Download attenuation in a ionospheric radio link

 ATTENUATION IN A IONOSPHERIC RADIO LINK Inês Martins Manique Instituto de Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais 1, 1049-­‐001 Lisboa, Portugal Abstract -­‐ This work addresses in the study of some relevant propagation phenomena in ionospheric radio links. The main objective is the calculation of the attenuation of a signal in a HF communication link between two points at the Earth's surface. Throughout the work, some simulations and calculations are made for the representation and analysis of some parameters. assumptions of topics one and two are used in the calculation of the attenuation in a communication between two points, where the signal suffers successive reflections in the ionosphere and the ground. Finally, topic five addresses the phenomenon of fading applied to the ionospheric links, with the different types and their influence on signal transmission as well as the appropriate treatment to each of these, making use of statistical distributions. I. INTRODUCTION The ionosphere, not being nowadays one of the mainstream media, it is still widely used in military and emergency communications. It is also seen as an alternative if the main media means are to fail. In the event of a natural disaster, terrorist attack or any other event that affects the communication systems, conventional communications via the ionosphere are able to restore communication. Thus, phenomenology associated with the ionosphere and how this affects the signal is still an important matter to be studied nowadays. This work aims to calculate the attenuation of the signal in a connection between two earth points, when there are successive reflections in the layers of the ionosphere and the ground, assuming rough ground. This paper is divided by four topics, all having theoretical bases, as well as some graphical simulations and calculations. The first topic addresses reflection in a rough surface. As a first approach, the effects of specular reflection in the ground are shown. Then, the reflection in a rough surface (diffuse reflection) and how this influences the signal obtained at the reception. The second topic focuses on the propagation via the ionosphere, assuming a model of layers, the constitution of the ionospheric plasma and also the measures that characterize the propagation in the ionosphere. On topic three the theoretical II. SCATTERING ON ROUGH SURFACES II.1 Specular reflection Fig. 1 – Specular reflection. Due to the presence of the Earth, phenomena like ground reflection and scattering of waves occur. The interference of the direct ray with the reflected ray causes fluctuations in the electric field and it can strongly change the signal at the receiving antenna, compared to the received signal in free space. The equation that represents the total electrical field as a sum of the direct ray with the reflected ray is 𝐸 = 𝐸! [1 + |𝛤|exp (𝑗𝛥𝜙)] !"! !
! !
where 𝐸! =
represents the free-­‐space !
field, Γ the ground reflection coefficient and 𝛥𝜙 the phase difference. The reflection coefficient depends on the polarization, which can be vertical or horizontal as represented in Fig. 2. 1 2𝜋𝛥𝑟
− arg 𝛤 = 𝑛𝜋 𝜆
II.2 Diffuse reflection (scattering) Fig. 2 – Reflection in horizontal and vertical polarizations [1]. The reflection coefficients for horizontal and vertical polarizations are given respectively by 𝑃𝐻: Γ! =
𝑃𝑉: Γ! =
𝑠𝑖𝑛 𝜓 − 𝑛! − 𝑐𝑜𝑠 ! 𝜓
𝑠𝑖𝑛 𝜓 + 𝑛! − 𝑐𝑜𝑠 ! 𝜓
𝑛! 𝑠𝑖𝑛 𝜓 − 𝑛! − 𝑐𝑜𝑠 ! 𝜓
𝑛! 𝑠𝑖𝑛 𝜓 + 𝑛! − 𝑐𝑜𝑠 ! 𝜓
Fig. 4 – Diffuse reflection. The electric field corrected for the case of a rough surface is given by The phase difference is related with the path difference between the direct ray and the reflected ray (Fig. 2) and is represented by !
𝐸 = 𝐸! 1 + 𝛤 𝑒 !! 𝑒 !∆! 𝛥𝑟
𝛥𝜙 = 𝑎𝑟𝑔 𝛤 − 2𝜋 𝜆
where 𝑔 =
!!
ℎ sin 𝜓 which translates the phase ! 𝑒
difference relative to any two points on the ground. The ℎ! parameter is related to the roughness of the ground. where 𝛥𝑟 = 𝑟! − 𝑟! . According to the Rayleigh criterion, the ground will behave as flat if the amplitude of the surface roughness is small in terms of wavelength. This criterion defends that the ground is flat if the following condition holds 𝑔 ≪ 𝜋 Fig. 3 – Representation of the direct and reflected rays. In the interference zone, the electric field oscillates between maxima and minima. These occur when exp 𝑗𝛥𝜙 = 1 and exp 𝑗𝛥𝜙 = −1, respectively. From the electric field equation, these are given by 𝐸
𝐸!
