Path Profile for Terrestrial Line of Site Microwave Link in the C-Band

In this paper, development of path profile for 6GHz C-band terrestrial line-of-site microwave link is presented. The path (elevation) profile data set is obtained using Geocontext online elevation software. With the path profile, the minimum antenna elevation and the minimum antenna mast heights for effective line of site installation are determined. According to the results, when path inclination is greater than zero, antenna elevation is 105.873m and 88.528m at the transmitter and receiver respectively, with antenna mast height of 36.712m at both the transmitter and the receiver and critical clearance of 4.787m at a distance of 1897.626m from the transmitter. However, when path inclination is equal to zero, antenna elevation is 88.528m at both the transmitter and receiver with antenna mast height of 19.367m and 36.712m at the transmitter and receiver respectively. In this case, the critical clearance is 0 m (zero meter) at a distance of 686.641m from the transmitter.


Introduction
At high frequencies such as the microwave frequencies, adequate planning is required to ensure line-of-site between the antennas at two distant communication link endpoints [1][2][3][4][5]. In this case, some factors must be taken into consideration in order to ensure clear line-of-sight; among the factors are, the earth curvature, the Fresnel Zone clearance, the atmospheric refraction and possible obstacles on the path of the communication link [6][7][8][9]. However, "in order to determine tower heights for suitable path clearance, a pat profile must be plotted" [10][11][12].
According to Standard (1996), path profile is a graphic representation of the physical features of signal propagation path; the path profile contains both endpoints of the path and shows the elevations in the vertical plane of points between the endpoints. The path profile also shows the Earth surface along with buildings, trees, and other features that may block the radio signal [13]. Importantly, proper planning of microwave and cellular path profile can help network planners to determine accurate tower heights for the antenna in order to achieve Line-of-Sight (LOS) clearance of the first Fresnel Zone or Fresnel Radius from obstacles that are along the radio propagation path and this will improve the Quality of Service (QoS) delivery of deployed systems [1,[14][15].
In this paper, approach for generating and plotting the path profile for terrestrial line of site microwave link in presented. In order to generate the path profile for terrestrial line of site microwave link, the elevation data along the signal path is required. The elevation data is used in conjunction with the signal frequency to generate and plot the various components of the path profile. The components of the path profile includes amongst others; elevation profile, earth bulge, Fresnel zone ellipsoid, minimum transmitter antenna height, minimum receiver antenna height and the location of the critical point for maintaining clear line of site. Sample path profile data set for a C-band link at 6GHz is generated and plotted for two cases, when the path inclination is equal to zero and when the path inclination is greater than zero. The signal path (or link) elevation profile (that is, elevation and distance) are obtained using Geocontext Online Elevation software [16]. With the path profile data and graph plots, the minimum antenna elevation and the minimum antenna mast heights for effective line of site installation are determined. The path profile ideas presented in this paper is very useful for terrestrial line of site microwave network designers and researchers.

Methodology
The following steps are used in generating the path profile for a C-band terrestrial line of site microwave link between University of Uyo Town Campus at Ipka Road and the Main Campus of University of Uyo which is at Use Offort:.
Step 1: The Signal Frequency The radius of the Fresnel Zone is a functions of frequency. As such, in this study the 6 GHz (in the C-Band) is considered.
Step 2: The Location (Longitude and Latitude) Of The Transmitter and The Receiver Let and be the longitude and attitude of the coordinates of the Let and be the longitude and attitude of the coordinates of the receiver respectively. transmitter respectively. University of Uyo Step 3: The Distance Between The Transmitter and The Receiver The path length (or distance), in Km between the transmitter and receiver is determined by using the Haversine formula and the coordinates (longitude and the latitude) of the transmitter and receiver. The Haversine formula is given as: Where LAT in Radians = The Elevation Data set for the given location is generated using an Geocontext Online Elevation software [15].
The elevation data is generated by entering the longitude and latitude of the transmitter ( and ) and the longitude and latitude of the receiver ( and ) into the source and destination coordinates textboxes on the Geocontext Online Elevation software. The elevation data set generated by the Geocontext Online Elevation software [15] includes: i. Points specified by their longitudes and latitudes, ii. The start point at the transmitter (transmitter location is the first point) iii. The end or the last point at the receiver (receiver location is the last point) iv. Distance of each of the points from the starting point's longitude and latitude v. The elevation at each point above sea level as the reference plane.
Step 5: The Earth Bulge The formula for calculating the Earth bulge at a distance 6 from the transmitter and distance from the receiver is given as follows: where, = >" # Height difference of Earth's Curvature at the point x between the transmitter and the receiver (m) 6 = Distance between the point and the transmitter (km) = Distance between the point and the receiver (km) B Effective Radius of Earth (km) Note: Usually taken as (1.333 rec.)actual radius to account for atmospheric refraction i.e. B 8,504km Step 6: The Radius of the First Fresnel Zone The radius of the C D Fresnel zone at point x is given as; where k = 1,2,3,… E FG" # is the radius of the C D Fresnel zone at point x. 6 is the distance of the point from the transmitter is the distance of the point from the receiver is the distance between the transmitter and the receiver where 6 (6) ʎ is the wavelength of the signal, where; where, C =Speed of light in a vacuum (3x10 8 ms -1 ) d =Total Distance (m) f = Signal frequency (Hz) Step 7: The Maximum Height Of Obstacle In The Terrain The maximum height of obstacle (= K>L MNOP" # # is estimated from the knowledge of the terrain. In this research, the terrain within which the link is located is in Uyo metropolis. The obstacles expected in the terrain are mainly buildings. The buildings within the signal path in Uyo are mainly two storey buildings. As such, the obstacle height is estimated as 10 meters. Step Step 10: Generate the Fresnel Ellipsoid The Fresnel ellipsoid if formed around the centre of the Fresnel zone. In order to generate the Fresnel Ellipsoid, the centre line (line-of-sight) through the Fresnel zone is first generated. Then the radius of the first Fresnel zone is added to the value of the elevation at the centre line of the Fresnel zone (for the upper part of Fresnel ellipsoid) and subtracted from the value of the elevation at the centre line of the Fresnel zone (for the lower part of Fresnel ellipsoid).
Step 11: The Centre Line (Line-Of-Sight) Through The Fresnel Zone Let the elevation at the transmitter is B and the Elevation at the receiver be B , respectively.
Let the distance of the transmitter from the transmitter is and the distance of the receiver from the transmitter be .
Let the gradient (n ) of the line linking the transmitter and the receiver be defined as; The equation for the transmitter to receiver line that passes through the point ( , B F ) is given as: Where r`a (b) is the radius of the k de Fresnel zone at point x.
Step 13: The Path Inclination Path inclination | } is given as follows; where d (in Km ) is the distance between the transmitter and the receiver while = and = are in meters are the height of the transmitter and the receiver respectively.

