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

assumptions of topics one and two are used in the Abstract - This work addresses in the study calculation of the attenuation in a communication of some relevant propagation phenomena in between two points, where the signal suffers ionospheric radio links. The main objective is the successive reflections in the ionosphere and the calculation of the attenuation of a signal in a HF ground. Finally, topic five addresses the communication link between two points at the phenomenon of fading applied to the ionospheric Earth's surface. Throughout the work, some links, with the different types and their influence simulations and calculations are made for the on signal transmission as well as the appropriate representation and analysis of some parameters. treatment to each of these, making use of statistical distributions.

I. INTRODUCTION II. SCATTERING ON ROUGH SURFACES The ionosphere, not being nowadays one of the mainstream media, it is still widely used in II.1 Specular reflection 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 Fig. 1 – Specular reflection. associated with the ionosphere and how this affects the signal is still an important matter to be Due to the presence of the Earth, phenomena studied nowadays. like ground reflection and scattering of waves This work aims to calculate the attenuation of occur. The interference of the direct ray with the the signal in a connection between two earth reflected ray causes fluctuations in the electric points, when there are successive reflections in field and it can strongly change the signal at the the layers of the ionosphere and the ground, receiving antenna, compared to the received assuming rough ground. signal in free space. This paper is divided by four topics, all having The equation that represents the total theoretical bases, as well as some graphical electrical field as a sum of the direct ray with the simulations and calculations. The first topic reflected ray is addresses reflection in a rough surface. As a first approach, the effects of specular reflection in the � = �![1 + |�|exp (��)] ground are shown. Then, the reflection in a rough surface (diffuse reflection) and how this influences !"! ! where � = ! ! represents the free-space the signal obtained at the reception. The second ! ! topic focuses on the propagation via the field, Γ the ground reflection coefficient and �� ionosphere, assuming a model of layers, the the phase difference. The reflection coefficient constitution of the ionospheric plasma and also depends on the polarization, which can be vertical the measures that characterize the propagation in or horizontal as represented in Fig. 2. the ionosphere. On topic three the theoretical

2�� − arg � = ��

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

�� − �! − ��!� ��: Γ! = �� + �! − ��!� Fig. 4 – Diffuse reflection. �!�� − �! − ��!� ��: Γ! = �!�� + �! − ��!� 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 � = �! 1 + � � �

�� !! �� = �� − 2� where � = ℎ sin � which translates the phase � ! � difference relative to any two points on the ground. where �� = �! − �!. The ℎ! parameter is related to the roughness of the ground. 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

� ≪ �

Fig. 3 – Representation of the direct and reflected rays. The power received at the observation point due to the surface element �� of the rough In the interference zone, the electric field ground is given by oscillates between maxima and minima. These occur when exp �� = 1 and exp �� = −1, respectively. From the electric field equation, 1 1 these are given by ��! = �!�! � ! � �, � �� ! �! � 4��! 4��!

� = 1 + Γ , �� where the scattering cross section is given by �! !"# � = 1 − Γ , �� ! �! !"# 1 �� ≃ �� − �! �! and they occur when

where � defines the ground’s roughness and it’s �!�! ! �� − ! ! given by �! � 1 − � = ! ! �� ! � !! 1 − � 2ℎ! � = � ! ! ! where � = ! and � = ! are both The total power received at the observation ! ! ! point due to the dispersion in the rough ground is dimensionless parameters. � is seen as an given by indicator of the level of the ground’s roughness , since it is inversely proportional to �. 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 ! !! The effective dispersive area (EDA) defines the area that effectively contributes to the total �!�! �� − scattered power collected by the receiving � 1 − �! ! �(�, �) = antenna. � 1 − �! !

Fig. 5 – Effective dispersing area. Fig. 6 – Representation of �(�), as a function of t.

The transversal dimension �! of the EDA is given by Analysing the graph, it is noted that for high values of t, the contributions to the integral are �! = � � ℎ centered at � =0, which corresponds to the specular point. Whenever � < 1, the largest contribution to the integral comes from the region whereas the longitudinal dimension �! is in the proximity of the antennas. Based on this expressed by result, we can now classify the ground in two types, depending on the values of t: reflecting ground (� > 1) and diffusing ground (� < 1). � ! ℎ � � , �� ≫ � �(�) � � = 2 2 � � Fig. 7 represents �!, where ! is the ! � ℎ ℎ − , �� ≪ � maximum value of the scattering cross section, 2 2 � � 2 � � according to

After obtaining the previous expressions, we �(�) �!�! can finally calculate the total power received by = �� − � 1 − �! ! scattering on the ground, and it’s given by !

