Abstract - The impairment to radio signal propagation in clear-air environment requires accurate prediction method and modeling for terrestrial line of sight links. This is necessary because of the unstable nature of the environment the signal is traversing. Prediction methods based on global radioclimatic models of the ITU-R can currently be made for three significant clear-air propagation effects on terrestrial line of sight links: multipath fading, distortion and depolarization. In addition, such predictions can also be made for multipath fading on very low angle satellite links, and interference between terrestrial and satellite communication systems resulting from duct propagation beyond the horizon. All these predictions explicitly or implicitly use world wide contour maps of refractive index gradient statistics for the lower 100m of the atmosphere. This paper focus on multipath propagation modeling in clear-air environment which can be used for line of sight link design application. The investigation was carried out using clear-air signal level measurement on a terrestrial line of sight link set up between the Howard College and Westville Campuses of the University of KwaZulu Natal, Durban, South Africa for a period of one year in 2004. Index Terms—Multipath Propagation, Digital Elevation Model (DEM), k-factor

I. INTRODUCTION

ECHNIQUES for predicting the deep-fading range of the multipath fading distribution for average worst month have been available for several years [1]. Most of these

techniques were based on empirical fits of Rayleigh-type distributions (i.e. with slopes of 10 dB/ decade) to fading data for individual countries. The best known techniques in this regard are those of Moritas [2] for Japan, Barnette [3] and Vigants [4] for USA, Pearson [5] and Doble [6] for the United Kingdom, Nadenenko [7] for the former Soviet Union and that of International Radio Consultative Committee (CCIR) [8] for the North-West Europe.

The single-frequency or narrow-band prediction equations [1] were based on the power-law form originally introduced by Morita and Kakita [9] in 1958. They showed the influence of path length on the number of hours containing deep fading or so-called Rayleigh fading. Morita and Kakita fitted the number of measured hours with deep fading in the worst “season” to path length for 4 GHz links in Japan, but they did

not make it clear how to relate the measured time with fade depth. Seven years later, Pearson [5] presented a set of curves for predicting the fade depth exceeded for 0.1% of the worst month at 4 GHz in the UK, taking the path length and terrain fade roughness s as predictor variables.

Like the model of Morita and Kakita, his model gave a linear relationship between the fade depth expressed in decibels and the logarithmic path length (i.e. the power-law form in probability), but it did not give a linear dependence on terrain roughness. Pearson also assumed a distribution slope of 10 dB/decade for fading exceeding 10 dB. Morita [2] added a dependence on frequency f later by analyzing new data for different frequencies. He used a partial regression technique, fitting the path length d dependence first and the frequency f dependence afterwards. Also he introduced discrete geoclimatic variability by giving geoclimatic factors for three regions: plains, mountains and coast.

In Southern Africa, Baker and Palmer proposed a model for the cumulative probability distribution of the k-factor [12]. While using available data for South Africa and Namibia, they concluded from regression analysis that there are climatic factors that need to be incorporated into the basic model. They concluded that the model would assist in predicting large values of the k-factor that may only be exceeded relatively rarely in the inland summer rainfall areas.

Afullo et al also reported on radio refractivity and k-factor studies for Botswana [13]. Using measurements taken over three years (1996 – 1998), the median value of k was determined to be 1.1, while the effective value, ke being 0.7. On the other hand when ducting data were included, they found the median k to be 1.03, while ke was 0.61. In [11] a framework for the modeling of the pdf of k, f(k), was developed and the model determined, based on radiosonde data collected in Botswana for the period 1996-1998. It was observed that at height spans 0-500m and 0-200m above ground level (a.g.l), the all-year median value of k, µk is 1.12 and the standard deviation is found to vary between 0.13 – 0.16 in all months, except in August when the deviation becomes lower at 0.067. The effective value of k, ke , is found from the analytical expression in [13] to be 0.7 for height span 0-500m a.g.l., while it is 0.61 for the lower height span 0-200m a.g.l.

Multipath Propagation Modeling and Measurement in a Clear-Air Environment for LOS Link Design Application

Peter K. Odedina, Member, IEEE and Thomas J. Afullo, Senior Member SAIEE School of Electrical Electronic and Computer Engineering,

King George V Avenue, Howard College Campus. University of KwaZulu-Natal, P.O. Box 4041, Durban South Africa

odedina@ukzn.ac.za, afullot@ukzn.ac.za

T

In this paper, we model multipath propagation in a clear-air environment using a line of sight link set up in Durban, South Africa. We use a signal level measurement result of ten months experiment in two of the campuses of University of KwaZulu Natal. Various parameters on the link path were investigated and how this affect the transmitted signal is explained.

