Antenna Applications Corner
Nuria Llombart EEMCS, Delft University of Technology Mekelweg 4, 2628 CD, Delft, The Netherlands E-mail:
[email protected]
Sudhakar Rao Northrop Grumman Aerospace Systems One Spacepark Redondo Beach, CA 90278 USA Tel: +1 (310) 813-5405 E-mail:
[email protected]
RF Field Mapping Inside a Large PassengerAircraft Cabin Using a Refined Ray-Tracing Algorithm Balamati Choudhury1, Hema Singh1, Jason P. Bommer2, and R. M. Jha1 Computational Electromagnetics Lab. CSIR-National Aerospace Laboratories Bangalore, India Tel: 080-25086582; Fax: 080-25268546 E-mail:
[email protected];
[email protected];
[email protected] 1
Boeing Research & Technology Seattle, USA E-mail:
[email protected] 2
Abstract Radio-frequency (RF) field mapping and its analysis inside a large passenger aircraft is a complex EM analysis problem, owing to its inherent concavity. The further hybrid surface modeling required for such concave enclosures leads to ray proliferation, thereby making the problem computationally intractable. In this paper, a large passenger-aircraft cabin is modeled as a single curved elliptical cylindrical cavity having a floorboard and windows. Unlike the available ray-tracing packages that use extensive numerical search methods, a quasi-analytical ray-propagation model is proposed here. This involves uniform ray launching, an intelligent scheme for ray bunching, and an adaptive reception algorithm to obtain the ray-path details inside the concave cabin. Although the image method yields precise point-to-point solutions, it cannot be used for curved concave environments. The developed method is therefore validated with respect to the RF field inside a cuboid. The RF field at the receiver within the cabin is determined using the ray-path descriptions and the constitutive EM parameters of the aircraft’s cabin materials. The convergence analysis of the RF field buildup is carried out with respect to the propagation time and the number of bounces. Keywords: Refined ray tracing; analytical surface modeling; RF field mapping; aircraft cabin; aircraft; ray tracing
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A
1. Introduction
lthough wireless access is easily available in all public places around the world, this is still not true for air passengers during the flight. The deployment of wireless technology inside aircraft is an important issue, due to uncertainties related to interference. Radio-frequency (RF) field mapping and its analysis inside a large passenger-aircraft cabin is hence of immense interest. Aircraft manufacturers will benefit from this technology by exploiting wireless networks, leading to the reduction of cable complexity, and hence the weight of the aircraft. Moreover, new in-flight services, such as onboard service/meal selection, service requests, and video on demand, could be made available to all passengers. Ray tracing has been employed in the past for site-specific indoor propagation models [1-3]. It has been shown that multiple reflection is dominant compared to the phenomenon of diffraction for the build-up of the RF field within the cavity [4]. Although ray tracing was used earlier for electromagnetic (EM) analysis of aircraft-cabin-like enclosures, a closer scrutiny revealed that these analyses predominantly employed measurements to merely fit their predictions, or to validate their empirical models [5-7]. Ray tracing inside a concave structure is known to become complex due to multiple reflections, transmission, and diffraction. Two routes to ray tracing are available for closed rectangular cavities, viz., ray casting [8, 9] (brute-force ray tracing), and the image method [10, 11]. While the image method yields precise point-to-point solutions, in contrast the ray-casting method involves iterative algorithms for convergence of the ray-path solutions. The image method can be readily applied to cubes, cuboids, and other similar planarfaceted structures, but not for curved concavities as encountered in aircraft cabins. For such applications, a refined raytracing method is developed and reported in the present paper. For EM environment analysis within the aircraft cabin’s interior, attempts have previously been made to overcome the computational complexity [12] by approximating the curved surfaces with large planar faceted plates. However, this leads to a completely different ray solution set, which may not necessarily approximate the case of curved surfaces. Work was reported earlier for the EM analysis for convex structures, including double-curved structures, using high-frequency methods in conjunction with an analytical ray-tracing technique such as the Geodesic Constant Method (GCM) [13]. However, this method is restricted to only external geometries, i.e., the convex part of such aerospace structures. Ray tracing becomes extremely cumbersome for the important applications of crevices and concavities within an enclosure (such as space modules, an aircraft engine, and passenger cabins), due to ray proliferation arising from multiple reflections, transmission, and diffraction. In fact, the only route to ray tracing available in such cases is ray casting. However, this improves the prediction only when the spatial rays are increasingly dense, leading to computational intractability. A feasible ray-tracing method is hence required to generate ray-path data for practical applications. The ray-path IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013
