International Journal of Scientific & Engineering Research, Volume 4, Issue 10, October-2013 1169

ISSN 2229-5518

Computation of Cross-Polarisation Due to Rain over Durban, South Africa

1Oluwumi Adetan, 2Thomas.J. Afullo

Abstract—The aim of this paper is to compute the cross polarisation caused by rain (XPD) at frequency band 10-35 GHz over Durban (29o52'S, 30o 58'E), a city along the eastern coast of South Africa. Two elevation angles of 23o and 55oare assumed for wave propagation along the coastal region. The globally accepted lognormal drop size distribution model for tropical region has been used to compute the raindrop sizes assumed to be spherical at 20oC. The power law relationship between attenuation and rain rate based on the measured complimentary cumulative distribution of rain rates in Durban is used to estimate the total attenuation. The ITU-R procedure in recommendation 618-9 (ITU-R, 2007) is employed in the estimation of the cross polarisation discrimination due to rain on earth-satellite

path. From our results, a linear difference of about 9dB between 0.1% and 0.01% of time is observed at all frequencies over the elevation angles. The XPD observed at 0.1% of time is higher than that of 0.01% at the same elevation angle and frequency. A lower value of XPD results in higher cross-talk or high interference between the two orthogonal channels at the satellite receiver station. The variation of the estimated values of XPD with co-polar attenuation (CPA), frequencies and rain rates at these elevation angles is also examined. The circular polarisation for earth-satellite propagation paths is assumed for the purpose of analysis.

Keywords— Depolarisation, Cross polarisation discrimination (XPD); Copular attenuation (CPA); Cross-talk.

—————————— ——————————

1 INTRODUCTION

he orientation of the lines of the electric flux in an electromagnetic (EM) field is generally referred to as wave polarisation. The use of orthogonal polarisations allows two independent information channels using the same frequency band to transmit signals over a single link. This method is useful in satellite communication systems to effectively increase the available spectrum. However, some degrees of interference between these channels are inevitable due to depolarizing effects caused by scattering and absorption of the hydrometeor (rain, ice, etc.), along the propagation path. This depolarisation is due to the non- spherical symmetry of the raindrops (the top and bottom are flattened), along with their tendency to have a preferred orientation. Depolarisation results in cross talk between two orthogonal polarized channels, transmitted on the same path and frequency band [1]-[7]. As a result of this, radiowaves propagating through them suffers differential attenuation and phase shift. This also may constitute a problem in communication systems using polarisation orthogonality to maintain isolation between channels. Differential attenuation and phase below 18 GHz increases with frequency for a given rain event, they however decrease for a given fade depth [1]. This is partly because less deformed smaller drops make a greater relative

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1Oluwumi Adetan is currently pursuing his doctoral degree program in electronic engineering in University of KwaZulu-Natal South Africa. His research interest is to study the effects of rain on microwave and communication systems. E-mail: oadetan@gmail.com.

2Thomas J. Afullo is a Professor in the School of Engineering, University of

KwaZulu-Natal, South Africa. His research interest includes

contribution to the total attenuation as frequency is increased.
Polarisation can be linear or circular (elliptical).The most general case of polarisation is the elliptical or circular polarisation. The electric field vector E (t), as expressed by [2] in equation (2) composed of two sinusoidal components,
having different amplitudes |𝐸𝑥 | and �𝐸𝑦 � and a phase

difference 𝑎𝑟𝑔 �𝐸𝑦 �:
𝑬(𝑡) = R 𝐸𝑥𝑒𝑗𝑤𝑡 = R ��𝑢 𝐸 + 𝑢 𝐸 �𝑒𝑗𝑤𝑡 � (1)
= 𝑢𝑥 |𝐸𝑥 | cos(𝑤𝑡) + 𝑢𝑦 �𝐸𝑦 � cos(𝑤𝑡 + 𝜙) (2)
where 𝑢𝑥 , and 𝑢𝑦 are the units vectors in the x- and y-
directions respectively; ω is the angular frequency and t is
the time. The phase is taken relative to the phase of 𝐸𝑥. As
observed in (1), the polarisation may be frequency
dependent and time varying as the hydrometeor change.
Oftentimes, EM waves transmitted along the principal
planes will arrive unchanged (magnitude) but, experience
differential attenuation and phase shifts. Consequently, any
transmitted polarisation that is not one of the link’s
principal planes will be cross polarized on reception [1-2]. It
is important to mention that the relative contribution of
differential attenuation and phase shift is different at
different frequencies. Differential phase shift appears to be
the dominant factor in rain induced depolarisation at
frequencies below 10 GHz and differential attenuation
becomes increasingly significant at higher frequencies.
Linearly polarized waves have an infinite axial ratio (the
ratio of the maximum to the minimum magnitude of the
electric field vector) while circularly polarized waves have
an axial ratio that lies between +1 and -1, corresponding to

