Microwave Basics

1. Do You know..?
by Ashish JAIN
Yet to complete..
These Pg’s are just based on my understanding & learning (based on Google Search).
Mail ID:ashish7aditya@gmail.com
Skype:ashish77aditya
It all started when I was asked by one of my colleague that why we keep Max Diversity improvement factor 200 in Pathloss 4.0 & what’s the Impact of Path Inclination on link performance ? It’s True that I
have a poor Memory & can’t keep things for a long stint in my mind. But I knew this can’t an answer to my colleagues Question. So, just started …(as simple as that) .

2. S.NO Topic
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General Notes
Snapshots
DIF
What we mean by Multipath
Multipath & DFM
Multipath Fade Probability
FSL
Multipath as SES or SES + Unavailability
Reliability Methods in Pathloss 4.0
Av Temperature
Rain Graph
P0
A pg on Interference Window
Pg#14'!A1

3. Path Inclination(Comments):
1
In the past Vigants model or the Fade occurance factor did not consider the path inclination wich is now part of P530 prediction models. This is mainly to take into account the probability of ducting.
2
The more the incident angle is increased (increase path inclination) the penetration propability increases without suffering reflection or refraction on these boundry surfaces.
3 Links planned with Inclination angle>10mr(aprox 0.6 degree) i.e Min angle of duct Penetration (escape Angle) are less likely to be entrapped.
Path Inclination Ep is given by:
H1
|Path Inclination (φ)|= |(H1-H2)/D|mrad
Ep= φ
Ht & Hr in m & d in Km. H2
The valid range of path inclination is 0 to 24mr..Pl4 doesn't impose any restriction on this value.. D
Also,Ep is inversely Prop to Link Avbty..
How to Reduce effect of Multipath Propagation:
Non-Diversity Tech's:
1) Antenna Tilt:
2) Path Inclination:
3) Reduction of path clearance:
Diversity Tech's:
Diversity techniques include space, angle and frequency diversity. Frequency diversity should be avoided whenever possible so as to conserve spectrum.
Antenna discrimination? EB,K-Factor.? C/I Ratio & RBER etc..
why to keep same Rx level at Star Hub node for radios with same sensitivity,B.W,Modulation.? RSL in pl4 is not only(Pt+G1+G2-FSL) but it include I think absorption loss also.noticed change in RSL value by changing water vpr density value.
Repeaters..? Scale in terrain? water vapr density ka impact? antenna decoupling effect of Multipath on XPD?
They measured MW hops in several frequency bands and of various distances, while typically reached improvements up to 200. The formulae for SD improvement factor are mostly derived from such measurements.
SD improvement factor" I is related to the "probability of outage" Pout. The simplest formula is
for uptilt(-ve) value & for uptilt(+ve) value in Antenna.
The pathloss program cannot calculate interference when the interfering transmitter and the victim receiver are at the same site such as in the case of a high low violation or frequency buck
The coupling between the transmitter and receiver is a near field situation which cannot be simulated with the antenna patterns or path lengths on the tower.
SRTM Version 2.0 instructions
The SRTM data uses the WGS84. NAD83 and NAD27 Coordinates are transformed automatically.
The conventional method for calculating outage times for analogue systems is based on the concept of single-frequency
fades and is therefore not directly applicable to high-capacity digital radio-relay systems. An increase in the fade margin,
which in analogue systems will tend to reduce the effect of thermal noise, will not improve the performance of
digital systems if multipath fading has already collapsed the eye-diagram amplitude to zero. It follows that increasing
the transmitter power cannot be employed as the only means of making digital radio systems meet their outage
requirements.
The appropriate spacing of SD antenna's is determined considering 3 factors:
1)To keep Clearance of lower antenna as low as possible.
2)To achieve specified diversity improvement factor.
3)To min the chance that the sgn on one diversity antenna will be faded by surface multipath when the sgn on the other antenna is faded.
When SD is used,the improvement depends on th extend to which sgn in two diversity branches of the system are uncorrelated.
Note:You can notice Effective FM when you select DFM(not signature method) & that too only if there will be dispersive component in that link.
In Pathloss,Vigants-Banett Menthod use C-Factor to calc fade prob.C-Factor in turn depend on Terrain Roughness & Climatic factor.
So,if you are using this method of relibility,then you will be required C-Factor value.
Actually different method to calc Fade Prob involve different Profile parameters:Like C-Factor(which in turn depnd on terrain roughness & Climatic fctr) in Vigant-B method;Geoclimatic fctr in ITU530-6;
Index
I've computed a comparison of error performance computed on three hops comparing the Vigants, P.530-5/6, P.530-7/8, and P.530-9/10/11 models. I found that at least for these three hops the computed error performance
(outage time) gets lower (better) in that order, i.e. from Vigants to P.530-5/6 to P.530-7/8 to P.530-9/10/11, with P.530-9/10/11 having the best performance (lowest outage). You can use PL4 having all four outage models to do
these comparisons.