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data, consisting of the direct plus cumulative reflected rays up to the Nth bounce, is required for the estimation of the RF field inside a generic aircraft cabin. In the present work, a novel refined ray-tracing method is developed for RF field computation inside a generic aircraft cabin, including for microwave frequencies in the GHz region. A quasi-analytical refined ray-tracing method is implemented in conjunction with analytical surface modeling for a typical generic aircraft cabin. A generic aircraft cabin of practical dimensions currently in vogue is considered [14]. A large passenger-aircraft cabin is modeled as a singly curved elliptic cylindrical cavity. At this point, it is mentioned that the large middle section of the aircraft can be accurately described by employing an elliptic cylindrical-section model. A planar floorboard and all the windows are included. A transmitting source is placed inside the generic aircraft cabin, and the test rays are launched from the transmitter. The rays are allowed to propagate inside the cavity. As the cabin model involves the use of parametric equations, the ray-propagation model accounts for the surface normal at different incident points. The surface normal of the elliptic cylinder is readily expressed in analytical equations [13], which significantly reduces the raypath computation time. The RF field distribution within the cavity is determined using the ray-path descriptions and the constitutive parameters of the generic aircraft cabin’s material. It is well known that unlike the convex surfaces, RF field mapping inside a concave structure is an extremely complex problem, dominated by the proliferation of reflected ray solutions. In this paper, an empty generic aircraft cabin is hence considered to analyze the problem of concavity. The transmitting and the receiving antenna are taken as directional antennas (half-wavelength dipoles). The simulation results for the RF field build-up within a generic aircraft cabin are presented for both the perpendicular and parallel polarizations. The field build-up at the receiving point is taken as a coherent sum of the fields associated with each ray reaching the receiver. The results are presented for a metallic generic aircraft cabin, followed by a metal-backed dielectric generic aircraft cabin. The convergence analysis of the field build-up is carried out with respect to the propagation time and the number of bounces that the rays undergo before reaching the receiving point.
2. Refined Ray-Tracing Method The SBR/image (shooting-bouncing-ray/image) approach, in conjunction with UTD (Uniform Theory of Diffraction) was also reported to be a good tool for analyzing radiowave propagation in furnished rooms [4]. There are several ray-path models, viz., the Fast 3D Model (FM) and the Full 3D Model (FUM) that have been used for prediction of the power level inside an aircraft cabin. The Fast 3D Model uses shooting and bouncing rays for the determination of the propagation paths, when the transmitters and receivers are close to the ground in height compared to other objects. In contrast, the Full 3D Model uses both shooting and bouncing rays and the image method. It 277
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gives more-accurate results, and there is no constraint on the object’s shape. However, it is computationally intensive. Other popular EM propagation prediction tools include Wireless Insite (WI), Site Planner [15], and Enterprise Planner [16], these having been used to model and simulate the EM environment in aircraft cabins. An aircraft cabin is an inherently concave structure, leading to a multiplicity of feasible ray-path solutions. The material properties, such as the roughness, conductivity, and dielectric properties, further affect the ray-path solutions. The EM propagation inside the aircraft’s cabin is thus complex in terms of visualization. For the ISM band (2.4 GHz, 5.2 GHz), ray-tracing models offer high-frequency solutions, and are of practical importance. Kwon et al. [17] recommended that a raybased technique could be successfully employed to study EM shielded enclosures without relying on any measurements. In this paper, a refined ray-tracing method is first implemented inside a lossy metal-backed dielectric cuboid. The ray-path data generated are compared with the ray-path data of the image method. The refined ray-tracing algorithm described below is then implemented inside the aircraft cabin.
