Radio Propagation Theory 1

PROPAGATION ISSUESIN DIGITAL RADIO LINK ENGINEERING

1997, Siemens ICN , Milano, Italy

Foreword

This Course covers the main topics in Radio Propagation, with application to theEngineering of Digital Radio-Relay Links. The aim is to provide the radio engineerwith the basic knowledge and understanding of radio propagation phenomena andtheir impact on the operation and performance of digital radio systems.

The Course makes reference to fundamentals in Radio Propagation Physics (withoutneed of complex mathematical tools in Electromagnetics theory). From this, it derives thebasic concepts in Radio Link Engineering. A detailed presentation of proceduresand computer tools for the Engineering and Planning of Radio Systems is out of thescope of this course.

The Course User is assumed to be familiar with elementary notions in Digital RadioModulations, Equipments, and Systems, as well as in Interference Analysis andPlanning and in Regulatory Issues. Some topics in the above areas are discussed, butonly in connection with propagation aspects.

Hypertextual techniques have been adopted. It is expected that this choice will improvesignificantly the flexibility and effectiveness of Computer Based Training, both inClass Presentations and in Individual (or Small Group) Use.

RADIO PROPAGATION TUTORIAL

Copyright : 1997 Siemens ICNViale P. e A. Pirelli 10, Milano, ItalyPhone +39-2-27331

Author : Luigi MorenoRadio Engineering ServicesVia Asti 10. Torino, ItalyPhone & Fax +39-11-8194575E-mail : [email protected]

USER GUIDE

Navigation through the Radio Propagation Tutorial is controlled by clicking onthe following symbols :

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RADIO PROPAGATION TUTORIAL

Copyright : 1997 ITALTEL SISTEMIVia Tempesta 2, Milano, ItalyPhone +39-2-43881 Fax +39-2-48000190

Author : Luigi MorenoRadio Engineering ServicesVia Asti 10. Torino, ItalyPhone & Fax +39-11-8194575E-mail : [email protected]

INDEX

1. Introduction Radio Link Equation Radio Link Engineering

2. Refraction through the Atmosphere Ray Curvature - Clearance and Diffraction

3. Refraction through the Atmosphere Multipath Propagation

4. Ground Reflections

5. Atmosphere and Rain Attenuation Rain Scattering and Absorption Absorption without rain

6. Propagation Related Topics Regulatory Background Interference Scenarios

HELP

About ...User Guide

1.1 - POINT-TO-POINT RADIO LINK

Tx Rx

The diagram shows the basic elements in any point-to-point radio link.

TRANSMITTER : Frequency, Tx Power, Capacity (bit/s, tel. chs., ...).ANTENNAS : Frequency range, Gain.RADIO HOP : Hop Length.RECEIVER : Frequency, Rx Threshold (related to Rx Signal Quality).

1.2 - BASIC RADIO LINK EQUATION (FREE SPACE)The basic parameters in a Point-to-Point Radio Link (see Block Diagram) areput together in the Radio Link Equation. The Radio Link Equation computesthe Rx Power in the absence of any propagation anomaly (free spacepropagation):

PR = PT + GT + GR - 92.4 - 20 Log (F) - 20 Log (L)PT = Transmitted power (dBm)PR = Received power (dBm) (normal propagation)GT = Tx antenna gain (dB)GR = Rx antenna gain (dB)F = Frequency (GHz)L = Hop length (km)

Warning : The constant 92.4 is correct only if the frequency is expressed inGHz and the hop length in km. If other units are used, the constant 92.4 mustbe modified accordingly (e.g. : with hop length in miles, the constant is 96.6).

1.3 - FREE SPACE LOSS (FSL)The Radio Link Equation can be also written as : PR = PT + GT + GR - FSLFSL is the Free Space Loss : FSL (dB) = 92.4 + 20 Log(F) + 20 Log(L)The Free Space Loss is often referred as Loss between Isotropic Antennas.In fact, for Isotropic Antennas (Gain = 0 dB), we have : PR = PT - FSL

The FSL increases 6 dB if : the hop length is doubled;

or the frequency is doubled.

Examples:

1.9 GHz 60 km FSL = 133 dB 3.8 GHz 60 km FSL = 139 dB 7.6 GHz 30 km FSL = 139 dB15.2 GHz 30 km FSL = 145 dB

0 5 10 15 20130

135

140

145

150

155

Frequency (GHz)

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60 km40 km

20 km

1.4 - ANTENNA GAIN

The antenna directivity mainly depends on the D/ ratio (antenna diameter towavelength ratio). The maximum gain is proportional to (D/)2.

Parabolic antenna : G = (pipiD/)2 = Antenna Efficiency = 0.55 - 0.65In dB units : G = 20 Log(D) + 20 Log(F) + 18.2 + 0.5 (depending on ).

Antenna gain is 6 dB higher if :

antenna diameter is doubled, for a given frequency.

frequency is doubled, for a given diameter.

0 5 10 15 2030

34

38

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46

50

Frequency [GHz]

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1.5 - LINK BUDGET

By using Logarithmic units (dB, dBm), the Radio Link Equation is put in avery convenient form. Gains and Losses are added with positive or negativesign, as in financial budgets. The Radio Link Equation is presented in the formof a simple Link Budget.

Example of a 50 km 7GHz link :Power Gains Losses

Transmitter Power PT 30 dBmTx Antenna Gain (3 m diam.) 42.5 dBFree Space Loss 143.3 dBRx Antenna Gain (3 m diam.) 42.5 dBReceived Power PR - 28.3 dBm

A more detailed Link Budget may include additional losses caused by Tx/Rxcomponents (feeders, branching, etc.) and by propagation impairments.

1.6 - TERRESTRIAL RADIO-RELAY LINKS

ELECTROMAGNETIC WAVE PROPAGATIONIN THE LOWER ATMOSPHERE, CLOSE TO GROUND,

AT FREQUENCIES IN THE RANGE 1 TO 40 GHz

In comparison with Free Space Propagation, a terrestrial radio-relay link isaffected by the presence of the atmosphere and of the ground. They producea number of phenomena which may have a severe impact on radio wavepropagation.

Propagation anomalies mainly depend on :

FREQUENCY;HOP LENGTH;METEOROLOGICAL AND CLIMATIC CONDITIONS;GROUND CHARACTERISTICS.

Propagation anomalies produce additional attenuation, which reduces the Rxpower. In most cases such phenomena are of short duration. In particularcases the Rx signal is also distorted in some measure.

1.7. - MAIN PHENOMENA RELATED TO RADIO PROPAGATIONIN THE LOWER ATMOSPHERE

Effects of the Atmosphere : Atmospheric Absorption (without rain); Refraction through the atmosphere: Ray Curvature; Refraction through the atmosphere: Multipath Propagation.

Effects of the Rain : Raindrop Absorption; Raindrop Scattering; RF Signal Depolarization.

Effects of the Ground : Diffraction through Obstacles; Reflections.

1.8 - RADIO LINK ENGINEERING - FADE MARGIN

In a well designed Radio-Relay Link, the Rx Power should be close to theFree Space Level for most of the time.

The Radio Link is usually designed in such a way that the Received Power PR(normal propagation conditions) is much greater than the Receiver ThresholdPTH .

The Fade Margin FM is defined as : FM (dB) = PR (dBm) - PTH (dBm)A Fade Margin is required to compensate for the reduction in Rx power causedby Propagation Anomalies.

The Fade Margin guarantees that the link will operate with acceptable quality,even if propagation anomalies causes Additional Losses (AdL), as long as theAdditional Loss is lower than the Fade Margin :

AdL < FM.

1.9. - OUTAGE PREDICTION

Generally speaking, an Outage is observed when the Rx power is below the RxThreshold (PR < PTH). So, the Outage Probability is :

Prob {Outage} = Prob {PR < PTH} = Prob {AdL > FM}

Fade Margin

Received Power Normal Propagation

Outage Time

Time

Threshold

1.10 - LINK BUDGET

A more complete Link Budget example (7GHz, 50 km link) is :Power Gains Losses

Transmitter Power PT 30 dBmTx Feeder & Branching Loss 1.4 dBTx Antenna Gain (3 m diam.) 42.5 dBFree Space Loss 143.3 dBAdditional Propagation Losses 3.0 dBRx Antenna Gain (3 m diam.) 42.5 dBRx Feeder & Branching Loss 1.4 dB

-------------------------------------------------

Net Path Loss 64 dBReceived Power PR - 34 dBm

Assuming the RX Threshold PTH = -77 dBm, then the Fade Margin is :

FM = PR - PTH = 43 dB

END OF CHAPTER

2.1 - ATMOSPHERE REFRACTION

The radio waves propagate along a straight line only if the electromagneticparameters in the propagation medium are homogeneous.

In the atmosphere, the Refractive Index modifies as the distance from groundincreases (Vertical Refractivity Gradient). This is due to the vertical gradientof basic atmosphere parameters, such as temperature, humidity, andpressure.

Several anomalies in EM propagation are produced by variations in therefractive index :

Ray Curvature

Multipath Propagation

Duct Propagation

2.2 - RAY CURVATURE IN ATMOSPHERIC PROPAGATION

Up to about 1 km height, the Refractive Index usually decreases with height,at a constant rate. This means that the Refractivity Gradient (rate of variation)is constant.

As a result, the path (radio ray) from the Tx to the Rx antenna is bent in somemeasure. The ray curvature is proportional to the Refractivity Gradient :thus it depends on the atmosphere parameters at any given time.

To check the visibility between the Txand Rx antennas, the joint effects ofthe Radio Ray Curvature, of theEarth Curvature, and of the terrainprofile have to be considered.

The Clearance CL is defined as thedistance of the radio ray to theground. A negative Clearance means

that a ground obstruction is higher than the ray.