Results and Discussions
A sample microwave link is used to demonstrate the effectiveness of the path profile algorithm presented in paper. The path profile data set and graph plots are presented for two cases; when the path inclination is equal to zero and when the path inclination is greater than zero. The results for the sample path profile studied are presented in this section 4.
Step 1: The Signal Frequency In this study, the C-band is considered and the frequency selected is 6 GHz. Step

Figure 1. Screenshot of The Google Map View Of The Location Of The Transmitter at University of Uyo Town Campus and The Receiver at the Main Campus of.
Step 4: The Elevation Data and The Elevation Profile Between The Transmitter and Receiver Some portions of the 512 records in the elevation dataset for the given transmitter and receiver location are given a in table 1. The dataset is generated using a Geocontext Online Elevation [15]. As shown in Figure 1, the transmitter is located at University of Uyo Town Campus, Ikpa Road with longitude of 7.919108 and latitude of 5.042362 while the receiver located at the Main Campus of University of Uyo, Use Offort at longitude of 7.976615 and latitude of 5.040823. The elevation profile plot for all the 512 data points in the full dataset is given in Figure 2. From Table 1 and Figure 2, the elevation at the transmitter is 69.161m (Column 5, Data Point Number 1) whereas the elevation at the receiver is 51.816m (Column 5, Data Point Number 512).  Some portions of the 512 records in the complete path profile dataset for the given transmitter and receiver location and microwave signal at 6GHz are given in Table 1. The path profile plot for all the 512 data points in the full path profile dataset is given in Figure 3. For Path Inclination (ɛp) >0 and in Figure 4. For Path Inclination (ɛp) = 0.  The link midpoint is indicated as the vertical green line in Figure 3 and Figure 4.
On the other hand, according to Table 2 Furthermore, in column 9 and column 2 of row Data Point Number 56 in table 2, the critical point for line of site has 0m clearance distance (in meters) between obstacle and the first Fresnel zone and it is located at a distance of 686.641m from the transmitter. The critical point for line of site is indicated as the vertical red line in Figure 4. The clearance distance between obstacle and the first Fresnel zone at the link midpoint (in column 2 and column 9 of row Data Point Number 250 and 251 in table 2) is above 27m.
When Path Inclination (ɛp) > 0, the transmitter and receiver antenna elevation and mast heights can be determined from the data in  In table 3, is can be seen that for Path Inclination (ɛp) = 0 antenna mast height of 36.712m is required at the transmitter and at the receiver. However, for Path Inclination (ɛp) > 0 antenna mast height of 19.367m is required at the transmitter and antenna mast height of 36.712m is required at the receiver.

Conclusion
The approach for generating and plotting the path profile data for terrestrial line of site microwave link in presented. Sample path profile data set for a C-band link at 6GHz is generated and plotted for two cases, when the path inclination is equal to zero and when the path inclination is greater than zero. The signal path (or link) elevation profile (that is, elevation and distance) are obtained using Geocontext Online Elevation software. With the path profile data and graph plots, the minimum antenna elevation and the minimum antenna mast heights for effective line of site installation are determined. Also, the critical location where the line of site condition can easily be violated is also determined. The path profile tool presented in this paper is very useful for wireless network designers.