# MODELING WIRELESS SIGNAL STRENGTH WITHIN A DEFINED ENVIRONMENT

A disclosed system quantifies the power distribution of a wireless signal within a constrained environment using non-sequential ray tracing. For each ray, one or more ray-reflecting surface is prescreened to identify collision-eligible surfaces and identify a collision surface from the collision-eligible surfaces, wherein the collision surface is the first ray-reflecting surface that a ray collides with. A power distribution component, indicating the position and power of a ray at a particular elevation within the environment, is added to a cumulative power distribution. If a reflected ray corresponding to each collision is calculated and satisfies ray eligibility conditions, a collision surface may be determined for the reflected ray. Collision surfaces may be identified by evaluating a target function for a number of ray positions, where the target function evaluates to zero when displacement between the ray and the ray-reflecting surface is zero.

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**Description**

**CROSS REFERENCE TO RELATED APPLICATIONS**

Not applicable.

**STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT**

Not applicable.

**REFERENCE TO APPENDIX**

Not applicable.

**BACKGROUND OF THE INVENTION**

**Field of the Invention**

Disclosed subject matter pertains to wireless communication and, more particularly, modeling of wireless signal power distributions within specific environments.

**Related Art**

Many commercial airlines offer in-flight wireless access networks, including some form of IEEE 802.11 (WiFi) network, that permit passengers to access Internet content in flight. However, ever increasing passenger demand for uninterrupted internet access via connections capable of supporting data intensive applications including, as non-limiting examples, high definition video and audio signals remains largely unaddressed.

Demand is also increasing for high performance, in-flight mobile communication services capable of supporting, as a non-limiting example, an in-flight call, made by a passenger while in the passenger's seat using the passenger's mobile device, to a landline or mobile phone on the ground. Currently, cellular communication during flight is often restricted or prohibited for safety reasons because electromagnetic interference (EMI) associated with the cellular communication signals transmitted by most mobile devices can interfere with electronic devices on an aircraft. However, because it is extremely easy to activate a cellular phone, whether intentionally or accidently, and extremely difficult for a crew member to detect, mobile phones can be a source of flight safety concern.

Whether to identify the source of a particular cellular communication signal or to provide broadband wireless access to hundreds of closely spaced mobile devices, an understanding of the power distribution of electromagnetic signals within an enclosed, densely populated environment characterized by a large number of discontinuities, including chairs, overhead cabinets, etc., is needed.

**BRIEF SUMMARY OF THE INVENTION**

Subject matter included herein discloses a method and system for determining wireless signal power distribution within an enclosed environment such as the interior of an aircraft cabin. Embodiments may employ a non-sequential ray tracing technique to model signal power distribution within an aircraft cabin equipped with a leaky antenna array. Disclosed methods and systems may model wireless signal coverage inside the aircraft cabin, taking into consideration various parameters such as the dimensions and materials of the aircraft cabin itself as well as the chairs, overhead storage bins, and other structures within the cabin. Embodiments may also model the power distribution attributable to wireless communication signals transmitted by the mobile devices of one or more passengers to monitor electromagnetic interference or to model the signal power distribution for wireless signals transmitted from the leaky antenna array. Although disclosed subject matter emphasizes an aircraft cabin environment, disclosed methods and systems are applicable to other enclosed or specialized environments including, as non-limiting examples, tunnels, buildings, ships, and trains.

Although descriptions of disclosed systems and methods may include references to WiFi signals or networks, WiFi is a non-limiting example of a wireless signal for which a power distribution within an enclosed environment such as an aircraft cabin is modeled. Accordingly, disclosed subject matter encompasses modeling of the power distributions for other wireless signals including, as a non-limiting example, cellular communication signals including, without limitation, global system for mobile communication (GSM) signals and the like. Currently, the use of cellular communication devices is frequently restricted or entirely prohibited on board an aircraft, primarily due to electromagnetic interference (EMI) concerns. However, developing technologies for suppressing or containing GSM-induced EMI may pave the way for in-flight cellular communication services and such services may employ a leaky feeder antenna to provide reliable connectivity. Thus, disclosed systems and methods for characterizing the signal power distribution associated with a particular antenna within a particular enclosed environment may be beneficially employed to implement and optimize onboard wireless network systems enabling airborne passengers to use their mobile devices to text or call people on the ground or otherwise communicate from within the enclosed environment. In this respect, disclosed systems and methods might be employed not only to characterize and optimize the desired GSM signal, but also to characterize and minimize any associated EMI signals.

Disclosed methods include methods performed by a central processing unit (CPU) executing executable instructions stored in a suitable memory devices or storage device. Disclosed embodiments include embodiments incorporating methods and operations that improve performance with little or no loss of accuracy.

Disclosed methods and systems quantify a power distribution for a wireless communication signal within a constrained environment that includes a leaky antenna array with a plurality of antenna slots. For each slot, operations referred to herein as surface selection operations are performed on each propagation ray of a ray tracing model that includes a plurality of propagation rays representing the radiation pattern of each antenna slot. In at least one embodiment, the surface selection operations performed for each propagation ray include screening ray-reflecting surfaces to identify collision-eligible surfaces and collision-ineligible surfaces. The collision-eligible surfaces are then processed to identify a collision surface for the ray. A reflected ray resulting from the propagation ray colliding with the collision surface is identified. If the reflected ray meets one or more criteria including, as a non-limiting example, sufficient power intensity, the surface selection operations are performed on the reflected ray to identify a collision surface for the reflected ray and to identify a subsequent reflected ray where each subsequent reflected has less lower power than its predecessor. This process continues until the power of a reflected ray is below a threshold value or until some other one or more criteria are not met. A signal power component is determined for each propagated and reflected ray where the signal power component may indicate a power and position of the ray as the ray intersects with a particular plane, such as a passenger level plane, within the enclosed environment. The accumulation of the signal distribution components from each the rays and reflected rays represents the signal power distribution.