CLTxRx

R Real Earth

2.3 - EQUIVALENT EARTH CURVATURE

An "Equivalent Earth Curvature" canbe defined by altering the real EarthCurvature in order that the radio raypath be straight.

The Real Earth and the Straight Raydiagrams are equivalent : the verticaldistance CL from the radio ray to theearth surface is the same in any pointof the two diagrams.

In the Equivalent Earth representationthe Earth Radius R is multiplied by afactor k. The value of the k-factordepends on the curvature of the radioray.

CLTxRx

R Real Earth

CL

Tx Rx

kREquivalent Earth

2.4 - WHAT DOES THE k-FACTOR MEAN ?

The k-factor is a measure of the ray curvature effect, produced by the variation inthe Atmosphere Refraction Index with height. So, the k-factor is related to theVertical Refractivity Gradient G. The k-factor indicates the atmosphere state ata given time and its effect to the radio ray curvature.

In a well-mixed atmosphere (Standard Atmosphere), the Refractivity decreaseswith height at a constant rate. This corresponds to the so-called StandardCondition, with a stable k-factor, equal to about 4/3.

Other k-factor conditions are :

k < 4/3

Sub-refractive Atm. Ray Path closer to the earth.

The lowest k value corresponds to the highest probability that the radio raybe obstructed

by the ground.

k > 4/3

Super-refractive Atm. Ray Path more distant from the earth.

The range of the radio transmission can be significantly expanded. Unexpectedinterference can be observed.

2.5 - FLAT EARTH REPRESENTATION

The Flat Earth Representation is analternative way to plot the Radio Raypath from the Tx to the Rx antenna.

The earth profile is forced to be flat,and the Radio Ray curvature is alteredaccordingly.

The Real Earth and the Flat Earthdiagrams are equivalent: the verticaldistance CL from the radio ray to theearth surface is the same in any pointof the two diagrams.

The Radio Rays representing differentk values

can be shown on the sameFlat Earth diagram. This is the moreusual representation, particularly incomputer aided link design.

CLTxRx

R Real Earth

CL

TxRx

Flat Earth

2.6 - REVIEW OF RADIO RAY REPRESENTATIONS

Equivalent Representations :CL equal in the three diagrams.`

Real Earth Diagram :

Equivalent Earth Diagram :(or Straight Ray)

Flat Earth Diagram :

CLTxRx

R Real Earth

CL

Tx Rx

kREquivalent Earth

CL

TxRx

Flat Earth

2.7 - VISIBILITY

Point-to-Point Radio Relay Links are usually designed under the requirementof Visibility

between the two Hop Terminals.

Two factors to be considered in Defining Visibility Criteria in a Radio Path:

Variability in Atmospheric conditions producing different ray curvatures

Tool : Statistical distributions of the k-factor.Objective : Find the Typical and Minimum k-factors appropriate for that path.

Effects of partial obstructions along the radio path

Tool : Fresnel Ellipsoids and Diffraction Analysis.Objective : Identify the Clearance Rules to be applied (minimum distance between the Radio Ray and the Ground).

2.8 - VARIABILITY OF THE k-FACTOR

The k-factor is related to the atmosphere Vertical Refractivity Gradient G(measured in N-units / km). In Standard Atmosphere G = - 40 N-units/kmand k = 4/3.

The Vertical Refractivity Gradient G and the k-factor are time varyingparameters, depending on daily and seasonal cycles and on meteorologicalconditions. Their range of variation is more or less wide, depending on theclimatic region.

In cold and temperate regions the range is rather narrow, while in tropicalregions it is very wide. Experimental observations show for example that theprobability of k 2.75), in different months.

2.9 - MINIMUM k-FACTOR

When atmospheric conditions determine the minimum k-factor, then the RadioRay is closer to the ground (maximum obstruction probability).In a radio hop an Effective k-Factor kEFF can be defined, taking into accountthe local k-factor values along the hop. For given climatic conditions, kEFF is afunction of the hop length (on long hops, kEFF is likely close to standard values;extreme atmosphere conditions are probably not present on the whole hop).

The ITU-R gives a curve ofminimum kEFF values as afunction of hop length (temperateclimate).This curve can be used inestablishing the worst casecondition to check VisibilityCriteria.

10 20 50 100 200

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Path Length [km]

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2.10 - THE FRESNEL ELLIPSOID

The Fresnel ellipsoid gives an estimate of the space volume involved in thepropagation phenomena from Tx to Rx. The points on the Fresnel ellipsoidsatisfy the relation : TxP + PRx = TxRx + /2

A radio wave through thepath Tx-P-Rx arrives at thereceiver with 180 degphase shift

with respect tothe direct path Tx-Rx.

About half of the Rx signalenergy travels through theFresnel ellipsoid. So, anyobstruction within theFresnel ellipsoid

has someimpact on the Rx power.F1 is the Fresnel Ellipsoid Radius, depending on distance L1 from the hopterminal.

TxRx

L1 L2

PF1

2.11 - THE FRESNEL ELLIPSOID - Examples

The Fresnel Ellipsoid Radius at a distance L1(km) from one hop terminal is :

F L L L FL1 300 1 1== ( ) / ( ) (m) F = Frequency (GHz) L = Hop length (km)

Note : F1 depends on the signal frequency.

In the figure : Fresnel Ellipsoid Radiusat the middle of the path (L1=0.5L).Other Path positions

:

R (L1=0.3L) = 0.92 * R (L1=0.5L)R (L1=0.1L) = 0.6 * R (L1=0.5L)R (L1=0.01L) = 0.2 * R (L1=0.5L)

0 20 40 60 80 1000

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7 GHz12 GHz

2.12 - OBSTRUCTION LOSS

The Clearance (CL) is the vertical distance from the radio ray to the ground.The Obstruction Loss depends on :

Obstruction height (normalized clearance CL/F1) Obstruction shape (knife-edge, earth curvature, ..)

In the figure : Loss in Rx Powercaused by obstructions withdifferent shapes

:1)

Knife-edge; 2) Earth curvature(beyond the horizon link);3)

Intermediate case.

The Normalized Clearance (x-axis)is positive for obstacles below theray, and negative for obstaclesabove

the ray.

1

32

-1.5 -1 -0.5 0. 0.5 1.Normalized Clearance Cl/F1

O

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2.13 - CLEARANCE CRITERIA

In any point of the Radio Path, the Clearance CL is the distance from the RadioRay (depending on the k-factor) to the ground .1) Typical and Minimum k-factors :

If possible, derive the k-factors from local data.For Temperate Climate, Minimum k-factor from ITU-R data.In the absence of specific data : Typical k = 4/3 Minimum k = 2/3.

2) Clearance Criteria : at any point between Tx and Rx :

CL > 100% F1 with Typical k CL > 60% F1 with Minimum k

When a frequency below 2 GHz is used :

CL > 60% F1 with Typical k CL > 30% F1 with Minimum k.

END OF CHAPTER

3.1 - MULTIPATH PROPAGATION

When atmospheric stratification issuch that the refractivity varieswith altitude according to particularprofiles, it may happen that theenergy from the Tx travels to the Rxover several spatially distinct paths(Multipath Propagation).

Under Multipath Propagation conditions,several "echoes" of the Tx signal arrive atthe Rx antenna with random amplitude,delay, and phase shift. The received signalcan be represented as the addition of multiple Vectors.

Tx Rx

Refractive Layer

total Rx

echo 1

n4

3

2

3.2 - IMPAIRMENTS DUE TO MULTIPATH PROPAGATION

The received power level is determined by combining a number of signalechoes.

Depending on the instantaneous phase shifts of echo components, the Rx signal is subject to fast amplitude variations. For this reason, multipath propagation is responsible of fast fading phenomena.

Echo phase shift are frequency dependent. The fade depth produced at a given time by combining signal echoes varies with frequency. Multipath fading is "frequency selective".

The frequency selective fading has a significant impact on wide-band digital signals : Amplitude and Group Delay distortions are produced (this causes Intersymbol Interference).The XPD (Cross Polarization Discrimination)pol.) is reduced during Multipath events. This enhances the Interference between X-pol. channels.

3.3 - MULTIPATH FADING EVENTS

Multipath events are observed with daily and seasonal cycles, whenatmospheric stratification is more likely to happen. They are more frequent withstrong evaporation (high temperature and humidity), absence of wind, and flatterrain.

During multipath propagationevents, the Rx signal levelvaries very fast. It may bealmost cancelled, for shortperiods (fraction of a second, orfew seconds). A multipathactivity period can last someminutes or even one hour ormore.

Multipath activity depends onenvironmental conditions and on

radio link parameters.Particularly in tropical climates, long multipath eventscan be observed.

Time

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3.4 - MULTIPATH FADING STATISTICS

When the Rx signal is produced by a large number of components (vectors withrandom phases), then the Rx power level is variable, with Rayleigh statistics.

The Probability of having a fadedepth A (dB) greater than a givendepth Ao is (Rayleigh formula) :

Prob {A>Ao} = Po 10-Ao/10

Po = Multipath OccurrenceFactor. It is a measure of themultipath activity in a radio hop.

? How to know Po ?

Operating Hop : Po is estimated by monitoring the Rx Power and by processing the measured data.

Hop under Design : Po is predicted by empirical propagation models.

0 10 20 30 40 50

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3.5 - MULTIPATH OCCURRENCE FACTOR

The Multipath Occurrence Factor Po depends on : Frequency;

Hop Length;

Climatic conditions;

Terrain.