𝐸
𝐸!
𝛿𝑃! = 𝑃! 𝐺! 𝑒
1
1
𝜎 𝑖, 𝑠 𝛿𝑆
𝐴 𝑟 !
4𝜋𝑟!
4𝜋𝑟! ! !
= 1 + Γ , 𝑒𝑣𝑒𝑛 𝑛 !"#
= 1 − Γ , 𝑜𝑑𝑑 𝑛 !"#
and they occur when The power received at the observation point due to the surface element 𝛿𝑆 of the rough ground is given by where the scattering cross section is given by 𝜎 ≃
1
𝑡𝑎𝑛! 𝛾
𝑒𝑥𝑝
−
𝑠!
𝑠!
2 where 𝑠 defines the ground’s roughness and it’s given by 2ℎ!
𝑠=
𝑙
The total power received at the observation point due to the dispersion in the rough ground is given by 𝑃! =
𝛿𝑃! The effective dispersive area (EDA) defines the area that effectively contributes to the total scattered power collected by the receiving antenna. 𝑃!
𝑡
= 𝑃!
𝜋
!
𝑡 !𝑢!
1 − 𝑢!
1 − 𝑢! !
𝑒𝑥𝑝 −
!!
!
𝑑𝑢 !
where 𝑢 = ! and 𝑡 =
!
! !
!! !
are both dimensionless parameters. 𝑡 is seen as an indicator of the level of the ground’s roughness , since it is inversely proportional to 𝑠. Fig. 6 represents the contribution of the different regions of the ground for the scattered power. To obtain these results, it is computed the !
integrand function of ! !!
𝑡 !𝑢!
𝑡 𝑒𝑥𝑝 − 1 − 𝑢 !
𝑓(𝑡, 𝑢) = 1 − 𝑢! !
𝜋
!
Fig. 5 – Effective dispersing area. Fig. 6 – Representation of 𝒇(𝒖), as a function of t. The transversal dimension 𝑦! of the EDA is given by 𝑦! = 𝑠 𝜏 ℎ whereas the longitudinal dimension 𝑥! is expressed by 𝑑 !
𝜏 𝑠 ,
2
𝑥! =
𝑑
ℎ
−
,
2 2 𝜏 𝑠
ℎ
≫ 𝑑 2 𝜏 𝑠
ℎ
𝑓𝑜𝑟 ≪ 𝑑 2 𝜏 𝑠
𝑓𝑜𝑟 𝜎(𝑢)
Fig. 7 represents 𝜎! , where 𝜎! is the maximum value of the scattering cross section, according to After obtaining the previous expressions, we can finally calculate the total power received by scattering on the ground, and it’s given by Analysing the graph, it is noted that for high values of t, the contributions to the integral are centered at 𝑢 =0, which corresponds to the specular point. Whenever 𝑡 < 1, the largest contribution to the integral comes from the region in the proximity of the antennas. Based on this result, we can now classify the ground in two types, depending on the values of t: reflecting ground (𝑡 > 1) and diffusing ground (𝑡 < 1). 𝜎(𝑢)
𝑡 !𝑢!
= 𝑒𝑥𝑝 −
𝜎!
1 − 𝑢!
!
3 ionosphere. There are various models for the analytical expression of the electron density. The first model was developed by Chapman, where the electron density is given by Fig. 7 – Representation of 𝜎(𝑢)
𝜎! , with varying t. The conclusions are similar to those of Fig. 6, the ground contribution is concentrated around the specular point when the ground is flat and along all the paths between the antennas when the ground is rougher. III. IONOSPHERIC COMMUNICATIONS The ionosphere has the ability to reflect and absorb electromagnetic waves, depending on the frequency and the ionization degree of the region. In terms of radio communications, the most important feature of the ionosphere is its capacity to reflect. The wave can be reflected between the ionosphere layers and the surface of the earth over thousands of kilometers, enabling the intercontinental transmission of short waves. The ionosphere is structured in layers (Fig.7), which are discretized by the electron density and the collision frequency. As the sun is the major source of ionization, the layers vary from day to night. 𝑁! = 𝑁! !"# 𝑒
!!!!!"# ! ! !!
!
!!!
