System and method for geospatial planning of wireless backhaul links

Aspects of the subject disclosure may include, for example, calculating a Fresnel zone about a line of sight (LoS) between a pair of antennas positioned on antenna mounts. The Fresnel zone is projected onto a geospatial grid of 3D cells, each having a height above a horizontal plane. Cells that intersect the Fresnel zone projection are selected to obtain a subset cells with constraint heights determined according to heights of the subset cells that are adjusted according to the Fresnel zone. The LoS is revised according to an algorithm to obtain a set of updated LoS. Those updated LoS that do not intersect the set of adjusted constraint heights are identified as solutions that include an optimal solution, should one exist. Other embodiments are disclosed.

FIELD OF THE DISCLOSURE

The subject disclosure relates to a system and method for geospatial planning of wireless backhaul links.

BACKGROUND

Telecommunication networks are facing a rapidly growing demand for network services. Internet applications like live broadcast, teleconferencing and streaming media are increasing the load on network infrastructures, which leads to a continuous requirement for network upgrades. For example, the deployment of 5G is expected to accelerate this process by further increasing the traffic rate of cellular networks. To cope with that, new cellular towers are connected to the network and new 5G antennas are deployed.

A backhaul network or link of a telecommunication network typically consists of Fiber-optic links between towers, but the deployment of optical fibers is slow and expensive, especially when trying to connect remote or isolated geographical places. Hence, fiber-optic links are often replaced by wireless links, such as microwave and/or free space optical transmissions between antennas located on network towers. Due to their high frequencies, microwave and/or free-space optical transmission may be formed as a narrow beam without interfering with other transmissions. Furthermore, waves in the high-frequency band of the electromagnetic spectrum, including microwaves and millimeter waves, carry much more information than low-frequency transmissions, but they are easily blocked by obstacles like buildings, foliage, and the terrain. When planning the network and positioning towers, antennas and transceivers, each connected pair of transmitter and receiver should have a line of sight (LoS) between them, and preferably without any obstruction within a first Fresnel zone about the LoS.

DETAILED DESCRIPTION

The subject disclosure describes, among other things, illustrative embodiments for systems and methods adapted for efficiently computing antenna heights for wireless communication links while maintaining clearance of at least a first Fresnel zone to identify solutions that optimize antenna heights. Other embodiments are described in the subject disclosure.

One or more aspects of the subject disclosure include a device, including a processing system having a processor and a memory that stores executable instructions. The instructions, when executed by the processing system, facilitate performance of operations. The operations include identifying a line-of-sight (LoS) between first and second antennas, wherein the first and second antennas are positioned within first and second height regions upon first and second towers at first and second geospatial locations. A Fresnel zone is calculated about the LoS and projected onto a geospatial grid to obtain a Fresnel zone projection. The geospatial grid comprises three-dimensional (3D) cells, each 3D cell having a base area within in horizontal plane and a height above the horizontal plane, and wherein the first and second antennas mounted upon the horizontal plane. A subset of the 3D cells are determined as those cells of the geospatial grid intersecting a projection of the Fresnel zone upon the horizontal plane. A set of constraints is generated according to the Fresnel zone projection, wherein the constraints comprise a set of constraint heights obtained from the subset of the 3D cells within a vertical plane containing the first and second towers. The set of constraint heights are adjusted according to the Fresnel zone to obtain a set of adjusted constraint heights within the vertical plane containing the first and second towers. The LoS is updated according to an LoS adjustment strategy to obtain a set of updated LoS. The operations further include identifying a subset of LoS of the set of updated LoS that do not intersect the set of adjusted constraint heights, wherein the subset of the LoS comprises an optimal solution, should one exist.

One or more aspects of the subject disclosure include a process that identifies, by a processing system including a processor, a line between first and second antennas, wherein the first and second antennas are positioned within first and second height regions upon first and second towers at first and second geospatial locations. The process further includes calculating, by the processing system, a Fresnel zone about the line and projecting, by the processing system, the Fresnel zone onto a geospatial grid to obtain a Fresnel zone projection. The geospatial grid includes three-dimensional (3D) cells, each 3D cell having a height above a horizontal plane, wherein the first and second antennas are mounted upon towers extending vertically upward from the horizontal plane. The process further includes selecting, by the processing system, cells of the geo spatial grid that intersect a projection of the Fresnel zone upon the horizontal plane to obtain a subset of the 3D cells and determining, by the processing system, a set of constraint heights according to heights of the subset of the 3D cells, the set of constraint heights located within a vertical plane containing the first and second towers. The set of constraint heights are adjusted, by the processing system, according to the Fresnel zone to obtain a set of adjusted constraint heights within the vertical plane containing the first and second towers. The LoS is adjusted according to an LoS adjustment criterion to obtain a set of updated LoS. The process further includes identifying, by the processing system, a subset of LoS of the set of updated LoS that do not intersect the set of adjusted constraint heights, wherein the subset of the LoS comprises an optimal solution, should one exist.

One or more aspects of the subject disclosure include a non-transitory, machine-readable medium, including executable instructions that, when executed by a processing system including a processor, facilitate performance of operations. The operations include calculating a Fresnel zone about a line between first and second antennas, wherein the first and second antennas are positioned within first and second height regions upon first and second antenna mounts at first and second geospatial locations. The Fresnel zone is projected onto a geospatial grid to obtain a Fresnel zone projection, wherein the geospatial grid comprises three-dimensional (3D) bins or cells, each 3D cell having a height above a horizontal plane, and wherein the first and second antennas are mounted upon towers extending vertically upward from the horizontal plane. Cells of the geospatial grid that intersect a projection of the Fresnel zone upon the horizontal plane are selected to obtain a subset of the 3D cells, and a set of constraint heights are determined according to heights of the subset of the 3D cells, the set of constraint heights located within a vertical plane containing the first and second antenna mounts. The set of constraint heights are adjusted according to the Fresnel zone to obtain a set of adjusted constraint heights within the vertical plane containing the first and second antenna mounts. The LoS is varied according to an LoS adjustment algorithm to obtain a set of updated LoS. A subset of LoS of the set of updated LoS are identified that do not intersect the set of adjusted constraint heights, wherein the subset of the LoS comprises an optimal solution, should one exist. In at least some embodiments, testing includes determining whether at least a first 3D Fresnel zone defined about the LoS is intersected by any of the 3D cells, such that the optimal solutions may also be free from any obstructions within at least the first 3D Fresnel zone.

Planning and optimization of radio networks has been studied in many papers. Planning the topology of networks has been investigated for cellular networks, long-range WiFi, and microwave links. Deployment of microwave links for non-line-of-sight cases has also been explored. Various data management tools were developed for managing and querying the topology of communication networks. However, while the focus of these papers is on planning the network topology, or querying it, they do not show how to effectively test the viability of a wireless link between towers, from a geospatial perspective, how to manage the geospatial data, and how to apply such tests at a large scale, e.g., testing that the LoS between a receiver-transmitter pair is not obstructed, while considering Fresnel zones.

Others have studied the selection of locations for antennas and microcells in cellular networks, by focusing on a theoretical optimization problem of how to create an optimal cellular network while satisfying graph properties like connectivity. For example, Ben-Shimol et al. studied the CMBS (Connecting Multiple fixed access Base Stations) problem: Given a terrain and a set of base stations, connect all the base stations in that set by positioning the smallest possible set of relay stations while considering the terrain properties. CMBS and other positioning problems are NP-hard. CMBS is also MAX-SNP-hard so there is no approximation algorithm for it. Thus, these papers at best present heuristics for the antenna-positioning problem, e.g., heuristics for the Steiner Tree Problem by computing a Minimal Spanning Tree.

These approaches, however, focus on a creation of the topology for wireless networks and not on large-scale LoS computation and they do not show how to compute optimal antenna heights for a pair of antennas. Computing visibility between given objects by testing LoS has received attention over the years, e.g., studying LoS over raster Digital Terrain Model (DEM) and topological surfaces. For example, Franklin and Ray studied visibility methods over a raster terrain. De Floriani and Magillo showed how to compute different types of LoS for points, lines, and regions. De Floriani et al. studied a problem very related to the one we are studying—positioning transceivers based on visibility; however, their study does not show how to handle Fresnel zones or how to compute optimal heights for receivers and transmitters.

The systems, processes and machine-readable instructions disclosed herein present a solution to large-scale wireless link planning, by exploiting geospatial data management methods. Namely, the disclosed techniques address efficient computation of optimal heights for the antennas. The disclosed techniques include computations that consider clearance of two-dimensional (2D) and/or three-dimensional (3D) Fresnel zones. Further, the disclosed techniques may be executed over a large-scale geospatial database. Results have been obtained for and tested over an entire area of continental USA. The disclosed techniques further address management of geospatial data by combining a database management system with the disclosed algorithms.

Microwave backhaul links are often used as wireless connections between telecommunication towers, and particularly in places where deploying optical fibers is impossible or too expensive. The relatively high frequency of microwaves increases their ability to transfer information at a high rate, but it also makes them susceptible to obstructions and interference. Hence, when deploying wireless links, there are two conflicting considerations. First, the antennas height, selected from the available slots on each tower, should be as low as possible. Second, there should be a line of sight (LoS) between the antennas, and a buffer around the LoS defined by a first Fresnel zone should be clear of obstacles. The LoS can be represented by a straight line between the two ends of a backhaul link. The line is straight but extends over a curved earth that may include terrain elevation variations and/or other potential obstructions, such as buildings, trees, billboards, bridges, and the like. Thus, a planning system for wireless links may include managing geospatial information regarding elevation and obstacles between the towers, and executing Fresnel-zone clearance tests, e.g., over a 3D model of a deployment area.

