FUNDAMENTAL CONSIDERATIONS FOR DIGITAL MICROWAVE LINK DESIGN

Kishori Sharan MATHUR

Dept. of Electronics & Communication, JJT University, Jhunjhunu 333001, Rajasthan., India Tel: +91- 9971652846, Email: kishorimathur@hotmail.com

Abstract

This paper mainly describes design considerations for Digital Microwave Communications links.

It describes method of path profiling, multipath fading phenomenon, signal attenuation. Also

counter measures for multipath propagations are discussed. In the last rain specific attenuation and

rain intensity statics are discussed.

Keywords-Path Profiling, Fresnel zone, Multipath Fading, Signal Attenuation, Rain Intensity

Model

1. Introduction

This paper mainly describes the method of path profiling, multi path propagation

considerations and estimation of rain specific attenuation.

Once the overall route map has been established and possible repeater sites identified, the

critical work of producing path profiles must take place. Radio repeaters are often built based on

the analysis of the path profile. For multi path propagation considerations; first refractivity

conditions are discussed and the received signal impairments are presented. Multi path activity

statistics are described, according to Rayleigh model and the multi path occurrence factor is

defined. These models are applied for outage prediction. Finally, multi path counter measures are

considered. In estimation of rain specific attenuation, interactions of an EM wave with molecules

encountered throughout the propagation path in the atmosphere are discussed. This leads to an

estimate of rain specific attenuation, as a function of rain intensity, signal frequency and

polarization. Statistical data on rain intensity is considered, as required by the ITU-R rain

attenuation model, which is presented as the basic tool to predict rain unavailability in any region,

in the world, at frequencies up to about 40 GHz.

2. Path Profiling

Path Profiling is very significant for long rural links, as physical checking for optical LOS

may be difficult or impossible as compared to urban links where usually it is essential to carry out

a radio survey to physically check the LOS.

Usually, a 1:50,000 maps are required and the contour line elevations recorded from a

straight line are drawn between the two points on the map. The earths bulge and the curvature of the radio beam need to be taken into account. Another important consideration is Fresnel zone

clearance. While designing microwave link information about all obstacles in the region between

the transmitter and receiver is identified and drawn on a profile plot. On the same profile plot, first

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Fresnel zone radius is also plotted which gives an indication of LOS clearance of any peak which

is required to remain outside this Fresnel zone radius.

3. Fresnel Zones

When microwave energy arrives 1800 out of phase (/2) at the receiving antenna with the

direct wave diminishes the boundary of first Fresnel zone. The second and third Fresnel zones are

defined as the boundary consisting of all point within the microwave links from which the

additional path length is 2 half and 3 half-wave lengths, respectively. So, at any point along the

path, there is a set of concentric circles whose centers are all on the direct line of sight path line,

denoting all the fresnel zone boundaries (See fig. 1).

The distance Fn (in meters) from the line of sight path to the boundary of the n th Fresnel zone is

approximated by the relation,

n. d1. d2

F n = 17.3 __________ 1

f. D

Where, d1 = distance from one end of the path to the reflection point (Km)

d2= distance from the other end of the path to the reflection point (Km)

D = d1 + d2

f = frequency (GHz)

n = number of Fresnel zones (1st, 2

nd,etc.)

The Fresnel zone radii have significant consequences when obstacles such as tree or hills

within the microwave path approach the first Fresnel zone radius. For determining the higher

Figure 1

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order, (n th) Fresnel zone radii when first Fresnel zone radius is known, following equation is

used:

Fn = F1 n __________________ 2

To achieve unaffected transmission by the presence of obstacles, the transmission path

should have a clearance from these obstacles of at least 0.6 times the first Fresnel zone radii.

Following process is adopted for implementing path profiling manually: -

1. A terrain profile ignoring earth curvature is plotted on Cartesian graph paper choosing any suitable vertical and horizontal scales.