!
where 𝜉 =
, and 𝑋 represents the angle !
between the sun and the vertical of the earth. There are also the linear, exponential and parabolic models, which were developed in order to simplify Chapman’s mathematical expression. When there is a separation of free electrons and ions, a plasma is originated and the plasma frequency is given by 𝑓! =
𝜔!
1 𝑞 ! 𝑁!
=
2𝜋 2𝜋 𝑚! 𝜀!
where 𝑞 represents the electron’s charge and 𝑚! the electron’s mass. The Fig. 9 illustrates the plasma frequency variation as a function of altitude and time of day, during April 2015, as measured by the Ebro Observatory ionosonde in Spain. Fig. 9 – Plasma frequency variation with altitude and time of day. Fig. 8 – Ionosphere stratification. The ionosphere is mainly composed of a cold plasma, which shows variations in the electron density depending on the amount of electromagnetic energy received from the sun. Knowing the solar flux, it is possible to calculate both the ion and electron density of the From around 07:00 to 21:00, at an altitude of 300 km, the plasma frequency takes its highest values, ranging from 7 MHz and 9 MHz. This altitude corresponds to the F2 layer, which reaches the maximum value of their reflective characteristics around 12h. The electromagnetic waves, when penetrating the ionosphere, transfer a considerable amount of energy to the electrons. This energy affects the 4 moving components of the ionospheric plasma by a process of collision between the electron and heavier particles. The higher the collision frequency (𝜗), the greater the attenuation. To obtain the attenuation constant, a very simple model is considered, in which are despised the action of the magnetic field and the collision losses. Manipulating some key expressions, one comes to the expression of the propagation constant, given by the expression 𝑘=
𝜔
𝑐
1−
𝜔! !
𝜔! ! 𝜗
−
𝑗
= 𝛽 − 𝑗𝛼 2 𝜔! + 𝜗 !
2𝜔 𝜔 ! + 𝜗 !
Finally, the attenuation constant is given by 𝛼=
𝜔! ! 𝜗
2𝑐 𝜔 ! + 𝜗 !
There are also some other measurements that allow the characterization of a radio signal propagating in the ionosphere. Some of the most important ones are the virtual height, the critical frequency and the maximum usable frequency. They are very useful for short wave communications, as they make it possible to forecast the path of the signal. These three measures are respectively given by 3×10! ×∆𝑡
ℎ! =
2
𝑓! =
Once returned to the Earth, the wave can be reflected on the ground and return to the ionosphere. Thus, there are several successive reflections of the wave, producing n jumps, that allow the signal to reach long distances. These successive reflections cause attenuation in the signal, namely free space attenuation, attenuation when crossing the layers of the ionosphere, and also attenuation due to reflection in the earth's surface, due to rough ground properties. There are two study cases considered in this paper, expressed in Fig.11 and Fig.12. The first case considers only one jump and the second case two jumps, for a distance of 2000km between the antennas. For both of them the total attenuation suffered by the signal is calculated, considering that the ionospheric reflection occurs in the F2 layer. Three frequencies are considered: 5 MHz, 15 MHz and 30 MHz. 80.55𝑁! !"# 𝑀𝑈𝐹 = 𝑓! sec 𝜃 IV. ATTENUATION IN A IONOSPHERIC COMMUNICATION Fig. 10 represents the electromagnetic waves, which are transmitted between two points on Earth. The wave transmitted by the antenna is reflected by the ionosphere layer, returning to Earth. This phenomenon is commonly termed as jump. Fig. 10 – Ionospheric waves, jump representation. Fig. 11 – Study case one, for one jump. Fig. 12 – Study case two, for two jumps. 5 To accurately characterize the paths of ionospheric waves, it is necessary to determine the relationship between the jump distance 𝑑 , the virtual height ℎ! and the angle of incidence 𝜓. 𝐴! = 32,5 + 20 log 𝑑 !" + 20 log 𝑓(!"#) [𝑑𝐵] Considering the distance and frequencies previously chosen, the values obtained for 𝐴! are expressed in Tab. 1. 𝐴!
