International Journal of Antennas and Propagation

Volume 2016 (2016), Article ID 4138329, 8 pages

http://dx.doi.org/10.1155/2016/4138329

## The Effect of Refractivity on Propagation at UHF and VHF Frequencies

^{1}Department of Electrical Engineering, Bahria University, Shangrilla Road, Sector E-8, Islamabad, Pakistan^{2}Department of Electrical Engineering, University of Engineering and Technology, Mardan Campus, Mardan, Pakistan

Received 20 June 2016; Revised 22 August 2016; Accepted 26 October 2016

Academic Editor: Larbi Talbi

Copyright © 2016 I. Alam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper is using weather parameters to investigate the effect of refractivity on propagation in the first kilometer of the atmosphere over the English Channel for a long transhorizon path of 140 km. Different refractivity profiles are constructed based on meteorological data taken from the UK Meteorological Office in order to investigate the effects of refractivity on propagation. The analysis is made for the hourly experimental path loss between the transmitter and receiver obtained from the experimental setup comprised of two communication links. The frequency of operation of the first link is 2015 MHz and that of the second link is 240 MHz. Parabolic equation method is modelled to get an hourly modelled path loss corresponding to each hourly experimental path loss to be analyzed for the said communication links. The correlation between the modelled path loss and experimental path loss is computed for refractivity distribution recommended by the ITU and predicted profiles. It is inferred from the simulated and experimental results that little or no influence exists by the evaporation duct upon path loss at 2015 MHz specifically for a long path of 140 km over the sea.

#### 1. Introduction

Radio communication links are significantly affected by highly variable propagation conditions of the atmosphere. Weather parameters can be used to predict distribution of refractivity responsible for these conditions. Assessing these variable conditions and providing a better prediction of refractivity potentially help the designers of communication, navigation, and radar systems to improve performance. Refractivity predictions are very useful in many applications of wireless communication, navigation, and surveillance systems. Such predictions are important in order to cope with the problems encountered where anomalous propagation and unpredicted path loss affect the performance of these systems. The influence of these unpredicted propagation effects is sometimes so severe that a complete communication breakdown occurs between transmitter and receiver or a radar misses its target completely. It is mandatory for a propagation engineer to take into account the deviation of the propagating wave due to the changes in the distribution of refractivity.

In this paper the phenomenon of ducting where a propagating wave trapped in the form of a duct is investigated in the first kilometer of the atmosphere over the English Channel for oversea propagation at UHF (2015 MHz) and VHF (240 MHz) frequencies in the radio spectrum. Ducting is classified into four different types with emphasis on the evaporation duct over the sea. The most important parameter to consider the effect of evaporation duct or the depth of the electromagnetic duct is evaporation duct height (EDH) which in turn determines how refractivity is affecting communication between transmitter and receiver.

The theory of the methodology used in this research for the simulation of radio wave propagation is provided in Section 2 where it is described in detail why the method of parabolic wave equation is selected. The experimental setup is provided in Section 3 while the construction of modified refractivity profiles is given in Section 4. Analysis and results from the implemented model are discussed in Section 5 with a number of cases for different EDHs for two oversea communication links. These links are labelled as “Link 1” for long path at UHF and “Link 2” at VHF. Finally, the conclusion of the work is presented in Section 6.

#### 2. Parabolic Equation Method

Different methods and techniques for measuring refractivity, for example, refractometer, radar, GPS occultation, and lidar, are in use. These methods are limited in many ways especially their practical implementation. For instance, the performance of lidar is limited by the background noise levels and high extinction conditions [1]. The parabolic equation method (PEM) was originally proposed by [2] for long range radio wave propagation in 1944. In 1946, [3] provided PEM solution to electromagnetic waves problems. In 1977, [4] decomposed an elliptical wave equation into two equations through the choice of an arbitrary constant reference wave number, one of which resulted in the development of the standard parabolic equation (also called the narrow angle parabolic equation) [5]. This technique gained popularity quite quickly and a number of researchers started using it by developing different solution methodologies [6–11]. This technique has been used for many years to model radio wave propagation in the troposphere especially over the sea.

PEM provides a reliable wave solution for the prediction of electromagnetic field in which real refractivity profiles are considered unlike the initially used rays-based solution techniques and mode theory-based solutions techniques. In contrast to PEM, ray-based and mode theory-based solution techniques like geometrical optics [12], physical optics [13], normal mode analysis, coupled mode analysis [14], and hybrid methods [15] resulted in an inappropriate solution [16].