In accordance with disclosed subject matter, a system and method for quantifying a power distribution of a wireless communication signal within a constrained environment includes performing particular operations for each of one or more antenna slots of a leaky antenna disposed within a constrained environment. Performing the particular operations may include performing surface selection operations for each propagation ray in a ray tracing model of each antenna slot wherein the ray tracing model includes a plurality of propagation rays.

The surface selection operations may include screening one or more ray-reflecting surfaces with respect the propagation ray to identify collision-ineligible surfaces and collision-eligible surfaces. A collision surface may then be determined from the collision-eligible surfaces, wherein the collision surface comprises a first ray-reflecting surface with which the propagation ray collides. A power distribution component corresponding to the propagation ray may be added to a cumulative power distribution. The power distribution component may indicate the position and power of the propagation ray as the ray intersects the passenger level plane or some other plane of interest.

One or more parameters of a reflected ray resulting from the propagation ray colliding with the collision surface may then be calculated or otherwise determined. The reflected ray parameters may include, as non-limiting examples, a power parameter and directional parameter. To illustrate, the power of a reflected ray may be determined based, at least in part, on the power of the propagation ray, the propagation ray's angle of incidence with respect to the collision surface, and an attenuation factor assigned to the collision surface. If the parameters of the reflected ray satisfy each of one or more ray eligibility criteria, the reflected ray is treated as a new propagation ray and processed in the same manner as its predecessor, i.e., the propagation ray whose collision with the collision surface resulted in the reflected ray, to determine a power distribution component and a collision surface for the reflected ray. This process may be repeated until, eventually, a reflected ray has insufficient power or fails to satisfy one or more of the ray eligibility criteria.

Screening a ray-reflecting surface may include identifying the ray-reflecting surface as either a collision-eligible surface or a collision-ineligible surface based on an original position of the propagation ray, a velocity vector or another indicator of a direction of motion of the propagation ray, and a surface displacement indicative of a position of the ray-reflecting surface relative to the original position of the propagation ray.

Identifying a ray-reflecting surface as either a collision-eligible or a collision-ineligible surface may include comparing one or more coordinates of a velocity vector for the propagation ray to a corresponding one or more coordinates of the displacement vector for the ray-reflecting surface. In at least one embodiment, if sign consistency is detected between each of the one or more coordinates of the velocity vector and its corresponding one or more coordinates of the displacement vector, the ray-reflecting surface is identified as collision-eligible surface.

In alternative embodiments, identifying ray-reflecting surfaces may include defining an eligible surfaces volume based on an initial position of the propagation ray and an enclosing volume wherein the enclosing volume is of a size sufficient to enclose the enclosed environment. The eligible surfaces volume may comprises a cuboid wherein a diagonal of the cuboid extends from the initial position of the propagation ray to an intersection point, wherein the intersection point is the point at which the propagation ray intersects the enclosing volume.

Identifying the collision surface may include identifying the collision surface using a target function that determines a target function value indicative of a displacement between a propagation ray and a ray-reflecting surface. The target function may evaluate to zero when displacement between the propagation ray and the ray-reflecting surface is zero and the target function value may increase monotonically with increasing displacement.

In an exemplary embodiment, a ray-reflecting surface corresponds to a triangle ABC defined by points A, B, and C, the position of the propagation ray comprises a point O, and the target function receives A, B, C, and **0** as inputs. In at least one embodiment, the target function evaluates to (S1+S2+S3)−S0 wherein S0 represents an area of triangle ABC, S1 represents an area of a triangle OAB defined by points O, A, and B, S2 represents an area of a triangle OBC defined by points O, B, and C, and S3 represents an area of a triangle OCA defined by points O, C, and A.

Exemplary operations for identifying the collision surface may include calculating initial slopes of target function plots for each collision-eligible surface, where each target function plot comprises a plot of target function values versus propagation ray positions. Ray-reflecting surfaces associated with positive value initial slopes may be identified as collision-ineligible surfaces and discarded from further processing. For each collision-eligible surface remaining after said identifying, each target function plot may be extrapolated in accordance with its initial slope to identify a projected distance value for each collision-eligible surface. The collision-eligible surfaces may be ordered in accordance with the projected distance values, e.g., surface associated with lowest projected distance value is processed first or otherwise prioritized. Processing a collision-eligible surface may include calculating a minimum target function value for the collision-eligible surface and, responsive to detecting a minimum target function value greater than zero, identifying the surface as a collision-ineligible surface and discarding the surface from further consideration with respect to the current propagation ray. Responsive to detecting a minimum target function value of zero, the ray-reflecting surface may be identified as the collision surface for the corresponding propagation ray.

**BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS**

Drawings are not to scale unless stated so. Embodiments of methods, systems, and/or articles of manufacture disclosed herein are described with reference to the following figures, in which like reference numerals indicate like elements unless indicated otherwise and in which a hyphenated form of reference numeral indicates an instance of the corresponding element, which may also be referenced generically or collectively with an un-hyphenated form of the reference numeral. e.g., “ . . . a first widget **11**-**1** and a second widget **11**-**1** . . . wherein each widget **11** includes . . . and wherein widgets **11** further include . . . .”