2. For all points on the path profile likely to give rise to poor clearance e.g. local maxima, path midpoint, etc. the height of the earth buldge is calculated using formula:

d1. d2

h B =

2 a

Where, d1, d2 = the distances from each site in kilometers, and

a = earth radius (= 6371 Kms)

3. The effect of tropospheric refraction (hTR) on clearance is calculated using hB and k is a factor to give:

H TR = h B (k-1 1) meters

4. The required fresnel zone clearance is calculated using:

H FZC = f. r1

Where, rn = n. d1. d2

d1 + d2

Typically, f = 0.6 for k = 0.7 and f = 1.0 for k = 4/3

5. An estimate is obtained for the Terrain Cover Height, hTC.

6. Finally, h TC + h B + h FZC are plotted on the terrain path profile.

7. A straight line passing through the highest of plotted points than allows appropriate antenna heights at each end of the link to be established. Once the path profile is drawn, the

preceding information can be used to adjust the profile for k-factor variations. Now a days

computer programs are used to draw the modified profiles.

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If adequate Fresnel Zone clearance cannot be guaranteed under all conditions then

diffraction may occur leading to signal fading. So far, discussion was confined to perfectly

reflecting surfaces.

But in practice, this applies to paths that pass over surfaces such as water or desert. Such

highly efficient reflective surfaces are known as smooth spheres diffraction paths. But the majority

of microwave paths have an obstacle clearance in the category known as knife-edge diffraction.

Diffraction is a characteristic of electro-magnetic wave, which occurs when a beam passes over an

obstacle with grazing incidence (i.e. just touching the obstacle) (see Fig2).

Figure 2

The beam energy is dispersed by an amount, which depends on the size and shape of an obstacle.

Loss in an area beyond an obstacle is described by shadow loss. The loss is dependent on

frequency. The high frequency waves tends to follow straight line of sight and not to be diffracted

into shadow area behind the obstacle. At lower frequencies, more diffraction occurs, producing

higher shadow loss since stronger signals exist in the shadow area. For smooth sphere grazing, the

loss could be up to 15 dB depending on clearance whereas knife-edge diffraction causes approx.

6dB of loss. The height of antenna must be sufficient to prevent the reflected losses due to varying

propagation conditions. Particular attention should be paid to this matter for paths crossing water

or desert.

3. Multipath Fading

One of the frequently occurred fading is due to beam bending. The microwave beam can be

influenced by a change of refractive index of the air. K = 4/3 is considered to be standard

atmospheric conditions with vertical refractivity gradient, G = -40 N/Km (k = 1.33). When

refractive index of the atmosphere is different from standard the beam will bend upward or

downward, depending on k-factor when k 1.33; G -40 N/Km is often called sub-refractive or

substandard condition. When k 1.33; G -40 N/Km is known as super refractive or super standard condition.

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When the EM ray trajectory suffers the same curvature, at any elevation in atmosphere, it is

known as constant vertical refractivity gradient. Under this condition, a direct ray trajectory is

identified. From the Tx antenna to the Rx antenna, with launching angle is given by,

H T - H R

= - arctg +

2. RE

Where, = D2 -- HT HR 2

RE is the equivalent earth radius (8500 km with standard k factor, k = 1.33).

HT & HR are the antenna heights at the transmitter and receiver respectively &

D is the path length.

In general, the vertical refractivity gradient may deviate from a constant gradient model. It

may be assumed as constant within atmospheric layers of limited height (stratified atmosphere). In

the real case, the transition from one layer to another is smoothed in some measure.

A stratified atmosphere model is useful in explaining the different bending of ray

trajectories, when they travel at different elevations in the atmosphere. In these conditions, the

gradient profile may be such that not only a direct ray, but multiple rays, with different launching

angles reach the receiver antenna through several spatially disjointed paths. This is called multi path propagation (see Fig3).

Figure 3

As a result, the received signal is made by several components (signal echoes), adding

together with random amplitude, delay and relative phase shift.

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4. Signal Attenuation Using a vectorial representation of signals, the received signal, under multi path propagation, can

be viewed as addition of multiple vectors (Fig4). The component vectors may interfere each other,

at a given time instant, in a constructive or destructive way, depending on the relative phase shifts.

Figure 4

The relative phase of component vectors depend on the difference in the path length

traveled by each signal component. Note that the wavelength is of the order of centimeters and

even small movements in atmospheric layers may significantly modified the path distances and the

relative vector phases so, at different time instants, variations in the component vector phases may

produce sudden variations in the resultant vector amplitude; the received signal power may be

almost canceled, for short periods (fraction of a second or few seconds). (Fig5). Clearly, during

multi path events, the received signal power may fade below the hop threshold, so that a system

outage is observed.