Disclosed herein are examples of systems, processes and non-transitory machine-readable instructions adapted for computing height of antennas by testing LoS and clearance of Fresnel zones. The systems, processes and/or software are adapted to process enormous geographic regions, e.g., covering all of the USA, at significant distances between towers, e.g., up to 80 kilometers or more. In at least some applications, application of the disclosed techniques may produce results within a few minutes for up to thousands of pairs of antennas, e.g., in a batch mode operation. The disclosed techniques provide efficient computation of antenna heights that permit effective modeling and management of large-scale geospatial data as would be necessary for network operation, maintenance, and planning, under real-world conditions.

Given two antennas, a Fresnel zone is a buffer shaped as a prolate spheroid around the LoS, as illustrated inFIG.2D. Its radius changes as a function of the distance from the antennas and the frequency of the transmission. It is maximal at the center point—the point that is equidistant from both antennas—and gets smaller while moving away from the center point. When deploying a transmitter-receiver pair, or two transceivers, at least a first Fresnel zone around the LoS must be clear of obstructions.

Many considerations are involved in the planning of the network and the deployment of the wireless links between towers, including tower locations, available space on the towers, tower-height limits, transmission frequencies and geospatial obstructions in the area. Without proper tools, network engineers must visit potential tower locations and examine manually if a deployment is possible in that location. Any process that relies on site visits is expensive, slow and does not scale. The techniques disclosed herein offer assistance to network planners by reducing a need for field visits.

Given a pair of towers that should be linked, a planning system computes heights for antennas on those towers. Planning antenna heights includes a balancing two conflicting goals. On the one hand, it is impossible to install all the antennas at the highest slot, so the goal is to position antennas as low as possible, to reduce installation and maintenance costs. On the other hand, for each transmitter-receiver pair, their height should guarantee LoS and clearance of the Fresnel zone around the LoS. Note that the antenna height is restricted by the tower height and that there is often a tradeoff—a higher height on one tower might allow lowering the height on the other tower, while maintaining LoS, and vice versa. Hence, an optimal (or effective) deployment may be defined, and corresponding antenna heights computed accordingly.

Application of the techniques disclosed herein to the planning of backhaul links offers numerous contributions. For example, the techniques include novel methods for testing LoS and Fresnel zone clearance for towers that are far from one another. Alternatively or in addition, novel algorithms are introduced for computing optimal antenna heights for pairs of towers. (3) The techniques may be embodied in a system for planning wireless backhaul links, that demonstrate effective management of the geospatial data for supporting large-scale planning. In particular, the disclosed techniques address the challenges involved in implementing a planning systems that are capable of efficiently testing LoS for distances of 80 kilometers (50 miles) or more, over a real-world elevation model of a substantial geographic region, such as an entire country, e.g., the entire continental USA.

In at least some embodiments, the communication system100includes a geospatial analyzer180adapted to analyze LoS backhaul links according to the techniques disclosed herein based on antenna tower locations, antenna height ranges and geospatial data. The communication system may include a geospatial data storage system183, such as a database management system. The geospatial data storage system183may store geospatial data including one or more of terrain elevations, descriptive and/or heights of natural and/or artificial structures overlaying a geospatial grid. The geospatial data storage system183may store antenna mounting structure location, such as tower locations, types, heights, owners, and information regarding other antennas as may already be installed on the towers. In at least some embodiments, the communication system100may include a user interface182adapted to facilitate user interaction with the geospatial analyzer, e.g., accepting user input identifying backhaul links, such as endpoints, intermediate points, tower locations, frequency bands of operation, and the like. The user interface182may include a graphical interface portion adapted to display graphical information, such as maps, tower locations, LoS links, Fresnel zones, 3D grid information, and analysis results.

One or more of the broadband access terminal112or the data terminals114, may include a Geospatial analyzer client190a,190b, adapted to facilitate LoS link analysis in cooperation with the geospatial analyzer180according to a client-server architecture. Likewise, one or more of the media terminal142or the display devices144, e.g., smart display devices, may include a Geospatial analyzer client194a,194b, adapted to facilitate LoS link analysis in cooperation with the geospatial analyzer180according to a client-server architecture. In at least some embodiments, one or more of the media mobile devices124, including smart devices, e.g., according to an Internet of Things, or vehicles126, e.g., may include a Geospatial analyzer client192a,192b, adapted to facilitate LoS link analysis in cooperation with the geospatial analyzer180according to a client-server architecture.

FIG.2Ais a block diagram illustrating an example, non-limiting embodiment of a LoS analyzer system200functioning within the communication network100ofFIG.1in accordance with various aspects described herein. The example LoS analyzer system200includes an LoS evaluator module201adapted to implement one or more algorithms adapted to identify optimal LoS solutions. The LoS analyzer system200further includes an LoS server202, a tile server204and in at least some embodiments, a tile preprocessor205(shown in phantom). In at least some embodiments, the LoS analyzer system200includes a database management system (DBMS)203adapted to store and/or serve supporting information, such as geospatial data, terrain maps, elevation data, possibly, analysis results, whether there be a solution or not, possibly including interim results, such as LoS calculations, Fresnel zone calculations, precalculated terrain elevation points and the like. Without limitation, the DBMS203may be replaced with any suitable storage system adapted to store and retrieve supporting information, such as a storage device, e.g., a hard disk drive, a flash drive, and the like.

It is envisioned that the LoS analyzer system200may include a user interface207, e.g., a local and/or remote operator console at which a network planner may select input values, such as one or more of definitions of link endpoints, towers, antennas, operating frequencies or wavelengths, data rates, customer identities, and so on. In at least some applications, the operator may select which algorithms to be applied, and/or which order multiple algorithms may be applied, and so on. In at least some embodiments, the LoS analyzer system200may be implanted according to a client server module, in which the LoS evaluator hosts a server application servicing client applications, such as the user interface207for one or more other subscribers208.

According to the illustrative embodiment, the DBMS203is in communication with the LoS server202and the tile server204. The DBMS203may store elevation grids and/or elevation points associated with one or more particular LoS under investigation. In at least some embodiments, the DBMS203may be in further communication with one or more of the tile preprocessor205and/or the LoS evaluator module201. To the extent preprocessing is applied, e.g., to combine elevation data with other terrain features, such as vegetation types and/or heights, building locations and/or heights, and the like, the resulting elevation points may be provided to the DBMS203to support current analyses and/or future analyses that may involve the same towers and/or operating frequencies or wavelengths. It is envisioned that in at least some embodiment, interim analysis values and/or analysis results, including indications of solutions and/or no-solutions may be provided by the LoS evaluator module201for storage at the DBMS203. In at least some embodiments, stored results may include graphical results, e.g., representations of the 3D terrain grid bins over a map with indications of possible interference and/or clearance for LoS operations of the applicable link.

In at least some embodiments, the DBMS203includes a database management system adapted to store geospatial data set used by the LoS server202and/or the LoS evaluator and/or by the Tile Server. It is understood that in at least some embodiments, the tile server204may include virtually any information retrieval and/or database management system. Examples include, without limitation, MySQL® database management systems, Oracle® database services, SQL® Server, and the like. It should be clear that the selection of PostgreSQL® database management systems. Such database management systems and/or services may be arbitrary in their application, such that selection of any particular one, e.g., for the tile server204, may be based on business considerations, rather than technical ones. In at least some embodiments, the data may be stored according to a PostgreSQL 12 (see, e.g., https://www.postgresql.org/), with PostGIS for the geospatial functionality (https://postgis.net/). It is understood that geospatial data is relatively static, hence, it may be stored according to an index, such as a clustered index, to promote efficient retrieval of data. For generality, a GiST index is described in the illustrative examples, however, it is understood that any spatial index be used. The example geospatial data uses bins of size 10×10 meters for most areas, and bins of size 1×1 meters for some urban areas, covering all of the USA and having a size of approximately 20 TB.

The tile server204may present a map, e.g., by serving Mapbox MBTiles to a client (see https://docs.mapbox.com/help/glossary/mbtiles/). The tiles may be vector tiles. By way of illustrative example, an effective storage and/or retrieval of the MBTiles, the tiles may be managed using the SQLite® downloadable software for creating searchable database to fashion an in-memory database (see, e.g., https://www.sqlite.org/). The tile server204may include a service, e.g., written in Rust, that is adapted to serve both as a static and a dynamic tile server model. A static tile server generally serves existing tiles per user request, whereas a dynamic tile server may create tiles on the fly and then serve them as needed. Such a dynamic approach reflects real-time changes in the underlying database. One or more of the tile server204, the LoS server202and the LoS evaluator may be implemented according to multithreaded processing. For example, a multi-threaded LoS evaluator may initially spans up to 50 threads, with this number being increased as needed.

The LoS server202may executes one or more backend computations. For example, the LoS server202may receive input data from a frontend and perform LoS computations, e.g., publishing results to topics, e.g., according to a publish-subscribe architecture, for frontend components to read and display. In at least some embodiments, the LoS algorithms for fixed-drain height and for min-max may be written in Python. Alternatively or in addition, any of the algorithms for antenna-height computation, such as the algorithm for min-sum, may be implemented in C, e.g., using shared libraries. It is understood that, more generally, any of the algorithms disclosed herein may be implemented in Python, e.g., using a connector module to access the database, in C, or in any other programming language.

The user interface207, or frontend may include a Web-based client, e.g., using JavaScript libraries for visualization of towers, 3D bins, terrain elevation and Fresnel zones (clearance or obstructions), seeFIG.2B. The frontend may be adapted to display an interactive map, to handle user input and/or to present LoS results. The front end may also communicate LoS data to other devices, such as the LoS evaluator module201.

One or more of the LoS evaluator module201and/or the user interface207may be adapted to host a profiler. The profiler may provide a performance monitoring function that listens to published topics in order to measure timing of LoS jobs. The other subscribers208(shown in phantom) may include one or more other various applications that can be subscribed to receive information related to the analyses, e.g., messages from a message broker in communication with the LoS evaluator module201. In at least some embodiments, the LoS evaluator module201is adapted to perform a testing function, e.g., executing experiments and/or measuring test results.