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 , with varying t. �! !!! where � = !, and � represents the angle ! The conclusions are similar to those of Fig. 6, between the sun and the vertical of the earth. the ground contribution is concentrated around There are also the linear, exponential and the specular point when the ground is flat and parabolic models, which were developed in order along all the paths between the antennas when to simplify Chapman’s mathematical expression. the ground is rougher. When there is a separation of free electrons and ions, a plasma is originated and the plasma frequency is given by

III. IONOSPHERIC COMMUNICATIONS ! �! 1 � �! �! = = The ionosphere has the ability to reflect and 2� 2� �!�! absorb electromagnetic waves, depending on the frequency and the ionization degree of the region. where � represents the electron’s charge and �! In terms of radio communications, the most the electron’s mass. important feature of the ionosphere is its capacity The Fig. 9 illustrates the plasma frequency to reflect. The wave can be reflected between the variation as a function of altitude and time of day, ionosphere layers and the surface of the earth during April 2015, as measured by the Ebro over thousands of kilometers, enabling the Observatory ionosonde in Spain. 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.

Fig. 9 – Plasma frequency variation with altitude and time of day.

From around 07:00 to 21:00, at an altitude of Fig. 8 – Ionosphere stratification. 300 km, the plasma frequency takes its highest values, ranging from 7 MHz and 9 MHz. This The ionosphere is mainly composed of a cold altitude corresponds to the F2 layer, which plasma, which shows variations in the electron reaches the maximum value of their reflective density depending on the amount of characteristics around 12h. electromagnetic energy received from the sun. The electromagnetic waves, when penetrating Knowing the solar flux, it is possible to calculate the ionosphere, transfer a considerable amount of both the ion and electron density of the energy to the electrons. This energy affects the

moving components of the ionospheric plasma by a process of collision between the electron and heavier particles. The higher the collision frequency (�), 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. Fig. 10 – Ionospheric waves, jump representation. Manipulating some key expressions, one comes to the expression of the propagation constant, given by the expression Once returned to the Earth, the wave can be reflected on the ground and return to the ! ! ionosphere. Thus, there are several successive � �! �! � � = 1 − − � = � − �� 2 �! + �! 2� �! + �! reflections of the wave, producing n jumps, that allow the signal to reach long distances.

These successive reflections cause attenuation Finally, the attenuation constant is given by in the signal, namely free space attenuation,

attenuation when crossing the layers of the � !� ! ionosphere, and also attenuation due to reflection � = ! ! 2� � + � in the earth's surface, due to rough ground

properties. There are also some other measurements that There are two study cases considered in this allow the characterization of a radio signal paper, expressed in Fig.11 and Fig.12. The first propagating in the ionosphere. Some of the most case considers only one jump and the second case important ones are the virtual height, the critical two jumps, for a distance of 2000km between the frequency and the maximum usable frequency. antennas. For both of them the total attenuation They are very useful for short wave suffered by the signal is calculated, considering communications, as they make it possible to that the ionospheric reflection occurs in the F2 forecast the path of the signal. layer. Three frequencies are considered: 5 MHz, These three measures are respectively given by 15 MHz and 30 MHz.

3×10!×∆� ℎ! = 2

�! = 80.55�!!"#

�� = �! sec �

IV. ATTENUATION IN A IONOSPHERIC COMMUNICATION Fig. 11 – Study case one, for one jump.

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. 12 – Study case two, for two jumps.

�! = 32,5 + 20 log � !" + 20 log �(!"#) [��] To accurately characterize the paths of ionospheric waves, it is necessary to determine � the relationship between the jump distance , the Considering the distance and frequencies virtual height ℎ! and the angle of incidence �. previously chosen, the values obtained for �! are expressed in Tab. 1.

� = 5 �� = 15 �� = 30 ��

�! 112,50 �� 122,04 �� 128,06 ��

Tab. 1 – �� for � = �� and three frequencies.

Fig. 13 – Geometry of the trajectory of the wave that reflects the ionosphere.