You see borders of the atmosphiric layers are always parallel to the Earth's surface so basicly when you have a signal incident angle very small on these boundry surface you will suffer total reflection and thus you will have a
total loss in the signal.
1000.atan[(|Ht-
Hr|)/1000.d]milliradians
H2=Twr
Ht+AMSLH1=Twr
Ht+AMSL
More will be path inclination,less will be angle between Normal to Refractive layer w.r.t
Incident ray & thus less chances of TIR.
The effects of slow relatively non-frequency selective fading (i.e. “flat fading”) due to beam spreading, and faster frequency-selective fading due to multipath propagation can be reduced by both non-diversity and
diversity techniques.
Technique known to reduce the level of surface reflections is to tilt the antennas slightly upwards. Detailed information on appropriate tilt angles is not yet available. A trade-off must be made between the resultant loss in
antenna directivity in normal refractive conditions that this technique entails, and the improvement in multipath fading conditions.
Links should be sited to take advantage of terrain in ways that will increase the path inclination, since increasing path inclination is known to reduce the effects of beam spreading, surface multipath fading, and atmospheric
multipath fading.The positions of the antennas on the radio link towers should be chosen to give the largest possible inclinations,particular for the longest links.
Another technique that is less well understood involves the reduction of path clearance. A trade-off must be made between the reduction of the effects of multipath fading and distortion and the increased fading due to sub-
refraction.However, for the space diversity configuration one antenna might be positioned with low clearance.
In general, antennas which are tilted towards the ground experience deeper fading, for a given time percentage, than those tilted upwards [35]. A combination of space and angle diversity, where the upper antenna is
untilted while the lower antenna is tilted upwards, provides better fading, and cross polar discrimination performance [35]. However, on paths over the sea,where there is a strong stationary standing wave, a space
diversity system can be improved by tilting the lower antenna towards the sea floor [35]. Finally, severe ducting can be tackled using two transmitting antennas which are separated by a large vertical distance [35], but
this approach requires high, expensive towers.
The limit of max. improvement factor of 200 comes from measurements performed by A. Vigants during 1970s.
The SD formula can give you any improvement number, but because of limited precision of the SD mathematical models (and concerning their conditions of applicability), it is not guaranteed, that you will reach extremely large
improvement in the field.
It doesn't mean, that values greater then 200 are impossible, but they are practically rather rare. Value 200 in Pathloss therefore serves as a conservative safety limit.
Pout(with SD) = Pout(without SD) / I .
"Availability" A is related to the "probability of outage" Pout via "(cumulative) probability of the fading event lasting more then 10 consecutive seconds" Rho d(10). See Pathloss v.4.0 manual - Module Worksheet (Reference).
The Vigants-Barnett model is one of the two Bell Labs employees Vigants A., ("Space Diversity Engineering", Bell System Technical Journal, January 1975) and WT Barnett, ("multipath propagation at 4, 6 and 11 GHz, "Bell System
Technical Journal 51, February 1972) developed in the 70s and again slightly modified and adapted formula, which is based primarily on empirical data. We use it in the form of
The data can be downloaded at ftp://e0srp01u.ecs.nasa.gov/srtm. These files are compressed using pkzip. You will need to unzip the files before they can be used.
Select either the Version1 or Version2 directory. If you are not sure which one to select read the following PDF file. For most users you will select Version2. Some North American users may want to use Version1 as there is data in 1 second resolution for the USA, but this could change.
File names refer to the latitude and longitude of the lower left corner of the tile - e.g. N37W105.HGT.ZIP has its lower left corner at 37 degrees north latitude and 105 degrees west longitude. To be more exact, these coordinates refer
to the geometric center of the lower left pixel.
In the Pathloss program click "Configure" – "Terrain Database" and select "SRTM" from the drop down list (at the bottom of the list).
Click "Setup Primary" (or "Setup Secondary" depending on your selection) an index of SRTM files will appear.
In the menu click "File" and then "BIL-HDR-BLW" and browse to find the file that you have downloaded and unzipped. It will have an .HGT extension. The program is now setup to use the selected SRTM file.

5. MAIN PAGE Rough Work
First Question:Why we keep Max Diversity Improvement Factor=200 in Pathloss or anyother planning tool..?
To Answer this & to see how this parameter affects Link Availability,just let we go through few basic equations.
Eq-1
where:
Pnon-div:Non-selective outage Probability for single Receiver.
I.F:Diversity Improvement Factor
For Space Diversity,
ITU-R 530 relates I.F (SD) as:
[1-exp{-3.34*(10^-4)*(S^0.87)*(f^-0.12)*(d^0.48)*(P0^-1.04)}]*[10^{(A-V)/10}] Eq-2
Vigants Method:
Where:
A:Fade depth(db) for unprotected path
P0:Fade Occurance Factor F:18GHz;D:23.75m,S:8m for Left,6m for right;V:0
S:Vertical Spacing C-to-C(m).
f:Freq(GHz) IFsd is same as calc in eq-3.
d:Pathlength(Km)
V:difference b/w Gain of two Receiving Antenna's
With Same symbols, Bell labs(Vigants) formula gives(S<15m):
{1.2*(10^-3)*(S^2)*F*(d^-1)}*[10^{(A-V)/10}] Eq-3
same apply for FD I.F factor also..