The backend component(s) may be deployed on one or more machines. One machine may be adapted to maintains a database, while the other machine is providing a Web server function that may include a module that executes the antenna-height computations (including testing LoS and Fresnel-zone clearance).

Positioning antennas on towers while examining the line of sight between the antennas requires knowledge of any geospatial obstructions that may exist between the towers. Digital surface models (DSM), sometimes referred to as a digital elevation models (DEM) provide elevation data corresponding to terrain. For example, a DSM may provide a height above sea level at different geographical points. Elevation values of the geographical points may be referenced according to their corresponding latitude, longitude pairs. Alternatively or in addition the elevation values may be indexed according to a grid structure that may, in turn, be referenced according to a predetermined reference location, such as a fixed latitude-longitude, a landmark, and/or some other suitable reference. In at least some embodiments, a DSM may be constructed according to a predefined resolution α. The grid structure may be rectangular, e.g., having square grid elements with a resolution of α=10 meters. Alternatively or in addition, the grid may be any regular polygon, such as triangular, diamond, hexagonal, and so on, and combinations thereof. It is envisioned that, without limitation, the grid elements may be regular shapes of a common size, irregular shapes of the same or similar area size and/or regular or irregular shapes of different sizes. For example, sizes may be determined according to features of a terrain, with relatively uniform terrains defined according to a relatively large grid, whereas varying terrains, e.g., hills, valleys, mountains, vegetation, buildings and so on, defined according to a finer resolution.

According to illustrative examples provided herein, a DSM may be created by a partition of an entire planning area, e.g., a state, group of states, or the entire USA, into bins of size α×α. (In practice, in different areas there could be bins of different size, according to the resolution of the geospatial data.) An elevation or height may be assigned to each bin. In at least some embodiments, the height is determined as a sum of a terrain elevation, e.g., from a DEM, and height above ground of objects, such as buildings, utility poles, bridges, and vegetation, e.g., crops, trees, vegetation. The summations may be carried over a grid of elevation values, such as elevation values over an area of exploration. For example, a terrain grid may be denoted by G, where G={(s, h), . . . } provides a set of pairs of a squared polygonal area s and height h. In at least some instances, a cell s in combinations with its corresponding height h, may be referred to as a 3D bin.

Antennas may be free standing or mounted on a supporting structure. Antenna supporting structures may include, without limitation, antenna masts or towers, utility poles, buildings, natural features, such as hills, and so on. The examples discussed herein refer to towers, but any suitable support structure may be used. A tower T has a corresponding location that may be referenced to a grid. The tower location l may be identified as a pair of longitude and latitude coordinates. At least some antenna towers may offer a range of possible antenna mounting locations. T=(l, hmin, hmax) and the minimum (maximum) height hmin(hmax) for antennas on this tower. A wireless backhaul link operating at higher frequencies, e.g., microwaves, millimeter waves, or even higher, relies on a line of sight (LoS) between each end of the link. Accordingly, the illustrative examples disclosed herein consider one or more LoS links between pairs of antenna and/or free-space optical towers. A solution may be referred to as a valid pair of antenna heights for both towers, as discussed herein below.

Given a pair of towers, a solution may include a respective antenna height for each tower, such that a direct line between the antennas does not intersect any 3D bin of a terrain grid describing ground heights and/or obstruction heights within a vicinity of the LoS link. It is understood that in at least some embodiments, a solution may include an LoS link having a Fresnel zone determined about the LoS path, such that the Fresnel zone does not intersect any 3D bin. Under certain constraints, a solution may include height of each antennas falling within applicable boundaries [hmin, hmax] defined for either or both towers. It is understood that a solution may not be available in view of one or more constraints, such as LoS path length, available tower heights and/or terrain elevations and/or obstructions, e.g., according to an applicable terrain grid G.

A solution for an LoS link between two towers, T1and T2may be denoted by sol[T1, T2] (h1, h2), a predicate that returns “True” if the pair (h1, h2) is a solution for the pair of towers T1and T2. In at least some applications, a notation sol(h1, h2) may be used when T1and T2are clear from the context.

Depending upon the details of any particular LoS link, there may be some instances in which many solutions are available, and other instances in which no solutions are available. To the extent there is no solution, an LoS analysis system adapted to perform one or more of the analyses disclosed herein may indicate one or more bins of the terrain grid responsible for any LoS limiting obstruction when the antenna heights on both towers are maximal.

Considering a pair of towers constituting ends of an LoS link under investigation, one may be referred to as a drain and the other as target. Typically, the drain is a tower that is already connected to the network and the target is a new tower. Thus, the antenna height on the drain tower is sometimes fixed. Nonetheless, there is still a need to compute the height of the antenna on the target tower.

Consider a pair of drain and target towers, Tdand Ttin correspondence. Several alternative approaches for determining optimal antenna heights are possible, of which three are described in detail herein. It may be appreciated that a goal of a solution, sometimes referred to as an optimal solution, is to install one or both antennas as low as possible. One of the illustrative solutions is referred to herein as a “fixed-drain” solution, in which a height hdof an antenna on the drain tower is fixed and cannot be changed, whereas a height htof an antenna on the target tower may vary within a range. Given the height hdof the antenna on the drain tower, an optimal fixed-drain solution may include a solution (hd, ht) such that the following condition is satisfied:
hd≤h′,for any solution(hd,h′)  (1)

Another one of the illustrative solutions is referred to herein as “min-max” solution. The min-max solution aims to reduce a height of a higher one of the drain or target antennas, with respect to a lowest available height, e.g., a base of the tower, referred to herein as hmin. For example, a solution of (40, 110), the numbers referring to a height dimension, such as meters or feet, in this case would be less desired than a solution of (60, 100), because a solution, e.g., an LoS link may be supported in which the higher antenna among the two, i.e., the antenna at 110 meters could be lowered to 100 meters in the second instance.

According to a min-max solution, let hdminand htminbe the lowest available elevations, e.g., the base elevations of the drain and target towers, respectively. An optimal min-max solution would be a solution (hd, ht), such that for every solution (hd′, ht′), the following condition is satisfied:
max{hd−hdmin,ht−htmin}≤max{hd′−hdmin,ht′−htmin}  (2)

Yet another one of the illustrative solutions is referred to herein as “min-sum” solution. In some applications, a total sum of heights may be more important that reducing a maximum height of either antenna. According to a min-sum solution, a solution having drain, target heights (40, 110) would be preferred over a solution having drain, target heights (60, 100), because the sum of heights in the first case is 150, whereas the sum of heights in the second case it is 160. An optimal min-sum solution, may be defined as a solution (hd, ht) that satisfies the following condition for every solution:
(hd′,ht′),hd+ht≤hd′+ht′  (3)

It is understood that the processes disclosed herein, such as determinations of one or more of the fixed drain, the min-height or the min-sum solutions may be performed for a single link, e.g., a single pair of drain and target towers. Alternatively or in addition, the processed may be applied to multiple links in a simultaneous, concurrent and/or sequential fashion. Evaluations of the various solutions may be referred to as a workload, e.g., having a set of pairs of drain and target with their corresponding height ranges and/or limits. When processing a workload, height may be computed for each given pair of towers, according to one or more different solution types, such as one or more of the fixed drain, the min-height and/or the min-sum solutions.

In an effort to obtain reliable solutions, the processes disclosed herein may be adapted to take Fresnel zones into account in network planning. A consequence of Fresnel zones on shortwave transmissions may include zones of destructive interference between direct and reflected electromagnetic waves, e.g., in high frequency bands of the electromagnetic spectrum. A brief description of Fresnel zones and their computation follows. Consider the antennas depicted in an example LoS link scenario230FIG.2Cand an LoS transmission from antenna A1to antenna A2having a corresponding wavelength λ. A direct beam231, going via point p and comprising the segments d1and d2, with a beam that is redirected from an obstruction, in this example, a building233, below the direct beam231. The redirected bean consists of the segments x1and x2. A shift of half a wavelength between the direct and the redirected beams leads to a destructive interference and a significant reduction in the signal strength. This happens when x1+x2=d1+d2+n·λ/2, for any odd integer n. By assigning (xi)2=r2+(di)2, for i=1, 2, the following relationship is obtained:

Note that i refers to an index to exploit the symmetry of the problem. Let zi=(r/di)2, for i=1, 2. Then,

When r<<di, we get that zi≈0. A Taylor series of the function di(1+zi)1/2around 0 yields di(1+½ zi+O(zi2)). By neglecting the O(zi2) component of the series, the following relationships are obtained:

That is,

r≈n⁢λ⁢d1⁢d2(d1+d2).(8)
The maximum radius occurs when d1=d2, that is, when the point p occurs at a midpoint of the direct beam231. An example Fresnel zone232obtained according to the foregoing relationships is illustrated about the direct beam231. The Fresnel zone232decreases when getting closer to either one of the antennas A1, A2. Note that the approximation r/di≈0 should not be applied when diis very small, e.g., occurring very close to either one of the antennas. When the point p is at one of the antennas, a radius of approximately nλ/2 may be used, perpendicular to the direct beam231and a radius of nλ/4 in a direction opposite the second antenna. Symmetry of the function may be appreciated with respect to d1and d2.

In practice, network engineers may focus primarily on a first Fresnel zone, in which n=1. It is understood, however, that applying the test with other values of n merely requires a change of the parameter and affecting the buffer width.

For a transmission frequency f, the wavelength is λ=c/f, where c≈2.997×108 m/s is the speed of electromagnetic waves in air. For example, consider two antennas located at a distance of D=20 km from each other, and a transmission with frequency f=30 GHz. Then, λ=0.01 meter and the radius of the first Fresnel zone at the midpoint is √{square root over (0.1·10,0002/(2·10,000))}≈22 meter.