According to Fig. 13, the angle of incidence � is IV.2 Ionospheric attenuation given by 2ℎ′ The attenuation suffered by the radio waves in � = tan!! � the layers of the ionosphere, considering that the stratification of the ionosphere layer is flat, is given by 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 � is the attenuation constant and � 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 � is

�� = sin �

where �� is the thickness of each layer of the ionosphere (30 km, 50 km, 70 km and 200 km for Fig. 14 – Angle of incidence � . D, E, F1 e F2, respectively), and � is given by Fig.

14.

The values of ionospheric attenuation IV.1 Free space attenuation obtained, for one jump, are expressed in Tab. 2. When electromagnetic waves propagate in the atmosphere, they undergo an attenuation which is � = 5 �� = 15 �� = 30 �� proportional opposition to the distance they �! travel, which is called the free space attenuation. This attenuation, considering isotropic antennas, �� 171,25 �� 19,05 �� 4,76 �� is given by

�� 23,25 �� 2,60 �� 0,65 ��

13,46 �� 1,50 �� 0,37 �� = 5 �� = 15 �� = 30 �� 1 �!

�� 2 28,24 �� 3,14 �� 0,78 �� ℎ�� 2,032 �� 3,921 �� 8,321 ��

Tab. 2 – �� for the four layers of the ionosphere and for �� three frequencies.

�� 5,869 �� 9,109 �� 13,773 �� 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. Tab. 4 – �� for three frequencies. The results are expressed in Tab. 3. It is noted that the vertical polarization has more impact on the rough ground attenuation. � = 5 �� = 15 �� = 30 �� Also, the attenuation value is greater the higher the frequency.

� !!"#$"%&'()_!! 207,96 �� 23,15 �� 5,78 �� IV.4 Total attenuation = �!! + �!! + � !!! It is now possible to calculate the total attenuation in both cases, for one jump and two Tab. 3 – Total attenuation for a reflection suffered in layer jumps. F2, for three frequencies. The total attenuation of the signal, for the case of one jump, is given by

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 whereas for two jumps, the total attenuation of rough ground is given by the signal is given by

! !!! �! = Γ � � �!"!#$ = �! + 2�! + �! !!"#$% !"#$"%&'()_!!!"""

where � = 1, due to the assumption of flat Earth.

For obtaining the values of the reflection The parameter �! corresponds coefficient Γ, the considered distance is now !"#$"%&'()_!!!""" 1000km, as it’s illustrated in Fig. 12 . Consulting to the ionosphere attenuation considering a the graph of Fig. 13, the corresponding angle of distance of 1000 km, since there are two jumps incidence to that distance is � = 34,99!. and the total distance of the link is divided by two, Calculating the parameters Γ (for both as shown in Fig. 11. horizontal and vertical polarization) and �, we come to the values of the attenuation by the The results for the total attenuation for a link rough ground, expressed in Tab. 4. 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.

� = 5 �� = 15 �� = 30 �� 1362,30 ��1366 ,13 ��264 ,86 ��270 ,05 ��171 ,06 ��176 ,51 �� !"!#$ � = � � �� 320,46 �� 145,19 �� 133,84 ��

� ...... �� = ⋯ � ��

329,87 �� 333,71 �� 149,90 �� 155,09 �� 142,36 �� 147,81 �� Tab. 6 – Total attenuation values for three frequencies for two or more jumps of 2000km each. Tab. 5 – Total attenuation values for three frequencies and for one and two jumps.

V. FADING IN IONOSPHERIC COMMUNICATIONS

Analysing the overall results it appears that, for Among the many adverse effects of lower frequencies, the value of total attenuation is ionospheric propagation, signal fading is one of much higher compared to higher frequencies. The the most difficult to remove due to its vertical polarization exhibits higher values of unpredictable nature. Fading is a phenomenon attenuation, in relation to the horizontal where the fluctuation of the signal’s amplitude polarization. In general, the attenuation values for between the transmitter and the receiver, caused both cases are close enough, so two conclusions by variations of environment. In the limit, the can be drawn. The first is that the difference signal might totally disappear, when its input between the attenuations suffered in the amplitude falls below the minimum level for ionosphere for 1 jump and 2 jumps turn out to be receiver detection. considerably small for clearly preferring one over There are typically two types of fading, the the other. The second conclusion is that the slow fading and the fast fading. attenuation corresponding to the reflection on the rough ground has little impact when compared to the attenuation in the ionosphere. The use of two V.1 Slow fading or more jumps can be advantageous in situations where a greater angle of fire is of interest and it is While going through the ionosphere, the radio intended to achieve higher distances, difficult to wave loses some of its energy to the ions and free achieve with only one jump. electrons of the layer, causing a decrease in signal The attenuation values for two or more jumps, strength. The greater absorption of the signal considering jumps of 2000 km each, are expressed occurs in the lower region of the ionosphere, in Tab. 6. where the ionization density is higher.