The basic theoretical development of parabolic equation starts with the reduction of the well-known 3-dimensional Maxwell’s equations, representing the existence of a full electromagnetic wave, to 2-dimensional time harmonic Helmholtz equations in range () and altitude (). This reduction is performed under the considered “paraxial propagation domain” in which the energy of the propagating wave travels in the form of a cone having vertex at the transmitting antenna and making a small “grazing angle” (term used for angle made by the wave with the horizontal direction of wave propagation). The horizontal and vertical polarized components of the field are propagating independently inside the cone with a time dependence of where is the angular frequency of the propagating wave and is the time [17].

Generally, two methods of finite difference method (FDM) [18] and split step Fourier transform (SSFT) [19] are used to get the numerical solution of the reduced parabolic wave equation. An excellent comparative description of the two methods can be found in [20]. The first method requires huge computational resources because of getting the solution of large system of simultaneous equations in large number of unknowns and the specification of radiation boundary conditions [21] on a closed domain [22]. FDM solves the wave equation explicitly in the time domain only without dropping the carrier frequency and hence a great amount of computing time and storage is needed. In this research SSFT algorithm is chosen as it uses larger range steps, which makes it more efficient computationally.

Split step Fourier transform technique works on the principle of marching the solution forward in short steps until converged solution is obtained. In other words, the solution to the problem of interest is obtained by splitting the solution in a series of phase screens (steps) orthogonal to the direction of propagation of the field. First the initial field is propagated and then a phase screen modulated by refractive index variations is applied to it. The resulting field is then forward propagated through the medium to the next phase screen and so on. A more detailed technical mathematical derivation for this technique with its application to tropospheric propagation problems as well as its implementation by using different solution methods can be found in [17]. In order to investigate the characteristics of refractivity and its impact on wave propagation, a propagation model is developed in MATLAB using PEM. The greater details about mathematical formulation of the propagation model using PEM and having implementation in MATLAB can be found in [18–21]. The model is used to get an hourly modelled path loss corresponding to the experimental path loss for all communication links.

#### 3. Experimental Setup

The experimental setup is comprised of two long (One at UHF and other at VHF) transhorizon paths of 140 km over the English Channel. The first link named as “Link 1” is from Jersey St John’s Quarry to Portland Bill Lighthouse at 2015 MHz frequency. Similarly, the second link named as “Link 2” is from Jersey St John’s Quarry to Alderney (Isl De Raz) at 2015 MHz frequency.

The height of the UHF transmitting antenna at Jersey St John’s Quarry is 16.5 m (AMSL) and that of VHF antenna is 17.5 m (AMSL). The height of the receiving antennas at Portland Bill Lighthouse is 12 and 13.4 m (AMSL) for UHF and VHF, respectively, with vertical polarization. The experimental half power beam width of the antennas is 17°.

For each communication link a set of 6000 values of the received signal strength per hour (i.e., 25 values in 2 seconds, 4 times per minute) were recorded by both receiving antennas. The median value for each set of 6000 recorded received signal strengths is calculated which resulted in a new data set termed as an “hourly data set.” The analysis made in this work is based on the hourly data set; the reason for doing so is that the meteorological data is available in an hourly format. From the median set of hourly data experimental path loss (EPL) is calculated for each communication link according to the relation given in where is the recorded received signal strength in dBm and is the conversion factor in dBm from signal strength (dBm) to path loss (dB).

The conversion factor (CF) is used to take into consideration all the gains and losses at the transmitters, receivers, amplifiers, feeders, and so forth. The value of CF for “Link 1” and “Link 2” are 89.7 and 68.2 dBm, respectively. Conversion factor is a specifically calculated value obtained by using different parameters for each link which converts the recorded received signal strength into path loss. The formula for getting this value is given in (2). The detailed link budget and calculation of the individual parameters used in (2) is given in [24]. The values for all these parameters are tabulated in Table 1 to get a corresponding CF value for each link.where is the power of transmitting source in dBm; and are the power gains of the amplifiers at the transmitter and receiver systems in dB, respectively; and are the feeder losses at the transmitter and receiver sites in dB, respectively; and are the gains of the transmitter and receiver antennas in dB, respectively.