Fig. 13 – Geometry of the trajectory of the wave that reflects the ionosphere. 𝑓 = 5 𝑀𝐻𝑧
𝑓 = 15 𝑀𝐻𝑧
𝑓 = 30 𝑀𝐻𝑧
112,50 𝑑𝐵
122,04 𝑑𝐵
128,06 𝑑𝐵
Tab. 1 – 𝑨𝟎 for 𝒅 = 𝟐𝟎𝟎𝟎 𝒌𝒎 and three frequencies. IV.2 Ionospheric attenuation The attenuation suffered by the radio waves in the layers of the ionosphere, considering that the stratification of the ionosphere layer is flat, is given by 𝐴! = 𝑒 !!∝𝜘 According to Fig. 13, the angle of incidence 𝜓 is given by 2ℎ′
𝜓 = tan!!
𝑑
The value of the angle as a function of distance is represented in Fig. 14, considering for values of ℎ! : 80 km, 100 km, 250 km and 350 km. where 𝛼 is the attenuation constant and 𝜘 is the distance travelled by the wave in the ionosphere, and it is obtained for each layer by adapting the second Martin's theorem on the absorption. The expression for 𝜘 is 𝜘 =
Fig. 14 – Angle of incidence 𝜓 . IV.1 Free space attenuation When electromagnetic waves propagate in the atmosphere, they undergo an attenuation which is proportional opposition to the distance they travel, which is called the free space attenuation. This attenuation, considering isotropic antennas, is given by 𝑒𝑠𝑝
sin 𝜓
where 𝑒𝑠𝑝 is the thickness of each layer of the ionosphere (30 km, 50 km, 70 km and 200 km for D, E, F1 e F2, respectively), and 𝜓 is given by Fig. 14. The values of ionospheric attenuation obtained, for one jump, are expressed in Tab. 2. 𝐴!
𝑓 = 5 𝑀𝐻𝑧
𝑓 = 15 𝑀𝐻𝑧
𝑓 = 30 𝑀𝐻𝑧
𝐿𝑎𝑦𝑒𝑟 𝐷
171,25 𝑑𝐵
19,05 𝑑𝐵
4,76 𝑑𝐵
𝐿𝑎𝑦𝑒𝑟 𝐸
23,25 𝑑𝐵
2,60 𝑑𝐵
0,65 𝑑𝐵
6 𝐿𝑎𝑦𝑒𝑟 𝐹1
13,46 𝑑𝐵
1,50 𝑑𝐵
0,37 𝑑𝐵
𝐴!
𝐿𝑎𝑦𝑒𝑟 𝐹2
28,24 𝑑𝐵
3,14 𝑑𝐵
0,78 𝑑𝐵
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 Tab. 2 – 𝑨𝒊 for the four layers of the ionosphere and for three frequencies. The total attenuation suffered in the ionosphere is the sum of the attenuations of each of the previous layers to the layer where the reflection occurs which, in this case, is layer F2. The results are expressed in Tab. 3. 𝐴! !"#$"%&'()_!!
= 𝐴! ! + 𝐴! !
𝑓 = 5 𝑀𝐻𝑧
𝑓 = 15 𝑀𝐻𝑧
207,96 𝑑𝐵 23,15 𝑑𝐵
𝑓 = 30 𝑀𝐻𝑧
5,78 𝑑𝐵
+ 𝐴! !! Tab. 3 – Total attenuation for a reflection suffered in layer F2, for three frequencies. IV.3 Rough ground attenuation In the case where there are two jumps, the signal will be reflected on the surface of the Earth. The attenuation of the signal reflected in the rough ground is given by !
𝐴! = Γ ! 𝑒 !! 𝐷 where 𝐷 = 1, due to the assumption of flat Earth. For obtaining the values of the reflection coefficient Γ, the considered distance is now 1000km, as it’s illustrated in Fig. 12 . Consulting the graph of Fig. 13, the corresponding angle of incidence to that distance is 𝜓 = 34,99! . Calculating the parameters Γ (for both horizontal and vertical polarization) and 𝑔, we come to the values of the attenuation by the rough ground, expressed in Tab. 4. 𝑓 = 5 𝑀𝐻𝑧
𝑓 = 15 𝑀𝐻𝑧
𝑓 = 30 𝑀𝐻𝑧
2,032 𝑑𝐵
3,921 𝑑𝐵
8,321 𝑑𝐵
5,869 𝑑𝐵
9,109 𝑑𝐵
13,773 𝑑𝐵
𝑝𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑝𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛
Tab. 4 – 𝑨𝒔 for three frequencies. It is noted that the vertical polarization has more impact on the rough ground attenuation. Also, the attenuation value is greater the higher the frequency. IV.4 Total attenuation It is now possible to calculate the total attenuation in both cases, for one jump and two jumps. The total attenuation of the signal, for the case of one jump, is given by 𝐴!"!#$ !!"#$ = 𝐴! + 𝐴! !"#$"%&'()_!! whereas for two jumps, the total attenuation of the signal is given by 𝐴!"!#$ !!"#$% = 𝐴! + 2𝐴! !"#$"%&'()_!!