Po can be predicted using empirical formulas, proposed by ITU-R and by

operating companies or research labs. A general formula is :

Po = K Q Fa Lb where : F = Frequency; L = Hop Length;

K = Geo-climatic Coefficient;Q = Terrain Coefficient;

The Frequency Exponent is close to unity. This means that the fading activityin a given hop is proportional to the frequency (at 11 GHz is approximately twicethan at 5.5 GHz).The Distance Exponent is in the range 3 - 3.6. This means that the fadingactivity , for a given frequency, climate, and terrain, is increased about ten timesif the hop length is doubled.

3.6 - MULTIPATH OCCURRENCE FACTOR - Examples

6 GHz hop : According to the prediction models, Po expected in the ranges :

30 km 50 km 65 kmDry climate, mountains 0.01 - 0.05 0.05 - 0.2 0.12 - 0.5Temperate clim., average terrain 0.05 - 0.12 0.2 - 0.6 0.5 - 1.5Tropical, humid clim., average terrain 0.15 - 0.4 0.8 - 2.0 1.8 - 4.5Tropical, humid clim., wet terrain 0.4 - 2.0 2.0 - 10. 5.0 - 20

Linear scaling to other frequencies :

3 GHz

divide by 2 the Po values computed for the 6 GHz hop

12 GHz

multiply for 2 " " " " " " "

? How to use Po predictions ?

Po = 1

Fade Depth > 30 dB for 2600 seconds / one month.

Any Fade Depth :

divide seconds by ten for 10 dB deeper fade

(e.g. Po = 1 Fade Depth > 40 dB for 260 seconds / one month).Other Po values : linear scaling

(number of seconds proportional to Po).

3.7 - FREQUENCY SELECTIVE FADING

The phase shift between signal echoes depends on frequency. As a result, thefade depth is varying with frequency

(frequency selective fading).During Multipath Events, a signalbandwidth of some 20 MHz maybe subject to slope distortion(fade depth maximum at one endand minimum at the other), or tonotch distortion

(maximum fadedepth within the signal band)Amplitude distortion is associatedto Group Delay distortion.

Frequency selectivity is fastvarying. This dynamic effectcan be observed as a fast-varying slope or even as a fast moving notchtrough the signal bandwidth.

FrequencyF

a

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SlopeNotch

3.8 - EFFECTS OF FREQUENCY SELECTIVE FADING

If the signal bandwidth is narrow (few MHz), the selective fading effect isnegligible. Multipath fading is assumed as a flat attenuation.

On the other hand, for wide-band signals (medium and large capacity digitalsignals), the attenuation within the signal band produces a significantdistortion in the received signal.

When a digital signal is distorted by selective multipath fading, the Bit Error Rate(BER) may be at the threshold level (10-3)

even if the Rx power is higherthan the Rx threshold. The final effect is a reduction in the Fade Margin.

Narrow-Band signals Wide-Band Signals

(almost) Flat Attenuation Frequency Selective Attenuation

Reduction in Rx Power Reduction in Rx Power + Signal Distortion

3.9 - SIGNATURE MEASUREMENT

The sensitivity of a digital radio equipment to multipath distortions can beestimated by laboratory measurements ("Equipment Signature").The Tx signal passes through a simulated multipath channel, modelled by adirect path plus echo (2-path channel). This produces a frequency selectiveresponse : Notch Depth = maximum Fade Depth within the signal bandwidth;

Notch Frequency = notch position, relative to the signal carrier.

The Notch Depth and Frequency arevaried (adjusting amplitude and phase ofdirect and echo signals). In each conditionthe Bit Error Ratio (BER) is measured.In the Notch Depth / Notch Frequencyplane, the Signature gives the region(Notch parameters) with BER > 10-3 (orany other threshold). The area below theSignature

gives a measure of the receiversensitivity to multipath distortions.

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Relative Notch Position [MHz]-10 -5 0 5 10 15-15

BER > 10-3

BER < 10-3

3.10 - MULTIPATH FADING OUTAGE TIME PREDICTION

Outage Events are usually defined as time periods with Bit Error Rate (BER)

higher than a threshold (usually 10-3).Note :

More complex definitions are required if reference is made to qualityevaluation on errored blocks (ITU-T Error Performance Rec. G.826).The Probability of Outage due to Multipath Events can be predicted by meansof a Multipath Fading Statistical Model. It must include specific models for :

Flat Attenuation (Po prediction);Frequency Selective Fading (prediction of channel dispersion and its effect on receiver performance);XPD Degradation (prediction of reduction in XPD associated to signal attenuation).

3.11 - MULTIPATH FADING OUTAGE TIME PREDICTIONWIDE-BAND SIGNALS

With Wide-Band signals, Fading Selectivity must be considered. Severalstatistical models have been proposed; some are described in ITU-R Recs.

A general formula for the Outage Time Tout, during the observation period To,is :

Tout = To POUT = To [ PT + PS ]PT = Po 10-FM/10 Non-Selective Outage Probability (related to signal

attenuation only; same as for narrow-band signals);PS = Selective Outage Probability (related to signal distortion). Computed on

the basis of the Receiver "Signature" (sensitivity to signal echoes).An alternative formula for combining PT and PS is :

Tout = To [ PT/2/2 + PS/2/2] 2/ = 1.5 - 2 is an empirical constant.

3.12 - MULTIPATH COUNTERMEASURES

Techniques used to reduce the multipath fading impairment in digital systems :

Adaptive Signal Equalization at the Receiver.

Diversity Reception : Space Diversity;Angle Diversity;Frequency Diversity.

For each Multipath Countermeasure, the Improvement Factor IF is defined :

IF = Tout (Unprotected) / Tout (with Countermeasure)where Tout = outage time.

The Improvement Factor can be predicted by means of Statistical Modelsincluding the effect of each specific countermeasure. When both Equalizationand Diversity

are used, the overall Improvement Factor is approximately givenby the product of the factors relevant to each technique (Synergistic Effect).

3.13 - ADAPTIVE EQUALIZATION

An Adaptive Equalizer is a circuit used at Rx, to partially compensate forsignal distortion. Adaptativity means that the equalizer response modifies,depending on the received signal.

In the Intermediate Frequency (IF) implementation, the equalizer amplifies thespectral components more deeply attenuated by fading. In the Base Band (BB)implementation, the equalizer cancels from each signal sample the componentdue to Intersymbol Interference (ISI). This technique is usually more effective.

The effectiveness of a signalequalizer can be appreciated bycomparing the receiver signatureswith and without the equalizer.The reduction in the area below thesignature curve gives a measure ofthe improvement provided by theequalizer.

N

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Notch Frequency [MHz]-10 -5 0 5 10 15-15

With Equalizer

Without Equalizer

3.14 - SPACE DIVERSITY

Two antennas are usually arranged on a single structure, with a suitable

vertical spacing. Typical spacing : 150 - 200 wavelengths.

The correlation of fade depth at the two antennas decreases as the antennaspacing increases. Thus the probability of deep fading at the two antennasat the same time can be made sufficiently low, with a suitable antennaspacing.

The relation between antenna spacing and correlation in signal distortion ismore controversial. It appears that also with small spacing a low correlationis obtained.

Signal Processing Options : Technique : Switch to the best signalCombine

both signalsObjective : Maximum Power

Minimum DistortionImplementation : at RF, IF, or BB.

3.15 - FREQUENCY DIVERSITY

Multipath fading is frequency selective. In multi-channel radio systems(usually with about 20 - 30 MHz spacing), not all the RF channels are deeplyfaded at the same time.

An RF stand-by channel is usually available (In 1+1 or N+1 arrangement) forequipment failure. It can be exploited also for multipath protection.

The traffic of a low quality (deeply faded) working channel can be switched tothe stand-by channel, with high probability of a significant quality improvement.

In some cases, the stand-by channel can be in a different RF band (Cross-band frequency diversity). Example : 7 GHz system with 11 GHz protection.Fast quality detector and switching circuits

are required (Hitless Switching:without errors or frame loss caused by the switching itself).

3.16 - PROPAGATION THROUGH DUCTS

In extreme cases, atmospheric layering may be such that radio propagation isconfined within a sort of waveguide

(radio duct). Ducts are classified as :Surface Ducts :

if the duct lower boundary is the earth surface;Elevated Ducts :

if the duct lower boundary is above the earth surface;

Duct propagation is characterized by attenuation well below the free spacevalue. So, if the Rx antenna is within the duct, the Rx signal may be muchhigher than in normal conditions. On the other hand, If the Rx antenna is out ofthe duct, rather long signal fadings are observed. Duct propagation may bealso responsible of unexpected interference at very long distance.

There is no general approach for a statistical prediction of duct events.However, in specific cases, the analysis can be based on the identification ofrefraction conditions leading to the duct formation. Then, if statistical localdata on refractivity gradient distribution

are available, the ducting probabilitycan be estimated.

END OF CHAPTER

4.1 - GROUND REFLECTIONS

Depending on the Path Profile, it may happen that a portion of the Tx radiosignal is reflected by the ground toward the Rx antenna. At the receiver, inaddition to the direct signal (D), a reflected signal (R) arrives.In most cases, the presence of a ground reflection is rather critical :

Fluctuations in the Rx signal level, even for long time periods; Enhancement of Multipath Activity (the reflected signal is not added to a stable direct signal, but to the fast-varying multipath signal);

Reduction of Space Diversity effectiveness as a countermeasure to multipath.

As far as possible, reflections should be avoided by :

Route Planning (in particular over-water paths);Site Selection : Obstruction of the reflected ray can be obtained in some cases,by suitable selection of the radio sites and of antenna heights.

4.2 - REFLECTION GEOMETRY

Geometrical parameters related to the Reflection mechanism :

Reflection point P;

Grazing angle ;

Direct path length D;

Reflected path lengthR1+R2;

Angles 1, 2 betweenDirect and Refl. Rays.

These parameters are varying with time, because of varying propagationconditions (k-factor).