It is understood that the Fresnel zone exists a a three-dimensional (3D) surface. As illustrated in the scenario235ofFIG.2D, the Fresnel zone234is represented as an ellipsoid drawn about the direct beam231, with a major axis of the ellipsoid aligned with the LoS direct beam. The Fresnel-zone radius changes according to a distance from either one of the antennas A1, A2. According to an evaluation or testing of a line corresponding to an LoS path between the antennas, given coordinates of a point below the line between the antennas, we need to know the width of the buffer above the point, based on a proper distance computation. Because the computations are on a sphere, we start by computing the angle used in the computation of a great-circle distance (see https://mathworld.wolfram.com/GreatCircle.html), i.e., the angle between vectors from earth center to given points corresponding to locations of pairs of antennas or the ends of LoS paths under investigation.

Consider two points P1and P2corresponding to antenna towers211a,211b, generally211, in which a longitude λiand latitude φiare the coordinates of point Pi, for i=1, 2, as depicted inFIG.2E. The central angel Au between the vectors from the center of a spherical earth213to the points may be represented by:
Δσ=arccos(sin φ1/sin φ2+cos φ1cos φ2cos(|λ2−A1|))  (9)

The computed distance is depicted inFIG.2E. For simplicity, it may be assumed that both towers211have the same height h. The tower locations are denoted l1and l3, whereas l2denotes a location of a point below the LoS, between the towers211. The computed distance is the distance from the antennas to point Q on the LoS. Let O denote the center of earth213. The points P1and P2are the locations of the antennas on the towers211. The point M corresponds to a midpoint between the points P1and P2. The distance between O and P1, denoted OP1, corresponds to Rearth+h, where Rearthis earth radius in point P1and h is a height of the first tower211a. Note that under the assumption of equal tower heights, OP1=OP2.

The angle ∠P1OM=Δσ/2 is computed using Eqn. 9. The angle ∠P1OQ may also be computed using Eqn. 9, over the coordinates of points l1and l2. Then, ψ=∠QOM=∠P1OM−∠P1OQ.

Referring next toFIG.2F, a case is depicted in which there is a height difference between the towers211a′,211b′, e.g., due to variations in tower construction and/or the terrain212. Let δ represent the height difference. Then, the distance P1P2may be approximated by ((P2P3)2+δ2)1/2. The angle ξ=∠P1P2P3≈arctan(δ/P2P3). Accordingly, Q1P2≈QP2/cos(ξ) and Q1P1=P1P2−Q1P2. The above computations provide for a given point l2on earth, located below the LoS, and a point Q, directly above it on the direct beam LoS, the distance between Q and the antennas on both sides. This yields the values d1and d2that may be applied to a computation of a Fresnel zone radius at that point. A distance between locations l1and l2, as described above, may be denoted as dist (l1, l2).

Example algorithms for computing LoS heights for receiver-transmitter antenna pairs are described below. In particular the example algorithms include one or more of fixed-drain solutions, min-height solutions and/or min-sum solutions. In at least some embodiments, the algorithms are applied according to a two-dimensional (2D) Fresnel zone. Alternatively or in addition, the algorithms may be modified the to address a three-dimensional (3D) Fresnel zone. A 2D Fresnel zone may be defined as a Fresnel zone buffer limited to directions down and up from the LoS, that is, an intersection of the Fresnel zone with a vertical plane that contains the LoS and a center of the earth.

According to an initial step of the computation an elevation, e.g., an elevation profile, is determined for terrain below the LoS. In at least some embodiments, the elevation profile may include data obtained from a digital terrain map and/or heights or elevations determined according to one or more items above a surface of earth within the vertical LoS plane, such as buildings, towers, trees, and the like. Referring toFIG.2G, let l1and l2correspond to locations of the towers211a,211bfor which the test is conducted, and let L correspond to a line that connects them. The towers211are positioned with respect to a grid G214. The grid214includes 3D bins of interest having a squared polygonal area s218, and a corresponding height h, (s, h) such that a squared polygonal area of interest s218intersects the line L. When L intersects s, an elevation may be denoted as (L, s)=(Lm, h), in which a point at a location lmis defined as follows. If the line L intersects s in a single point, lmmay be taken as that point. If the line L intersects s in two points, the reference lmmay be taken as a middle point between these two points of intersection. If the line L intersects s at an edge of the polygonal area s, the reference lmmay be taken as a midpoint of the edge.

According to this initial step, a set S of elevation points (points with height) is determined, where the points are on a line L that connects the towers211, exactly below the LoS, i.e., a line drawn between antennas at their respective heights on the towers. Each elevation point (lm, h) may also be represented as a line obstacle (lm, h) perpendicular to earth surface, starting from the point on the surface of earth and having length, or height h extending above the earth surface. These lines are depicted between the towers inFIGS.2H,2I,2J. According to the example 2D computation, a solution may be obtained for a given pair of towers Tdand Ttand set S of elevation points, each having corresponding heights. The set S of elevation points may be considered as potential obstructions or interferers to one or more of a LoS and/or a corresponding Fresnel-zone.

According to some applications, antenna heights may be calculated according to step-by-step processes, e.g., in which calculations may be performed according to a minimum height on both towers, or a given fixed height for the drain. Then, in subsequent each step, the LoS and/or clearance of a Fresnel zone may be computed. If the test fails, the height of the antennas may be raised on one of the sides. This LOS and/or Fresnel zone computation may be repeated iteratively until a solution is discovered. There are, however, several limitations to such an approach. First, it does not find an optimal solution and the solution depends on the increment step. Second, the computation is inefficient, because the LoS and clearance tests are conducted per each step. If, for example, the tower height is 500 meters and the step increment is 10 meters, there might be a need to conduct up to 50 clearance tests for increments on just one side and 100 tests for increments on both sides. That is, the step-by-step algorithm has O(kn) time complexity, where n is a number of points in S and k is a ratio of the tower's height to the step size. Third, an intersection of a bin with a prolate spheroid (or an ellipse) is a complex and expensive computation. Such techniques may be applied to 2D Fresnel zones, but may not provide an ability to test clearance of 3D Fresnel zones. The following example algorithms offer improvements over such techniques.

An example technique for computing a fixed-drain solution is disclosed herein. Let a drain antenna tower Tdhaving a range between minimum and maximum available antenna heights be identified by Td=hdmin, hdmax). Likewise, let a target antenna tower Tthaving a range between minimum and maximum available antenna heights be identified by Tt=(lt, htmm, htmax). Locations ldand ltare identified for the towers, as well as a set S of elevation points of terrain and/or potential interfering objects. For a fixed-drain computation, the height hdof the antenna on tower Tdis given.

Table 1, provided below, includes an example pseudo code, referred to as a 1stalgorithm. The 1stalgorithm computes optimal drain and target antenna heights (hd, ht) in a single pass over the elevation points in S. Initially, the 1stalgorithm computes a slope for a potential LoS, where a height on the target tower Tdis a minimum height (Line 1 of the example pseudo code of Table 1). Then, for each elevation point (li, hi), the 1stalgorithm computes a Fresnel-zone radius at point h (Line 4 of the example pseudocode of Table 1), adds that to the height hiand finds the slope of the LoS that would prevent intersection with that elevation point (Line 6 of the example pseudocode of Table 1). A maximal slope per all the points in S and the slope for the minimum height htminis computed. Based on this maximal slope, a maximal slope height htis computed (Line 9 of the example pseudocode of Table 1). If the maximal slope height htis above the maximal height for the target tower, i.e., ht>htmaxthere is no solution. Otherwise, the pair (hd, ht), computed with the maximal slope and representing an optimal solution for a fixed-drain scenario, is returned at the end of the loop.

When a solution is returned, it satisfies all the conditions of an optimal solution. That is, the solution of the 1stalgorithm is optimal, at least because any lower value of htwould lead to an intersection of the Fresnel zone with a bin in a location for which the maximal slope was discovered.FIG.2H, provides an illustration of different slope calculations for an example backhaul link scenario240having a first tower241aseparated from a second tower241b, by a distance D. A straight line drawn between a drain antenna at hdand a target antenna htrepresents an LoS244. An ellipse242drawn about the LoS represents an intersection of a Fresnel-zone ellipsoid with a plane containing the antenna towers and the LoS. The different slopes are computed for obstacles243determined according to the set S of elevation points that may have different heights as illustrated. The obstacle height values S may be adjusted according to the Fresnel zone242, e.g., increased by a width of the Fresnel zone, AS, determined at a location of the obstacle. A largest slope, after obstacle height values are adjusted according to the Fresnel zone, may be selected and used for computing ht. Note that the computed solution guarantees that htwould not be above hmax.

A solution of an antenna height for each tower, if available, would satisfy the conditions that a direct line between the antennas does not intersect any 3D bin, that a corresponding Fresnel zone does not intersect any 3D bin, and that the height of each antennas falls within an applicable antenna height boundaries [hmin, hmax] defined for that tower. The maximum slope solution, if one exists, represents an optimal solution for a fixed-drain scenario240, because it is the lowest height ht, at which an unobstructed LoS may be obtained taking into consideration a Fresnel zone, at least within a plane containing both towers and the LoS244. Accordingly, the optimal target antenna height may be identified by applying the slope calculations over a single pass of the obstacle height values S.

According to the example 1stalgorithm, computation requires a single pass over the elevation points in S, and it has O(n) time complexity, where n is a number of points in S, i.e., n=4 according to the simplistic example. In some embodiments, the points in S may be sorted before evaluating the different slopes. For example, the points in S may be sorted according to height at a beginning of the computation. Such a sorting of heights would allow the computation to start with the highest obstacles and then stop the computation early, i.e., before evaluating every single obstacle in the set S, if there is no solution. Although it seems intuitive, it was found that such a pre-sorting of the heights has an O(n·log(n)) time complexity, which may slow the computation compared to proceeding without a presorting. Hence, in at least some embodiments, the points S do not need to be sorted as part of the computation.