**DETAILED DESCRIPTION**

The figures referenced above and the written description of specific structures and functions below are not presented to limit the scope of what the Applicant has invented or the scope of the appended claims. Rather, the figures and written description are provided to teach any person skilled in the art to make and use the inventions for which patent protection is sought. Those skilled in the art will appreciate that not all features of a commercial embodiment of the inventions are described or shown for the sake of clarity and understanding. Persons of skill in this art will also appreciate that the development of an actual commercial embodiment incorporating aspects of the present disclosure will require numerous implementation-specific decisions to achieve the developer's ultimate goal for the commercial embodiment. Such implementation-specific decisions may include, and likely are not limited to, compliance with system-related, business-related, government-related and other constraints, which may vary by specific implementation location and vary from time to time. While a developer's efforts might be complex and time-consuming in an absolute sense, such efforts would be, nevertheless, a routine undertaking for those of ordinary skill in this art having benefit of this disclosure. It must be understood that the inventions disclosed and taught herein are susceptible to numerous and various modifications and alternative forms. The use of a singular term, such as, but not limited to, “a,” is not intended as limiting of the number of items. Further, the various methods and embodiments of the system can be included in combination with each other to produce variations of the disclosed methods and embodiments. Discussion of singular elements can include plural elements and vice-versa. References to at least one item or to one or more items may refer to one item or to multiple items. Also, various aspects of the embodiments could be used in conjunction with each other to accomplish any disclosed objectives, advantages, or benefits. Unless the context requires otherwise, the term “comprise” or variations such as “comprises” or “comprising,” should be understood to imply the inclusion of at least the stated element or step or group of elements or steps or equivalents thereof, and not the exclusion of a greater numerical quantity or any other element or step or group of elements or steps or equivalents thereof. The device or system may be used in a number of directions and orientations. The order of steps can occur in a variety of sequences unless otherwise specifically limited. The various steps described herein can be combined with other steps, interlineated with the stated steps, and/or split into multiple steps. Similarly, elements have been described functionally and can be embodied as separate components or can be combined into components having multiple functions.

**101** deployed within an aircraft cabin **100**. The leaky antenna array **101** illustrated in **106**. The vertical displacement **108** between the elevation of leaky attention array **101** and the passenger level elevation **106** may be, as one example, 1.85 meters. In other embodiments, vertical displacement **108** may be greater than or less than this displacement.

The passenger level elevation **106** may represent the height or elevation above a base elevation or floor **104** at which a mobile device of a passenger is most likely disposed when the passenger is seated. By way of a non-limiting example, the passenger level elevation **106** may lie within a range of elevations between a first elevation corresponding to the elevation of the seating surface of a passenger seat and a second elevation corresponding to an elevation of an upper end of a seat back that defines an operational regime for a typical passenger or other user of wireless signals.

The leaky antenna array **101** illustrated in **102** and leaky antenna section **103**, wherein each leaky antenna section **102** includes one or more segments of varying lengths. As illustrated in **102**-**1** is disposed in a first section **107**-**1** of aircraft cabin **100**, leaky antenna section **103**-**1** is disposed in second section **107**-**2** of aircraft cabin **100**, leaky antenna section **102**-**2** is disposed in third section **107**-**3** of aircraft cabin **100**, and leaky antenna section **103**-**2** is disposed in fourth section **107**-**4**, where sections **107** of aircraft cabin **100** may be defined by walls and/or other structures.

Leaky antenna array **101**, also sometimes referred to as a leaky feeder or leaky feeder antenna, is a communication system device suitable for use within enclosed environments including tunnels, mines, aircraft, and the like. A leaky antenna may include a coaxial cable in which slots or slots have been incorporated into the outer conductor along the length of the cable. The slots allow electromagnetic signals to leak into and out of the cable. Line amplifiers may be employed at regular intervals within the cable to maintain signals at functional levels.

The leaky antenna array **101** illustrated in **102** and a second leaky antenna **103**. A first section **102**-**1** of leaky antenna **102** is disposed in a right rearward section **107**-**1** of aircraft cabin **100**, a second section **102**-**2** of leaky antenna **102** is disposed in a right forward section **107**-**3** of aircraft cabin **100**, a first section **103**-**1** of leaky antenna **103** is disposed in a left rearward forward section **107**-**3** of leaky antenna array **101**, and a second section **103**-**2** of leaky antenna **103** is disposed in a left forward section **107**-**4** of aircraft cabin **100**.

Although **101** that includes two leaky antennas (**102**, **103**), each of which includes two or more straight line segments, other embodiments may include more or fewer leaky antennas and each leaky antenna may include more or fewer straight line segments. In still other embodiments, the leaky antenna array **101** may include a leaky antenna with one or more curved sections (not depicted in

**110** suitable for use as a leaky antenna section **102** in the leaky antenna array **101** illustrated in **110** illustrated in **110** include an inner conductor **111** and an outer conductor **112**. Outer conductor **112** defines or includes a leaky antenna slot **114** that permits electromagnetic signals to enter and exit leaky antenna **110**. Although **110** that includes just a single leaky antenna slot **114**, leaky antenna slots **114** may be disposed at various positions along leaky antenna **110**.

The leaky antenna **110** may be treated, in at least some embodiments, as an ideal or near-ideal Lambert surface for purposes of modeling its characteristic radiation pattern. The power or intensity of radiation from an ideal Lambert source is directly proportional to the cosine of the angle between the direction of the outgoing light and the surface normal. Treating the leaky antenna **110** of **110** in the configuration of leaky antenna array **101** illustrated in **110**. The power of far field radiation varies inversely with the square of the distance from the antenna or other object of interest. Thus, for example, if the far field power is P at a distance of 1 unit from an antenna or other object of interest the power at a distance of 2 units is ¼×P.

**120** corresponding to at least one embodiment of the leaky antenna **110** illustrated in **100** (

Ray tracing algorithms include sequential and non-sequential algorithms. A sequential ray tracing algorithm traces rays through a pre-defined sequence of surfaces while travelling from the object surface to the image surface. Sequential ray-tracing may yield insight into curvatures, ideal glass types, and number of lens elements required in an optical system. However, for a complex system such as the system represented by the surfaces within an aircraft cabin, analysis of the wireless signals inside an airplane, the order in which rays scatter and interact with objects depends on the relative direction and location of the ray. Accordingly, a non-sequential ray tracing algorithm may be preferred to determine wireless signal power distribution within an aircraft cabin or within other geometrically large and complex environments.