TxRx

PR1 R2

D1

2

4.3 - RX SIGNAL WITH REFLECTION

In the presence of reflection, the overall received signal (S) is given by the(vectorial) addition

of the direct (D) and the reflected (R) signals :S = D + R

The result of adding the two vectors D and R depends on:

Relative amplitude of D and R :

reflection loss : depends on the surface type (worst case : 0 dB e.g. water); divergence factor : due to the spherical earth surface (usually a small loss); antenna directivity : depends on path geometry and antenna beamwidth.

Phase shift between D and R :

direct and reflected path length difference (expressed in multiples of the wavelength ; 360 deg. phase shift for each ) ; reflection shift : depends on frequency, grazing angle, and surface type

(usually close to 180 deg;).

4.4 - RX SIGNAL LEVEL

If the antenna height is varied, then the path length difference and the phaseshift between the Direct and the Reflected signal change. As a result, theRx signal level is a function of the Antenna Height.

Direct and Reflected signals co-phased Maximum Rx level" " " " phase-opposed Minimum Rx level

The exact positionscorresponding to themaximum andminimum Rx levelchange withpropagationconditions (k-factor).

Rx Level

TxRx

4.5 - SPACE DIVERSITY IN REFLECTION PATHS

The Rx level varies with the antenna height, but the position of the maximum Rxlevel is not stable, due to varying propagation conditions (k-factor). With twoantennas, a good Rx level can be expected at least at one antenna.

Space Diversity Engineering : Antenna Spacing : The optimum value is computed, but again it depends on the k-factor. Design Rule : Compute Spacing for k=4/3 and check for higher and lower k-factors.

Position of the lower antenna : In general, as low as possible, in order to :Obstruct (at least partially, if possible) the reflected ray;Minimize path difference and reflected signal delay.

Clearance : For the Lower Antenna, in most cases, Clearance=0 is enough;Usual rules for the Higher Antenna.

Implementation Options : BB Switching to the best signal; RF or IF Adaptive Combining (as for Multipath countermeasure); RF Combining (Anti-Reflection System).

4.6 - EFFECT OF ECHO DELAY

The Reflected Ray Delay must be compared with the Symbol Period Ts

ofthe digital signal. Depending on and Ts, the reflection effects are :

5.1 - PROPAGATION THROUGH RAIN

Main phenomena associated to Radio Propagation in the presence of Rain :

Scattering : part of the EM energy is re-irradiated by the raindrops in every

directions.

Absorption : part of the EM energy is transferred to the water molecules in

the raindrops.

De-polarization : the polarization plane (e.g. Vertical) of the incident radio

signal is rotated, thus producing a cross-polarized (e.g. Horizontal) component.in the signal at the receiver.

These phenomena are sensitive to :

Signal Frequency (wavelength compared to the drop size);

Signal Polarization (this is related to not-spherical drop shape);

Rain Intensity.

5.2 - RAIN ATTENUATION

A radio wave travelling throughrain drops is subject to scatteringand absorption phenomena. Inthis process, part of the signalenergy

directed to the receiver islost.

The Rain Attenuation : is measured in dB/km; increases with frequency, but can be assumed as uniform (flat) within a radio channel bandwidth;

increases with rain intensity; with Horizontal Pol. is higher than with Vertical Pol.;

produces fades usually several minutes long.

20

100

5

1

0.2

0.05

0.01100 5002051

0.25 mm/h

1.25

5

25

100

Frequency [GHz]

S

p

e

c

i

f

i

c

A

t

t

e

n

u

a

t

i

o

n

[

d

B

/

k

m

]

5.3 - ITU-R RAIN REGIONS

In temperate climates, frequencies below about 10 GHz are not significantlyaffected by rain. On the other hand, in tropical climates rain effects are to beconsidered even at 5-6 GHz. The ITU-R provides a world map of rain regions.

For each region, the rainrates

(mm/h) for giventime percentages arereported.

Rain Attenuation Modelsmake reference to RainRates corresponding tosmall time percentages(0.01 %).

5.4 - ITU-R RAIN ATTENUATION MODEL

A step-by-step procedure is recommended by ITU-R :

1) Find the rain rate R for 0.01% of time (from ITU-R maps, or from local data).2) Compute the specific loss ((

(dB/km) corresponding to the rain rate R and tothe wave frequency and polarization (H or V) (formulas are given by Rec. 838).3) Compute the Effective Hop Length Leff (km) (the real length is reduced,taking into account the rain cell size) (formulas are given by Rec. 530).4) Compute the Attenuation for p = 0.01% of time : A0.01 (dB) = (( Leff.5) The attenuation for other time percentages (in the range 1% to 0.001%) iscomputed from A0.01, (formulas are given by Rec. 530).As a result, a curve can be plotted of Rain Attenuation vs. Time Percentage,valid for given rain region, frequency, polarization, and hop length)

5.5 - RAIN UNAVAILABILITY PREDICTION

From the Time % vs. RainAttenuation curve, theUnavailability is computedas the time percentagewith attenuation greaterthan the Fade Margin.

In the Figure a 38 dB FadeMargin is assumed. Thenthe Rain Unavailability isabout 0.0025% (about 12minutes / year)..The prediction methodderives from long-term rain

rate statistics. Therefore, the Rain Unavailability Prediction must beconsidered as an average, to be expected during a period of several years.

0 10 20 30 40 500.001

0.01

0.1

1

Attenuation [dB]

Region L 50Km11GHz Pol. H

FM

%

o

f

T

i

m

e

5.6 - OTHER RAIN IMPAIRMENTS

Effect of De-Polarization : In radio links using the co-channel plan (twocross-polar radio channels at the same frequency) the C/I ratio is guaranteed bythe isolation between H and V polarizations. In the absence of rain, theantenna XPD

can provide a C/I ratio well above 25 dB.

Rain de-polarization reduces the C/I ratio at the receiver. A statistical model

is proposed by ITU-R Rec. 530. Example : In a 13 GHz link, with 40 dB rainattenuation, the XPD is reduced to about 16 dB (according to the ITU model).While an increase in Tx power (and in fade margin) reduces rain unavailabilitydue to rain fading, it is of no help for rain de-polarization.

Effect of Scattering : The scattering of radio wave energy produced by rain

drops may cause interference to other radio systems. This effect is particularlysignificant with high Tx power (e.g. interference from satellite earth stationsto radio-relay links). The procedures for the evaluation of the Co-ordinationArea around Earth Stations (ITU-R Rec. 615) include an estimate of this effect.

5.7 - ATMOSPHERIC ABSORPTION

The power loss caused by Atmospheric Absorption is usually not significant andcan be neglected in the Link Budget. Only in particular frequency bands thiseffect is to be considered.

Frequency Bands affected byAtmospheric Absorption Peaks :

22.5 GHz (water vapour) Max Attenuation = 0.18 dB / km

60 GHz (oxygen)Max Attenuation = 16 dB / km.

The figure is valid for :sea leveltemperature : 15 Cwater vapour : 7.5 g/m3

H2O

O2

10 20 50 1000.01

0.1

1

10

Frequency [GHz]

A

t

t

e

n

u

a

t

i

o

n

[

d

B

/

k

m

]

5.8 - USE OF 22.5 AND 60 GHz FREQUENCY BANDS

Radio systems operating in the 22 - 23 GHz bands are only marginallyaffected

by atmospheric absorption. In temperate climates, hop lengths aregenerally limited below 10 - 12 km because of rain attenuation. The additionalattenuation due to water vapour absorption is small (2 to 3 dB depending ontemperature and humidity), but is to be considered in the link budget.The 60 GHz band is not presently in commercial use. It could be used for veryshort hops

(e.g. building-to-building links).

Propagation impact on Interference : The very high attenuation at 60 GHz

allows the re-use of the same RF carrier within a short distance, without mutualinterference (small re-use distance). A high efficiency in spectrum utilizationcan be achieved.

END OF CHAPTER

6.1 - REGULATORY ISSUES

Main topics, relevant to Digital Radio-Relay Systems, dealt with by Regulatorybodies :

Performance Objectives : The Error Performance and Availability Objectives

for Digital Networks are recommended by the ITU-T, regardless of thetransmission medium.

ITU-T Recommendations are taken into account in producing the ITU-R Errorperformance and Availability Recommendations, which are specific for the caseof Digital Radio-Relay Systems.

Use of RF Bands : The International Radio Regulations define the type of

radio services operating in each RF band, on a primary or secondary status.

For the RF bands assigned to the (Terrestrial) Fixed Radio Service, the ITU-Rrecommends the adoption of Frequency Plans, with detailed specification of theRF carrier position, channel spacings, guard bands, etc.

OBJECT. RF BANDS

6.2 - ITU PERFORMANCE OBJECTIVES FOR DIGITAL PATHS

ERROR PERFORMANCE OBJECTIVES based on :

Quality Parameters (among them : SES = Severely Errored Second i.e. a

period of 1 second with a severe performance degradation)

Max. Time Percentages for each quality param. below given thresholds.

AVAILABILITY OBJECTIVES based on :

Definition of Availability : After 10 consecutive SES events , Unavailability

is detected. The 10 seconds are part of the Unavailable time. After 10 consecutive non-SES events Availability is detected. The 10 seconds are part of the Available time.

Max. Unavailable Time Percentage

Note : Error Performance Objectives are checked only during Available Time.

6.2 - ITU-R AVAILABILITY OBJECTIVES

New ITU-T Rec. (and related ITU-R Rec.) under study.ITU-R Recs.for a 2500 km Reference Path, including High Grade, MediumGrade, and Local Grade Links.

High Grade Basic Objective : Unavailability < 0.3%Allocation Criteria : Distance scaling for Radio Sections down to 280 km;

Block Allocation for shorter Radio Sections.

Unavailability produced by : Propagation (usually 1/3 of objective) Equipment failures (usually 2/3 of objective).