Table 1. The total number of rays emanating from an isotropic source. Elevation Angle, θ [°]
Azimuth Angle, φ [°]
Total Number of Rays on a Sphere (FORTRAN Output)
18
18
134
9
9
522
8
8
656
5
5
1667
3
3
4616
2
2
10357
1
1
41345
0.1
0.1
4126183
0.01
0.01
4.125387 × 108
2.1 The Algorithm of the Refined Ray-Tracing Method In this approach, the transmitter and receiver are placed inside a lossy (metal-backed dielectric) cuboid, and the rays are launched from the transmitter using a uniform ray-launching scheme [10]. The increase in ray density with respect to the angular separation between the rays is shown in Table 1. Each launched ray is defined by its (θ , φ ) values and is allowed to propagate inside the cabin. The first intersection point is determined by considering the intersection formula between a line and the surface of the cuboid (six walls). An intermediate point on the reflected ray is then obtained [18] by taking the normal at the first incident point, and enforcing the condition of co-planarity. The same process is repeated for all subsequent bounces. The receiver is considered as a small adaptive reception sphere placed inside the cuboid. The center of the adaptive sphere is the receiving point. The rays that enter the adaptive reception sphere are considered to be the required rays. In fact, these rays appear in bunches, and the density of the ray bunches increases with an increase in the number of rays launched. It is hence essential to identify the ray bunches, rather than considering all the rays within a ray bunch. Towards this, an intelligent scheme for ray bunching is developed, which identifies the ray bunches and takes the ray nearest to the center as the representative ray path for the given ray bunch. This scheme identifies the same number of ray solutions, independently of the number of rays launched. The representative ray that iteratively converges to the receiving point represents the ray-path solution. All the converged rays within the adaptive reception sphere are considered to be rays required (Figure 1) for the RF field buildup inside the cuboid. 278
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Figure 1. The complete ray tracing up to five bounces for a cuboid, including all lower bounces and the direct ray. The source and receiver positions were S ( 0, 0, 0 ) and R ( 0.0,1.45, 0.1) .
2.2 The Algorithm of the Image Method In this method, all the possible ray paths at the receiver can be precisely obtained when both the source and receiver are within the cavity. This method considers the images formed with respect to a plane, and characterizes the images based on the order of these images. These images then act as secondary sources that give rise to higher-order images. Furthermore, each of these rays is tracked and segregated in time to help analyze the time-dependent solution. This method proves simple and accurate for ray-propagation studies within planar faceted surfaces. IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013
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2.3 A Comparison of the Refined Ray-Tracing Method and the Image Method Since the image method cannot be employed for the (curved) aircraft cabin, the RF field build-up inside a metalbacked lossy cuboid (1.83 m × 1.64 m × 1.40 m) was compared for the ray-path data, using the image method and the refined ray-tracing method. The numbers of rays received at the observation point (receiver) using both the refined ray-tracing method and the image method are given in Table 2. The trend of the field build-up was analyzed for up to a cumulative 25 bounces that the rays underwent before reaching the receiving point. Simulations were carried out at 2.4 GHz. A comparison of the RF field build-up inside the metal-backed lossy cuboid is shown in Figure 2, without loss of generality, for parallel polarization. The constitutive parameters of the dielectric wall were= ε r 10.74 − j 2.01 and a thickness of 4 mm. Figure 2 showed an excellent match between the RF field build-up using the refined ray-tracing and the image methods. This allowed us to use the refined ray-tracing method for aircraft cabin analysis (where the image method was not available, due to the intrinsic curved concavities of the aircraft’s cabin). The refined ray-tracing method is used in conjunction with analytical surface modeling to generate the ray-path details inside a generic passenger-aircraft cabin. A comparison of the CPU execution time in generating the ray-path data inside a cuboid using the image method and the refined ray-tracing method is given in Table 3. It was observed that for lower bounces, both of the methods took equivalent time. However, this was not true for higher bounces. The proposed refined ray-tracing method proved to be efficient compared to the image method. Moreover, the proposed method can be extended to aircraft-cabin applications, where the image method cannot be used.
3. Surface Modeling of the Aircraft’s Cabin
Table 2. The number of rays at the receiver. Bounces
Image Method
Refined RayTracing Method
1
6
6
2
18
18
3
38
38
4
66
66
5
102
104
10
402
401
15
902
903
20
1602
1570
25
2502
2490
Table 3. A comparison of CPU execution times for ray tracing inside a cuboid (Intel Core 2 Duo CPU E8400 3 GHz). Number of Bounces*
Image Method
Refined Ray-Tracing Method
15
33 s
27 s
20
2 m 11 s
44 s
25
8 m 15 s
1m7s
30
21 m 5 s
2m6s
Image method: for faceted concavities (e.g. cuboid); not extendible to aircraft cabin. Refined ray-tracing method: applicable to faceted concavities (e.g. cuboid); readily applicable to aircraft cabin. *Cumulative, i.e. includes all lower bounces and direct ray.