An example of another technique for determining optimal antenna heights is referred to herein as a min-max solution. The min-max approach minimizes a maximum height of either antenna of a backhaul link.FIG.2I, provides an illustration of min-max calculations for an example backhaul link scenario245having a first tower241aseparated from a second tower241b, by a distance D. A straight line drawn between a drain antenna at hdand a target antenna htrepresents an LoS249. An ellipse247drawn about the LoS represents an intersection of a Fresnel-zone ellipsoid with a plane containing the antenna towers and the LoS. As a starting point, two ends of a backhaul link, e.g., towers Tdand Tt, are identified. The towers may be located on a map or grid, e.g., according to their latitude-longitude coordinates. Give the tower locations, a set S of elevation points may be determined along a line and/or a path extending between the two towers. Initially, the slope is computed based on the minimum height of the two towers. Then, while maintaining the slope for each obstacle (the same increments on both sides), the antennas are elevated to prevent intersection with that obstacle, if needed. Note that the Fresnel-zone radius is added to the obstacle height when computing the elevation.

An example of 2ndalgorithm, the min-max algorithm, may be applied to the defined geometry and elevation points to obtain an optimal min-max solution for Tdand Tt. The example 2ndalgorithm may begin according to minimum height values of the towers, hdminand htmin, e.g., minimum heights at which any antenna may be mounted or otherwise installed. For the minimum height values, a height difference from a base or lower extent of an antenna mounting range for each tower Td, Ttis 0, that is hdmin−hdmin=0 and htmin−htmin=0. A slope may be computed whereby a vertical or height difference of the minimum heights between the towers may be determined as htmin−hdminmin, associated with a value Δy, while a horizontal, e.g., a straight-line distance between the towers, not necessarily accounting for curvature of the earth or any elevational differences may be determined as dist(ld, lt) and associated with a value Δx. A slope value, e.g., of a minimum height LoS247between the min height values at each tower, may be set according to a slope of the solution Δy/Δx and may be used in a computation of intermediate heights. Using the predetermined minimum-height slope value, a testing LoS may be determined by effectively moving the minimum height LoS247upward, away from the base, whereby distances between each antenna and its corresponding base level may be equal for both antennas. Such an equal vertical offset will ensure that a constant slope Δy/Δx is maintained.

In at least some embodiments, the 2ndalgorithm may proceed in an iterative manner, e.g., by testing elevation points along the set of elevation points S for possible interference with the LoS, considering height offsets ΔS to account for the Fresnel zone, and updating the heights htand hdwhen there is a need to increase the height to prevent intersection with an obstacle. If at some point, a height of one of the antennas, e.g., the 1stantenna at the drain tower hdaccording to the illustrative backhaul link scenario245, exceeds a maximum available height for that tower hdmax, there may still be an option to increase a height of the other antenna, e.g., the 2ndantenna at the target tower Tdaccording to the illustrative backhaul link scenario245. Should this situation occur, the 2ndalgorithm may call and/or otherwise incorporate the 1stalgorithm, by setting a height of the limiting antenna, e.g., the 1stantenna at the drain tower Td, to be fixed at its maximum value, e.g., hdmax.

First, the computed height is in the range of allowed heights, per each tower. Second, there is Fresnel zone clearance and LoS because hdand htare elevated to prevent interference, for all the points in S. Third, for any solution (h′d, h′t), if h′d<hdthen h′t>htand in this case max{h′d−hdmax, h′t−htmax}=h′t−htmin>max{hd−hdmin, ht−htmin}. Similarly, if h′t<htthen h h′d>hdand in this case max {h′t−htmin, h′d−hdmin}=h′d−hdmin>max {hd−hdmin, ht−htmin}. The computation only requires a single pass over S, so it has O(n) time complexity, where n is the number of points in S.

Once again, a solution of an antenna height for each tower, if available, would satisfy the conditions that a direct line between the antennas does not intersect any 3D bin, that a corresponding Fresnel zone does not intersect any 3D bin, and that the height of each antennas falls within an applicable antenna height boundaries [hmin, hmax] defined for that tower. To the extent there is a solution, the 1stalgorithm, called by the 2ndalgorithm, will return a valid result. However, to the extent a solution is not available or cannot be determined, a “No solution” message may be returned to the user. Likewise, if at some point, a height htof the 2ndantenna at the target tower Ttexceeds a maximum available height for that tower htmax, the 2ndalgorithm may call and/or otherwise incorporate the 1stalgorithm, with reversed roles. Namely, the target antenna height htmay be fixed and set to be htmax, while the 1stalgorithm finds a minimum value for a height of the drain antenna hd. Once again, to the extent a solution is not available or cannot be determined, a “No solution” message may be returned to the user.

In at least some embodiments, a “no-solution” result, e.g., as reported in a no-solution message may be accompanied by additional information. In at least some embodiments, one or more potential interfering elevation points in S may be identified responsive to a no-solution result. The results may be presented in a text message, a tabular form and/or in a graphical format. For example, any possible interfering points may be identified as points and/or regions on a map. An identification of the locations of any possible interferers alone or in combination with a map may allow a network planner to evaluate interferers and to identify mitigative measures, e.g., higher towers, new towers, alternative routes, and so on.

Referring toFIG.2B, a graphical display265of results of one or more of the techniques disclosed herein is illustrated. The example graphical display265shows a terrain map266. The terrain map may be a graphic, e.g., corresponding to one or more of a topological map, a road map, a geopolitical border map, a city or town planning map, and so on. Alternatively or in addition, the terrain map266may include photographic imagery as may be obtained from a drone and/or a satellite image. The illustrative example provides a bird's eye view satellite image showing vegetation, roads, and structures. More generally, the graphical display265be adapted to provide visualizations of one or more of the towers, the 3D bins, terrain elevations, and so on.

The illustrated portion of the terrain map is intersected by a LoS between two antenna towers, not shown. The LoS is a straight line between the antennas, having a first Fresnel zone defined about it. Depending upon terrain heights, the LoS and/or its first Fresnel zone may intersect one or more cells of a terrain grid. For example, the cells may encompass an area s, e.g., a square cell, with a corresponding height value h. One or more of the backhaul link planning and/or evaluation algorithms may be employed give the LoS and in view of the appropriate cells of the grid data. The grid cells may be identified as disclosed above, e.g., those cells intersecting a Fresnel zone of the LoS link projected onto the grid.

According to the illustrative example, bins of the grid that intersect, almost intersect or are far from the Fresnel zone may depicted in a distinguishable manner, e.g., according to different colors and/or shading. According to the example graphical display265, a first group of grid bins267athat intersect the Fresnel zone may be depicted as red, while a second group of grid bins267bthat almost intersect the Fresnel zone are depicted as yellow and a third group of bins267cthat is far from the Fresnel zone are depicted as green. Other bins268that are located under the Fresnel zone, but according to their heights, do not intersect with it may be displayed in yet another color, such as blue. In at least some embodiments, a user interface provides functionality allowing a link planner to adjust a display of planning data including results, e.g., by allow for adjustments including one or more of pan, rotate, zoom, colorization, and the like.

An example of yet another technique for determining optimal antenna heights is referred to herein as a min-sum solution. The min-sum approach minimizes a sum of the heights of both antennas of a backhaul link. Once again, as a starting point, two ends of the backhaul link, e.g., towers Tdand Tt, are identified. The towers may be located on a map or grid, e.g., according to their latitude-longitude coordinates. Give the tower locations, a set S of elevation points may be determined along a line and/or a path extending between the two towers. A 3rdexample algorithm may be applied to the defined geometry and elevation points to obtain an optimal min-sum solution for Tdand Tt. The example 3rdalgorithm may begin according to minimum height values of the towers, hdminand htmin, e.g., minimum heights at which any antenna may be mounted or otherwise installed.

The input consists of the drain and target towers Tdand Tt. We compute the elevation points S and then call the 2ndalgorithm, i.e., the min-max solution, with parameters Td, Ttand S for an initial solution. If the 2ndalgorithm does not find any solution, then the computation may return with a “No solution” message. To compute a min-sum solution from a min-max solution, the min-max solution may be tilted to achieve an optimal min-sum solution. See illustration inFIG.2J. Let ldbe a location of a first tower Td, with ldbeing a location of a second tower Tt, with lmbeing a location of a midpoint between them. If an obstacle from the set S of elevation points for which the height of the aforementioned min-max solution is between Itand lm, the algorithm attempts to lower a height on the second tower Tt, whereas if that obstacle is between ldand lm, the algorithm attempts to lower the height on the first tower Td. Consequently, a corresponding decrease of the height on one side is bigger than the increase of the height on the other side, such that a total sum of heights hd+htbecome smaller.

In at least some embodiments, an example of the 3rdalgorithm starts with a solution of the 2nd, min-max algorithm and tilts the slop if necessary. If the tilting point is between the first tower Tdand the midpoint between the towers lm, then the 3rdalgorithm attempts to increase hdand decrease ht, and vice versa. When increasing hd, the algorithm computes the slopes with hmaxon Tdand hminon Ttto ensure that the tilting does not exceed height boundaries (see lines 9 and 10 of the example pseudo code presented in Table 3). It then computes for each obstacle (li, hi) between the tilting point and tower Ttthe slopes of a line that goes through the top of the tilting obstacle and the top of (li, hi). A new slope, which is a tilt that satisfies all the constraints, is selected (see, e.g., line 15 of the pseudocode presented in Table 3).

If the selected constraint is between the tilt constraint and the midpoint lm, this elevation point replaces the tilt point, and the tilt is recalculated. Otherwise, the new slope is used to compute the new height values (hd, ht). Note that in each step of the loop, the tilting point gets closer to lmor the tilting ends, hence, the number of tilts is smaller than that number of points in S. Also note that each tilt decreases the sum of heights, until no decrease is possible anymore. The case where the tilting point is between tower Ttand the midpoint lmis symmetric and computed in the same way with reversed roles.