communication systems, electromagnetic theory, microwave and R F

communications. E-mail: afullot@ukzn.ac.za

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either left-hand circular polarisation (LHCP) or right-hand circular polarisation (RHCP) [2].
A reliable estimate of the depolarizing properties of tropical rainfall for terrestrial and earth space links therefore requires among other parameters; the investigation of the differential attenuation, differential phase shift, cross polarisation discrimination (XPD) in the orthogonal channels and the co-polar attenuation (CPA). The aim of this paper is to estimate the cross polarisation of millimeter waves in the Ku and Ka band frequencies caused by rainfall over Durban (29o52'S, 30o 58'E) at two elevation angles of 23o and 55o at frequency range 10-35
GHz. The elevation angles 23o and 55o are for links above the Indian Ocean Region (IOR) and over the Atlantic Ocean Region (AOR) respectively. The ITU-R P.618-9 [8]; recommendation for propagation data and prediction methods required for the design of Earth-space telecommunications systems is adopted for the purpose of computation. An attempt is made to determine the variation of the XPD with co-polar attenuation (CPA), rainfall rate and frequency. The raindrop sizes are assumed spherical at 20oC and the circular polarisation for Earth- satellite propagation paths is also assumed for the purpose of computation.

2 OVERVIEW OF RELATED WORKS AND EXPERIMENTAL SET UP

2.1 Related Work



A good number of researchers have determined the propagation effects of cross polarisation caused by rain. Experimental results have shown the existence of a relationship between attenuation and depolarisation especially when rain depolarisation is dominant. This has been extensively discussed by Nowland et al,[9], Dissanayake et al.[10]and Chu [11]. In their separate studies, Ajewole [4] and Oguchi [5]showed that rain induced cross polarisation of radio waves has its roots in the differential attenuation and differential phase shift produced between the two polarisation states and in the slight tilt of the axis of symmetry (canting angle) of the raindrop away from the vertical due to wind effects. By assuming a constant canting angle of raindrops along a propagation path, Oguchi and Hosoya [12] estimated the cross polarisation due to different rainfall rates. Similarly, Ajewole et al. [13] computed XPD due to rain for four tropical types of rain by adopting the method earlier proposed by Oguchi [14].The effects of varying the canting angles of the raindrops was also investigated by Ajewole et al. [15] using different types of rain and raindrop sizes on cross polarisation discrimination and established that XPD improves by about 4-7 dB over those models having equal orientation. Recently, the dependence of XPD on co-polar attenuation, frequency and rainfall was estimated by Ojo [16] over some stations in Nigeria at various elevation angles and frequencies.
In this work, the computation of XPD at frequency range
10-35 GHz and at elevation angles of 23o and 55o is carried
out over the eastern coast of South Africa assuming a spherical raindrop sizes at 20oC. The variation of the estimated values of XPD with other parameters such as co- polar attenuation, rain rate and frequency is also discussed.

2.2 Experimental Set Up

Durban (29o52'S, 30o 58'E) is a coastal city located along the eastern coast of South Africa. The city is characterized by four different seasons per annum. It is often referred to as a humid subtropical region due to its high rainfall intensity which often occurs during the summer months [17-19].
In this report, the rainfall rate data measured over a period of one year (January - December, 2009) using a Joss- Waldvogel (JW) RD-80 disdrometer measuring system has been utilized to estimate the cross polarisation caused by rain over Durban. The equipment is installed at the roof top of the School of Electrical, Electronic and Computer Engineering building, University of KwaZulu Natal, (Howard College), South Africa. The minimum and

TABLE 1

RAIN RATE DISTRIBUTION AT VARIOUS PERCENTAGES

OF EXCEEDENCE IN DURBAN

maximum rainfall rate values are 0.003mm/h and
117.15mm/h respectively. The disdrometer converts the
momentum of each falling drop impacting on the sensor’s
surface into an electric pulse of commensurate voltage. The

detectable diameter range is divided into 20 intervals [20].

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120
100
80
60
40
20
0
0.001 0.01 0.1 1 10
Percentage time values ordinate is exceeded (%)

Fig.1. Rainfall rate complementary cumulative distribution function (CDDF) for Durban (Jan -Dec.

2009).

