. As mentione above, the calculation of optical istance to each of these points must be accurate. Since the current implementation uses only plane p reflections, we can use a simple istance calculation ( = (x) + (y) + (z) ) from each point on the wall to an image of the source. One problem with this solution is the number of square root calculations involve. One optimization is to calculate the istances to the three corners of the intersection (since the cone is well-behave, the area of intersection will always be a triangle) an use bilinear interpolation to etermine the istances to the intermeiate points. This will be faster, but it is less accurate. The inaccuracy results from the fact that the istance between two points oes not vary linearly as one point moves in an arbitrary plane. Fig. shows a two-imensional cross-section of a cone intersecting a wall. In this figure, the istance ~ is the result of varying the istance from the origin linearly between the two enpoints (i.e. ~ = t1 + (1? t) ; 0 t 1). The maximum error cause by this ifference (in the three imensional case) is boune by the following [9]: r 1 + cos Error max " # 1 + cos? 4 + (1)

3 α ~ 1 (x,y) Figure : Cross-section of a cone where max is the maximum istance along any of the three corner rays, an is the largest angle between two rays. While this equation still contains a square root, istance is use only as a multiplier. Therefore, the contents of the square brackets above can be calculate ahea of time, an a table lookup can be use at runtime, since the angle of emission is boune by the largest angle use in sening the initial cone. If the error is too large, then we can subivie the cones. B. Subivision There are three reasons for subiviing our cones into smaller cones. The first occurs if we are using linear interpolation to simplify the istance calculation an the error is too large. Since the three corners are alreay known, only one new ray must be trace. This can be one by aing a single ray through the centroi, an recursively examining each of the three cones create by joining an existing ege to this point. Alternatively, one coul use either a four-to-one or a two-to-one subivision of the cones. Initial Intersection Resulting Cones a c a c b b Figure : (left) A wall is misse, but will be etecte in the next iteration. (right) A wall is misse, an will not be etecte. Another reason for subiviing is to prevent the cones from getting so large that they might strale a wall. Since the current implementation etects interactions with walls only when a corner point intersects one, allowing the ege length to get as large as wall sizes coul result in cones passing through walls without having any interaction etecte. Because ege length epens on the angle at which the cone is cut, a choice must be mae about what shoul be boune. We chose to use the I I lengths of the eges forme when the cone is cut by a plane perpenicular to its irection of propagation, an at a istance equal to the length of the longest ege intersecting a wall (the test is one immeiately after etermining the intersections of the corner rays). Since there exists a minimum ege-length for walls, this provies a guieline for choosing a maximum cone size. In practice, 0% of the minimum ege-length has worke well. It shoul be note here that pieces of the signal that o not strike the other walls will be etecte, as in the left example of Fig.. In that case, the portion of the cone that i not strike any of the (up to) three walls etecte will be recursively passe back to the tracing function, at which time the new wall will be etecte. In the right example of Fig., the whole cone struck parts of the walls that were etecte, so there are no remaining fractions to be passe to the next iteration, an the walls that were not etecte will remain unetecte. However, for our application we o not expect this to occur as we only consier large walls an our limit on the cone size will ensure that all walls are etecte. C. Occlusion Another ifficulty in etermining which parts of cones strike walls is the occlusion of one wall by another. The natural solution to this problem is to process the closest wall first, clip on the borers of that wall, an pass the remaining fragments of the cone to the remaining walls. The ifficulty with this is the usual problem with occlusion: how to efine closest. We cast three rays for each cone to fin which walls these rays intersect. We then use a variation of the painter s algorithm to etermine an orering on these walls. Details of our variation on the painter s algorithm can be foun in [9]. One particular aspect of our metho is worth mentioning here. The stanar painter s algorithm sorts the polygons base on their istance from the eye-point, using a coorinate system having the eyepoint at the origin an with the viewing irection along one axis. However, we will be casting our