**130**, including a plurality of propagation rays **131**, corresponding to and generated based on the far field intensity pattern **120** illustrated in **130** includes N propagation rays **131** wherein the direction of each propagation array **131** is chosen by random selection. Other embodiments, may employ a different technique for converting a radiation pattern to a ray tracing model.

The value of N, the number of propagation rays **131**, necessary to accurately represent the corresponding radiation pattern and accurately predict the resulting signal power distribution varies depending upon the application. Generally, the value of N should be the smallest value that produces accurate results. This value of N, which may be referred to herein as Nmin, may be determined empirically by observing changes in predicted power distributions for different values of N. In at least one embodiment, Nmin may be defined as the least value of N for which a 10% increase in N results in less than 1% change in predicted power distribution. Other embodiments may employ more relaxed or more stringent conditions for convergence.

Ray tracing model **130** may be represented as a data structure that includes an entry associated with each propagation ray **131**. Each entry in such a data structure may include sufficient fields to fully describe each propagation ray **131**. These fields may include, as non-limiting examples, three or more fields uniquely defining an orientation for each propagation ray **131**, one or more fields for indicating a magnitude of each propagation ray **131**. In at least some embodiments, the data structure may be simplified by an assumption that all propagation rays **131** in ray tracing model 10 originate from the same point of origin, in which case the orientation and magnitude may be conveyed by a single set of three parameters corresponding to three dimensions, whether specified using a Cartesian coordinate system, a polar coordinate system, or another suitable system. In at least some embodiments, the data structure corresponding to the ray tracing model **130** illustrated in **110**. In other embodiments, the data structure for ray tracing model **130** may be derived from the far field intensity pattern **120** illustrated in

The accuracy of alternative models of electromagnetic propagation, including the finite element method (FEM) or finite-difference time-domain (FDTD) method in which antenna signals are treated as electromagnetic waves, depends on the mesh size being much smaller than the applicable wavelength. Such methods often require a comparatively large amount of computer memory and computational time to compute, which make them unrealistic to model wireless signals in an airplane. In contrast, ray tracing models require much less computer resources and achieves reliable results in a relatively short period of time.

Rays from different slots along leaky antenna array **101** undergo reflection and refraction as they impinge on surfaces of the cabin and structures within the aircraft cabin. In at least one embodiment, refracted rays are ignored without substantial loss of accuracy because the applicable surfaces, i.e., the surfaces of the aircraft shell and aircraft furniture have high attenuation and very low refraction.

In at least one embodiment, rays are maintained and propagated until either of two ray termination criteria has been satisfied. The two ray termination criteria may include a propagation length criteria and a power level criteria. The propagation length criteria may be configured to terminate a ray after the ray and its ancestors have an accumulated propagation distance exceeding a particular propagation distance, e.g., 60 M or longer. The power level criteria may terminate any reflected ray with a power intensity that is 10% or less of the initial intensity of the original ray.

The final result is a data structure that maps or otherwise indicates power levels at different positions within the passenger level elevation **106** inside aircraft cabin **100**, which represents an estimate of the wireless communication signal power available to passengers for their personal mobile devices.

**150** for determining, modeling, or estimating a signal power distribution (SPD) for a communication signal within an enclosed environment, such as the aircraft cabin **100** illustrated in **101** illustrated in **150** illustrated in **150** is illustrated in

Generally, the method **150** illustrated in **150** may include one or more attenuation parameters that determine, in conjunction with one or more intensity criteria, whether a reflected ray is to be further processed or discarded. Eventually, the intensity of a reflected ray will be insufficient to satisfy the applicable intensity criteria and the ray reflected will be discarded before loading the next ray from the ray tracing model.

A power value is determined for each propagation ray and for each reflected ray of sufficient intensity. The individual power values are summed or otherwise grouped, combined, or accumulated to produce the SPD. In some embodiments, each power level value represents a power level at a particular elevation within the enclosed environment. As a non-limiting example, at least one embodiment produces a passenger level SPD, i.e., an SPD based on the power value calculated for each ray as it passes through the passenger level **106** (

In some embodiments, method **150** is simplified by constraining an elevation parameter to a single value or to a comparatively small number of values representing some fraction of the total elevation of the aircraft cabin **100**. As suggested previously, for example, the SPD at passenger level elevation **106** may be thought of as the most useful SPD within the aircraft cabin **100** illustrated in **150** may generate a planar SPD representing the power intensity levels at a plurality of points, each of which lies within a plane disposed at the passenger level elevation **106** illustrated in **100** while still other embodiments may generate intermediate SPDs covering less than the entire aircraft cabin **100** but more than the SPD at a single elevation.

The flow diagram blocks of the method **150** illustrated in **152**) corresponding to operations for retrieving certain data described below, an initialization block (block **154**) corresponding to operations for configuring the system performing method **150**, a slot selection block (block **156**) corresponding to operations for selecting a leaky antenna slot, a ray processing block (block **161**) corresponding to operations for processing propagation rays associated with the leaky antenna slot as described below, and a remaining slots block (block **176**) corresponding to an operation for determining whether any leaky antenna slots remain.