A large passenger-aircraft cabin section can be modeled as a single curved right elliptic cylinder with end caps. The typical dimensions of the aircraft cabin were taken from open-domain sources [14]. In analytical surface modeling, the surfaces are defined by parametric equations.
3.1 The Geometry of the Aircraft Cabin The internal dimensions of the generic large passengeraircraft cabin section considered were taken as •
Internal fuselage length of the cabin:
34 m
•
Internal width of the cabin:
4m
•
Fuselage height:
4.2 m
•
Internal height:
2.2 m
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Figure 2. A comparison of the RF field build-up at the receiver inside a metal-backed lossy cuboid using the image method and the refined ray-tracing method. 279
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3.2 Calculation of Shaping Parameter The parametric equations of a right elliptical cylinder are given by [13] x = a cos φ ,
y = c sin φ ,
(1)
v1 ≤ z ≤ v2 , where a and c are the semi-major axis and the semi-minor axis of the elliptic cylinder, φ is its azimuth angle (which varies from 0° to 360°), and v1 ≤ z ≤ v2 represents the finite length of the elliptic cylinder. Figure 3. The dimensions of the aircraft cabin.
4. Propagation Inside the Aircraft Cabin After analytical surface modeling of the aircraft cabin, the ray-path details between the transmitter and receiver were determined using a refined ray-tracing algorithm, described below. The transmitter and receiver were located inside the aircraft cabin, without loss of generality, at S ( 0.8,1.4, −15 ) and R ( −0.7, 0.9,16 ) .
4.1 Refined Ray Tracing Inside the Aircraft Cabin Initially, a uniform ray-launching scheme [10] was used within the aircraft cabin from the isotropic source (transmitter), which was subsequently adapted for convergence of ray solutions at the receiver.
Figure 4. The aircraft cabin, modeled using Boeing AGPS. The aircraft fuselage was hence modeled as an elliptic cylinder, having a semi-major axis of 2.1 m and a semi-minor axis of 2 m. The finite length of the elliptic cylinder was taken to be 34 m. A floorboard was placed at a height of 2 m from the bottom of the fuselage, so that the height from the floorboard to the top was 2.2 m (Figure 3). The floorboard acted like a reflecting surface, so that the rays were bounded by the floorboard and the upper part of the elliptic cylinder. According to the dimensions of the fuselage, 50 windows on either side of the fuselage were considered. The width of a window was taken to be 0.216 m, and the height of a window was taken to be 0.376 m. The spacing (pitch) between windows was 0.33 m. Windows were placed 1 m above the floorboard. The aircraft cabin, modeled using Boeing AGPS software [19], is shown in Figure 4. 280
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Each ray was uniquely defined by its (θ , φ ) values, where θ and φ are the angles that the ray made with the z axis and the x axis. The rays were then allowed to propagate inside the cabin. The first intersection point was determined by the intersection formula between a line and the surface of the corresponding hybrid structure [18]. As the hybrid structure of a closed aircraft cabin has four surfaces at different heights, the y and z coordinates of the first intersection point was checked, and the equation was accordingly adopted for calculation of the first incident point. The corresponding four surfaces of the generic aircraft cabin are: Plane: Elliptic cylinder: Plane: Plane (floorboard):
z = −17 −17 > z > 17 z = 17 y = −0.1
The unit surface normal vector at the first incident point was determined by taking the normal equation of the corresponding surfaces [13]. Figure 5 presents the surface normal of an elliptic cylinder. IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013
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The unit surface normal equation of a second-degree quadric patch is given by Nˆ = xN iˆ + y N ˆj + z N kˆ ,
(2)
which for a right elliptic cylinder is expressed as xN =
yN =
a cos φ1 a 2 cos φ12 + c 2 sin φ12 c sin φ1 2
a cos φ12 + c 2 sin φ12
,
,
(3)
zN = 0 .
Figure 5. The unit surface normal vector representation of a right elliptic cylinder.