Index
The Diversity outage Probability(Pdiv) for No-selective Fading is given by:
Pdiv= Pnon-div/I.F
I.Fsd=
I.Fsd=
Theoritically tool will calc Pdiv as per Eq-1 but Practically it goes limited.The limit of max. improvement factor of 200 comes from measurements
performed by A. Vigants during 1970s.They measured MW hops in several frequency bands and of various distances, while typically reached
improvements up to 200.It doesn't mean, that values greater then 200 are impossible, but they are practically rather rare.
So, placing a limit on Max SD I.F is because of the concern that in actual you don't achieve I.F>200,so pre-consider outage Probability with Diversity(Eq-
1) taking this in note rather then just relying on theoritically calc values.
So, it means Pathloss calculate SD improvement factor & if it comes <Max Limit we have set(say 200) it will use that value for rest of the parameter
analysis but if > 200 then it will use 200 as SD improvement fact for rest of the analysis.

6. MAIN PAGE Rough Work
#1 Remark:
#2 Remark:
#3 Remark:
#4 Remark:
Index
what we mean by
multipath ..?
Why during
multipath
fading,Amplitude
varies very fast.?
why multipath
fading is frequency
selective.?Impact of
Multipath fading on
XPD.
This explain why in
gereral Selective
fading multipath is
noticed for Wide
band signals & not
for narrow band
signals.
Shows RSL graph
during multipath
fading.Fast variation
is RSL can be a sign
of Multipath fading.

7. MAIN PAGE ROUGH WORK & COMMENTS
Multipath propagation Reliability:
Fading of a Mw link can result from any of the following:
}
1) Atmosp MultiPath.
OR
2) Rain Attenuation.
Frequency Selective Fading+Interference+Thermal Noise3) Diffraction fading (@low K).
4) Fades produced by Specular reflections. The total outage time will dependent on these three contributors.
5) Propagation anomalies produced by Atmph ducts or layers.
The Fade Probability P, is a funtn of Frequency,Path Length & Fade Margin of a radio link & takes the following General form:
P
Ȣ
{(f)^b}{(d)^c}.{(10)^(A/10)} Eq-1
where:
d:Path length
f:Freq
A:FM in dB
In Pathloss,5 methods are available to calc Fade Probability:
1) Vigants-Barnett
2) ITU-R P.530-6
3) ITU-R P.530-7/8
4) ITU-R P.530-9/10
5) K.Q Factor;K.Q Factor including Terrain roughness.
Additional Performace Parameters can be calc from Fade Probability P,as follows:
1) Worst Month unavailability(%): 100.P
}2) Worst Month availability(%): 100(1-P) Eq-2
3) Worst Month outage time(sec): P.sec_month
Assuming 3 heavy fading months per year (0.25 a Yr),the annual performance can be expressed as :
1) Annual unavailability(%): 100.(P)0.25
}2) Annual availability(%): 100(1-0.25P) Eq-3
3) Annual outage time(sec): 0.25Psec_year
Multipath fading is a warm weather phenomenon.The length of the fading season is propotional to Av annual temperature.The fade duration ,"To" expressed as a fraction of a year is given as:
To =0.25(t/50)
thus ,Eq-3 can be modified as:
1) Annual unavailability(%): 100.(To.P)0.25
}2) Annual availability(%): 100(1-0.25To.P) #### Eq-4
3) Annual outage time(sec): 0.25To.P.sec_year
FADE MARGIN:
Fade Margin(Effective Fade Margin)
Flat Fade Margin Dispersive Fade Margin
Thermal Fade Margin + Interference Fade Margin
1)Thermal Fade Margin:
2)Interference Fade Margin:
3)Flat Fade Margin:
Eq-5
where,
Af:Flat FM
At:Thermal FM in dB
Ai:Interference FM in dB
4)Dispersive Fade Margin: DFM= Eq-6
where,
Δf:Signature width of Equipment
B:Notch depth of equipment
Dispersion(i.e Variation w.r.t Freq) .
Let we also understand here two type of fading (w.r.t Frequency)
Intersymbol Interference:
Comment#1
Again, DFM is a hardware parameter of the MW radio, from which Pathloss (or other SW tool) calculates the probability of outage caused by selective multipath fading.
Comment#2:
4.1)Procedure to construct W-Graphs:
The Transfer function of two ray radio channel is given by:
Eq-7
Where,
a:amplitude of direct ray.
at f=fo
a[1-b]
20log|a| +20log|(1-b)| dB Eq-8
Note:The Width of the signature is independent of ray delay & the Amplitude of the signature is proportional to the ray delay value.
4.2) Dispersive Fade Occurance Factor(in Pathloss):
The Dispersive Fade margin measurements procedure is based on the fade statistics of a 26mile path from PALMETTO to ATLANTA,Georgia.In general Dispersive Multipath Fading depends on the following:
For Good Propagation conditions:0.5-1
Extremely difficult conditions:9.