cones in a large number of irections. We coul transform all the polygons to a coorinate system base at the cone s origin, but instea we istinguish epth using the cone s origin, a point on each polygon, an the normal to one of the polygons, as illustrate in Fig. 4. This calculation is performe after any require splitting. III. Results Lecours et al. [] evelope a simulator base on ray tracing, an publishe its behavior in both real an imaginary situations. The real situations emonstrate goo agreement, an that was presente as an argument that the analysis of imaginary situations also reflecte a realistic approximation of the actual signal behavior. As a emonstration of their technique, Lecours et al. generate signal intensity graphs for a single strip of the imaginary room. The reaer is referre to the Lecours et al. paper f or etails of the wall sizes an material properties of this room. We teste our technique on the Lecours et al. imaginary room. Fig. shows the results of our technique for the portion of this room use in their paper. These are the signal strength preictions for an isotropic raiator one meter from the front wall, an one meter below the ceiling. The graphs show the signal strength meters above the floor, along a line one meter from the left wall (the position of this line relative to the room

4 Pick a point in each half-plane. Let S be in half-plane 1, P be in half-plane, E be the eye point, an N be a normal to half-plane I ((S-E) ot N) * ((P-S) ot N) > 0 then 1 might occlue. E S-E S #1 P-S P N # (In this example, #1 might occlue #.) Figure 4: Metho for etermining possible occlusion between two half planes Figure 6: The signal strength preicte by cone tracing the Lecours et al. room (transmitter is at the left sie). Darker areas represent regions of highest signal strength. The black line is the strip use in Fig. an is not part of the signal strength ata Figure : Cone tracing signal strength for Lecours et al. room. The top row are our simulations. The bottom row are their results. The left column simulates the floor only. The right column simulates the complete room. The y-axis gives the signal strength in ecibels, an the x-axis is the istance from the back wall. Differences in magnitue are ue to antenna gain. an transmitter is illustrate Fig. 6). The room is six meters by twelve meters in imension. Our results match theirs for the simple case of floor only, an also once the ceiling an sie walls are ae, in that both sets of results show an area of poor reception in the region from four to six meters along the sie wall. In both cases, reception improves in an area six to eight meters along the wall, an the signal quickly egraes after passing the nine meter mark. This latter region (from nine to twelve meters) is strongly influence by reflections from the en wall, once that wall is ae to the moel. While the large-scale behaviors agree between our metho an the Lecours et al. metho, there is isagreement about the small-scale signal behavior. These ifferences can be explaine by the failure of the current implementation of cone tracing to consier angle of incience when fining reflection coefficients. The values use were the coefficients for a 4 egree angle of incience. However, there is actually a significant variation in reflection as a function of incience angle [1]. This variation accounts for the ifferences between our results an the results of Lecours et al. Theoretically, the agreement of the two methos is not a sur- Figures from []. Reprinte by author s permission Y 1e+04 1e+0 1e+0 Times vs. Max Bounces Figure 7: Execution times for four rooms room 1 room room room 4 prise. Although blocks of signal are consiere, instea of infinitely thin components, the same reflections are use, so the total interference shoul be similar. What this experiment shows, however, is that the cone tracing technique can be applie in practice. The graphs in Fig. were generate by a post-analysis loop through one row of the signal strength matrix, an represent only one strip of the room. In fact, by the time they were known, the analysis for the whole room was complete (Fig. 6). This particular analysis took thirty secons on a lightly loae RS/6000. Timings were mae for four moels. Each room was analyze for various limits on the number of bounces permitte. Ten trials were performe for each bounce limit in each room, an the averages were use. The user time elapse was roughly exponential with respect to the bounce limit (Fig. 7). Exponential growth seems natural, since each cone gives birth to some group of aughter cones, an the average number of aughter cones from an incient cone shoul be inepenent of the generation numbers of the cones involve. However, another interesting iscovery arising from these trials was how low the bounce limit coul be set without significantly affecting the results. The results (shown in Fig. 8) emonstrate that, while the time cost of each step increases, the effect on results ecreases. Note that the bounce limit counts only reflections. This allows the weaker signals foun in rooms istant from the transmitter to still interfere with each other, even though they may have been severely attenuate by intervening walls. Combining these results suggests that setting a low limit on X