Once the surface normal at the point (where the ray was incident) was determined, the reflected ray was obtained by employing the laws of reflection. This process was repeated for the subsequent bounces. A receiver was considered to be at the center of an adaptive reception sphere placed inside the generic aircraft cabin. These ray-paths tended to appear as ray bunches (Figure 6), which traversed nearly parallel paths before reaching the reception sphere. An intelligent ray-bunching scheme was hence developed to identify the ray bunches. The ray nearest to the center of the adaptive sphere within a bunch (the red colored ray in Figure 6) was selected for further convergence. This ray converged iteratively by refining the angular separation to yield the ray solutions at the receiver (the green colored ray in Figure 6).
4.2 Results and Visualization of Ray Path
Figure 6. A single bunch of rays reaching the reception cube. The converged ray (green-colored ray) reached the receiving point (a front view with respect to Figure 4).
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The ray-path propagation characteristics were verified for reflection i.e., co-planarity and equality of angles. These data were utilized for the ray-path visualization. In this ray procedure, a total of 4,126,183 rays were launched, corresponding to a nominal angular spacing of 0.1°. Out of these, only 42 rays cumulatively reached the receiver, up to three bounces, besides the direct ray. Of these 42 rays, there were four rays
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ray-path data up to 30 bounces (i.e., the direct ray, all the onebounce rays, all the two-bounce rays, ..., up to all the 30-bounce rays), as discussed in the next section.
5. RF Field Build-up Inside the Aircraft Cabin The RF field-mapping problem was formulated in three steps, viz., (i) analytical surface modeling of the generic aircraft cabin enclosure, (ii) ray-path data generation within the enclosure using a refined ray-tracing algorithm, followed by (iii) frequency- and polarization-dependent RF field computation for the field mapping inside the generic aircraft cabin. The estimation of the RF field build-up within a closed cavity utilized the ray-path description and the coordinates of the reflection point(s) obtained using the novel adaptive threedimensional ray-tracing procedure that was explained in the previous sections. Although the ray tracing became computationally complex when numerous ray paths and their multiple reflections were considered, it nevertheless offered an efficient method for volumetric ray tracing within the concave environment. The total electric field at an observation point, P, inside a cavity [20] is given by E ( P ) = ∑ Ei ( P ) ,
(4)
i
where Ei ( P ) is the electric field due to the ith ray from the transmitting antenna to the receiver point, P, after undergoing a finite number of reflections corresponding to its unique ray path. The number of reflections depends on the angle at which the ray originates from the transmitting antenna.
Figure 7. The cumulative rays that reached the receiver up to (a) three bounces, and (b) five bounces, inside the aircraft cabin.
that reached after one bounce, 10 rays that reached after two bounces, and 28 rays that reached after three bounces. Figure 7a cumulatively shows the rays until the third bounce at the receiver inside an aircraft cabin. Figure 7b gives the three-dimensional perspective of the ray-path details inside the generic aircraft cabin up to five bounces, which showed the increase in the complex ray density. In fact, in the present paper, the ray-path data was generated up to 30 bounces, which were then sorted with respect to their propagation times. It is pointed out that for the RF field mapping application under consideration, it was sufficient to cumulatively generate the 282
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The time-independent field expressed in Equation (4) is the sum of an infinite number of field-contribution terms within a closed metallic cavity. However, for a time snapshot, the computation was limited to a finite time. Furthermore, the phase of each ray (reaching the receiving point at a different instant of time) was adjusted to get coherent superposition of the EM field contributions. Each individual ray-field contribution, Ei ( P ) , was determined by ray tracing within the enclosed generic aircraft cabin structure according to the laws of Geometrical Optics (GO) [21]. The value of the field, besides the direct ray, depended on the number of reflections an individual ray underwent while traversing from the transmitter to the receiver, and other EM parameters such as constitutive material of the wall, the geometry of the environment, etc. One thus had to follow (i.e., trace) the ray path in order to compute the corresponding ray field. After N reflections, the complex electric field (in V/m) due to the ith ray at the receiving point P [20] is given by = Ei ( P ) E0 Fti Fri {Π l Rl } e − jkd Li ( d ) ,
(5)