The sampling time, T of the disdrometer is 60s with the sampling area, A of 50cm2 (0.005 m2).Rainfall samples with overall sum of drops less than 10 were discarded to compensate for the dead-time errors. The instrument is located at an altitude of 139.7m above sea level. Although there is generally high wind variability in Durban, the location site is free of disturbances due to unwanted noise and shielded from abnormal winds.Fig.1 and Table 1 show the complementary cumulative distribution function (CDDF) of the rainfall rate for the one year data in Durban and the specific relationship between the percentages of time the rain rate is exceeded. Rainfall rate values of 32.33 mm/h, 66.25mm/h and 101.56mm/h were estimated at 0.1%,
0.01 % and 0.001 % of time exceeded respectively.

3 COMPUTATIONAL PROCEDURES

The ratio (in dB) of the power in the copolarised wave to the power in the crosspolarised wave that was transmitted in the same state is termed the cross polarisation discrimination due to rain (XPDrain ). In other words, it is the appearance in the course of propagation of a radio wave through the atmosphere, of a polarisation component which is orthogonal to the desired polarisation.
Mathematically, it can be expressed by [2]-[5] as:
𝐸𝑥𝑥
𝐶𝑓 = 30 log 𝑓 for 8 ≤ 𝑓 ≤ 35 𝐺𝐻𝑧 (4)
where f is the frequency in GHz.
Step 2: Calculate the rain attenuation dependent term:
𝐶𝐴 = 𝑉(𝑓) log 𝐴𝑝 (5)
where Ap is the estimated rainfall attenuation (in dB)
exceeded for the required percentages of time. This may
also be computed from [7].
𝑉(𝑓) = 12.8 ∗ 𝑓0.19 for 8 ≤ 𝑓 ≤ 20 𝐺𝐻𝑧
𝑉(𝑓) = 22.6 for 20 < 𝑓 ≤ 35 𝐺𝐻𝑧
Step 3: Calculate the polarisation improvement factor:
𝐶𝜏 = −10 log[1 − 0.484(1 + cos 4𝜏)] (6)
where 𝐶𝜏 = 0 for τ = 45o and reaches the maximum value
of 15 dB for τ = 0o or 90o.
Step 4: Calculate the elevation angle dependent term:
𝐶𝜃 = −40 log(cos 𝜃) for θ ≤ 60o (7)
Step 5: Calculate the canting angle dependent term:
𝐶𝜎 = 0.0052𝜎2 (8)
where σ is the effective standard deviation of the raindrop
canting angle distribution (in degrees). It takes the value 0o,
5o, 10o and 15o for 1%, 0.1%, 0.01% and 0.001% of the time
respectively. In this work, the value of 10o is used.
Step 6: Calculate rain XPD not exceeded for p% of the
time:
𝑋𝑃𝐷𝑟𝑎𝑖𝑛 = 𝐶𝑓 − 𝐶𝐴 + 𝐶𝜏 + 𝐶𝜃 + 𝐶𝜎 (dB) (9)

4 RESULTS AND DISCUSSIONS

The variation of XPD at various elevation angles and frequencies 12, 15, 20 and 35 GHz are shown in Fig. 2. In general and at all frequencies, XPD decreases as frequency

𝑋𝑃𝐷𝑟𝑎𝑖𝑛 = 20log10
𝐸𝑥𝑦
� (dB) (3)
increases for all the elevation angles. As the elevation angle increases for a given frequency, the XPD increases. A larger value of XPD is observed as the percentage of time also
where 𝐸𝑥𝑥 and 𝐸𝑥𝑦 are the co-polarized and cross
polarized waves transmitted in the same polarisation states
respectively. The ITU-R step-by step methods to compute
the XPDrain statistics are stated as follows:
Step 1: Calculate the frequency-dependent term:
increases. A difference of about 8-9 dB is observed between
0.1 % and 0.01% of time while a difference of about 5-6 dB
is noticed between 0.01 % and 0.001% of time. A low value
of XPD implies an increased interference (cross-talk) at the
receiver station of the satellite. The following sub-sections
further explain the variation of XPD with co-polar

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attenuation, rainfall rate and operating frequencies for 40
different elevation angles. 35

30

50
45 25
40 55o
35
30 23o
25
20
15

20

15 55o

10

5

23o

0

10
5
0
0.001 0.01 0.1 1

percentage of time values ordinate is exceeded

(%)

(a) 12 GHz

45
40
35
30
25
20
15 55o
10
5 23o
0
0.001 0.01 0.1 1

Percentage e values ordi is exceeded

0.001 0.01 0.1 1

Percentage of time values ordinate is exceeded

(%)

(d) 35GHz

Fig.2. Cross polarisation discrimination (XPD) over different elevation angles at f = 10-35 GHz in Durban (R0.01 = 66.25 mm/h).