4.1. Multi path Activity Modeling

Multi path events are observed with daily and seasonal cycles, when suitable refractive

gradient profiles are more often observed. A multi path activity period can last tens of minutes or

even one or several hours.

A prediction model of multi path activity is implemented by correlating significant radio link and

environmental parameters with statistical observation of multi path events.

Figure 5

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4.2. Radio and Environmental Parameters

Radio link parameters, which have been recognized as affecting multi path events, are:

i) Working frequency ii) Path length iii) Path inclination

Environmental conditions, which are likely to produce multi path events, are:

i) Flat terrain ii) Strong evaporation (high temperature and humidity) iii) Absence of wind.

It is often useful to identify climatic regions with specific characteristics, so that multi path

activity can, in some measure, be correlated with regional parameters. Particularly in tropical

climate, long multi path events can be observed.

4.3. Statistical observation of Multi path events

By monitoring a radio hop during multi path events, a number of recordings, similar to the

previous figure no 5, can be collected. This enables to build up statistical data about the time

periods with fade depth, below given threshold.

A large amount of similar, experiments have shown that fade depth statistics are well

approximated by Rayleigh distribution (at least for fade depth greater than about 15 dB).

According to that distribution, the probability that the signal fade depth A (in dB) is deeper than a

given value A0 is given by,

-A0/10

Prob A A0 = P 0 . 10

Where, P0 is called multi path occurrence factor.

Note that, if the reference fades depth A0 increases 10 dB, than the corresponding probability is

lower by a factor 10 (see Fig6), (the diagram slope is 10 dB/decade).

Figure 6

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5.4. Multi path Occurrence Factor

The Rayleigh model for multi path fade depth is described by a single parameter P0. We

can imagine collecting fade depth statics on a given radio hop in different time periods, or on radio

hops with different lengths, working frequency, and/or indifferent climates. We accept that, in

some measure, the experimental results approximate the Rayleigh formula given above, even if

different P0 value will apply in each case. So, the P0 parameter gives a measure of the multi path

activity on a given hop and within a given time period.

The above example suggests an experimental means to estimate P0 factor when a radio hop

is already working. However, the radio engineer needs prediction tools to estimate P0 while a radio

hop is at the design stage.

Several empirical formulas have been proposed, giving P0 as a function of radio hop

parameters and of environmental conditions.

Most of the formulas have the following structure:

P 0 = C . Q . F . D

Where, C = Geoclimatic coefficient

Q =Terrain profile coefficient

= frequency exponent

= Path length, exponent, is empirical parameters.

They are usually estimated by processing large amount of experimental data or can derive

from more complex formulas, again related to the results of field measurements. Generally, P0 is

proportional to frequency (the exponent is equal or close to 1), while the exponent is in the range of 3.0 to 3.6 (the multi path occurrence increases about 10 times when the hop length is

doubled).

The most popular model for P0 prediction is the Bell Labs formula (reported in paper by

WT Barnett and A Vigants, in early 70s). The general formula mentioned above is applied (frequency in GHz, distance in Km), with the following parameters:

= 1

= 3 C = 1 x 10

-5 for dry mountainous regions

= [2.1 x 10-5

for continental regions

= 3.1 x 10-5

for maritime temperature regions

= 4.1 x 10-5

for maritime sub-tropical, high humidity and temperature regions]

Q = 1/1.3

= Profile roughness, measured in meters as the standard deviation of terrain

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Elevation at 1km intervals (in any case, must be in the range of 6.0 m to 42.0 m).

Examples of Barnett and Vigants models are given in fig no7 (a), 7(b), 7(c), and 7(d).

5. Counter measures for multi path propagation

Several techniques have been devised to reduce impairments caused by multi path

propagation.

5.1. Space diversity

As with reflection paths, two Rx antennas, with suitable vertical spacing, receive the multi

path component signals with different phase patterns. So, in a well-arranged space diversity

configuration, the Rx signals at the two antennas will exhibit a low correlation and the probability

of deep fading at the same time can be significantly lowered. Typical spacing is of the order of 150

to 200 wavelengths. A diversity improvement factor ISD is defined as,

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Prob A1 A0 ISD (A0) =

Prob A1 A0, A2 A0

Where, A1 and A2 are the attenuations at the two diversity receivers, A0 is reference attenuation

and Prob X,Y means probability that events X & Y are true at the same instant (joint probability).