5) Effective Fade Margin:
Effective Fade Margin(EFM) combines the Flat & Dispersive Fade Margin components as:
EFM= Eq-9
Af:Flat Fade Margin in dB
Ad:Dispersive Fade Margin in dB
Rd:Dispersive Fade Occurance factor
NOTE:
When a digital signal is distorted by selective multipath fading,the BER may be at threshold level (10^-3) even if the Rx power is higher than the Rx threshold.The final effect is reduction in FM.
Narrow Band Signals Wide Band Signals
(Almost) Flat Attenuation Frequency selective Attenuation
Reduction in Rx Pwr Reduction in Rx Pwr + Signal distortion
Index
Each of these can contribute to overall propagation reliability & must be seprately analysed.The parameter of interest is the total time that RSL<Threshold level.
It is generally assumed that these events are mutually exclusive events & total time below threshold level is sum of the outage times for each mechanism.Ex-Multipath fading does not occur during heavy rainfall.So,Multipath &
rain outage time can be added together.
Atmph multipath fading is a result of number of rays with varying path lengths arriving at the Receive antenna.The different ray paths can result from both change in R.I Gradient & earth reflections.The Rays add vectorially in
receive antenna.
Multipath fading follows Rayleigh probability distribution.The Fade Probability Represents the fraction of the time (in the worst month),that the depth of multipath fades will exceed the fade margin.Note,that this fade
probability does not include any of the other fade mechanisms mentioned above & does not include the additional time required to reframe the signal following a fade which result in loss of framing.
Note:P is expressed as Fraction of time not %age. Eq-1 is valid for FM>15dB & applies to unprotected (Non-Diversity) system in one direction of transmission.The Exponents b,c & constant of proportionality are
based on empirical data.
"t" is Av annual Temperautre in °F
Note:In pathloss, Flat FM for Multipath will come in picture
,incase of interfernce on that link.else only Thermal FM.
A Radio Property,involved only
for selective Multipath Fading.
The Fade probability of a Mw Link is a functn of FM.The Fade margin consist of Flat component & Dispersive component.The Flat component deals with total power in pass band ,whereas DFM deals with Amplitude-Freq response in pass
band.Dispersive component is applicable to digital Radios only.Analog radios are not sensitive to the pass band freq response.The Flat FM is made up of Thermal FM & an interference FM.
It is defined as the diference between Free Space Received Signal & Receiver threshold level.This represent an additional Attenuation to free space received signal required to produce an outage due to thermal noise alone,independent of any
interference .
Interference effectively degrades the receiver threshold.This represent an additional Attenuation to free space received signal required to produce an outage due to interference alone,independent of any thermal noise.
Note that BER is just like a digital representation of S/N ratio.So, under interference,N increases.In order to maintain same S/N ratio or BER,"S" wanted signal also should be increased.Thus Threshold increases under interference & this
degradation is known as threshold degradation.
Af= ­10.log{10^(-At/10)+10^(-Ai/10)}
17.6-10log[{(2Δf)* e^(-B/3.8)}/158.4] dB
a) Flat Fading:Flat fading is just another way to describe a fade where all frequencies in the channel of interest are equally affected.The fading due to thermal noise & interfernce fall under this & thus Flat Fade margin is defined
for it.
b)Frequency Selective Fading:Frequency selective fading implies variation of Amplitude & group delay distortions across the channel B.W produced by multipath nature of X-mission media.
Dispersive Fade margin is defined as the average depth of multipath fade which will result outage(independent of thermal noise & interference).To make it more simple,understand & think DFM like an equivalent Fade Depth
exceeded for same number of seconds during worsth month as is the number of seconds of outage caused by selective multipath fading events during worst month.Selective multipath fading events happens,when multipath fading
notch penetrates inside the area of the system's signature curve(W-graph).
Hindi Mai: Ek arbitary or better say ek equivalent FM (say 50db) jo
exceed hota hai utne time keliye jitne time selective multipath fading ke
karan outage(time) hue at particular BER.
It is a form of distortion of s signal in which one symbol interferes with subsequent symbols.ISI is
usually caused by multipath propagation or in-herent non-linear frequency response of a channel
causing sussive symbols to Blur together.ISI in result impact on BER.Adaptive Equalizers are used
to fight against ISI.
Frequency selective fading lead to intersymbol interference & thus
channel distortion in digital radios.
DFM of 50db ka matlab hai ki agar Selective multipath fading 50 db tak horehe hai then systems
will not genereate ISI & channel distortion will be within tolerable limit but agar 50db se jada
Selective fading horehe hai then system will generate ISI which will be untolerable & will degrade
its BER.
Y-axis shows the depth [in dB] of the notch of the multiptath selective fading. For measurement purposes, this is the depth of the notch of a comb-filter realized by the test set-up representing two-ray model, as defined by
Rummler for tau = 6.3ns. Yes, this depth also depends on the ratio between direct and delayed signals.