5 Signal Level (B) 1e-01 1e-0 Signal Level (B) 1e-01 1e-0 1e-0 Lecours, Grenier, Baqarhi, an Cherkaoui room tmp.room1.xgraph.1.1 tmp.room1.xgraph..1 Lecours, Grenier, Baqarhi, an Cherkaoui room Distance (m) tmp.room1.xgraph..1 tmp.room1.xgraph..1 tmp.room1.xgraph.4.1 tmp.room1.xgraph..1 Distance (m) Figure 8: Bounce limits: The preicte signal strength for the room escribe in [] The top graph compares bounce limits of 1 vs., an the bottom shows,, 4, an together. Note that there is very little qualitative ifference between limiting the number of bounces to two, an limiting them to five. Compare this with the execution times shown in Fig. 7. the number of bounces will greatly benefit overall efficiency. IV. Conclusions This paper has shown an efficient application of cone tracing, which prouces useful approximations of signal behavior in specific inoor environments. Using the technique escribe avois the mathematical complexities of approximating a soli wavefront with a collection of rays, the reunancies of analyzing the same room for multiple receiver locations, an the inefficiencies of choosing arbitrary initial signal resolutions. It oes so by using cones instea of rays, recoring signal intensity for the entire room in one pass, an ynamically subiviing cones that become too big. In aition to many optimizations possible for our current technique (such as computing signal strength for a volume, improving the intersection technique, moeling non-isotropic raiators, etc), there are two interesting effects that coul also be moele. First, surfaces in the presence of an electric fiel can become seconary emitters. These seconary emissions are uniform in all irections, suggesting that a raiosity technique [4, p.79] coul moel them effectively. Secon, when a wavefront hits a corner or an ege of an object, iffraction effects cause the signal to propagate uniformly from the surface iscontinuity. For corners, this results in a spherical wavefront that can be moele as a new transmitter, but for eges the wavefront will be cylinrical an will require a new moel for the signal. A iscussion on how to implement these extensions can be foun in [9]. References [1] John Amanaties. Ray tracing with cones. In Computer Graphics (SIGGRAPH 84 Proceeings), pages 19 1, July [] D. C. Cox, R. R. Murray, an A. W. Norris. Measurements of 800 MHz raio transmission into builings with metallic walls. The Bell System Technical Journal, 6(9):69 717, November 198. [] D. C. Cox, R. R. Murray, an A. W. Norris. 800 MHz attenuation measure in an aroun suburban houses. The Bell System Technical Journal, 6(6):91 94, July- August [4] James D. Foley, Anries van Dam, Steven K. Feiner, an John F. Hughes. Computer Graphics (secon eition). Aison-Wesley, [] M. Lecours, D. Grenier, M. Baqarhi, an S. Cherkaoui. Measurements an simulation of receive signals in rooms an corriors at 900 MHz an in the 0-60 GHz ban. In 4n annual IEEE Vehicular Technology Conference, pages , 199. [6] W. C. Lee. Mobile Communications Engineering. Mc- Graw Hill, New York, 198. [7] John W. McKown an R. Lee Hamilton Jr. Ray tracing as a esign tool for raio networks. IEEE Network Magazine, pages 7 0, November [8] A. Motley an J. Keenan. Personal communication raio coverage in builings at 900 MHz an 1700 MHz. Electronics Letters, 4(1):76 764, June [9] Michael Ni. Using ray tracing for site-specific inoor raio signal strength analysis. Master s thesis, University of Waterloo, Waterloo, Ontario, Canaa, 199. [10] Keith D. Paulsen, Daniel R. Lynch, an Weiping Liu. Conjugate irection methos for helmholz problems with complex-value wavenumbers. International Journal for Numberical Methos in Engineering, :601 6, 199. [11] Scott Y. Seiel an Theoore S. Rappaport. A ray tracing technique to preict path loss an elay sprea insie builings. In Globecom 9, pages 649 6, 199. [1] Scott Y. Seiel an Theoore S. Rappaport. Site-specific propagation preiction for wireless in-builing personal communication system esign. IEEE Transactions on Vehicular Technology, 4(4): , November [1] Scott Y. Seiel, Kurt R. Schaubach, Thomas T. Tran, an Theoore S. Rappaport. Research in site-specific propagation moeling for pcs system esign. In 4n annual IEEE Vehicular Technology Conference, pages 61 64, 199. [14] Kari Sipilä an Kari Heiska. Can ray tracing be use as a faing generator in simulating micro-cellular mobile raio systems? In Wireless 96, volume, pages 8 44, Calgary, Alberta, Canaa, July TRLabs, TRIO, IEEE Canaa.