FIGS.2K and2Lillustrate tilts according to the 3rdexample min-sum algorithm, for the case where there are two tilts, i.e., the tilting point changes.FIG.2Killustrates a first scenario255in which a drain and target antenna towers Td, Ttare separated by a distance D. A straight line representing an LoS257is drawn between antennas at their respective heights on the towers, e.g., after implementing the min-max solution according to the 2ndexample algorithm. Give the tower locations, a set S of constraints or elevation points258may be determined along a line and/or a path extending between the two towers. Titling points are identified, and the tilts calculated according to the algorithm.FIG.2Lillustrates the same tower configuration, adding a Fresnel zone262about the LoS.

For each tilting point, the computation of (hd, ht) is in linear time in the size of S. At the worst case, the number of tilting points is O(n), where n is the number of points in S. However, in practice the number of tilting points is bounded, and the computation has linear time complexity in the size of S. As an optimization, elevation points may be ignored that are below the line L between hdmin, htmin, that connects the base points hdminand htminon the two towers.

According to the aforementioned 1st, 2ndand 3rdexample algorithms, solutions are determined according to testing for clearance of a 2D Fresnel zone, i.e., in a plane containing the towers Td, Tt and the LoS257. To keep the computation efficient in the case of 3D Fresnel zones, we apply a reduction of the 3D case to the 2D case. Intuitively, obstacles that are not directly below the LoS but may intersect the 3D Fresnel zone at a location not in the plane containing the Td, Tt and the LoS, are projected or otherwise moved into the same plane. Consequently, these other objects may be redrawn to appear below the LoS257, after adjusting for their respective heights. It is worth noting that the original set of elevation points S includes obstructions that fall directly below the LoS. The obstructions may extend outside of the LoS plane containing the towers Td, Tt, but their corresponding height is determined as their intersection with the LoS plane.

By way of example, and according to a first step of a computation the Fresnel zone is projected onto the ground, below the LoS. Bins (s, h) of the grid G having an area s, e.g., a squared area, that intersects the Fresnel zone projection are identified. These intersecting cells may be identified by the grid cells of G that are below the Fresnel zone. Let Lld,lt, be the line on the ground between the location ldof tower Tdand the location l1of tower T1. For each bin (s, h), if the line Lld,ltintersects s, we add to S a representative point of the intersected cell, e.g., a midpoint of the intersection segment, with the intersected segment having a corresponding height h. Alternatively or in addition, two vertexes of the intersected grid cell area s that are closest to Lld,ltmay be taken and added to the set of constraints S with heights h, if their distance from Lld,ltdoes not exceed the Fresnel zone radius at this location. In at least some instances, the midpoints and/or vertices may not be directly below the LoS. This considers potential obstructions at locations not within the LoS plane that includes the towers, but intersecting other regions of the Fresnel zone ellipsoid. Hence, given a vertex or point v that was added to s and is not below the LoS, the following steps may be applied. Referring next toFIG.2M, an adjusted point v′ may be found, which corresponds to a projection of the LoS onto the line Lld,ltat a point between the antenna towers. Note that the vertex v′ is below the LoS and in a plane perpendicular to the LoS that also contains the point v. Next, a first corresponding point223above v′ may be found on the LoS, and a radius r of the Fresnel zone computed at that point, based on a corresponding distance from the antennas. Then, for replacing a constraints in v by a constraint in v′, the height may be adjusted.

In at least some embodiments, a height adjustment may be accomplished in a manner that is illustrated in the scenario220FIG.2M, which illustrates a cross section221of the Fresnel zone ellipsoid, taken perpendicular to a corresponding LoS. According to the illustration, the LoS is perpendicular to the page, e.g., representing a cut of the Fresnel zone234(FIG.2D). Let l1and h1be a location and height of a point222above v, e.g., obtained from a terrain map and/or terrain development data. A location of v′223is represented by l2. The value d=dist(l1, l2) represents a distance between v and v′. A value x=(r2−d2)1/2may be computed and then a value of Δh=r−x determined as a difference between r and x. Accordingly:
h2=h1−Δh=h1−r+(r2−d2)1/2,  (14)

where r is the Fresnel zone radius at the point above v′.

In at least some embodiments, a geospatial data model is represented using 3D bins. Bin data may contain information about terrain, e.g., the local ground level relative to sea level and heights, e.g., local object heights relative to ground level. In at least some embodiments, a basic form of each type of bin data may be obtained from United States Geological Survey (USGS) map data. For example, a USGS Digital Elevation Model (DEM) may be used for terrain and a National Land Cover Database (NLCD) categories may be added to and/or otherwise combined with the DEM to produce heights. These are both examples of publicly available datasets, see: https://www.usgs.gov/core-science-systems/ngp-3dep/about-3dep-products-services; and https://www.mrlc.gov/data/nlcd-2016-land-cover-conus. It is understood that any other elevation data may be used in combination with and/or in lieu of these datasets, e.g., in places that are not covered by these datasets or in places where more accurate elevation data may be available.

The USGS DEM data may be available in resolutions as fine as a 1-meter grid, but presently the fine-resolution dataset does not provide complete nationwide coverage. In the interest of uniformity, terrain bin data may be determined according to ⅓ arc-second data, e.g., roughly 10-meter resolution, which is presently available in the U.S. with nationwide coverage. The NLCD data also comes in approximately 10-meter resolution, and is nationwide, so it is a suitable adjunct to the DEM data to produce a nationwide Digital Surface Model (DSM). According to the USGS, the vertical accuracy of the DEM is within 3 meters, with 95% confidence, whereas the NLCD is categorical data with accuracy that is considered to be between 71% and 97%.

Both sets of data are presently available in a raster format, which may be pre-processed for storage in an alternative format, e.g., as a partitioned PostGIS table with clustered geospatial indexing. Accordingly, the contiguous 48 USA states may be covered by 944 geospatial cells (USGS DEM), each containing as many as 100 million bins (or reference points). The NLCD comprises 8 billion geospatial reference points. A resulting database formed in this manner would represent approximately 12 TB of data, including the index information.

Alternatively or in addition, as a further optimization, the same terrain and height information may be stored in shared objects (shared library) on a solid-state drive (SSD). For example, a shared object may be created per each 1°×1° of latitude and longitude, including all of the 3D bins in an applicable area. Since indexing is inherent in the shared object structure, this storage is also quite compact (180 GB for DEM, 180 GB for NLCD).

Additional refinements to this approach are also available. For example, information that may be considered better, even if it is not nationwide, may be referenced as part of a hierarchical retrieval allowing better data to be used wherever it is available. This form of hierarchical retrieval may be done with proprietary terrain and height data providing results that are more accurate (more reliable and/or more recent) and have finer granularity, e.g., 1 meter resolution instead of 10 meters. At present, such data is mostly available for large metropolitan areas. It could also be done with the higher resolution (1-meter) USGS DEM data, if needed.

Referring next toFIG.2N, an example LoS scenario270is illustrated in which an LoS link is analyzed between first and second tower T1, T2. The first tower T1has a first antenna location range extending from a minimum height of h1minto a maximum height of h1maxand the second tower T2has a second antenna location range extending from a minimum height of h2minto a maximum height of h2max. A number of potential obstructions, referred to as constraints271, are located between the towers.

Let the points272in a set S represent the tops of the constraints271between the towers, after adjustment to a Fresnel zone radius. Suppose that Lminis a line that connects h1min, and h2min. All the points272in S that are below the line Lminare irrelevant for the computation and may be ignored. A modified set Scmay be defined as the set S after the removal of the points below the line Lminand after adding the points on the towers T1and T2at heights h1min, and h2min. According to the illustrative example, the black vertical bars represent the obstacles or constraints271, and the red circles or points at the top portions of at least some of the constraints271are the points in the modified set Sc.

An algorithm may be defined in which relevant points of the modified set Scare identified first. Next, a convex hull277aof the points in Scis determined according to a convex hull algorithm. A second set of points C, taken from the modified points Scdefine vertices of the convex hull277a. The set of points C are represented by the vertical bars with circles or points at the top, with a black dot drawn within the circle. To the extent that an LoS solution exists for the example LoS scenario270, it may be determined according to one of multiple, e.g., three options. Should a solution exist, such as the one depicted as case270(FIG.2N), that solution would be returned. Should one of the points in C closest to the midpoint273be h1minor h2min, then a solution as presented as case278(FIG.2P) may be returned. Should there be no solutions in either or both of cases270or278, then another solution, e.g., one where a line goes via h1maxor h1max, as in case275(FIG.2O), may be returned.

According to a first option, depicted as a first scenario275inFIG.2O, a first particular line 276 is defined via a first maximum height h1maxon tower T1and a point in C, where the point is between h1maxand a midpoint273between the first and second towers T1, T2. Additionally, the first particular line 276 does not intersect an interior of a convex hull277bformed according to the points in C. This first particular line 276 represents a the line having the largest slope among all lines via the first maximum height h1maxand any point in C. This first scenario275may also apply to a symmetric case for point h2maxof tower T2and a point between h2maxand the midpoint273.

According to a second option, depicted as a second scenario270inFIG.2N, a second particular line 274 is defined via the following two points in C—the point271that is closest to the midpoint273from the right and point272that is closest to the midpoint273from the left. Additionally, the following criteria are also met: (i) the second particular line 274 does not intersect a convex hull277bformed according to the points in C; (ii) an intersection of the second particular line 274 with the first antenna tower T1is within the range defined between h1min, h1max; and (iii) an intersection of the second particular line 274 with the second antenna tower T2is within the range defined between h2min, h2max.

According to a third option, depicted as a third scenario278inFIG.2P, a third particular line 279 is determined as the line via a point h2minwhen this point is in C that is closest to the midpoint from the right. This scenario may also be applied to a symmetric case for a point h1minof tower T1and a closest point to the midpoint273from the left.