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where E0 is the reference field at the source; Fti and Fri are the corresponding values intercepted on the radiation patterns of the transmitting and receiving antennas, respectively, in the direction of the ray; Rl is the reflection coefficient of the lth object [22, 23]; d is the total ray-path length; k is the wavenumber; and Li ( d ) is the path loss [17]. The dependences of the reflection coefficient on the material properties, viz., permittivity, conductivity, thickness, and the angle of incidence, were appropriately incorporated. For the theoretical analysis in this paper, a normalized E field of 1 V/m (or 0.125 mW/m 2 ) was assumed at the transmitter. In practice, a typical transmitting power inside an aircraft cabin is 0 dBm (or 1 mW/m 2 ) [24]. The above values are well within the human exposure limits, both for professionals as well as for the general public, in the operational wireless frequency range. These limits are 137 V/m rms (or 50 W/m 2 ) and 61.4 V/m rms (or 10 W/m 2 ), respectively, according to the IEEE standards for safety levels [25]. The RF-field simulation depends on the ray-path descriptions generated. This ray-path data in turn depends on the methodology used. For an indoor environment such as an aircraft cabin, the RF-field convergence depends on factors such as the cumulative bounces of the feasible ray paths considered, the propagation time, the constitutive parameters of materials, the angular separation between the rays launched, the source and receiver positions, the radiation characteristics of the excitation source (the antenna), and the obstacles within the environment. Simulations were done for (i) an empty cabin, (ii) a cabin with the floorboard, and (iii) a cabin with the floorboard and windows. The material of the floorboard was taken to be carpet ( ε r = 1.19 , tan δ = 0.02 , d = 20 mm), and the covering of the windows was assumed to be PMMA ( ε r = 2.66 , tan δ = 0.01 , d = 2.5 mm). Both the transmitting and receiving antennas were taken to be λ 2 dipoles. In this paper, the simulations were carried out both for a metallic ( σ = 106 S/m) and a metal-backed dielectric aircraft cabin. The launching of rays within an enclosure could be efficiently done for any angular separation. However, if the angular separation between the adjacent launched rays is too large, fewer test rays are launched, and the RF field at the receiver does not converge. There thus is a requirement for launching the test rays at increasingly smaller angles, which at the other extreme is beset with the obvious problem of computational intractability. It was observed that a tradeoff existed for the class of problems being analyzed here, optimally in the range of 0.1° to 0.25°. In this study, the RF field build-up at the receiving point inside the aircraft cabin was obtained for a ray angular separation of 0.1°. Simulations were carried out at 2.4 GHz for both parallel and perpendicular polarizations. The normalized RF field build-up at the receiving point inside an empty metallic aircraft cabin is shown in Figures 8a and 8b for the perpenIEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013
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Figure 8. The RF field build-up inside a metallic generic aircraft cabin (the frequency was 2.4 GHz, 0.1° ray angular separation, σ = 106 S/m), for (a) perpendicular polarization, and (b) parallel polarization. Since the walls were metallic, convergence was not achieved. dicular and parallel polarizations, respectively. For a given ray bounce, the complete set of rays is characterized by a distinct tmin and tmax . Here, tmin refers to the minimum time of the (shortest) ray path for a given bounce. Likewise, tmax corresponds to the maximum time of the (longest) ray within the set of rays for the same number of bounces. It is pointed out that for the preset number of bounces, tmin may be more than the propagation time of several rays of a lower bounce type, and even more than some of the rays of the higher bounce type. One of the focuses of this study was hence to analyze the RF-field convergence with respect to the cumulative bounce of the feasible ray paths (i.e., cumulatively all the ray paths up to a preset number of bounces). In the case of perpendicular polarization (Figure 8a), the field convergence required a very large number of bounces, and hence the time axis should be very large. However, the time window considered, until 3.5 µsec, was sufficient for practical 283