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5.2. Frequency Diversity

In this case, we exploit the frequency selective nature of multi path fading, so that two RF

channels with suitable frequency spacing exhibit the low correlation property, which guarantees a

low probability of deep fading in the two channels at the same time.

6. Rain Attenuation

An EM wave, traveling in a given direction through a rain cell, losses part of its power in

that direction as a result of absorption and scattering effects. In the impact with a raindrop, the total

power loss depends on the drop cross section; which is given by the sum of a scattering cross

section and an absorption cross section.

The drop cross section is a function of the drop radius and of signal wave length by

integrating the power lost in the impact with a single raindrop to all the rain drops in a given

volume (rain cell), the total loss produced within the rain cell can be estimated.

To do this, suitable statistical models are needed to relate the number of rain drops in a rain

cell and their size distribution to the rain intensity. Such models have been tuned on the basis of a

large amount of experimental data, coming from different regions in the world. As a result, the

specific rain attenuation (dB/Km) can be expressed, as a function of the rain rate R (in mm/Hr), by the following exponential formula:

= K . R

Where, the parameters K and are the functions of the signal wavelength and polarization.

ITU R Rec P-838 gives a table with the K and values, for vertical & horizontal polarizations, in the frequency range 1 to 400 GHz. Formulas are given for the case of any linear

or circular polarization.

Examples of specific rain attenuation as a function of rain rate are given in the figure no8.

Note that the increase in specific attenuation is about 100 times, when passing from 3 to 12 GHz.

Moreover, the vertical polarization is significantly less attenuated than horizontal polarization, at

the same frequency.

6.1. Worldwide rain intensity statics

An important input to any rain attenuation model is the expected rain activity in the region

where the radio hop will operate, as derived from long-term statics. More specifically, it was found

useful to refer to the low probability tails of rain statics, since we are mainly interested in one

event with very heavy rainfall.

The rain rate exceeded for 0.01% of the time is the significant parameter, useful to

characterize the rainfall activity in a given region. If possible, this rain rate should be derived from

reliable statistical data about the local rain events. When local data are not available, the procedure

recommended by ITU-R, P-837, and a new approach is reported to estimate the rain rate exceeded

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for any percentage of time, in any part of the world. This is based on data file, derived from 15

years of data of the European Center of Medium Range Weather Forecast (ECMWF). They cover

the entire world, with latitude and longitude grids in 1.50 steps.

Figure 8

To give approximate information about the rain rates used in rain attenuation predictions,

the ITU-R approach is reported, which was based on world maps with rain regions. Each region was labeled with a letter; the table below, each letter is associated with the corresponding rain rate

(in mm/Hr) exceeded for 0.01% of the time (see Table 1).

TABLE-I

A 08 D 19 G 30 K 42 P 95

B 12 E 22 H 32 L 60 Q 145

C 15 F 28 J 35 M 63 N 115

The ITU-R Rain regions for Asia and Oceania are shown in Fig No9.

7.2 ITU-R Rain attenuation Models

In order to apply rain cell models to the estimate of rain attenuation in radio hop, it is

necessary to consider how the rain cell sizes compare to the hop length. While in very short hop

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(below some 2-3 Km), the whole length may be affected by rainfall; in longer hops a rain cell

occupies only a portion of the whole distance.

ITU-R Rec P-530 defines an effective hop length DEFF, in order to take account of rain cell size,

D

DEFF = [R < 100 mm/Hr]

1 + D/ [ 35 e (-0.015R)

]

D

DEFF = [R 100 mm/Hr] 1 + 0.128 x D

Note that the effective length is a function of the local rain rate R (in mm/Hr). As shown in Fig

No10 the effective length is more compressed with high rain rates (a rain cell with high rain rate is

expected to occupy a smaller area). On the other hand, the effective length is close to the real

length as far as the later is approximately below 4 Km.

Figure 9

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Figure 10

References

1. Trevor Manning, (1999)" Microwave Radio Design guide", Airtech House Inc.

2. Ian Glover, Peter Grant, (1997)" Digital Communications", Prentice Hall.

3. Robert G Winch, (19993)" Telecommunication Transmission systems", Mc Graw Hill.

4. Darvid.M.Pozar (1999)Microwave Engineering John wileys & sons, Inc.