4.1 XPD-CPA Relations in Durban

Fig.3 shows the variation of the XPD and the rain attenuation exceeded for the required period of time, often called the co-polar attenuation (CPA) over the elevation angles at (a) f = 15 GHz and (b) 35 GHz. It can be observed that the CPA increases with decreasing angle of elevation. The cross polarisation discrimination degrades with increasing CPA. This shows an agreement with Ajewole et al. [13] and confirms the inverse relation between the CPA and XPD. This implies that signal degradation as a result of XPD is enhanced

of tim

(%)

nate

more by CPA for a given fade than due to XPD as the

(b) 15 GHz

frequency decreases.

45


45
40 55o
35 35
30 30
25 23o 25
20 20
15

15

10
5 10
0 5
-5 0

55o

23o

0.001 0.01 0.1 1

Percentage of time values ordinate is

exceeded (%)

0 10 20 30 40 50

Attenuation [dB]

(c) 20GHz

(a)

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40
35
30
25
20
15 55o

o

10
5 23o
0
0 50 100 150
Attenuation (dB)

(a)

(b)

Fig. 3. XPD versus Co-polar attenuation

4.2 Variation of XPD with Frequency

It is important to mention that the relative contribution of differential attenuation and phase shift is different at different frequencies. Differential phase shift appears to be the dominant factor in rain induced depolarisation at frequencies below 10 GHz and differential attenuation becomes increasingly significant at higher frequencies. The dependence of XPD on frequency at the elevation angles for different rain event is shown in Table 2. In general and for all the elevation angles, XPD decreases as the frequency of

55o

(b)

operation increases. However, at higher frequency above 30

GHz, a sharp change in XPD values is observed. This may

be due to the presence of ice crystals in the upper layer of
rainclouds producing a greater contribution to
depolarisation. Similarly, less deformed smaller drops
make a greater relative contribution to the total attenuation
as frequency is increased. The contributions of the
differential attenuation and phase shift to cross polarisation
at varying frequencies and the complex dielectric property
of water which depends on frequency are also probable
factors that may be responsible for the sudden change in
the XPD as the frequency increases. The differential
propagation reduces with frequency for a given fade depth.

TABLE 2

VARIATION OF XPD WITH FREQUENCY FOR DIFFERENT ELEVATION ANGLES

(a) R0.01 , (b) R0.1 .

4.3 XPD versus Rainfall Rate

The variation of XPD with rain rate at (a) f = 15 GHz and (b) f = 30 GHz is given in Fig 4 and Table 3 at the two elevation angles. An inverse relation is also observed between the XPD and rainfall rate at all angles of elevation. As the rainfall rate increases, XPD decreases. Table III shows the XPD-rain rate relation at different elevation angles operating at f= 12 and 30GHz. At a given rain rate, the cross polarisation discrimination increases with increase in elevation angles. The cross polarisation becomes poorer as the rain rate and frequency are raised. This results in poor interference level in the orthogonal channels.

50
40
30
20 55o
10 23o
0
0 50 100 150
Rain rate (mm/h)

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(a)

40
35
30
25
20
15
10
5
0
-5
55o
23o
elevation angles. The results obtained in this work will greatly be useful in the design of terrestrial and Earth-to- satellite link in southern Africa. However, due to inadequate of experimental data, it will be of interest to further investigate and validate this work in the nearest future and to estimate same for other regions across South Africa.

ACKNOWLEDGEMENT

Fruitful discussions with Professor Moses O. Ajewole and Dr. Joseph S. Ojo of the Center for Research and Developments (CERAD), Akure, Nigeria are highly appreciated.
0 50 100 150
Rain rate (mm/h)

(b)

Fig. 4. XPD versus rainfall rate at (a) f= 15GHz (b) f =

30GHz

TABLE 3

COMPUTED XPD VALUES AND RAINFALL RATES AT OPERATING FREQUENCIES of 12 and 30 GHz.

12 GHz

R0.01 (mm/h)

10.53

32.33

66.25

98.16

Elevation

23o

55o

31.297

43.667

18.714

30.469

9.978

21.636

4.648

16.234

angle

30 GHz

Elevation

23o

55o

24.497

35.609

12.214

22.795

4.142

14.757

-0.207

10.474

angle

5 CONCLUSION

The reliability of a transmission link is mostly determined from the quantities measured at one time or the other on the link. The computation of cross polarisation discrimination and its relationship to co-polar attenuation and other quantities along the Earth-space propagation paths at elevation angles of 23o and 55o and frequency band
10-35GHz has been carried out in this work. Our results show that cross polarisation discrimination degrades with increasing co-polar attenuation and decreases sharply as the elevation angle decreases due to the larger attenuation as a result of longer distance the signal travels at low

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