Ex- if you have planned RSL say of -30 db & your thermal FM is 60db meaning Radio threshold is
-90db.Now if DFM is 50db for this radio & if selective multipath fadings is >50db but less than
60db(say 55db) then also you will face degrade in BER value & outage .Multipath fading will
already collapse the Eye diagram Amplitude to zero(ISI).
The case where main path leads the secondary path(two ray path model) is referred as Min-Phase multipath case, and case where main path lags the secondary path is referred as Non-Min-Phase multipath case.Both cases should
be measured in order to obtain true picture of Radio against freq selective multipath fading.
So,never correlate or compare DFM with Thermal FM.DFM has nothing to do with it & other LB
parameters.It's a Radio parameter defined based on Signature Curves(W-Graphs).Radio will say that
I have this very DFM & it will be based on this signature Graph & signature curves in turn are
ploted as a practicle exercise/measurements for each radio in Laboratory.The procedure to construct W-Graphs requires that a notch be created at a given frequency offset from carrier frequency;notch depth is increased until a specified BER(say 10^-3 or 10^-4) is attained.The depth of the notch is then
plotted at this frequency offset.The shape of resulting plot is responsible for its name.
H(ω)= a[1-b*e^{-j(ω-ωo) }]Ϯ
Ϯ:delay(6.3ns)
fo=ω/2π determines the position of notch & thus Notch depth.
b:Relative amplitude of reflected ray.
H(ω)=
20log|H(ω)|=
The notch depth is: B = -20log(1-b) 0 <= b < 1, referring to the above formula.
A system signature curve (W-graph) represents this notch depth for which the reference BER was reached (10-3, 10-6), plotted against the frequency axis. Frequency axis is relative to the
nominal channel carrier frequency "fo". I.e. for "fo", the W-graph typically shows 0 MHz.
Notch is shifted alongside the frequency axis by changing the initial phase phi0 = ωo on the test set-up that generates the transfer function H(ω)=a[1-b*e^{-j(ω-ωo) }].Ϯ Ϯ
Also complex Modulation schemes will in general have
poor DFM .
- Terrain Roughness & Ground type
- Climatic conditions
- Path inclination
- Path Clearance.
To account for these factors ,it is necessary to adjust value of dispersive fade margin.This is accomplished by the term "Dispersive Fade Occurance Factor" in Pathloss.By definition,it is 1 for this link in discussion.As such there
are no published guidelines for this factor.By experience on different path it suggest:
-log[{10^(-Af/10)} +Rd{10^(-Ad/10)}]
If the signal B.W is narrow(few MHz),the selective fading effect is negligible.Multipath fading effect is assumed as a flat atennuation.On the other hand,for Wide-Band signals(medium & large capacity digital signals),the
attenuation within the signal band produces a significant distortion in the received signal.

8. MAIN SHEET ROUGH WORK
Two steps:
1)Outage probability due to Non­Selective(Flat) Component
2)Outage probability due to Selective(Dispersive) Component
1) Outage Probability due to Flat Multipath Fading(Pf):
K*(d^3.6)*(f^0.89)*{(1+|E|)^-1.4}*{10^(-A/10)} Eq-1
d:Pathlength(Km) 7Km<d<95Km
f:Freq(GHz) 2GHz<f<37GHz
|E|:Path Inclination(mrad) 0 mrad<|E|<24 mrad
A:Fade depth(dB)
Incase of Diversity,
where,
[1-exp{-3.34*(10^-4)*(S^0.87)*(f^-0.12)*(d^0.48)*(P0^-1.04)}]*[10^{(A-V)/10}] By ITU R-530 for Space Diversity
DIF= {1.2*(10^-3)*(S^2)*F*(d^-1)}*[10^{(A-V)/10}] By Bell labs(Vigants)
DIF= By Both ITU-R530 & Bell Labs(Vigants) For Frequency Diversity
2) Outage Probability due to Selective Multipath Fading(Ps):
Eq-2
where,
m:Mean time delay between two rays(nsec)=0.7[(d/50)^1.3] per hopϮ
This formula for P0 is as per ITUR P.530­7
r,m & r,nm:Reference delay used in signature measurement(nsec)Ϯ Ϯ
Incase of Diversity,
where:Ks is Selective Correlation Cofficient;Formulas to calc this for SD & FD are rather complex(See Rec 530).
Total Multipath Outage Probability:
Eq-3
α:Empirical Constant ,1.5<α<2
Index
Outage Probability due to Multipath Fading(in Worst month& for Narrow Band Signals):
Pf=
Pf,div= Pf/DIF
Pf:Outage Probability due to non diversity Flat Multipath fading
DIF is given by
I.Fsd=
(80/d*F)(ΔF/F)(10^A/10)
where:ΔF is Freq spacing (GHz)
Ps= 2.15η[Wm*{10^(-Bm/20)}*(Ϯm^2)/|Ϯr,m| + Wnm*{10^(-Bnm/20)}*( m^2)/| r,nm|]Ϯ Ϯ
η:Multipath Activity Factor=1­[e^{(­0.2)(P0)^0.75}]
P0:Multipath Fade occurrence Factor=[K*(d^3.6)*(f^0.89)*{(1+|E|)^­1.4}/100]
wm & wnm:Signature width for Minimum & Non­Minimum phase channel.