Unavilability is usually measured on a one year basis, but objectives should besatisfied as a multiple year average.

6.3 - ITU-T ERROR PERFORMANCE OBJECTIVES

Two approaches : Rec. G.821 Rec. G.826

First Issue 1980 1992

Ref. Connection 27,500 km 27,500 kmRadio Link part of : ISDN Connection PDH and SDH transport

ATM Connection

Bit Rate Below Primary Rate At or Above Primary Rate

Performance criteria Errored Bits Errored Blocks

Definition of Errored Second (ES) : One Second with >= 1 Errored Bit (Block).Different definitions for Severely Errored Seconds (SES).Only in G.826 : Background Block Error (BBE)ES / total available seconds : < 0.08 in G.821; depending on bit rate in G.826;SES / total available seconds : < 0.002 both in G.821 and G.826.

6.4 - ITU-R ERROR PERFORMANCE OBJECTIVES

Reference : ITU-T Rec. G.821

ITU-T Objectives are scaled to a 2500 km Reference Path, including HighGrade, Medium Grade, and Local Grade Quality.

High Grade Basic Objective : BER > 10-3 less than 0.054% of Available Time.Allocation Criteria : Distance scaling for Radio Sections down to 280 km; BlockAllocation for shorter Radio Sections.

Reference : ITU-T Rec. G.826

Objectives scaled to a 2500 km Reference Path, with International Portion andNational Portion

(intermediate or terminating countries)Allocation Criteria : Block Allowance Factor + Distance Allocation Factor.

6.5 - IMPACT OF PROPAGATION ON PERFORMANCE OBJECTIVES

Performance Impairment DegradationPeriod

Performance Objective

RainObstruction Fading (Sub-Refractive Conditions)Interference (Super-Refractive Conditions)

>= 10 seconds Availability

Multipath FadingShort Term Uncorrelated Interference

< 10 seconds Error Performance (SES)

Long Term Correlated Interference

Not Significant Error Performance (ES and BBE)

6.6 - ITU-R RECOMMENDED FREQUENCY PLANS

General characteristics :

Separate sub-bands for Tx and Rx channels, with a central guard band (one exception : U.S. TD 4 GHz plan, with alternate Tx and Rx channels).

Constant channel spacing between co-polarized channels.

Two types of channel arrangements : Interleaved PlanCo-Channel Plan

Criteria followed in the ITU-R Frequency Plan activity :

Below 12 GHz : Compatibility of Channel Arrangements in the transition from

Analog to Digital systems.

Above 12 GHz : Channel Arrangements optimized for Digital systems.

6.7 - INTERLEAVED CHANNEL ARRANGEMENT

x = Co-polar. .channel spacing

y = Centralguard band

z = Edgeguard band

Interferences : two adjacent X-pol. signals, channel spacing F = x/2two adjacent Co-pol. signals, channel spacing F = x

Comment : Recommended in analog systems (frequency reuse not possible)

Adopted also for digital systems below 12 GHz.

...

z

x

1

Pol.

H(V)V(H)

2

3

4 Ny

1

2

3

4 N

...

z

F

GO CHANNELS RETURN CHANNELS

N-1 N-1

x/2 x/2

6.8 - CO-CHANNEL ARRANGEMENT

x = Co-polar.channel spacing

y = Centralguard band

z = Edgeguard band

Interferences : one X-pol. signal at the same frequency (F = 0)two adjacent Co-pol. signals, channel spacing F = xtwo adjacent X-pol. signals, channel spacing F = x

Comment : Suitable for digital systems, short hops, simple modulations

Recommended in frequency bands above 12 GHz (only digital)Recently adopted in some frequency bands below 12 GHz (x-pol. interference canceller required for complex digital modulations)

...

z x

1

Pol.

H(V)V(H)

2

3

4 N

y

1

2

3

4 N

...

z

F


6.9 - INTERFERENCE CLASSIFICATION

From the Propagation point of view :

Correlated : the interfering signal is subject to the same propagation conditions

as the useful signal (same fade depth for the two signals, at the same time).Uncorrelated :

the interfering and the useful signals are subject to differentpropagation conditions (worst case: interference at the nominal level, while theuseful signal is at the threshold level).

From the Signal Source point of view :

Intra-System (Internal) Interference : coming from the same radio site or from

other sites in the same radio system. Signal parameters are known by thesystem designer in detail . It includes correlated and uncorrelated interference.

Inter-System (External) Interference : coming from other radio systems,

sometimes only partially known by the system designer. Usually, it has to beconsidered as uncorrelated interference.

6.10 - INTERFERENCE SCENARIO

In te rfe red R ece iv er

C lick o n

fo r d e ta ils

D esired S ig n a l In te rfe rin g S ig n a l P a th O th er U sefu l S ig n a ls

END OF CHAPTER

INTERFERENCE SCENARIO - Same Hop Interference

Co-Channel Frequency Arrangement : Same Frequency, X-pol.

Adjacent channel, Co-pol.

Interleaved Frequency Arrangement : Adjacent channel, X-pol.

INTERFERENCE SCENARIO - Same Frequency X-pol.

Type of Interference : Intra-System, Same Hop(only in Co-Channel Frequency Arrangement)

Frequency Spacing : zero

Polarization : X-polar

Discrimination from : Antenna XPD

Propagation issues : Multipath : Partially correlated interference. Multipath outage prediction models include the XPD degradation effect.

Rain : Correlated interference, but with XPD degraded by rain de-polarization effect.

INTERFERENCE SCENARIO - Adjacent Channel Co-pol.Type of Interference : Intra-System, Same Hop

(only in Co-Channel Frequency Arrangement).Frequency Spacing : x (x = co-polar minimum spacing)Polarization : Co-polar

Discrimination from : Tx & Rx Filtering (NFD)Propagation issues : Multipath : Partially Uncorrelated Interference.

Correlation can be evaluated by Frequency Diversity Models

Rain : Correlated interference (same fade depth as desired signal).

INTERFERENCE SCENARIO - Adjacent Channel X-pol.Type of Interference : Intra-System, Same Hop

(significant only in Interleaved Frequency Arrangement,usually negligible in Co-channel arrangement)

Frequency Spacing : Interleaved Plan x /2Co-channel Plan x (x = co-polar minimum spacing)

Polarization : X-polar

Discrimination from : Antenna XPD and Tx & Rx Filtering (NFD).Propagation issues : Multipath : Partially correlated interference. Multipath

outage prediction models include the XPD degradation effect.

Rain : Correlated interference, but with XPD degraded by rain de-polarization effect.

INTERFERENCE SCENARIO - Next Hop, Tx to Rx

Type of Interference : Intra-System, Any Frequency Arrangement

Frequency Spacing : > y (y = central guard-band)Polarization : usually X-polar, at least for min. spacing (not always)Discrimination from : Tx & Rx Filtering (NFD), Antenna back-to-back

decoupling.

Propagation issues : Uncorrelated interference.

Antenna Back-to-back decoupling degraded by nearby reflections.

INTERFERENCE SCENARIO - Next Site, Front-to-Back


Frequency Spacing : co-channel (worst case)Polarization : usually X-polar (not always)Discrimination from : Tx Antenna Front-to-Back discrimination.

Propagation issues : Rain : Correlated interference.

Multipath : Partially uncorrelated (space diversity effect)Antenna Front-to-Back discrimination degraded by nearby reflections.

INTERFERENCE SCENARIO - Adjacent HopType of Interference : Intra-System, Any Frequency Arrangement

Frequency Spacing : co-channel (worst case)Polarization : usually X-polar (not always)Discrimination from : Rx Antenna Front-to-Back discrimination

Propagation issues : Rain : Uncorrelated interference (partial correlation if raincell close to Interfered Rx).Multipath : Uncorrelated interference

Antenna Front-to-Back discrimination degraded by nearby reflections.

INTERFERENCE SCENARIO - Same Hop Tx to Rx


Frequency Spacing : > y (y = central guard-band)Polarization : usually X-polar, at least for min. spacing (not always)Discrimination from : Tx & Rx Filtering (NFD), Antenna Tx/Rx decoupling (or

antenna side-to-side decoupling if two antennas are used) .

Propagation issues : Uncorrelated interference.

Reflections nearby the radio site very dangerous if the Tx signal is reflected toward the Rx.

INTERFERENCE SCENARIO - Overreach


Frequency Spacing : co-channel

Polarization : Co-polar

Discrimination from : Tx and Rx Antenna angular discrimination (if hops are not in line). Additional Free Space Loss for interfering signal

Propagation issues : Rain : Correlated Interference, as far as the Interfering path is close to the desired signal path.

Multipath : Uncorrelated.

The check of Clearance for the Interfering signal path must be based on worst case assumption (effect of super-refractive propagation, k-factor > standard value).

INTERFERENCE SCENARIO - Other System

Type of Interference : Inter-System

Frequency Spacing : co-channel (worst case)Polarization : Co-polar (worst case)Discrimination from : Tx and Rx Antenna angular discrimination.

Tx & Rx Filtering (NFD) if not co-channelPropagation issues : Uncorrelated interference.

The check of Clearance for the Interfering signal path must be based on worst case assumption (effect of super-refractive propagation, k-factor > standard value).

INTERFERENCE SCENARIO - Node

Type of Interference : Inter-System

Frequency Spacing : Co-channel (worst case)Polarization : Co-polar (worst case)Discrimination from : Rx Antenna angular discrimination.

Tx & Rx Filtering (NFD) if not co-channelPropagation issues : Rain : Partially correlated if Rx angle is small

Multipath : Uncorrelated interference.