We start by describing the various radioclimatic parameters that is expected to be on the link path. Next we do an in depth topographical and detail contour mapping of the study area. Finally we do a comprehensive analysis and explanation of some of the plot of the signal level measurement between the transmitter and receiver for the link.

II. INVESTIGATION STUDY AREA

The investigation study area where the line-of-sight link was set up is in Durban, KwaZulu Natal province of South Africa. Durban is located on the coaster shore of Indian ocean on the geographical coordinate (Latitude

o29 97' S and Longitude o30 95' E ) the climatic region is coastal savanna [16].

The line-of-sight link was established between the Howard College and the Westville campuses of the University of KwaZulu-Natal, Durban. The transmitter station was setup on the roof of the Science building at the Westville campus on the azimuth angle of 30.980o and about 178 m above sea level and the receiver station on the roof of the Electrical Engineering building at Howard College campus on the azimuth angle of 30.943o and about 145 m above sea level [17]. The terrestrial link parameters are shown in Table 1. The expected noise power in the receiver when no signal is transmitted lies between – 80.5 to -80.2 dBm [18]. The power received at the receiver end can be calculated as follows [18]:

P P FSL + G G Lossesr t r ant t ant� � � � (1)

20 dBm 135 dB + 38.6 dBi +38.6dBi 2.2dB 1 dB� � � � 41 dBm��

where P = Power transmitted (taken as 100mW = 20 dBm);t

FSL = Free space loss; G Receive antenna gain;r ant �

G = Transmit antenna gain.t ant

III. CLEAR-AIR MULTIPATH PROPAGATION MODELING

In order to appropriately model the multipath propagation for the clear-air condition of our study area, there is need to get the correct digital terrain model and the contour mapping for the line-of-sight link of the study area. To this end, we have used the Arcgis software tool to develop the digital elevation model (DEM) map and the contour map of our study area; these are shown in Fig. 1 and Fig. 2. Information required for detailed link design calculation, for

the LOS link can be extracted from these plots as explained in [10].

The DEM of the study area is shown in Fig. 1. DEM can broadly be defined as a digital representation of the continuous variation of elevation over space [20]. Elevation can be any continuous variable that depends on geographic coordinates [21]. It is also customary to use the term ' DEM ' for what can be called ' gridded DEM ' so that the more general term should then be ' Digital Terrain Model ' (DTM). The digital elevation model is an extremely useful product of a GIS for land evaluation and production of maps [21]. It can be seen that more detail information on the topographical feature of our study area is revealed by the DEM map (see Fig. 1). Our link is surrounded by different geographical features such as road, river, vegetation and different undulating terrain as can be observed from Fig. 1. All these contribute in various ways to the signal degradation as was observed from the clear-air signal level measurement over 6.73 km, 19.5 GHz link. Though one can get a rough estimate of terrain height distribution of our study area from the DEM, it is still difficult to get the exact height of each point from the DEM. This is why we have produced a contour map of our study area using the same software as shown in Fig. 2. The contour map has the advantage of showing the exact height for each point in the study area. We have divided our path length of 6.73 km into an interval of 1 km from the transmitter to the receiver as can be seen from the two plots. This is done so that the procedure described in [10] can be implemented for our study area.

The procedure described in [10] for detail link design is stated as follows:

TABLE I TERRESTRIAL LINK PARAMETERS FOR THE LOS SHF SYTEM [17]

Parameter Description

Path Length 6.73 km Height of transmitting antenna above the ground

24 m

Altitude of transmitter station 178 m Height of receiving antenna above the ground

20 m

Altitude of receiver station 145 m Carrier frequency 19.5 GHz Bandwith under investigation 200 MHz Transmitting power 10 – 100 mW Transmitting/receiver antenna gain

38.6 dBi

Transmitting/receiver beam width

1.9 degrees

Free space loss 135 dBm Total cabling and connection losses

� 2.2 dB

Clear-air attenuation � 1dB Receiver bandwidth 100 kHz – 1GHz

As a first step, determine the geoclimatic factor and the

magnitude of the path inclination, |�p| (mrad), using the following relation:

4.2 0.0029dN1K = 10� �

(2)

dN

dN1 dh h 65m�

� (3)

The path inclination is determine as follows:

h hr e = p d

��

(4)

where hr is the altitude in meter of the receiver antenna, he is the altitude in meter of the transmit antenna and d is the path length in kilometer. From the profile of the terrain along the path, obtain the terrain heights, h, at intervals of 1 km, beginning 1 km from one terminal and ending 1 km to 2 km from the other. Using these heights, carry out a linear regression with the “method of least squares” to obtain the linear equation of the “average” profile:

h (x) = a + a x0 1 (5)

where x is the distance along the path from the transmitter. The coefficients a0 and a1 can be calculated from the relations [22]:

( )a = �h a �x /n0 1− (6)

�xh (�x �h)/n

a =1 2 2�x (�x) /n

− ⋅

− (7)

where the summations are over the number, n, of profile height samples. From (5), calculate h (0) and h (d), the heights of the average profile at the ends of the path, and the heights of the antennas above the average path profile:

h = h h (0)e1 − (8a)

h = h h (d)r2 − (8b)

For paths where the point of specular reflection is fairly obvious (such as on paths over water, partially over water, or partially over flat, level terrain), the height above the reflecting surface should be used for h1 and h2.