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applications, as shown later. The results were reported until 30 bounces (cumulative), which brought convergence within the ambit of computational tractability. Since the walls of the generic aircraft cabin were considered to be highly metallic ( σ = 106 S/m), the rays did not suffer significant attenuation at each reflection before reaching the receiver. It could be observed from Figures 8a and 8b that the level of the RF field build-up tended to broadly increase with the number of bounces considered. This was due to the fact that as the number of bounces increased, the number of rays reaching the receiver also increased. These numerous rays reaching the receiver arrived from different directions, and hence tended to substantially cancel, leaving only a small net (positive/negative) RF field. This small net field contributed to the earlier threshold of the RF field build-up in the incremental sense, thereby leading to the extremely slow rate of convergence for the metallic case. This was along expected lines, since convergence was reported not to have been achieved within a highly metallic reverberation-chamber-like environment [20]. Particularly initially, the amplitude of the total RF field build-up at the receiver fluctuated with the number of bounces. This may have been due to the fact that this study had emphasis with respect to the preset cumulative number of bounces, which was used as the cutoff that ignored the higher-bounce ray paths. Although the higher bounces tended to result in increasingly diminished (and hence negligible) electric-field contributions, their contributions during the initial RF build-up was not necessarily so, thereby leading to the observed RF fluctuations. However, with an increase in time, this error evened itself out. The RF field build-up inside the aircraft cabin with a metal-backed carpet floorboard was next computed. The walls of the cabin were taken to be metal-backed dielectric ( ε= r 10 − j 5 , d = 11 mm). The constitutive parameters of the wall material and the floorboard were employed in the estimation of the reflection coefficients [23] of each of the ray paths, as functions of polarization and of all the successive angles of incidence. The magnitudes and phases of the reflection coefficients of a metal-backed carpet floorboard for both perpendicular and parallel polarizations are reported in Figure 9. The floorboard was considered to be a plane. It acted like a reflecting surface for the rays traveling inside the cabin. The rays underwent reflections from the walls, the upper portion of the cabin, and the floorboard, and remained bounded in the region between the floorboard and the upper portion of the cabin. The contributions of each ray path reaching the receiver within the cabin were coherently summed up after adjusting them in phase. The resultant normalized RF field build-ups within the generic aircraft cabin for perpendicular and parallel polarizations are shown in Figures 10a and 10b, respectively. The y axis within these normalized field plots was limited to 0.005 to facilitate a closer scrutiny. It could be readily observed that for a metal-backed dielectric generic aircraft cabin, the ray contributions converged rapidly for both perpendicular and parallel polarization, both over time and over the number of bounces. 284
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Figure 9. The reflection coefficient of a metal-backed carpet floorboard (= ε r 1.19 − j 0.024 , d = 20 mm, f = 2.4 GHz): (a) magnitude, (b) phase.
This was ascribed to the lossy nature of the metal-backed dielectric wall and the floorboard (metal-backed carpet) upon which the rays were incident, leading to attenuation upon each reflection, and thus lower RF field amplitude and a rapid convergence. The case of the metal-backed cabin with a carpet floorboard and windows was next considered. Fifty equidistant rectangular PMMA windows (= ε r 2.66 − j 0.027 , d = 4.5 mm) on either side of the cabin were considered. These windows were placed 1 m above the floorboard. The rays propagating inside the cabin escaped (substantially) through these windows. This resulted in a much lower amplitude of field build-up at the receiving point inside the cabin. The RF field build-ups for the perpendicular and parallel components of the field build-up are shown in Figures 11a and 11b, respectively. The y axis within these normalized field plots was limited to 0.005 to facilitate a closer scrutiny. As expected, the rays escaped through the windows, leading to IEEE Antennas and Propagation Magazine, Vol. 55, No. 1, February 2013
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Figure 10. The RF field build-up inside a metal-backed dielectric ( ε = r 10 − j 5 , d = 11 mm) cabin with a carpeted floorboard (= ε r 1.19 − j 0.024 , d = 20 mm) (the ° frequency was 2.4 GHz, 0.1 ray angular separation): (a) perpendicular polarization, (b) parallel polarization. (Although the field was normalized, the y axis considered was only up to 0.005, to facilitate closer scrutiny of the plots).
Figure 11. The RF field build-up inside a metal-backed dielectric ( ε = r 10 − j 5 , d = 11 mm) cabin with a carpeted floorboard (= ε r 1.19 − j 0.024 , d = 20 mm) and PMMA windows (= ε r 2.66 − j 0.027 , d = 4.5 mm) (the frequency was 2.4 GHz, 0.1° ray angular separation): (a) perpendicular polarization, (b) parallel polarization. (Although the field was normalized, the y axis considered was only up to 0.005, to facilitate closer scrutiny of the plots).