0 5 10 15 2030

34

38

42

46

50

Frequency [GHz]

A

n

t

e

n

n

a

G

a

i

n

[

d

B

] 4m3m

2m

1m

0.5m

CLTxRx

R Real Earth

CLTxRx

R Real Earth

CL

Tx Rx

kREquivalent Earth

CLTxRx

R Real Earth

CL

TxRx

Flat Earth

10 20 50 100 200

1.1

0.9

0.7

0.5

0.3

Path Length [km]

k

e

f

f

TxRx

L1 L2

PF1

0 20 40 60 80 1000

10

20

30

40

50

60

Hop Length [km]

F

r

e

s

n

e

l

R

a

d

i

u

s

[

m

]

2 GHz4 GHz

7 GHz12 GHz

132

-1.5 -1 -0.5 0. 0.5 1.Normalized Clearance Cl/F1

O

b

s

t

r

u

c

t

i

o

n

L

o

s

s

[

d

B

]

-10

0

10

20

30

40

No

t

c

h

D

e

p

t

h

[

d

B

]

Relative Notch Position [MHz]-10 -5 0 5 10 15-15

BER > 10-3

BER < 10-3

No

t

c

h

D

e

p

t

h

[

d

B

]

Notch Frequency [MHz]-10 -5 0 5 10 15-15

With Equalizer

Without Equalizer

TxRx

PR1 R2

D1

2

Rx Level

TxRx

20

100

5

1

0.2

0.05

0.01100 5002051

0.25 mm/h

1.25

5

25

100

Frequency [GHz]

S

p

e

c

i

f

i

c

A

t

t

e

n

u

a

t

i

o

n

[

d

B

/

k

m

]

0 10 20 30 40 500.001

0.01

0.1

1

Attenuation [dB]

Region L 50Km11GHz Pol. H

FM

%

o

f

T

i

m

e

H2O

O2

10 20 50 1000.01

0.1

1

10

Frequency [GHz]

A

t

t

e

n

u

a

t

i

o

n

[

d

B

/

k

m

]

INTERLEAVED CHANNEL PLAN

...

z

x

1

Pol.

H(V)V(H)

2

3

4 Ny

1

2

3

4 N

...

z

F


N-1 N-1

x/2 x/2

CO-CHANNEL PLAN

...

z x

1

Pol.

H(V)V(H)

2

3

4 N

y

1

2

3

4 N

...

z

F


0 5 10 15 20130

135

140

145

150

155

Frequency (GHz)

F

r

e

e

S

p

a

c

e

L

o

s

s

[

d

B

]

60 km40 km

20 km

Prob {A>Ao} = Po 10-Ao/10 In this Figure : Po = 1

0 10 20 30 40 50

0.0001

0.001

0.01

0.1

1

Ao [dB]

P

r

o

b

{

A

>

A

o

}

10 dB/dec

-40

-30

-20

-10

0

10

Frequency

A

m

p

l

i

t

u

d

e

[

d

B

]

fo fo+1/

b=1

b=0.9

b=0.5

Frequencyfo fo+1/

b=0.5

b=0.9

b=0.95N

o

r

m

.

g

r

o

u

p

d

e

l

a

y

To Probe Further :

Glossary - Radio Transceivers Glossary - Antennas

To Probe Further :

Derivation of the Radio Link Equation Definition of Logarithmic Units

To Probe Further :

Loss vs. Distance in Radio and Cables Derivation of the Radio Link Equation

To Probe Further :

Glossary - Antennas Definition of Antenna Gain

To Probe Further :

Definition of Logarithmic Units

To Probe Further :

Atmosphere Structure and Refraction Effects of Vertical Refractivity Gradient

To Probe Further :

Fresnel Ellipsoid and Optical Analogy Diffraction Analysis

To Probe Further :

Effects of Vertical Refractivity Gradient Vectorial Addition of Multiple Signals

To Probe Further :

Vectorial Addition of Multiple Signals Rx Signal Level vs. Time and Frequency

during Multipath Events

To Probe Further :

Vectorial Addition of Multiple Signals

To Probe Further :

Vectorial Addition of Multiple Signals Formulas for Po prediction

To Probe Further :

Formulas for Po prediction

To Probe Further :

Rx Signal Level vs. Time and Frequency during Multipath Events

To Probe Further :

Effects of Multipath Distortion on Digital Signals

To Probe Further :

Signature Measurement

To Probe Further :

Selective Fading Prediction Models Signature Measurement De-Polarization due to Multipath

To Probe Further :

Formulas for Po Prediction Vectorial Addition of Multiple Signals

To Probe Further :

Selective Fading Prediction Model Signature Measurement De-Polarization due to Multipath Maximum Hop Length (Rain & Multipath)

To Probe Further :

Selective Fading Prediction Model

To Probe Further :

Angle Diversity

To Probe Further :

Vectorial Addition of Two Signals Reflection Coefficients

To Probe Further :

Anti-Reflection System

To Probe Further :

Vectorial Addition of Two Signals

To Probe Further :

Radio Wave Propagation through Rain De-Polarization due to Rain Other Hydrometeor Effects (fog, snow)

To Probe Further :

Radio Wave Propagation through Rain

To Probe Further :

ITU-R Model for Rain Unavailability Prediction De-Polarization due to Rain

To Probe Further :

ITU-R Model for Rain Unavailability Prediction Maximum Hop Length (Rain & Multipath)

To Probe Further :

De-Polarization due to Rain Other Hydrometeor Effects (fog, snow)

To Probe Further :

RF Bands Assigned to the Radio Fixed Service (FS)

To Probe Further :

ITU-T Error Performance Objectives

To Probe Further :

Status of ITU-R Recs. on Performance Objectives

To Probe Further :

RF Bands Assigned to the Radio Fixed Service (FS)

To Probe Further :

Formulas for Po prediction

To Probe Further :

Selective Fading Prediction Models Equalization Improvement

To Probe Further :

Angle Diversity Diversity Improvement Selective Fading Prediction Models

To Probe Further :

Diversity Improvement Selective Fading Prediction Models

To Probe Further :

Rain Rates in ITU-R Regions

GLOSSARY - Radio Transceivers

Tx Power : The RF power at the Radio Transmitter Output (usually manufacturer data do not include loss in the RF branching system).Tx Capacity : The amount of information delivered at the Tx input and available at theRx output (usually expressed in bit / second, or telephone chs, or TV chs., etc.).Path Bit Rate : Bit Rate (bit/second) actually transmitted on the radio path (it is usuallyhigher than the Tx Capacity, due to bits added by the Tx radio equipment for channelcoding, service channels, framing, etc.)Tx Frequency : The Carrier Frequency in the Emitted Signal.

Emitted Spectrum : The distribution of emitted RF energy at frequencies around the TxCarrier Frequency. It depends on the (Path) Bit Rate, Modulation technique and TxFiltering (Tx Spectral Shaping).Tx Spectral Shaping : The overall effect of Tx Filters in limiting the Emitted Spectrum.

Rx Power (nominal) : The RF power at the Radio Receiver Input in normal propagationconditions.

Glossary - Radio Transceivers

Rx Power (actual) : The RF power at the Radio Receiver Input, at a given time,including propagation losses present at that time.

Rx Threshold : The minimum RF power at the Rx input, required for the Receiver tooperate above a threshold of acceptable quality.

Reception Quality : The result of comparison between the original information deliveredat the Tx input and that available at the Rx output; it can be expressed by the Bit ErrorRatio (BER), or by other (more complex) parameters related to Bit Blocks.Rx Selectivity : The overall effect of the Receiver Filters in discriminating the desired signal from signals received on adjacent radio channels. It is expressed by an overalltransfer function, including the contribute of RF, IF, and BB filters.

Net Filter Discrimination (NFD) : The attenuation of the Interfering signal level at theRx decision circuit, as a result of the interfering signal Tx spectral shaping and of the Rxselectivity at the interfered receiver.

GLOSSARY - Antennas

Isotropic Antenna : An ideal source of Electromagnetic Radiation, that radiatesuniformly in all directions.

Omnidirectional Antenna : A Real Antenna, that approximates an Isotropic Antenna; inmost cases radiation is (almost) uniform at all azimuth angles, but within a limited rangeof elevatuion angles.

Directive Antenna : A Real Antenna, that concentrates most of the emitted radiationwithin a small angle in a given direction.

Reflector Antenna : A Directive Antenna, using one or more reflecting surfaces toconcentrate the emitted radiation in the desired direction.

Parabolic Antenna : A Reflector Antenna using a Parabolic Surface; the feeder positionis in the parabola focus.

Horn Antenna : A Reflector Antenna using a sector of a Parabolic Surface.

Cassegrain Antenna : A double Reflector Antenna: the primary reflector is a parabolicsurface, the secondary reflector is a hyperbolic surface.

Glossary - Antennas

Antenna Gain : See Definition.

Directivity Diagram : A plot of the antenna gain (usually relative to the maximum gain)as a function of the azimuth or elevation angle.

Far Field Region : The region sufficiently distant from the antenna, where the EM fieldcan be represented as a plane wave and the antenna diagram is stabilized. Closer to theantenna, the Near Field Region and the Fresnel (transition) Region are defined. Theboundary between the Fresnel and the Far Field Region is approximately at the distance:

dFF = 2 D2 / (D = antenna diameter)

Launch and Arrival Angles : The angle of the Radio Ray at the Tx or Rx antenna, withrespect to the Horizon; it varies with atmospheric conditions (k-factor).

Logarithmic UnitsLogarithmic units are widely used in Radio Link Engineering computations. The LinkBudget is put in a very convenient form by using logarithmic units. Gains and Losses areadded with positive or negative sign, as in financial budgets.