FIG.2Qdepicts an illustrative embodiment of a process280adapted for analyzing LoS links in accordance with various aspects described herein. The process280includes identifying at281a pair of towers between which an LoS link is sought. As disclosed herein, the towers may be referred to as a drain tower, Tdand a target tower, Tt. The towers Tdand Ttare identified in relation to a reference coordinate system. For example, each tower Td, Ttmay be located at a corresponding location ld, lt, which, in turn, may be identified by an x-y coordinate on a horizontal grid and/or a latitude-longitude. Each tower Td, Ttmay have an available antenna height location and/or a range of such available locations. The height values hd, htmay extend from some minimum value hdmin, htminto some maximum value hdmax, htmax. The heights may be determined according to one or more of a height of the tower, a range of heights at which antennas may be located that is less than the height of the tower, or a particular fixed height, e.g., at which an existing antenna is already mounted at.

It is envisioned that in at least some embodiments, the available range of available heights may be contiguous, e.g., extending from the minimum to maximum heights. Alternatively or in addition, the range of heights may include separate non-contiguous ranges of locations upon one or more of the towers. In at least some embodiments, the range of heights may include more than one discrete locations, e.g., of already mounted antennas and/or available mounting slots. It is understood that real estate on at least some towers may be a scarce commodity, e.g., being shared with competing applications.

Having established the endpoints of a link under analysis, an initial LoS estimate may be determined at282as a line joining the towers, without necessarily taking account of any height values. Such an LoS estimate would be sufficient to project onto a terrain grid to facilitate identification of terrain grid cells that intersect and/or are nearby to the estimated LoS. Alternatively or in addition, the LoS may be determined or otherwise calculated at282according to a pair of heights of the heights on the towers. The LoS is a straight line between the two endpoints.

The process280further includes determining Fresnel zone at283corresponding to the LoS. The Fresnel zone will depend upon a frequency and/or frequency band of operation. The Fresnel zone can be envisioned as a prolate spheroid, e.g., an ellipsoid, having its major axis aligned with the LoS. A width of the ellipsoid varies according to a location or displacement along the LoS, being widest at its midpoint.

The analyses may be determined according to a geometry of the ground and/or structures upon the ground along the LoS. In at least some embodiments, proximate geospatial data may be obtained at284. The geospatial data may include elevation data at latitude-longitude coordinate pairs, proximate geospatial data being identified according to proximity of the elevation data location in view of the LoS. For example, Geospatial data may be defined according to a square grid of area s, each area of the grid having a corresponding terrain height h. For example, obtaining proximate data may include selecting those grid tiles that intersect one or more of the LoS and/or the Fresnel zone. In at least some embodiments, the analyses may be conducted according to a buffer zone, e.g., a range extending beyond the Fresnel zone. The buffer zone may be a fixed value. Alternatively or in addition, the buffer zone may be variable, e.g., varying as a percentage of the Fresnel zone.

It is understood that locations of at least some grid cells may have additional structure that extends vertically above the ground elevation, e.g., an obstruction height that may be added to the elevation above mean sea level. Such obstructions may include natural structures, such as trees, crops, and the like. Alternatively or in addition, such obstructions may include one or more of man-made structures, such as buildings, utility poles, cables, other antenna towers, and the like. Some obstructions may be fixed, e.g., a building, whereas other obstructions may be mobile, e.g., vehicles upon a roadway, trains upon rails, shipping upon water, and the like. The set of elevation points may be determined at285as corresponding heights of each grid cell that intersects a projection of the LoS and/or that intersects a projection of the Fresnel zone alone or with a buffer, if applicable. The heights may include the terrain elevation added to an actual height of an obstruction upon the ground and/or an estimate height of such an obstruction, e.g., a max height of a vehicle for roadway applications.

A determination is made at286as to whether a fixed-drain scenario is applicable. To the extent at least one of the antenna towers offers only a fixed height, a fixed-drain scenario may be appropriate. To the extent the fixed-drain scenario applies, a fixed-drain algorithm is performed at287. The fixed drain algorithm may include an algorithm according to the pseudo code of Table 1. A determination is made at288as to whether a fixed-drain solution exists. To the extent a solution does exist, the solution results may be presented at289to a user, e.g., a network engineer, an analysist, and/or network operation and maintenance personnel. Presentation of the solution results may include one or more of a simple message or statement confirming the existence of a solution, a height value, or height values, a frequency or wavelength at which the results were accomplished, tower locations, and the like. In at least some embodiments, presentation of the solution results may include graphical results, e.g., showing the 3D grid cells with a color coding suggesting the link would be operable at the solution height(s).

To the extent a solution does not exist, the “no solution” results may be presented at290to the user. Once again, presentation of the solution results may include one or more of a simple message or statement confirming the lack of an available solution for the prescribed scenario, a height value, or height values, a frequency or wavelength at which the results were accomplished, tower locations, and the like. In at least some embodiments, presentation of the no solution results may also include graphical results, e.g., showing the 3D grid cells with a color coding to facilitate identification of those cells at which the elevation points interfered with LoS operation.

Application of the fixed-drain solution may be performed in a single pass, e.g., considering elevation heights of the set of elevation points and performing no more than one calculation for each elevation point. A solution indicates that an unobstructed LoS is possible for the prescribed terrain, with the variable height being the lowest height in a range of variable heights of the target tower.

To the extent it was determined at286that a fixed-drain scenario is not applicable, the process280may perform a min-max algorithm at291. The min-max algorithm may include an algorithm according to the pseudo code of Table 2. A determination may then be made at292as to whether a min-sum solution should be performed. To the extent it is determined at292that a min-sum solution should be performed, the process280may continue by performing a min-sum algorithm at293. In at least some embodiments, the min-sum algorithm may include steps according to the pseudo code of Table 3. A determination may then be made at288as to whether a min-sum solution exists. To the extent a min-sum solution does exist, the solution results may be presented at289and to the extent a solution does not exist, a no-solution result may be presented at290.

To the extent it is determined at292that a min-sum solution should not be performed, a further determination may be made at294as to whether the fixed drain algorithm should be run. For example, if a solution is not obtained for the min-max algorithm performed at291, the process280may continue by performing a fixed-drain algorithm at287. In such instances, a height at one of the towers Td, Ttwould have reached its maximum value without there being a solution according to the min-max algorithm. In such instances, a fixed drain height of the fixed drain algorithm may be set to the corresponding max height, understanding it may be the drain of the target. The fixed-drain algorithm would then be run at287and a determination made at288as to whether a solution was obtained. Likewise, to the extent a determination was made at294that the fixed drain algorithm should not be run, the process280also proceeds to step288to determine whether a solution exists. To the extent fixed drain solution does exist, the solution results may be presented at289and to the extent a solution does not exist, a no-solution result may be presented at290.

Experiments have been conducted to evaluate the system, that illustrate computation times with the settings described hereinabove. The experiments were designed to examine effects of different parameters on computation time. Examples of at least some of the parameters considered include a comparison of running times for height computation using different algorithms. According to observed test results, a retrieval time refers to a time taken to select and retrieve relevant bins from a database, whereas a computation time refers to a time taken to compute optimal antenna heights after retrieval of the bins. When testing Fresnel zone clearance in a 3D setting, the number of bins that participated in the test was much larger than the number of bins that are examined in a 2D setting, an effect also observed with respect to the computation times.

Other variants investigated included the effect of caching. For example storing information in a cache memory rather than bringing the data from a database, which typically helped speed up computations. Computation time was observed according to further variants included effects of distance between the towers, transmission frequency as it affects the Fresnel zone.

A simple algorithm that for a given pair of towers, Tdand Tc, incrementally tests LoS and clearance of the Fresnel zone was used as a baseline. It started with hd←hdminand ht←htmin. In each step, it tested a clearance of the Fresnel zone with respect to a given obstacles, e.g., obstacles retrieved via 3D bins of the grid. If there was no clearance, the lower height among hdand ht(or one of them, arbitrarily, if they are equal) is raised by an incremental value, e.g., 5 feet. The process was continued until a clearance of the Fresnel zone was obtained, or one of the heights exceeded a maximum height (hd>hdmaxor ht>htmax). This baseline algorithm was referred to as a step-by-step computation.

The step-by-step computation typically had an average error that was found to be about half the size of the step. Decreasing the step size improved the accuracy but increased the running time, and vice versa. For example, when applying the step-by-step algorithm to towers with a height of 300 feet using a step size of 20 feet, the expected error is of 10 feet, and approximately 30 steps were required to discover that there is no line of sight between the towers. For a step size of 10 feet, the error was around 5 feet, but about 60 steps were executed before discovering that there was no LoS. In comparison, the algorithms disclosed herein compute the optimal solution according to the definitions provided above; while requiring only a single pass over the obstacles. Namely, the effect of each obstacle on the overall solution was considered no more than one time in determining an optimal solution for a give tower configuration.

Although the step-by-step algorithms are inefficient and do not compute an optimal solution, they have been used by previous systems for computing antenna heights, as part of wireless backhaul planning. Hence, the step-by-step computation provided a suitable benchmark.

To test performances of the novel system different workloads were used. Each workload included a set of pairs of towers, namely, one pair of towers, and/or many pairs of towers. The workloads investigated were synthetic tower locations with distances between towers being generated according to a random number generator, to reflect a variety of areas and distances. Note, however, that the geospatial data used for LoS tests was real. Workloads were generated as follows. the input consisted of (1) a selected number of pairs to generate, (2) a distance range between the towers of every pair, and (3) a bounding box that the generated pairs should fall inside. A random number generator was used to pick a point l1for one tower. Then, a random distance d in the given range and an arbitrary angle α were selected. The position of a second tower was a point at a distance d from l1at angle α. Due to business confidentiality, no information about the network topology was used.

The evaluations also included effects of the frequency on computation times. Running times were observed and recorded in milliseconds, e.g., using a fixed-drain algorithm as a function of a distance between the towers, for different transmission frequencies. Reported times were obtained for 3D Fresnel zones while using cache. All reported times were presented as average time over a fixed number, e.g., 10, independent runs, for a fixed number, e.g., 10, different pairs of towers.