The ray processing block **161** illustrated in **161** includes a ray launching block (block **160**) corresponding to operations for selecting one of the propagation rays of the applicable ray tracing model, a surface filtering block (block **162**) corresponding to operations for identifying surfaces that are collision-ineligible with respect to the propagation ray being processed, a surface identification block (block **164**) for identifying the current propagation ray's collision surface, a power and angle determination block (block **170**) for determining a power and angle of a reflected ray resulting the propagation ray's collision with the collision surface, a reflected ray criteria block (block **172**) for distinguishing between reflected rays that should be further processed and reflected rays that require no further processing, and a remaining rays block (block **174**) for determining whether each propagation ray in the ray tracing model have been processed.

The method **150** illustrated in **152**) one or more data structures. In at least one embodiment, the first data structure is an environment geometry file corresponding to and indicative of the physical geometry of the applicable environment. In the case of an enclosed environment corresponding to the aircraft cabin **100** of **100**. A second data structure that may be input as part of block **152** illustrated in **130** illustrated in

After loading the applicable data structures in block **152**, the method **150** illustrated in **154**) one or more system parameters pertaining to the particular computing system performing method **150**. A leaky antenna slot may then be selected (block **156**) from a plurality of leaky antenna slots defined for a particular leaky antenna array **101**. Each leaky antenna slot may be defined by its latitudinal and longitudinal coordinates as seen from the top view of **100**. A leaky antenna data structure that includes the position information for each leaky antenna slot may be loaded as a fourth input in block **152**.

Once a leaky antenna slot is identified, the method **150** illustrated in **161** for each propagation ray **131** (**130** (**161** illustrated in **160**, **162**, **164**, **170**, **172**, and **174** as described herein.

The environment geometry file and the material file may include data defining hundreds or thousands of surfaces within aircraft cabin **100**. The block **162** illustrated in **162** are discussed in more detail with respect to

After filtering at least some surfaces in surface filtering block **162**, the method **150** illustrated in **164** to identify the surface with which the propagation ray under consideration first collides. This surface may be referred to herein as the first collision surface or, more simply, the collision surface associated with the propagation ray. Operations for identifying each propagation ray's collision surface are described in more detail below with respect to

Once the collision surface for a ray has been identified, an angle and power may be determined (blocks **170**) for the reflected ray produced by the collision of the original ray and the collision surface. The direction of the reflected ray can be determined by reflection law, and the reflection coefficient can be calculated according to Fresnel's equation. One or more attenuation factors may be stipulated and used to determine an intensity associated with the reflected ray. The method **150** illustrated in **172**, the reflected ray is effectively discarded and method **150** as illustrated in **174**. However, if the intensity of the reflected ray is sufficient to satisfy any one or more intensity thresholds or criteria, the method **150** illustrated in **162**, **164**, and **170** for the reflected ray.

When the intensity of a reflected ray fails to satisfy any intensity criteria, method **150** determines (block **174**) whether every propagation ray in the ray tracing model has been processed for the current antenna slot. If any propagation rays associated with the present antenna slot have not been processed, method **150** performs operations **160** through **172** for the next propagation ray. If every propagation ray has been processed for the current antenna slot, processing of the current antenna slot is complete and method **150** proceeds to block **176** to determine whether any other antenna slots remain.

If method **150** determines in block **176** that all antenna slots have been processed, method **150** terminates. Otherwise, method **150** performs operations **156** through **174** for the next antenna slot.

As stated above, surface selection block **164** finds the collision surface for a particular ray, i.e., the first surface with which a particular ray collides as the ray propagates forward over time. In at least one embodiment, identification of the collision surface associated with a particular propagation ray is facilitated by employing a target function F, as described herein, that generates a value indicative of the displacement between a propagation ray and a surface.

Referring to **131** and an exemplary surface **201** are depicted at two points in time to illustrate the target function F. Each surface in the environment geometry file and the material file corresponds to a triangle defined by three points in space. An exemplary surface **201**, most clearly shown in **131** is displaced from and propagating towards surface **201** while, in **131** has reached and collided with surface **201**. In **131**, forms a first triangular surface **202**-**1** with points A and B, a second triangular surface **202**-**2**, with points B and C, and a third triangular surface **202**-**3**, with points A and C.

In at least one embodiment, the target function F(A,B,C,O) is defined as:

*F*(*A,B,C,O*)=(*S*1+*S*2+*S*3)−*S*0

where S1 is the area of triangle OAB, S2 is the area of triangle OBC, S3 is the area of triangle OCA, and S0 is the area of triangle ABC. **201** corresponding to triangle ABC, i.e., S1+S2+S3=S0 if and only if the distance between point O and surface **201** is zero. In terms of the target function F, the collision surface for a propagation ray is the first surface that produces a target function value of zero as the ray propagates. Accordingly, one embodiment of surface selection block **164** (**131** propagates forward.

**164** for determining the collision surface of a propagation ray **131** (

The flow diagram blocks illustrated in **301**) for determining an initial slope of a target function plot for a collision-eligible surface, a filtering block (block **302**) for discarding certain surfaces based on their initial slopes, an estimation block (block **304**) for estimating a collision distance for a particular surface, a prioritizing block (block **306**) corresponding to operations for sorting or otherwise processing collision-eligible surfaces, a simulation loop block (block **307**) for determining a target function minimum for the current surface, and an identification block (block **320**) for identifying the collision surface for the present propagation ray.

The simulation loop block **307** illustrated in **310**) for selecting the collision-eligible surface with the shortest estimate collision distance, a minimum target function value block (block **312**) for calculating the minimum target function value of the current propagation ray with respect to the current collision-eligible surface, a decision block (block **314**) for determining whether the minimum target function value is zero (0), and a discard block (block **318**) for discarding surfaces that yield minimum target function values greater than 0.