The ratio R between the power P and a reference power PREF (both in the same unit,like W or mW) is expressed in decibels as:

R (dB) = 10 Log10 (P / PREF)If R>0, then P > PREF (gain). Otherwise, if R

Logarithmic Units

Examples of power levels expressed in different units :

Power in mW Power in dBm Power in dBW

0.001 -30 -60 0.1 -10 -40 1.0 0 -30 2.0 +3 -27 5.0 +7 -23 10.0 +10 -20 40.0 +16 -14 100.0 +20 -10 200.0 +23 -7 1000.0 +30 0 5000.0 +37 +710000.0 +40 +10

Derivation of the Basic Radio Link Equation

Let us assume that a radio signal is transmitted using an Isotropic Antenna, with powerPT. At the distance L from the antenna, the Power Density is : = PT / 4BBL2

If a Directive Antenna (gain GT) is used and assuming that the distance L is sufficientlylarge, in order that Far Field Conditions are satisfied, then the Power Density in theantenna pointing direction is :

= PT GT / 4BBL2

At the distance L, a receiving antenna with an Effective Area ARE is used. Then, thereceived power is :

PR = ARE = PT GT ARE / 4BBL2

The Effective Area is related to the Antenna Gain : ARE = GR 882 / 4BB (8 = wavelength)Then the Received Power can be finally expressed as :

PR = PT GT GR 882 / [4BBL]2 = PT GT GR [c / 4BBFL]2

where c is the propagation velocity and F is the signal frequency.

Derivation of the Basic Radio Link Equation

By transforming into Logarithmic Units, we get :

PR[dBm] = PT[dBm] + GT[dB] + GR[dB] - 92.44 - 20 Log (F[GHz]) - 20 Log(L[km])which is the usual Radio Link Equation. If frequency and distance are not expressed,respectively, in GHz and km, then the numerical constant 92.4 must be modifiedaccordingly.

Comments : Two equivalent forms of the Radio Link Equation have been derived above:

PR = PT GT 0 AR / 4BL2 (1)PR = PT GT GR [c / 4BFL]2 (2)

The antenna parameters used in (1) are the Tx gain GT and the Rx antenna area AR.The Rx power is proportional to GT, to AR and to PT; it is inversely proportional to thedistance squared. This probably sounds quite clear from the physical point of view.

On the other hand, formula (2) looks attractive for its symmetric form, since both the Txand Rx antenna gains appear. However, we must remember that, for a given antennaarea, the gain increases with frequency (see also Antenna Gain Definition). That's whythe frequency term appears in (2).

Definition of Antenna Gain

Let us imagine an Isotropic Antenna at the centre of a sphere (with radius L), radiatinga total power P. In every point on the sphere surface, a uniform EM power density could be measured :

()ISO = P / 4BBL2

Now, we substitute the Isotropic Antenna with a Directive Antenna and we measure theEM power density on the sphere surface, at the intersection with the antenna axis (wemaintain the same total emitted power P). The result is ()DIRThe antenna gain on the axis is defined as : g = (p)DIR / (p)ISOor, in logarithmic units : G (dB) = 10 Log (g) = 10 Log [(p)DIR / (p)ISO]The Antenna Gain depends on the physical dimensions of the antenna, normalized tothe signal wavelength 8. For Reflector Antennas we have :

G (dB) = 10 Log (4 BB

0

0

A / 88

2) = 10 Log (4 BB

AE / 882)where A is the reflector area, 0 is the Antenna Efficiency (generally in the range 0.55 -0.65) and AE = 00A is called Antenna Effective Area.

Loss vs. Distance in Radio (and Cable) LinksIn the Radio Link Equation, the factor 1/L2 (or -20 Log (L) in logarithmic units) shows howthe received signal power is reduced as the distance L from Tx to Rx increases.

We refer to the simple Isotropic Antenna example. The antenna is at the centre of asphere (with radius L), radiating a total power P. In every point on the sphere surface, theEM power density is:

= P / 4BB

L2

The Loss vs. Distance mechanism is directly related to the EM power density at the Rxantenna, which is proportional to 1/L2. This corresponds to a 6 dB increase in powerloss every time the hop length is doubled.

It must be recalled that the Radio Link Equation is valid for Free Space Propagation.Therefore, no interaction between the Electromagnetic (EM) radiation and thepropagation medium is responsible for power loss.

For the above reason, the term Free Space Loss could be slightly misleading.

A completely different mechanism is responsible of power loss at the receiver when the

Loss vs. Distance in Radio (and Cable) Links

EM energy interacts with the propagation medium and some phenomena of energytransfer or transformations produce the attenuation in the received signal.

This happens, for example, in coaxial cable transmission, where signal loss is mainlydue to dissipative phenomena (interaction of EM energy with conductive and dielectricmaterial in the cable). Depending on signal frequency and cable characteristics, somefraction of signal power is lost every kilometre travelled through the cable. So, the loss isusually expressed in dB/km.

Also in radio communications through the atmosphere, dissipative phenomena can beobserved. Absorption in the atmosphere is caused by water vapour, oxygen moleculesor by water in raindrops. Also for these phenomena, the power loss is usually expressedin dB/km.

However, in most cases (dry atmosphere, frequencies below 20 GHz), the interaction ofthe EM radiation with atmosphere components is almost negligible.

Atmosphere structure and refraction gradientThe Refractive Index is the ratio of the Velocity of Light in vacuum to the velocity in adifferent medium. Since the Velocity of Light in the atmosphere is very close to that invacuum, then the Refractive Index in the atmosphere is greater than, but very close to 1.

However, also small variation in the atmosphere Refractive Index have significant effectson the propagation of Electromagnetic Waves. For this reason, instead of using theRefractive Index n (close to 1), it is convenient to define the Refractivity N as :

N = (n - 1) 106

that is the number of parts per million that the Refractive Index exceeds unity. TheRefractivity is a dimensionless parameter, measured in N-units.

The atmosphere Refractivity is a function of Temperature, Pressure, and Humidity, andit is not constant with height. The ITU-R Rec. 453 gives the formula :

N = (77.6 / T ) ( P + 4810 e / T )where T = absolute temperature (Kelvin deg);

P = atmospheric pressure (hPa, numerically equal to millibar);e = water vapour pressure (hPa).

Atmosphere structure and refraction gradient

The average value of N at sea level is about No = 315 The ITU-R gives world mapswith the mean values of No in February and August.

The Vertical Refractivity Gradient G (measured in N-units per km, N/km) is defined as:G = (N1 - N2) / (H1 - H2)

where N1 and N2 are the refractivity values at elevations H1 and H2, respectively.

In a Standard Atmosphere model, the Vertical Refractivity Gradient is assumed asconstant in the first kilometre of the atmosphere : G = - 40 N/km. This corresponds tothe Standard Propagation conditions.

Deviation from the Standard Atmosphere condition leads to Anomalous Propagation.Such anomalies are usually associated with particular meteorological conditions, liketemperature inversion, very high evaporation and humidity, passage of cold air overwarm surfaces or vice versa.

In this conditions, the Vertical Refractivity Gradient is no longer constant. A numberof different profiles have been observed and measured. It is worth noting that, at greateraltitude, the Refractive Index is, in any case, closer and closer to 1; so the RefractivityN goes to zero, according to an exponential function.

Effects of Vertical Refractivity Gradient

In any point in the space, an Electromagnetic Wave propagates in the direction normalto the wave-front (iso-phase plane) in that point. In a homogeneous medium, iso-phase planes are parallel to each other and the propagation direction is a straight linenormal to them.

The Atmosphere is not an homogeneous medium. The Refractivity varies with heightand the Vertical Refractivity Gradient gives a measure of this variation.

Different Refractivity at different heights means different propagation velocity. Thewave-front moves faster or slower depending on the height, producing a rotation of thewave-front itself. Thus, also the propagation direction (normal to the wave-front) rotates.The ray curvature 1/r is a function of the Vertical Refractivity Gradient G : 1/r = - G 10-6.

In the Equivalent Earth representation, the ray path is made straight, by modifying theearth radius R (6370 km) to kR (k = equivalent earth factor). This condition means :

1/kR = 1/R - 1/r k = 1 / ( 1 - R/r) = 1 / ( 1+ R G 10-6) = 157 / ( 157 + G )For the Standard Atmosphere (G = -40 N units/km), this gives k = 4/3 ( = 1.33).


Anomalous propagation conditions :

Constant-G profiles : deviation from the Standard Atmosphere (k = 4/3), can result in :Sub-Refractive propagation (k < 4/3, G > -40 N-units/km) : usually associated to

atmosphere density increasing with height (warm air over cool air or moist surface). Theray curvature is reduced or even is bent upward ( k < 1, G > 0 ); the ray path is closer tothe ground (maximum obstruction probability when k is minimum).

Super-Refractive propagation (k > 4/3, G < - 40 N-units/km) : observed whentemperature inversion happens or other phenomena makes atmosphere densitydecreasing with height. (cool dry air over a warm body of water). The equivalent earthreduces its curvature; for k the ray is parallel to the earth and propagation mayextend its range (unexpected interference may appear). In extreme super-refractionconditions (G < -157 N-units/km, negative k) the ray is bent toward ground and no signalarrives at the Rx antenna (black-out).

Variable-G profiles : with better approximation, the Refractivity Gradient can beassumed as constant only in limited height ranges (layered atmosphere). Under thismodel, the ray curvature changes when passing from one atmosphere layer (G = G1)


to the higher (or lower) one (G = G2). Even if, in the real case, the transition from onelayer to another is smoothed in some way, a layered atmosphere model is useful inexplaining :

Multipath propagation : the different ray curvature in atmospheric layers mayproduce a number of separate propagation paths from the transmitter to the receiver.

Duct formation : the atmosphere layers are such that the rays at the duct lowerboundary tend to be bent upward, while rays close to the upper boundary tend to be bentdownward. The result is that propagation is confined within a limited height ranges, withattenuation much lower than in well mixed atmosphere. If the Rx antenna is within theduct, a stronger signal will be received. If the Rx antenna is out of the duct, rather longsignal fadings are observed.