�!"!#$ � = 5 �� = 15 �� = 30 ��

��

� 530,45 �� 534,29 �� 172,26 ��177 ,45 ��147 ,94 ��153 ,39 �� = �

� 738,41 �� 742,25 �� 195,41 ��200 ,60 ��153 ,72 ��159 ,17 �� = � Fig. 15 – Slow fading.

Slow fading behaviour is described by the log- There are two types of fast fading, very intense normal distribution, which probability distribution fast fading and weak fast fading. function is In the weak fast fading, one of the signals of � ln the multipath dominates over the other. This type 1 � � � = 1 − 1 + �� ! of fading is described by the Rice distribution, with 2 2� 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. The very intense fast fading is described by the Rayleigh distribution, with probability distribution function given by V.2 Fast fading �! Fast fading is related to multipath effect, � � = 1 − �� − �� 2 � ! when each ray arrives at the receiver coming from ! a different direction. When going through its path, the ray undergoes phenomena such as reflection This function is represented in Fig. 19. on the surface of the Earth, refraction in the ionosphere, among others, that affect the signal quality at the reception.

Fig. 17 – Multipath effect. Representation of three different paths (C1, C2 and C3). Fig. 19 – Probability distribution function, for the Rayleigh distribution.

The graphs of probability distribution functions The following topic calculations were made to for fading characterization are very convenient as, obtain the attenuation in a ionospheric link. Two given a certain median signal-to-noise ratio, these scenarios were studied, the first considering just allow to know the value of the achieved signal to one jump and the second considering two jumps, noise ratio for a given percentage of time. If the for three values of frequency. After analysing the S/N value found is below the value corresponding results, it is noted that, generally, the attenuation to the median, is considered a bad result. It is values of both cases are very similar, so one can actually what happens most of the time. conclude that the difference between the attenuations suffered in the ionosphere for 1 Considering a case of very intense fast fading, jump and 2 jumps turn out to not being � = 30 �� for a median signal-to-noise ratio of � considerably large to clearly prefer one case over and aiming to ensure that ratio 99% of the time. the other. It is also noted that the attenuation By consulting the graph on Fig. 19, we obtain a corresponding to rough ground reflection has little margin of 12 ��, which is below the median impact on the total attenuation. The use of two value, facing a bad result. Considering now a case or more jumps can be advantageous in situations of slow fading, in the same conditions, wanting to where the use of a greater angle of fire is of obtain the signal level that is exceeded 99% of the interest, and when it is intended to achieve higher time. Consulting the graph on Fig. 16, we obtain a distances, most difficult to achieve with the use of margin of −5 ��, again, a bad result. One way of only one jump. correcting these values, in order to improve them, Lastly, was made an approach to the fading would be to increase the transmission power, phenomenon, associated with the propagation in which sometimes becomes quite expensive. the ionosphere, referring to the types of fading Another solution would be to introduce spatial or that may occur. To characterize their behaviour, spectral diversity. The values of the fading margins three graphs were made to translate the fading should be added to the attenuation values types, using statistical distributions (lognormal, calculated in topic IV. Rice and Rayleigh). These graphs were consulted for calculating the fading margins, in order to predict the reliability of a connection. VI. CONCLUSIONS

This paper addressed the calculation of the signal attenuation in a ionospheric link between VII. REFERENCES two points at the Earth’s surface, when there are successive reflections in the layers of the ionosphere and the ground, assuming rugged [1] J. F. Figanier e C. A. Fernandes, Aspectos ground. de Propagação na Atmosfera, Lisboa: Secção de Propagação e Radiação, IST- The diffuse reflection and specular reflection DEED, 2002. were addressed, as well as the differences

[2] http://obsebre.es/ca/variabilitat-dia-a-dia between the two. Two simulations were made concerning the diffuse reflection, which allowed [3] IPS Radio and Space Services, to conclude that for � > 1 the ground is “Introduction to HF Radio Propagation”, considered reflector and for � < 1 the ground is [4] Silva, Henrique José Almeida da, considered diffusor. “Propagação na atmosfera”, May 2001 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.