The surface selection block **164** illustrated in **301**) initial slopes of target function plots associated with each collision-eligible surface, i.e., each surface that remains after the prescreening of surfaces performed in surface filtering block **162** (**351** for each of five collision-eligible surfaces, while in actual practice, the number of collision-eligible surfaces is likely to be significantly larger. Each target function plot **351** graphs the target function value F(A,B,C,O) of a propagation ray vs a distance parameter D representing the distance the propagation ray has traveled from its original position. An initial slope of each target function plot **351** is determined by calculating the target function difference, which corresponds to the difference between the propagation ray's initial target function value **353**, i.e., the propagation ray's target function value at D=0, and the propagation ray's delta target function value **355**, i.e., the propagation ray's target function value at D=dx, where dx is a small value. In one exemplary embodiment, a value equal to 10% of the applicable wavelength is used for dx. Other embodiments may, however, use larger or smaller values. The slope of the line connecting each initial target function value **353** and its corresponding delta target function value **355** represents the initial target function slope.

Returning to **302**) because a positive slope indicates that the corresponding propagation ray is moving away from the applicable surface. Referring to the exemplary set of target function plots **351** in **351**-**1** can be eliminated as a collision surface candidate because the initial slope of target function plot **351**-**1** is positive, i.e., the distance between the ray and the surface associated with target function plot **351**-**1** increases as the ray propagated away from its original position.

The surface selection block **164** illustrated in **304**) a distance, referred to herein as the collision distance estimate DO, where DO represents the value of D at which a linear extrapolation of the target function plot **351** intersects the D axis of plot **350**, i.e., the distance at which the target function value reaches zero along the linear extrapolation of the line between the initial target function value **353** and the corresponding delta target function value **355**.

The collision surface candidates, i.e., all collision-eligible surfaces remaining after discarding surfaces in block **302**, are then prioritized or sorted (block **306**) according to their collision distance estimates DO. The surface selection block **164** illustrated in **307** in which the collision surface candidate having the lowest collision distance estimate DO is selected (block **310**) for ray propagation simulation.

Ray propagation simulation for the selected surface is then performed by calculating a target function value for incremental positions of the applicable ray to identify (block **312**) a minimum target function value, Fmin, for the selected surface. Because the target function value decreases monotonically as a propagation ray approaches a particular surface and increases monotonically once the propagation ray collides with or passes by the particular surface, Fmin is the last target function value calculated before an increase in target function value is detected. Thus, if a sequence of incremental distances for a propagation ray is denoted as D(1), D(2), . . . , D(n−1), D(n), . . . , then:

*F*min=*F*(*A,B,C,D*(*x*)) where *F*(*A,B,C,D*(*x−*1))>*F*(*A,B,C,D*(*x*))<*F*(*A,B,C,D*(*x+*1))

Once Fmin is identified, the surface selection block **164** illustrated in **314**) whether Fmin equals zero is made. If the Fmin for a selected surface is zero, the selected surface is identified as the collision surface (block **320**). Conversely, if Fmin is positive, the propagating ray did not collide with the selected surface and the selected surface may be discarded (block **318**) as a collision surface candidate.

**361**-**1** through **361**-**5**. Each fully enumerated target function plot **361** corresponds to one of five collision-eligible surfaces and indicates the applicable surface's target function value for each incremental distance of the applicable ray. Comparing **351**-**5** in **361**-**4** is identified as the collision surface. Specifically, although the surface associated with fully enumerated target function plot **361**-**5** was the first surface evaluated as the collision surface based on the initial slope of target function plot **351**-**5** (**367**-**5**. The surface associated with fully enumerated target function plot **361**-**4** was subsequent identified as the actual collision surface when the Fmin value (**367**-**4**) for target function plot **361**-**4** was found to be zero.

**162** (**164** (

In **201** is performed and all surfaces **201** are considered collision-eligible surfaces that must be processed via surface selection block **164** (

**201** is identified as either a collision-eligible surface or a collision-ineligible surface with respect to the propagation ray based on the propagation ray's velocity vector **371** and a displacement vector (not illustrated explicitly), where the displacement vector indicates the position of the applicable surface **201** relative to the propagation ray's initial position (x0, y0, z0). In at least one embodiment, a surface **201** is identified as a collision-eligible surface if the coordinates of the displacement vector and the coordinates of velocity vector **371** have the same sign. If, as an example, the velocity vector **371** for a particular propagation ray has a positive y-coordinate value, any surface **201** positioned wherein the displacement vector has a negative y-coordinate value is a collision-ineligible surface because the propagation ray is moving away from the surface in the y-direction. This example is illustrated in **371** with a positive y-coordinate value. The positive y-coordinate value of velocity vector **371** renders all surfaces positioned in a “negative y direction” with respect to initial position (x0, y0, z0), collision-ineligible. Collision-ineligible surfaces **373** are illustrated in

The filtering of surfaces described in the preceding example can be expanded to filter surfaces based on any two of the three coordinates or based on all three coordinates. **371** has a positive value y-coordinate and a positive value z-coordinate. Therefore, any surface positioned wherein its displacement vector has a negative value y-coordinate or a negative value z-coordinate is collision-ineligible. Collision ineligible surfaces **375** are illustrated in

The coordinates of the three points defining each surface have maximum and minimum values in the x, y, and z planes and the filtering illustrated in **371** has a positive value y-coordinate. To filter only those surfaces that have zero probability of being the collision surface, the displacement vector may be defined in accordance with the surface's maximum y-coordinate value (ymax). If the ymax displacement vector has a negative value y-coordinate, then the entire surface is negatively positioned in the y-direction with respect to the propagation ray's initial position (x0, y0, z0) and, because the propagation ray is moving in a positive y direction, the propagation ray cannot collide with the surface and the surface can therefore be designated as collision-ineligible. By analogy, displacement vectors defined based on the maximum x-coordinate value, xmax, the maximum y-coordinate value, ymax, and the maximum z-coordinate value, zmax, may be used in the filtering of

**400** depicted in the flow diagram of

The flow diagram blocks illustrated in **401**) for loading all collision eligible surfaces, a construction block (block **402**) for constructing a first virtual box, a block (block **404**) for determining a point at which a vector associated with the propagation ray intersects the first virtual block, a construction block (block **406**) for constructing a second virtual block, and a block (block **408**) for identifying surfaces within the second virtual block as collision-eligible surfaces.