Fresnel Ellipsoid and Optical Analogy

The propagation of Radio Waves is often described in terms of Ray Trajectories, withimplicit reference to Geometrical Optics. Reflection and Refraction phenomena aremainly discussed in this context.

However, it is important to remember that the Geometrical Optics approach is adequateso long as any discontinuities encountered by an Electromagnetic Wave during itspropagation are very large compared with the wavelength.

The Fresnel Ellipsoid gives an indication of the space volume involved in the propagationfrom a source point (Tx) to a sensor (Rx). The ellipsoid radius is proportional to thewavelength square root.

In the optical field, the wavelength is so small (about 5 10-4 mm) that the radius ofthe Fresnel ellipsoid is negligible, at least as a first approximation. Only with accurateexperiments (unusual in our visual experience) diffraction phenomena can be observedand the role of Fresnel ellipsoid can be appreciated also in the optical field.

We are familiar with our optical experience, that can be of some help in describingsome aspects of propagation mechanisms. But this analogy can be misleading in othercase. For example, the concept of Visibility is quite different in Radio Engineering andin our visual experience.

Diffraction Analysis

Generally speaking, Diffraction effects can be observed when the wave propagation isaltered by an obstacle which has dimensions comparable to the wavelength in theplane normal to the propagation direction. Usually, this means that the obstacle is closeto the Fresnel ellipsoid (possibly with partial or total obstruction). The theoreticalcomputation of diffraction loss is rather complex. Usually, reference is made to twoobstacle models :

the smooth spherical earth ;the knife-edge obstruction.

They represent extreme and opposite conditions and most practical cases can beassumed as intermediate between these two models. The ITU-R Recs. 368 and 526include the analysis of the two models. In Rec. 526 the Knife-edge model is generalizedto rounded obstacles and the case of multiple obstructions is also dealt with.

An approximation for the knife-edge case is given by :

Diffraction Loss (dB) = 6.9 + 20 Log [ ( y2 +1 ) + y ]

where y = 2 CL/F1 - 0.1 is a function of the clearance CL normalized to the Fresnelradius F1, and the approximation is valid for y > - 0.8 (Note : CL is negative when aground obstruction is higher than the radio ray).

Vectorial Addition of Two Signals (deterministic)Let us consider a propagation channel where an echo (delayed) signal adds to the directsignal at the receiver. The Channel Transfer Function H(F) is :

H(f) = 1 - b exp [ - j (2pif - ) ] = 1 - b exp [ - j 2pi(f - fo) ]where : b = echo amplitude (direct signal amplitude normalized to unity) ;

= echo delay ; = echo phase (relative to direct signal).The substitution = 2pifo has beenused in order tointroduce the frequencyfo where the H(f)modulus is minimum :

| H(fo) | = 1 - bOther minimums in |H(f) | are found for anyfrequency fn = fo + n/ (n integer).-40

-30

-20

-10

0

Frequency

A

m

p

l

i

t

u

d

e

[

d

B

]

fo fo+1/

b=1

b=0.9

b=0.5

Vectorial Addition of Two Signals

The Group Delay is represented for different values of the echo amplitude b.

In the figure it isassumed b < 1(delayedsignal smaller than thedirect one). This gives aMinimum-PhaseTransfer Function. Ifthe delayed signal isgreater than the directone, then a Non-Minimum PhaseTransfer Function isproduced. This case isusually dealt with byassuming again the echoas the smaller signal,with a negative . TheGroup Delay diagram isgiven by the same figure, butreversing the ordinate axis.

Frequencyfo fo+1/

b=0.5

b=0.9

b=0.95

N

o

r

m

.

g

r

o

u

p

d

e

l

a

y

Vectorial Addition of Multiple Signals (statistic)Let us consider the case of N signals, adding together. They can be represented asvectors, with orthogonal components {x1, y1}, {x2, y2}, ..., {xN, yN}. Each vector hasrandom amplitude and phase (independent to each other, same statistics).The orthogonal components of the resultant vector are given by :

X = x1 + x2 + ... + xN Y = y1 + y2 + ... + yN (1)With N (number of signals) growing to infinity, reference can be made to the CentralLimit Theorem : X and Y are independent Gaussian Random Variables, whoseaverage value is zero and variance is 2 (we are not interested in investigating theprecise value of ). The amplitude R of the {X,Y} vector is given by :

R2 = X2 + Y2 (2)Given the statistical properties of X and Y (mentioned above), formula (2) defines R as aRayleigh Random Variable, with average value (pi/2). The Rayleigh CumulativeFunction gives :

Prob { R < c } = 1 - exp [ - c2 / 22 ] c2 / 22 (3)

Vectorial Addition of Multiple Signals

where the approximation holds when c

Reflection Coefficients

In many cases it is advisable to adopt the conservative assumption that the modulus ofthe Reflection Coefficient be equal to 1. For very small grazing angles and/or forHorizontal Polarization this is a realistic approximation.

For Vertical Polarization, the table gives the Reflection Coefficient modulus in the case ofsea reflection :

Grazing Angle Frequency 0.5 1 2 4

1 GHz -1.4 dB -2.8 dB -6.2 dB -12.0 dB 3 GHz -1.2 dB -2.3 dB -5.3 dB -10.9 dB10 GHz -0.8 dB -1.7 dB -4.3 dB -8.4 dB

Similarly, the phase of the Reflection Coefficient is very close to 180 with HorizontalPolarization (any grazing angle) and also with Vertical Polarization, for grazing anglesbelow 0.5.

With Vertical Polarization and larger grazing angles, the phase is smaller than 180,depending also on the frequency. However, in radio link design, the prediction of theReflection Coefficient phase is usually not required.


Space Diversity, as a Reflection Countermeasure, is usually implemented to maximizethe Rx power level, by switching to the best signal or combining in IF or RF. However,the maximized Rx signal is in some way a combination of the direct and the reflectedsignal.

In some cases it is required that the reflected signal be cancelled, to avoid signaldistortion (particularly with very long reflection delays). The Anti-Reflection system is anRF Space Diversity implementation with the objective of cancelling (or minimizing) thereflected signal component in the overall Rx signal..

The Antenna Spacing is such that thereflected signal arrives in phaseopposition at the two antennas.The phase shifter is used for finephase adjustment. The result at thehybrid is a co-phase addition of thedirect signal components from the twoantennas, and phase oppositioncancelling of the reflected signal components.

Hybrid Rx


The Space Diversity configuration can also be seen as an Antenna Array, with anoverall directivity pattern having a null toward the reflection point.

Also the Anti-Reflecting systems, as other Space Diversity implementations, are usuallyoptimized for standard propagation conditions. Then the solution is checked in the wholerange of expected k-factor values.

Multipath Propagation - Rx Level vs. Time and Frequency

In a Frequency &Time Plane, thefigure shows theaddition of multiplevectors with randomphases.

Each vectorrepresents one Rxsignal component,during a multipathevent.

The Rx signalamplitude changesfrom time t1 to t2, aswell as fromfrequency f1 to f2.

Multipath propagation is a dynamic event, both in the time dimension and in thefrequency dimension.

.

Rx

1

n4 3

2

Rx

1

n 4 3

2

Rx

1

n4

3

2

Rx1

n 43

2

Frequency

Time

f2

f1

t2t1


Rx SIGNAL vs. TIME :

Phase shifts are varying with time because of movements in atmospheric layers.Since the wavelength is rather small (e.g. 10 cm at 3 GHz), even a small change in thepath length produces a significant phase rotation. So the relative phases amongmultipath components are fast varying, as well as the reultant vector (Rx amplitude).The speed of change of the multipath channel is expressed in two ways.

1) Rx signal power variation in a given time interval : up to 10 dB in 100 ms (100 dB/s)has been observed, according to several authors.

2) Fade Notch (deepest attenuation) movement through the signal bandwidth : up to 10MHz in 100 ms (100 MHz/s) has been observed, according to several authors.The above estimates affect the design of multipath countermeasures, like adaptiveequalizers, combiners, and switches to the protection channel (frequency diversity).


Rx SIGNAL vs. FREQUENCY :

In a modulated signal, let us consider the spectral components at the edge of the signalbandwidth F : F1 = Fc - F/2 and F2 = Fc + F/2 (Fc = carrier frequency).Moreover, let us simplify the multipath propagation as the composition of a direct and adelayed (echo) signal.The phase shift between the F1 signal component and the delayed echo is :1 = 2pipiF1 where is the echo delay. Similarly, at F2, we have 2 = 2pipiF2.The multipath propagation produces an (almost) flat attenuation through the wholesignal bandwidth F, if the phase shifts 1 and 2 are equal (or very close) (samecomposition of the direct and echo signals at F1 and F2 ) :

= 2 - 1 = 2pi (F2 - F1) = 2pi F 0 that is 2pi pi F

Formulas for Po Prediction

Several formulas have been proposed to predict the Multipath Occurrence Factor Po.They can be derived from the general formula :

Po = C Q Fa Lb

where F is the Frequency in GHz, L is the Hop Length in km. The four parametersdefining the prediction model are : a = Frequency Exponent; b = Distance Exponent;C = Climatic Factor; Q = Profile Factor.

Formula from Bell Labs (USA) :This formula is the result of field measurements in the US, mainly reported by A. Vigantsand W.T. Barnett in several papers. The parameters in the general Po formula arespecialized as follows :

Frequency Exponent a = 1; Distance Exponent b = 3;C = from 10-5 (dry mountain climate) to 4.1 10-5 (climate with high humidity and temperature; coastal regions);Q = 1 / S1.3 where S = Profile roughness, computed from the hop profile.

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Radio Propagation Theory 1