Results indicated that computation time grew almost linearly as a function of the distance. This may be a result of a number of bins between the towers growing as a linear function of the distance between the towers. When comparing computations for towers with LoS between them and towers with no LoS between them, for the case when there was no LoS the computation was faster, because the algorithm was permitted to stop as soon as it discovers that there was no solution.

The frequency is the inverse of the wavelength, so as the frequency grows, the Fresnel zone radius gets smaller. Thus, for higher frequencies, there were less 3D bins to retrieve and process allowing the computations to be completed sooner, resulting in lower running times.

For cases in which the frequency was not given, it was determined as a function of the distance. Note that as the distance between the towers grew, the frequency decreased, while the Fresnel zone radius grew bigger. So, bigger distances require more attention to the Fresnel zone.

Computation of a 3D Fresnel zone was more expensive than computation of a 2D Fresnel zone, because more bins were involved in the computation, due to the transformation and inclusion in the computation of bins that are below the Fresnel zone but are not directly below the LoS. The effect on a running time of testing clearance of 3D Fresnel zones versus tests for 2D Fresnel zones for the case was observed for a case in which where there was no LoS, and another case in which there was LoS between the towers. As expected, computation with a 3D Fresnel zone was more expensive and affected all the algorithms. This may have resulted from many more bins being included in a computation when retrieving bins to test clearance of a 3D Fresnel zone instead of retrieving only the bins that are below the LoS.

With respect to caching, it was found that typically, cache can speed up computations significantly, because when using a cache, data are retrieved from a fast storage device like the memory instead of retrieval from the disk. To test the effect of the cache, all the experiments were executed in a cold-start mode e.g., shutting down the database management system and starting it again before the experiment, versus computation of a workload twice without shutting down the database management system between the runs. Although large machines were used with ample memory, the cache had no significant effect on the retrieval time. This result is most likely due to the very large workloads and the large-scale computations. Each set of computations fills-in the memory with new data, so the cache cannot be utilized to speedup computations.

It was observed that an existence of LoS affected the running time, because when there is no LoS the computations were permitted to terminate early. There were two steps to the computation. One step involved a retrieval of the bins. As expected, the bin-retrieval time (the time it takes to discover the relevant bins and retrieve them from the database) was not affected by the existence or lack of LoS. However, after bin retrieval, the running time was significantly affected by the existence or lack of LoS, due to the early termination in the case where there is no LoS.

In the interest of efficiency, the 3rdexample min-sum computation algorithm was implemented in C using shared libraries. Accordingly, in this algorithm retrieval time was not distinguished from computation time. A total running time for this algorithm for NYC and Nationwide workloads was obtained. Since selection and retrieval of the bins was inseparable, the effect of the existence or lack of LoS was diminished. In particular, local computations were observed to be much faster than the nationwide computations. Overall, in a local workload fewer shared objects were retrieved and processed, even for short distances, because many LoS computations were conducted over overlapping areas. In practice, planning is often executed over a restricted area, and a local workload of 5000 pairs with an average distance of 10 miles between towers takes about (5000×0.125)/60≈10 minutes. The computation times reported herein were those times obtained with particular equipment available at that time. It is understood that computation times may vary according to different equipment as may be used.

Disclosed herein are systems, processes and non-transitory, machine-readable media adapted for wireless backhaul planning. The illustrative techniques have been developed with a goal to be more accurate and faster than alternative existing systems. In an initial version of the system, there were scripts that selected and uploaded the necessary data into the database, per workload, and another script executed the computations in a naive way. In that approach, the pre-processing for about 5000 pairs was about two weeks and the computation after the pre-processing took between 40 to 60 minutes. The current system computes a workload of 5000 pairs in about 10 minutes altogether. This refers to all the steps, including bin selection and retrieval from the database. This is done while coping with a more challenging task (3D Fresnel zone computation instead of 2D Fresnel zone and more accurate distance computation).

It can be appreciated that coping with long distances between towers is challenging. There is a twofold increase in the number of bins as a function of the distance, because there are more bins between the towers but also the radius of the Fresnel zone increases. Thus, effective retrieval of bins from the database with proper optimizations is essential for efficient overall computation.

It has been observed that practicing the techniques disclosed herein affords a substantial reduction in computation time as a result of the various optimization techniques. For example, computation efficiency may result from data inserted into a database with clustered indexes and according to a compact representation. Computation efficiency may be further improved by retrieval of bins from a database in an optimized manner using a suitable bounding buffer and an index, e.g., retrieving the minimal number of bins necessary per each computation. This may be accomplished by computing a tight buffer around a projection of the Fresnel zone on a map of the terrain, e.g., the earth and retrieving only bins that are below the Fresnel zone and relevant for the computation. In at least some embodiments, the computation may be multithreaded, using efficient algorithms that permit early termination, as disclosed herein.

Referring now toFIG.3, a block diagram is shown illustrating an example, non-limiting embodiment of a virtualized communication network300in accordance with various aspects described herein. In particular a virtualized communication network is presented that can be used to implement some or all of the subsystems and functions of system100, the subsystems and functions of LoS analyzer system200, and process280presented inFIGS.1,2A-2Q, and3. For example, virtualized communication network300can facilitate in whole or in part efficient testing LoS links for clearance of Fresnel zones to identify solutions that optimize antenna heights.

In at least some embodiments, the virtualized communication network300includes a geospatial analyzer180adapted to analyze LoS backhaul links according to the techniques disclosed herein based on antenna tower locations, antenna height ranges and geospatial data. The communication system may include a geospatial data storage system183, such as a database management system. The geospatial data storage system183may store geospatial data including one or more of terrain elevations, descriptive and/or heights of natural and/or artificial structures overlaying a geospatial grid. The geospatial data storage system183may store antenna mounting structure location, such as tower locations, types, heights, owners, and information regarding other antennas as may already be installed on the towers. In at least some embodiments, the communication system100may include a user interface182adapted to facilitate user interaction with the geospatial analyzer, e.g., accepting user input identifying backhaul links, such as endpoints, intermediate points, tower locations, frequency bands of operation, and the like. The user interface182may include a graphical interface portion adapted to display graphical information, such as maps, tower locations, LoS links, Fresnel zones, 3D grid information, and analysis results. One or more of the geospatial analyzer180, the geospatial data storage system183and the user interface182may be implemented in whole or in part according to the virtualized network function cloud325, according to the cloud computing environment375. One or more of the broadband access110, wireless access120, media access140may include a Geospatial analyzer client390a,390b,390cadapted to facilitate LoS link analysis in cooperation with the geospatial analyzer180according to a client-server architecture.

Turning now toFIG.4, there is illustrated a block diagram of a computing environment in accordance with various aspects described herein. In order to provide additional context for various embodiments of the embodiments described herein,FIG.4and the following discussion are intended to provide a brief, general description of a suitable computing environment400in which the various embodiments of the subject disclosure can be implemented. In particular, computing environment400can be used in the implementation of network elements150,152,154,156, access terminal112, base station or access point122, switching device132, media terminal142, the LOS analyzer system200, and/or VNEs330,332,334, etc. Each of these devices can be implemented via computer-executable instructions that can run on one or more computers, and/or in combination with other program modules and/or as a combination of hardware and software. For example, computing environment400can facilitate in whole or in part efficient testing LoS links for clearance of Fresnel zones to identify solutions that optimize antenna heights.

Turning now toFIG.5, an embodiment500of a mobile network platform510is shown that is an example of network elements150,152,154,156, the LOS analyzer system200, a user interface207, a client device of a client-server embodiment of the LOS analyzer system200, and/or VNEs330,332,334, etc. For example, platform510can facilitate in whole or in part efficient testing LoS links for clearance of Fresnel zones to identify solutions that optimize antenna heights. In one or more embodiments, the mobile network platform510can generate and receive signals transmitted and received by base stations or access points such as base station or access point122. Generally, mobile network platform510can comprise components, e.g., nodes, gateways, interfaces, servers, or disparate platforms, that facilitate both packet-switched (PS) (e.g., internet protocol (IP), frame relay, asynchronous transfer mode (ATM)) and circuit-switched (CS) traffic (e.g., voice and data), as well as control generation for networked wireless telecommunication. As a non-limiting example, mobile network platform510can be included in telecommunications carrier networks and can be considered carrier-side components as discussed elsewhere herein. Mobile network platform510comprises CS gateway node(s)512which can interface CS traffic received from legacy networks like telephony network(s)540(e.g., public switched telephone network (PSTN), or public land mobile network (PLMN)) or a signaling system #7 (SS7) network560. CS gateway node(s)512can authorize and authenticate traffic (e.g., voice) arising from such networks. Additionally, CS gateway node(s)512can access mobility, or roaming, data generated through SS7 network560; for instance, mobility data stored in a visited location register (VLR), which can reside in memory530. Moreover, CS gateway node(s)512interfaces CS-based traffic and signaling and PS gateway node(s)518. As an example, in a 3GPP UMTS network, CS gateway node(s)512can be realized at least in part in gateway GPRS support node(s) (GGSN). It should be appreciated that functionality and specific operation of CS gateway node(s)512, PS gateway node(s)518, and serving node(s)516, is provided and dictated by radio technology(ies) utilized by mobile network platform510for telecommunication over a radio access network520with other devices, such as a radiotelephone575. In at least some embodiments, the radiotelephone575may include a Geospatial analyzer client590, adapted to facilitate LoS link analysis in cooperation with the geospatial analyzer180(FIGS.1and3) according to a client-server architecture.

Turning now toFIG.6, an illustrative embodiment of a communication device600is shown. The communication device600can serve as an illustrative embodiment of devices such as data terminals114, mobile devices124, vehicle126, display devices144or other client devices for communication via either communications network125. For example, computing device600can facilitate in whole or in part efficient testing LoS links for clearance of Fresnel zones to identify solutions that optimize antenna heights.