Next, we calculate the “average” grazing angle φ (mrad), corresponding to a 4/3-earth radius model for refraction (i.e., ae = 8500 km) from

h +h 21 2 = 1 m (1 + b )

d�

� ��� �

(9)

Where

2d

m = 4a (h + h )e 1 2

(10)

| h h |1 2

h +h1 2�

�� (11)

m+1 1 3 3mb 2 cos � 3 Arcos 33m 3 2 (m+1)

�� �� � �� � � � �� �� � � �� � �� �

(12)

Fig. 1 A digital elevation model (DEM) of the study area

Fig. 2 Contour Map of the Study Area

In calculation of the coefficients m and ς , the variables ae ,

d, h1 and h2 must be in the same units. The grazing angle φ will be in the desired units of milliradians if h1 and h2 are in meters and d in kilometers. If desired, the distances de and dr from terminals e and r to the point of specular reflection on the average profile can be determined from:

h > h1 2d = (1 ± b)d/2e h < h1 2

�������

(13a)

and h > h1 2d = (1 b) d/2 r h <h1 2

�������

� (13b)

such calculations can be useful in choosing a suitable regression interval on the path profile.

Finally, calculate the percentage of time, P, that the fade depth, A(dB), is exceeded in the average worst month using (14)

3.3 0.93 1.1 1.2 A/10P Kd f (1 | |) 10p� �� � �� � � (14)

where the symbols have their usual meaning.

It should be noted that the latest revision of the ITU-R recommendation on the above subject has incorporated and embedded in (14) the grazing angle φ and by virtue of this latest revision, (14) can now be written as (see [23]):

3.2 0.97 0.032 0.00085 A/10P Kd (1 | |) 10 f hLp�� � �

� � � (15)

IV. RESULTS

The procedure described above was followed and after useful information have been extracted from the DEM and the contour map of the study area (see Fig. 1 and Fig. 2) we are

able to calculate the required multipath modeling parameters highlighted in (2) – (15) and the results are shown in table 2, Fig. 3 and Fig. 4 respectively.

TABLE 2 MULTIPATH MODELING PARAMETERS FOR ITU-R METHOD 2 LINE OF

SIGHT LINK DESIGN

Distance from

Transmitter (km)

HEIGHT PROFILE

Other Parameters

h(x) Value (m)

Parameter Value

0 h(0) 178 a0 -8.761 1 h(1) 80 a1 36.534 2 h(2) 150 hr 165 3 h(3) 120 he 202 4 h(4) 110 h1 24 5 h(5) 80 h2 20 6 h(6) 80 n 8

6.73 h(7) �

h(d)

145 φ 0.002162

0.000001

0.00001

0.0001

0.001

0.01

0.1

Jan Feb Mar Apr May Jun July Aug Sept Oct Nov Dec

Months

Exc

eeda

nce

Pro

bab

ility

(%)

pw Durban_Meth1 A=30 dB pw Durban_Meth2 A = 30 dB

Fig. 3 Percentage of Time that Fade Depth A = 30 dB is exceeded in the average worst month in Durban Links for ITU-R methods 1 and 2 (19.5GHz)

Fig. 4 Clear-air Signal Level Measurement over 6.73km LOS Link over 24 hrs on June 14 2004

V. DISCUSSION Multipath propagation modeling has been presented using both clear-air signal level measurement and detailed ITU-R line of sight link design process. The detail ITU-R method was achieved by extracting needed topographical information from the digital elevation model (DEM) map plotted using the Argis software. The DEM map and the contour map (See Fig. 1 and Fig. 2) reveal the detailed information about the link characteristic and implementation of ITU-R method two was possible. The different multipath modeling parameters obtained using this process is shown in table 2.

On the other hand, due to the rugged, hilly, and non flat nature of the intervening terrain (see Fig. 1), multipath fading contribute about 1 dB. Water vapour attenuation is another contributor with highest contribution in summer with an average pressure of about 27mb (see Table 3 in [24]), giving an average attenuation of 0.34 dB/km, or 2.2 dB over the 6.7 km path.