Bm,Bnm:Signature depth for min & non­Min Ph channel.
Ps,div= (Ps^2)/η(1-Ks^2)
Ptotal= [{Ps^α/2 + Pf^α/2}^2/α]

9. ROUGH WORK
Remark:
Index
It must be recalled (after reading these Pg's) that FSL is valid for free
space,so no interaction between the EM radiation & propagation medium
is responsible for power loss.
A complete different mechanism is responsible for power loss when EM
wave interacts with propagation medium which lead to attenuation in
signal.
Pg# 1.pdf
Pg# 2.pdf
Pg# 3.pdf

10. MAIN SHEET ROUGH WORK
ITU G.821 & G.826 has defined following two terms
1) SES
2) UNAVAILABILITY
It is universally agreed that a rain fade will always last longer than 10 consecutive seconds & is classified as Unavailability only.
So,it comes that Multipath fading will be classified either as SES or UNAVAILABILITY 6.31= 6.25+0.06 Site-A
G.821 & G.826 states performace objective in terms of SES & Unavailability & stating that: 3376.64= 3050.07+326.57 Site-B
Worst Month time below level= SES + UNAVAILABILITY
Figure­1
A B
Index
Fades lasting 10 consecutive seconds or longer as UNAVAILABILITY & all other fades as SES.
these results are in line with ITU statement that "Worst Month time below level=
SES + UNAVAILABILITY"
A period of unavailable time begins at the onset of 10 consecutive Severely Errored Second (SES) events. These 10 seconds are considered to be part of unavailable time. A new period of available time begins at
the onset of 10 consecutive non-SES events. These 10 seconds are considered to be part of available time. Figure 1 illustrates the transitions between the availability states.
You can select any of the two options.You will have benchmark KPI for both
SESR(sec/month) & Annual unavailability.If you select,"Treat Multipath as SES only"
then you will notice high SESR(sec/month) value but better annual availability like in
LEFT side picture & if you select, "Treat Multipath as SES+ Unavailability" then you
will notice low SESR(sec/month) value but low annual availability like in righ side
picture.
Like you agree that we should have 99.999% avlbty,>30db FM etc you will have
agreed benchmark for SESR & unavailability(min/yr).
Both these options for Multipath Treatement will come under ITU G.821 & G.826 calc
only,not under Total Annual below Level as it doesn't invlove & relate SES.
T1306350­95
Detection of unavailable state Detection of available state
< 10 sec 10 sec < 10 sec 10 sec
Availab le state Unavailable state Available state
SES
Non­SES
Error­free s econd

11. MAIN SHEET ROUGH WORK
Following methods are available for Reliability Options:
1)Vigants­Barnett
2)ITU­R P.530­6
3)ITU­R P.530­7/8
4)ITU­R P.530­9
5)KQ
also ITU has defined 530­11,12,13,14… but not included in pathloss4.0
1)Vigants-Barnett: Prob(A>A0)=[6*(10^-7)*C*F*(d^3)]*10^(-A0/10)
2)ITU-R P.530-6: Prob(A>A0)=[0.01*K* (d^3.3)*(f^0.93){(1+ |Ep|)^-1.1}*(φ^-1.2)]*10^(-A0/10)
2.1) Geoclimatic Factor(K):
then, K is calculated as mentioned below:
K= Eq-1
where,
α: Numeric value based on Path Classification(<700m,>700,over sea,Ovr large water bodies etc..)
Note:Both the constants values are available to you Mr Jain.check Your batabase.
Logarithmic Geoclimatic Factor is used in Canada
Please note that this Geoclimatic Factor (K) is different from Earth Radius Factor(K).
2.2)Grazing Angle:
It's an angle of incidence or reflection at the reflection point of a reflective plane(for Earth Radius factor K=4/3).
Major challenge in low grazing angle is that angular separation between direct & reflected paths is smaller than the B.W of the receiving antenna.hence reflected signal can't be filtered.
Ψ:Grazing Angle
fmin=[15/pathlength(Km)]GHz
The valid range of Grazing Angle is 1­12mrad,though Pathloss 4.0 doesn't impose any upper limit(just like on Path inclination 0­24mr) .
3) ITUR P.530-7/8: Prob(A>A0):[0.01*K*(d^3.6)*(f^0.89){(1+|Ep|)^-1.4}]*10^(-A0/10)
Though equation for K in this method is not one like in 530­6 but is very similar & only constants /cofficients have different values.
Note:The constants & Cofficient's values are available to you Mr Jain.check Your batabase.
4)ITUR P.530-9: Prob(A>A0):[0.01*K*(d^3.2)*{(1+|Ep|)^-0.97}*{10^(0.032f-0.00085hL)}]*10^(-A0/10)
Equation for K in this method is not one like in 530­6 or 530­7.