+ 𝐴! !"""
The parameter 𝐴! !"#$"%&'()_!!
corresponds !"""
to the ionosphere attenuation considering a distance of 1000 km, since there are two jumps and the total distance of the link is divided by two, as shown in Fig. 11. The results for the total attenuation for a link between two points of the Earth’s surface, considering a distance of 2000 km between them, and reflection in layer F2 of the ionosphere, for one and two jumps, are expressed in Tab. 5. 7 𝑓 = 5 𝑀𝐻𝑧
𝐴!"!#$
𝑓 = 15 𝑀𝐻𝑧
𝑓 = 30 𝑀𝐻𝑧
1362,30 𝑑𝐵 1366,13 𝑑𝐵264,86 𝑑𝐵 270,05 𝑑𝐵171,06 𝑑𝐵 176,51 𝑑𝐵
𝒏
= 𝟔 𝟏 𝒋𝒖𝒎𝒑
320,46 𝑑𝐵
145,19 𝑑𝐵
133,84 𝑑𝐵
... 𝒏
𝟐 𝒋𝒖𝒎𝒑𝒔
𝑃𝐻
𝑃𝑉
329,87 𝑑𝐵 333,71 𝑑𝐵 𝑃𝐻
149,90 𝑑𝐵 𝑃𝑉
155,09 𝑑𝐵 𝑃𝐻
142,36 𝑑𝐵 𝑃𝑉
147,81 𝑑𝐵 Tab. 5 – Total attenuation values for three frequencies and for one and two jumps. 𝑓 = 5 𝑀𝐻𝑧
𝑃𝐻 𝒏
𝑃𝑉 𝑓 = 15 𝑀𝐻𝑧
𝑃𝐻 ... ...
... ...
= ⋯ Tab. 6 – Total attenuation values for three frequencies for two or more jumps of 2000km each. V. FADING IN IONOSPHERIC COMMUNICATIONS Analysing the overall results it appears that, for lower frequencies, the value of total attenuation is much higher compared to higher frequencies. The vertical polarization exhibits higher values of attenuation, in relation to the horizontal polarization. In general, the attenuation values for both cases are close enough, so two conclusions can be drawn. The first is that the difference between the attenuations suffered in the ionosphere for 1 jump and 2 jumps turn out to be considerably small for clearly preferring one over the other. The second conclusion is that the attenuation corresponding to the reflection on the rough ground has little impact when compared to the attenuation in the ionosphere. The use of two or more jumps can be advantageous in situations where a greater angle of fire is of interest and it is intended to achieve higher distances, difficult to achieve with only one jump. The attenuation values for two or more jumps, considering jumps of 2000 km each, are expressed in Tab. 6. 𝐴!"!#$
...
𝑃𝑉 Among the many adverse effects of ionospheric propagation, signal fading is one of the most difficult to remove due to its unpredictable nature. Fading is a phenomenon where the fluctuation of the signal’s amplitude between the transmitter and the receiver, caused by variations of environment. In the limit, the signal might totally disappear, when its input amplitude falls below the minimum level for receiver detection. There are typically two types of fading, the slow fading and the fast fading. V.1 Slow fading While going through the ionosphere, the radio wave loses some of its energy to the ions and free electrons of the layer, causing a decrease in signal strength. The greater absorption of the signal occurs in the lower region of the ionosphere, where the ionization density is higher. 𝑓 = 30 𝑀𝐻𝑧
𝑃𝐻 𝑃𝑉 530,45 𝑑𝐵 534,29 𝑑𝐵 172,26 𝑑𝐵177,45 𝑑𝐵147,94 𝑑𝐵153,39 𝑑𝐵
=𝟐
𝒏
= 𝟑 738,41 𝑑𝐵 742,25 𝑑𝐵 195,41 𝑑𝐵 200,60 𝑑𝐵153,72 𝑑𝐵 159,17 𝑑𝐵
Fig. 15 – Slow fading. 8 Slow fading behaviour is described by the log-­‐
normal distribution, which probability distribution function is 𝐹 𝑥 =1−
1
1 + 𝑒𝑟𝑓
2
𝑥
ln
𝑥!