The filtering method **400** illustrated in **401**) and constructing (block **402**) a first virtual box **381** of a size that is just sufficient to enclose all surfaces or slightly bigger. In at least one embodiment, first virtual box **381** is a parallelepiped defined by the xmin, xmax, ymin, ymax, zmin, and zmax planes where xmin is the minimum x-coordinate value of all surfaces, xmax is the maximum x-coordinate value of all surfaces, and so forth. The propagation ray's velocity vector **371** is then linearly extrapolated, starting from the propagation ray's initial position at (x0, y0, z0), to calculate or otherwise determine (block **404**) an intersection point (x1, y1, z1) where velocity vector **371** intersects first virtual box **381**.

A second virtual box **383** is then constructed (block **406**) using the propagation ray's original position (x0, y0, z0) and the intersection point (x1, y1, z1) as opposing corners of the second virtual box. Surfaces **201** may then be identified (block **408**) as collision-eligible or collision-ineligible based on their respective positions relative to second virtual box **383**. Surfaces **201** that are entirely exterior to second virtual box **383** may be identified as collision-ineligible surfaces.

Table 1 below indicates exemplary times for processing a leaky antenna array using each of the four surface-filtering options illustrated in **6720** surfaces, Option 2 required less than 50% of the time required to process the antenna array via Option 1, while Option 3 required just 35% of the processing time required by Option 2, and Option 4 required just over 20% of the processing time required by Option 3.

**450** illustrated in **451** coupled to a flash storage device **452** to store, for example, basic I/O system (BIOS) code or the like. The CPU **451** is further illustrated coupled to memory **455**. Memory **455** may include CPU-executable program instructions, that, when executed by CPU **451**, cause system **450** to perform one or more of the operations disclosed herein including operations disclosed with respect to the flow diagrams of **451** is further illustrated coupled to one or more I/O devices **460**-**1** and **460**-**2** through a chipset device identified as I/O Hub **457**. I/O devices **460** may include, as examples, wireless and/or wireline network interface devices enabling system **450** to communicate with other systems via the Internet or one or more private networks.

The invention has been described in the context of advantageous and other embodiments and not every embodiment of the invention has been described. Obvious modifications and alterations to the described embodiments are available to those of ordinary skill in the art. The disclosed and undisclosed embodiments are not intended to limit or restrict the scope or applicability of the invention conceived of by the Applicant, but rather, in conformity with the patent laws, Applicant intends to protect fully all such modifications and improvements that come within the scope or range of equivalents of the following claims.

## Claims

1. A method of quantifying a power distribution for a wireless communication signal within a constrained environment, wherein the method comprises:

- performing first operations for each of one or more antenna slots of a leaky antenna disposed within a constrained environment, wherein the first operations include: performing surface selection operations for each propagation ray in a ray tracing model of each antenna slot, wherein the ray tracing model includes a plurality of propagation rays, wherein the surface selection operations include: screening one or more ray-reflecting surfaces with respect the propagation ray to identify collision-ineligible surfaces and collision-eligible surfaces; identifying a collision surface from the collision-eligible surfaces, wherein the collision surface comprises a first ray-reflecting surface with which the propagation ray collides; adding a power distribution component corresponding to the propagation ray to a power distribution data structure; calculating a reflected ray resulting from the propagation ray colliding with the collision surface; and responsive to determining that the reflected ray satisfies each of one or more ray eligibility conditions, performing the collision surface operations for the reflected ray.

2. The method of claim 1, wherein screening a ray-reflecting surface includes identifying the ray-reflecting surface as either a collision-eligible surface or a collision-ineligible surface based on:

- an original position of the propagation ray;

- a direction of motion of the propagation ray; and

- a surface displacement indicative of a position of the ray-reflecting surface relative to the original position of the propagation ray.

3. The method of claim 2, identifying a ray-reflecting surface as either a collision-eligible or a collision-ineligible surface includes comparing one or more coordinates of a velocity vector for the propagation ray to a corresponding one or more coordinates of the displacement vector for the ray-reflecting surface.

4. The method of claim 3, further comprising:

- responsive to detecting, based on said comparing, sign consistency between each of the one or more coordinates of the velocity vector and its corresponding one or more coordinates of the displacement vector, identifying the ray-reflecting surface as a collision-eligible surface.

5. The method of claim 1, wherein screening includes defining an eligible surfaces volume based on an initial position of the propagation ray and an enclosing volume wherein the enclosing volume is of a size sufficient to enclose the enclosed environment.

6. The method of claim 5, wherein the eligible surfaces volume comprises a cuboid and wherein a diagonal of the cuboid extends from the initial position of the propagation ray to an intersection point, wherein the intersection point comprises a point at an intersection of the propagation ray and the enclosing volume.

7. The method of claim 1, wherein identifying the collision surface comprises identifying the collision surface using a target function, wherein the target function determines a target function value indicative of a displacement between a position of the propagation ray and a ray-reflecting surface.

8. The method of claim 7, wherein the target function value is zero when displacement between the propagation ray and the ray-reflecting surface is zero and wherein the target function value increases monotonically with increasing displacement.