5.1) KQ Factor:
Prob(A>A0)=[K.Q.(f^b)*(d^c)]*10^(-A0/10)
5.2) KQ Factor Including Terrain Roughness(S): Prob(A>A0)=[{K.Q.(f^b)*(d^c)}/(S^1.3)]*10^(-A0/10)
Index
All these Reliablibity methods involve either
same or different path profile parameters to
calc fade probability(& Fade occurrence
Factor P0).
Normally Equation for Fade Probability goes
like:Prob(A>A0)=P0.10^(-A0/10).It is then
this P0 which is defined differently under
ITUR P530­6,7,9… & VB & KQ methods of
Reliability.
All these reliability methods involve different Path-profile parameters.
In Pathloss,Vigants­Banett Menthod use/depends on C-Factor to calc fade prob. C-Factor in turn depend on Terrain Roughness & Climatic factor.So,if you are using this method of relibility,then you will
be required C­Factor value.
In Pathloss,ITU­R P.530­6 method use/depends on Pathinclination,Av Grazing angle & Geoclimatic Factor(K).
Geoclimatic Factor (K) is calculated from "the Percentage of time PL that the av refractivity gradient in the lower 100m of the earth atmosphere is less than -100N units/Km".
The Value of PL can be calculated from Contour maps for that region in discussion.
10^-{(α-Clat-Clon)(PL^1.5)}
Clat &Clon:Depending on Latitude & longitude has different value.
In Pathloss 4.0 ,this reliability method involves or depend only on Pathinclination & Geoclimatic factor(K).No Av Grazing Angle is involved.
In Pathloss 4.0 ,this reliability method involves or depend only on Pathinclination & Geoclimatic factor(K).
About different versions of 530 and relevant formulas for probability (and Po), I suggest to use the very last version (530­14). Previous formulas were revised
because a number of ITU delegates reported to ITU­R meetings their critical comments, so each revision should be, according to most and qualified delegates,
more appropriate than previous version.

12. MAIN SHEET ROUGH WORK
# Multipath Fade occurrence Factor or Fade Occurrence Factor or Multipath Activity Factor(P0):
Prob(A>A0)=P0.10^(-A0/10) Eq-1
P0 basically gives a measure of the Multipath Activity on a given link within a given time period.
Many Emperical formulas have been proposed ,giving P0 as a function of radio hop parameters and environmental conditions. Most of them have following general structure:
Eq-2
where C=Geoclimatic Coefficient,
Q=Terrain profile Coefficient,
α=Frequency exponent,
β=Path length exponent.
Example for P0 by ITUR P 530­6: Example for P0 by Vigants Barnett :
They are usually estimated by processing large amount of experimental data,or can derive from more complex formulas,again related to field measurements.
Below mentioned are formulas for P0 under different Reliability methods :
P0 by ITUR P 530-6:※
Eq-3
where:
|Ep|:Path Inclination(mr)
φ:Av Grazing Angle(mr)
K: Geoclimatic Factor
P0 by ITUR P 530-7:※
P0:0.01*K*(d^3.6)*(f^0.89){(1+|Ep|)^-1.4} Eq-4 Example for P0 by ITUR P 530­7:
Example for P0 by K.Q :
P0 by ITUR P 530-9:※
Eq-5
Where,hL:Height of the lower antenna(out of site A & B).This Height is Antenna Height + AMSL
P0 by Vigants-Barnett:※
P0=6*(10^-7)*C*F*(d^3) Eq-6
hL=105.89m considered b=1,c=3.5 & K.Q=1.4^10­8
P0 by KQ Method:※
P0=K.Q.(f^b)*(d^c) Eq-7.1 Example for P0 by ITUR P 530­9: Example for P0 by K.Q with Terrain Roughness:
when included terrain roughness,
P0={K.Q.(f^b)*(d^c)}/(S^1.3) Eq-7.2
Note:The constants(K.Q) & exponent's values are available to you Mr Jain.check Your batabase.
considered b=1,c=3.0 & K.Q=4.1*10^­5*(S)^­1.3
Index
By Monitoring a Radio link during multipath events , a number of recordings , similar to above figure can be collected.This enables to build up statistical data about the time periods with Fade depth below given
thresholds.
A Large amount of similar experiments have shown that fade depth statistics are well approximated by a Rayleigh distribution (atleast for fade depth greater that 15dB).According to that distribution,the
probability that the signal fade depth A(in dB) is deeper than a given value A0 is given by:
where P0 is called "Multipath Occurrence Factor"
P0=C.Q.(F^α).(D^β)
P0=0.01*K* (d^3.3)*(f^0.93){(1+ |Ep|)^-1.1}*(φ^-1.2)
P0:0.01*K*(d^3.2)*{(1+|Ep|)^-0.97}*{10^(0.032f-0.00085hL)}
Where,C:C­Factor,just like K Factor(Geoclimatic factor) in ITU­R P 530…This C­Factor in turn depends on Terrain roughness & climatic factor(cf)

13. World Average Annual Temperature In C

15. MAIN SHEET ROUGH WORK
To keep myself on track & to be precise ,will talk to the point only..