2𝜎
There are two types of fast fading, very intense fast fading and weak fast fading. In the weak fast fading, one of the signals of the multipath dominates over the other. This type of fading is described by the Rice distribution, with the probability distribution function illustrated on Fig. 18. This function is represented in Fig. 16, for four values of variance, 10 dB, 15 dB, 20 dB and 30 dB. Fig. 18 – Probability distribution function, for the Rice distribution. Fig. 16 – Probability distribution function, for the log-­‐normal distribution. V.2 Fast fading Fast fading is related to multipath effect, when each ray arrives at the receiver coming from a different direction. When going through its path, the ray undergoes phenomena such as reflection on the surface of the Earth, refraction in the ionosphere, among others, that affect the signal quality at the reception. The very intense fast fading is described by the Rayleigh distribution, with probability distribution function given by 𝐹 𝑥 = 1 − 𝑒𝑥𝑝 −
𝑥!
𝑙𝑛 2 𝑥! !
This function is represented in Fig. 19. Fig. 17 – Multipath effect. Representation of three different paths (C1, C2 and C3). Fig. 19 – Probability distribution function, for the Rayleigh distribution. 9 The graphs of probability distribution functions for fading characterization are very convenient as, given a certain median signal-­‐to-­‐noise ratio, these allow to know the value of the achieved signal to noise ratio for a given percentage of time. If the S/N value found is below the value corresponding to the median, is considered a bad result. It is actually what happens most of the time. Considering a case of very intense fast fading, for a median signal-­‐to-­‐noise ratio of 𝑆 𝑁 = 30 𝑑𝐵 and aiming to ensure that ratio 99% of the time. By consulting the graph on Fig. 19, we obtain a margin of 12 𝑑𝐵, which is below the median value, facing a bad result. Considering now a case of slow fading, in the same conditions, wanting to obtain the signal level that is exceeded 99% of the time. Consulting the graph on Fig. 16, we obtain a margin of −5 𝑑𝐵, again, a bad result. One way of correcting these values, in order to improve them, would be to increase the transmission power, which sometimes becomes quite expensive. Another solution would be to introduce spatial or spectral diversity. The values of the fading margins should be added to the attenuation values calculated in topic IV. VI. CONCLUSIONS This paper addressed the calculation of the signal attenuation in a ionospheric link between two points at the Earth’s surface, when there are successive reflections in the layers of the ionosphere and the ground, assuming rugged ground. The diffuse reflection and specular reflection were addressed, as well as the differences between the two. Two simulations were made concerning the diffuse reflection, which allowed to conclude that for 𝑡 > 1 the ground is considered reflector and for 𝑡 < 1 the ground is considered diffusor. On the second topic, a theoretical approach was made to the ionosphere communications, including its constitution, referring to the model of layers, and the measures that characterize its propagation, such as plasma frequency, critical frequency, virtual height, maximum usable frequency and attenuation constant. The following topic calculations were made to obtain the attenuation in a ionospheric link. Two scenarios were studied, the first considering just one jump and the second considering two jumps, for three values of frequency. After analysing the results, it is noted that, generally, the attenuation values of both cases are very similar, so one can conclude that the difference between the attenuations suffered in the ionosphere for 1 jump and 2 jumps turn out to not being considerably large to clearly prefer one case over the other. It is also noted that the attenuation corresponding to rough ground reflection has little impact on the total attenuation. The use of two or more jumps can be advantageous in situations where the use of a greater angle of fire is of interest, and when it is intended to achieve higher distances, most difficult to achieve with the use of only one jump. Lastly, was made an approach to the fading phenomenon, associated with the propagation in the ionosphere, referring to the types of fading that may occur. To characterize their behaviour, three graphs were made to translate the fading types, using statistical distributions (lognormal, Rice and Rayleigh). These graphs were consulted for calculating the fading margins, in order to predict the reliability of a connection. VII. REFERENCES [1] J. F. Figanier e C. A. Fernandes, Aspectos
de Propagação na Atmosfera, Lisboa:
Secção de Propagação e Radiação, ISTDEED, 2002. [2] http://obsebre.es/ca/variabilitat-dia-a-dia
[3] IPS
Radio
and
Space
Services,
“Introduction to HF Radio Propagation”,
[4] Silva, Henrique José Almeida da,
“Propagação na atmosfera”, May 2001 10