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a significant reduction in the converged field amplitude at the receiving point, as compared to the case of the aircraft cabin with a floorboard (Figure 10). The RF build-ups converged both over the propagation time and the number of bounces for both perpendicular and parallel polarizations. The simulations were carried out for both the parallel and perpendicular polarizations to consider existing antennas of linear polarization. However, it is also known that circularly polarized antennas may be better employed in many situations of wireless communication applications. The benefits of circular polarization include superior propagation and penetration with less susceptibility to outside interference and multipath signals, high gain, less fading, and minimal polarization mismatch with wireless sensors and the linearly polarized antennas of access points mounted on aircraft [26]. However, the effects of a reverberant cavity on the average received power have been reported, indicating that the potential advantages of exploiting circular polarity are diminished in the cabin [27]. This implies the analysis for linear polarization can be applied without any loss of generality when considering practical cabin installations where line-of-sight coupling is not likely dominant. In the case of an aircraft passenger cabin, the rows of seats and the overhead baggage cabins are distinctive features. These passenger seats have finite thicknesses and curved profiles. Furthermore, the material of the seat may be dielectric in nature, with some parts that are characterized by finite conductivity. Such a scattering enclosure will undergo diffraction. The free-space ray-path propagation – rather than surface waves on the scatterer – is the dominant propagation mechanism. This remains an important assumption while modeling the dielectric seats and finitely conducting materials for the path-loss prediction in the aircraft in-cabin environment. The material properties become the dominant loss mechanism, rather than the diffraction effect, in such cases. It was reported by other researchers elsewhere that diffraction effects were less and had minimal effects [4]. In any case, in an empty cabin (bereft of seats), diffraction effects are not likely to manifest themselves, and would appear only when seats were included in a more-complex environment. To summarize, the effect of the permittivity of the material is more dominant than the multiple reflection and diffraction effects of obstacles and obscurations in building up the RF field within the cabin. Owing to their lossy nature, an aircraft cabin with seats and passengers would result in further attenuation of the RF field associated with the rays propagating within the cabin.
6. Conclusion The RF environment inside a generic aircraft cabin was analyzed based on a novel ray-tracing algorithm proposed here,
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in conjunction with analytical surface modeling, for a generic aircraft cabin. The refined ray tracing yielded the required raypath data, which also facilitated visualization of all the rays that reached a particular adaptive reception sphere placed inside the generic aircraft cabin. An intelligent scheme of ray-bunching was developed to differentiate the ray solutions as ray bunches that identified the same number of ray solutions arising at the adaptive sphere, independently of the (increasing) number of rays launched. A refinement algorithm was then employed to identify the ray path within this ray bunch, which eventually converged onto the receiving point. This algorithm cumulatively generated the complete data for all the ray paths up to a given number of bounces. In this study, the RF field build-up at the receiving point inside a generic aircraft cabin was obtained for rays launched at an angular separation of 0.1° within the cabin. For the class of generic aircraft cabin problem analyzed in this work, it was sufficient to cumulatively consider the ray paths up to 30 bounces for RF-field convergence, which was within the realm of computational tractability. The RF field build-up at the receiving point was obtained as a coherent sum of the fields associated with each ray reaching the receiver, after being adjusted in phase. Simulations were carried out at 2.4 GHz. The results for the RF field build-up were shown for (i) an empty metallic aircraft cabin, (ii) a metal-backed dielectric aircraft cabin with carpet floorboard, and (iii) a metal-backed dielectric aircraft cabin with carpet floorboard and PMMA windows. The number of rays reaching the receiver increased with the number of ray bounces. These numerous rays incident from different directions tended to cancel out, leaving but a net (positive/negative) RF field. Despite the large number of rays, it was only this small net RF field that contributed to the incremental rise or fall in the threshold of the RF field build-up. This led to the slow rate of convergence. In the case of both perpendicular and parallel polarization, the RF field buildup inside a metallic generic aircraft cabin tended to broadly increase with the number of bounces considered. This trend was along the expected lines, since it is well known that the RF field convergence is not achieved within a highly metallic reverberation chamber. For a metal-backed dielectric aircraft cabin with carpet floorboard or with carpet floorboard and PMMA windows, the RF field build-up converged rapidly, both with respect to the elapsed time and to the number of bounces. This was due to the lossy nature of the metal-backed dielectric wall and the metalbacked carpet floorboard of the generic aircraft cabin enclosure. Moreover, the rays falling on the PMMA windows escaped out, resulting in a much lower build-up threshold at the receiver within the cabin. The RF-field estimation demonstrated the efficiency of the proposed ray-tracing algorithm in analyzing the RF-field mapping within this type of enclosure, such as an aircraft cabin, a tunnel, a corridor, etc.
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