9. The method of claim 8, wherein:

- the ray-reflecting surface corresponds to a triangle ABC defined by points A, B, and C;

- the position of the propagation ray comprises a point O; and

- the target function evaluates to (S1+S2+S3)−S0 wherein: S0 represents an area of triangle ABC S1 represents an area of a triangle OAB defined by points O, A, and B; S2 represents an area of a triangle OBC defined by points O, B, and C; and S3 represents an area of a triangle OCA defined by points O, C, and A.

10. The method of claim 9, wherein identifying the collision surface includes:

- calculating initial slopes of target function plots for each collision-eligible surface, wherein each target function plot comprises a plot of target function values versus propagation ray positions;

- identifying ray-reflecting surfaces associated with positive value initial slopes as collision-ineligible surfaces;

- for each collision-eligible surface remaining after said identifying: extrapolating each target function plot in accordance with its initial slope to identify a projected distance value for each collision-eligible surface; ordering the collision-eligible surfaces in accordance with the projected distance values; processing the collision-eligible surfaces in accordance with the ordering, wherein processing a collision-eligible surface includes: calculating a minimum target function value for the collision-eligible surface; responsive to detecting a minimum target function value greater than zero, identifying the surface as a collision-ineligible surface; and responsive to detecting a minimum target function value of zero, identifying the surface as the collision surface.

11. A system comprising:

- a central processing unit;

- a non-transitory computer readable memory including processor executable program instructions that, when executed cause the CPU to perform operations comprising: performing first operations for each of one or more leaky antenna slots disposed in a leaky antenna array disposed within a constrained environment, wherein the first operations include: performing first operations for each of one or more antenna slots of a leaky antenna disposed within a constrained environment, wherein the first operations include: performing surface selection operations for each propagation ray in a ray tracing model of each antenna slot, wherein the ray tracing model includes a plurality of propagation rays, wherein the surface selection operations include: screening one or more ray-reflecting surfaces with respect the propagation ray to identify collision-ineligible surfaces and collision-eligible surfaces; identifying a collision surface from the collision-eligible surfaces, wherein the collision surface comprises a first ray-reflecting surface with which the propagation ray collides; adding a power distribution component corresponding to the propagation ray to a cumulative power distribution; calculating a reflected ray resulting from the propagation ray colliding with the collision surface; and responsive to determining that the reflected ray satisfies each of one or more ray eligibility conditions, performing the collision surface operations for the reflected ray.

12. The system of claim 11, wherein screening a ray-reflecting surface includes identifying the ray-reflecting surface as either a collision-eligible surface or a collision-ineligible surface based on:

- an original position of the propagation ray;

- a direction of motion of the propagation ray; and

- a surface displacement indicative of a position of the ray-reflecting surface relative to the original position of the propagation ray.

13. The system of claim 12, wherein the operations include:

- identifying a ray-reflecting surface as either a collision-eligible or a collision-ineligible surface includes comparing one or more coordinates of a velocity vector for the propagation ray to a corresponding one or more coordinates of the displacement vector for the ray-reflecting surface.

14. The system of claim 13, wherein the operations include:

- responsive to detecting, based on said comparing, sign consistency between each of the one or more coordinates of the velocity vector and its corresponding one or more coordinates of the displacement vector, identifying the ray-reflecting surface as a collision-eligible surface.

15. The system of claim 11, wherein screening includes defining an eligible surfaces volume based on an initial position of the propagation ray and an enclosing volume wherein the enclosing volume is of a size just sufficient to enclose the enclosed environment.

16. The system of claim 15, wherein the eligible surfaces volume comprises a cuboid and wherein a diagonal of the cuboid extends from the initial position of the propagation ray to an intersection point, wherein the intersection point comprises a point at an intersection of the propagation ray and the enclosing volume.

17. The system of claim 11, wherein identifying the collision surface comprises identifying the collision surface using a target function, wherein the target function determines a target function value indicative of a displacement between a position of the propagation ray and a ray-reflecting surface.

18. The system of claim 17, wherein the target function value is zero when displacement between the propagation ray and the ray-reflecting surface is zero and wherein the target function value increases monotonically with increasing displacement.

19. The system of claim 18, wherein:

- the ray-reflecting surface corresponds to a triangle ABC defined by points A, B, and C;

- the position of the propagation ray comprises a point O; and

- the target function evaluates to (S1+S2+S3)−S0 wherein: S0 represents an area of triangle ABC S1 represents an area of a triangle OAB defined by points O, A, and B; S2 represents an area of a triangle OBC defined by points O, B, and C; and S3 represents an area of a triangle OCA defined by points O, C, and A.

20. The system of claim 19, wherein identifying the collision surface includes:

- calculating initial slopes of target function plots for each collision-eligible surface, wherein each target function plot comprises a plot of target function values versus propagation ray positions;

- identifying ray-reflecting surfaces associated with positive value initial slopes as collision-ineligible surfaces;

- for each collision-eligible surface remaining after said identifying: extrapolating each target function plot in accordance with its initial slope to identify a projected distance value for each collision-eligible surface; ordering the collision-eligible surfaces in accordance with the projected distance values; processing the collision-eligible surfaces in accordance with the ordering, wherein processing a collision-eligible surface includes: calculating a minimum target function value for the collision-eligible surface; responsive to detecting a minimum target function value greater than zero, identifying the surface as a collision-ineligible surface; and responsive to detecting a minimum target function value of zero, identifying the surface as the collision surface.

**Patent History**

**Publication number**: 20190380044

**Type:**Application

**Filed**: Jun 6, 2018

**Publication Date**: Dec 12, 2019

**Applicant**: BAYLOR UNIVERSITY (Waco, TX)

**Inventors**: Jonathan HU (Woodway, TX), Liang DONG (Woodway, TX), Yang LI (Waco, TX)

**Application Number**: 16/001,415

**Classifications**

**International Classification**: H04W 16/22 (20060101); H04B 17/391 (20060101);