After the multipath modeling parameters have been obtained, the line of sight link implementation was done using the path link parameters stated in table 2. This helps to calculate the percentage of time that a particular fade depth A is exceeded for the average worst month in Durban as shown in Fig. 3. It should be noted that the fade depth shown here is for A =30 dB for all the months for the two ITU-R methods. While the first ITU-R method is the multipath process that does not involve detail link information such as the grazing angle φ , the second ITU-R method incorporate the grazing angle into the calculation as seen above. The first method has been implemented elsewhere [24] and that is why we have made a comparison with the second method (see Fig. 3).

Comparing these two ITU-R methods shows that they both have similar pattern distribution for the different months in Durban for the chosen fade depths (see Fig. 3). The worst months in Durban are February and August as shown in Fig. 3 for both methods, this is in agreement with our previous results in [24]. This shows that the link designer need to make adequate plan for the months of February and August in Durban to avoid link outages in these seasonal months. While the pattern distribution is similar for all the months for both methods in Durban at the chosen fade depth, it can be observed that the first ITU-R method underestimate the percentage exceedance probability value for all the months for the chosen fade depth in Durban. This show that the second ITU-R method is an improved method compared to the first ITU-R method.

The clear-air signal level measurement plot at the receiver is shown in Fig. 4. The expected signal level at the receiver is -41 dBm as explained in section 2, but it can be seen that the actual signal levels are 1 – 4 dB below the expected free space value of – 41dBm. Several factors contribute to this; k-factor fading arises due to the fact that the value of k used in the design is 1.33, while the median value of k-factor for Durban is 1.21, with a value of k = 0.5, exceeded 99.9% of the time[14, 15]. The “worst” month for k-factor fading is February (with value of k � 0.2 exceeded 99.9% of the month), while the month of August has k-factor value exceeded 99.9 % of the time of 0.9. Note also that the median value of k for August is 1.27 as opposed to the 1.21 for February [15]. Thus this type of fading may contribute 1 – 1.5 dB over the path (see [14]).

On the other hand in winter, the average water vapour pressure is about 13mb (see Table 2 in [18]), resulting in attenuation of about 0.13 dB per km, and 0.9 dB over the 6.7 km path [25]. Thus, water vapour attenuation contributes about 1 dB in winter and 2.2 dB in summer. Due to the coastal nature of Durban, as well as the industries, fog attenuation is also a contributor. At the operating frequency of the link of 19.5GHz, an average attenuation of 0.1dB/km is expected, resulting in a value of 0.7 dB along the propagation path [26]. This thus account for the difference in the clear-air signal level measurement shown in Fig. 4 from the expected value of – 41dBm.

VI. CONCLUSION

This paper has presented a multipath propagation modeling using digital elevation model (DEM) and contour map to extract useful topographical terrain information. This topographical terrain information made it possible to implement the ITU-R detailed line of sight link design process as described in [10]. This ITU-R detailed LOS link design method is then compared with its initial planning purpose method counterpart. It was discovered that the initial method underestimate the percentage of time that a particular fade depth (A = 30 dB) is exceeded in the average worst month in Durban compared to that of the ITU-R detailed method. Hence the ITU-R method two (detailed link method) is considered to produce an improved result compared to its initial planning counterpart. Clear-air signal level measurement plots were also done using the line of sight link set up between Howard college campus and Westville campus of University of KwaZulu-Natal. The plots reveals that the receive signal level at the receiver differs from the expected free space loss value of – 41dBm by 1 – 4 dB. This difference is attributed to various clear-air radioclimatic variables such as; the k-factor value used for the design is different from that of the Durban environment. Also contributing to this difference is the multipath, water vapour, terrain, fog and industry pollution among other things. The results in this paper will be found very useful by radio link designers in South Africa.

ACKNOWLEDGMENT

The Authors wish to thank the South African Weather Service for availing the radiosonde data used in this presentation.

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Peter K. Odedina holds a B.Sc. in Physics (Electronics Specialization), from, Federal University of Technology Akure (FUTA), Nigeria. An M.Sc. in Electrical Engineering from University of KwaZulu-Natal Durban, South Africa, and currently pursuing a PhD degree in Electronics Engineering at the same University. He has been an IEEE member for five years.

Thomas J. Afullo holds the B.Sc (Hons) Electrical Engineering from University of Nairobi, Kenya, the MSEE from West Virginia University, USA, and the License in Technology and PhD in Electrical Engineering from the Vrije Universiteit Brussel (VUB), Belgium. He has held various positions in industry and university for more then 25 years. He is currently an Associate Professor, Dept. of Electrical Engineering University of KwaZulu-Natal, Durban, South Africa.