Eq-1
where:Td0 is allowable Threshold degradation specified in the interference dialog box.
Nrx is receiver noise threshold in dbm.
When T/I & Rx Threshold @ BER10^­6 is availble from radio file, then Nrx can be calc as
Eq-2
If the receiver noise threshold is not available due to missing data, the default minimum interfering level will be used as the objective.
The difference between the transmitter and receiver frequencies is greater than the specified maximum.
The transmitter is located at the same station as the receiver.
The interfering path length is greater than the specified coordination distance. The path length is calculated from the receive and transmit coordinates.
NOTE:
Interpretation#1 This value you will see in brackets of Ifl(Interfering Tx case line)
Interpretation#2 Default Minimum Interference Level has nothing to do till the time you have radio files defined with Rx threshold @BER10^­6 & T/I .
If these data value are missing in radio files then default Minimum Interf Level becomes Iobj.
Interpretation#3 As we know Iobj reflects total power in the victim receiver passband which will degrade the receiver threshold by the specified amount.
─92dbm
─98dbm ─107dbm
Ifl IObj Ifl
How Interference calc is Made:
Ignore Adjacent Channels:
Index
Coordination Distance:Interference is not calc. if interfering path length is > the specified coordination distance. Meaning V­I distance which will fall under defined coordination
distance will be taken into consideration,rest will be ignored.
Maximum Frequency Separation:Interference is not calculated if difference between interfering transmitter & victim receiver freq is greater than the specefied Max value.
Default Minimum Interference Level:The interference analysis calc will determine the INTERFERENCE OBJECTIVE using Threshold Level @ BER 10^­6 & Threshold to
Interference(T/I) ratio specified in radio file.IF,note that If these data values are missing in radio file,default minimum interference level will be used as the Objective.
Margin:It sets a tolerance on the reporting of interference cases.Meaning if the Interference Level Objective for the receiver under test is ­104dbm & Margin defined is 10dB,then all
interference cases greater than ­114dbm will be reported.
Digital Interference objective:The objective is specified in terms of the allowable receiver threshold degradation. For frequency coordination with other operators, the
usual value is 1 dB; however, for intra system interference, the final criteria is determined by the increased outage times resulting from the actual threshold degradation.
This threshold degradation objective will be converted to an interference level objective(Obj) for each receiver in the calculation.Thus you will see Obj only for Victim Receiver & not
for Interfering transmitters…
Interference Level Objective is calculated for each receiver as follows:
Iobj= 10log10[10^(Nrx/10) x {10^(Td0/10) ­1}]
Nrx=RxTh­T/I+5.868 dBm
This interfering level objective represents the total power in the victim receiver passband which will degrade the receiver threshold by the specified amount. At this point
of calc, the frequencies and the bandwidths of the interfering transmitter and victim receiver are not considered. These will be used later to calculate the filter
improvement.
As the calculation proceeds, an interference case will be rejected at any point if its interfering level is less than the reporting threshold(Iobj­margin), Several other conditions to reject an
interference case are as follows:
Margin has nothing to do with Interference Objective or default Minimum Interference level… No nothing.. It just allow tool to consider or reject interference cases. Tool will consider all
those interference cases for which Ifl≥ [IObj based on Eq­1 ­ Margin].
Saying again it has nothing to do with "Interference Objective or default Minimum Interference level" . Iobj which you will see in case report(Receiver) will be calculated based on either
Eq­1 or Default Min Interference Level in case of missing data in radio file only. You don't or never add Margin Value to it.
Margin Value helps you to consider or discard interference cases for that receiver under test. Meaning if You set Margin 0 , then tool will consider only those cases for which Interfering
signal (Ifl) is ≥Iobj calculated. If you set margin 10, then all cases for which Interfering signal (Ifl due to interfering transmitter) ≥ OBJ­Margin will be considered.
Iobj­ Ifl≤Margin
So, do not get confussed if you see ifl say ­128dbm when Obj=­120dbm & default Min interf level =­115dbm & margin=10db. Because Default min interfe level will come in picture when
Obj can't be calc from radio Threshold & T/I. And if Default min Intef level is in picture then Yes it will become Interference level Objective & then you can't have case with ifl=­128dbm
when margin is set 10db & default interferenece level is ­115dbm.
Thus, if we have Obj=­104dbm & Ifl is less than this Obj say Ifl=­113dbm(where Margin=10db) then definetly this Ifl have lower impact towards
threshold degradation (specified).Because we required a signal of strength of interfering signal = Obj which will degrade the Receiver threshold by
specified amount.
So, any time if you notice Obj­Ifl(value in brackes) a positive value , it will have low Threshold degradation as compared to one with negative value
for Obj­Ifl.If both two cases under comparison have Positive value for Obj­Ifl ,then one with lower value will tend to have more threshold degradation.
Similarly if both two cases under comparison have negative value for Obj­Ifl ,then one with high negative value will tend to have more threshold
degradation.
Specify Threshold Degradation==>Tool accordingly sets Obj level based on eq­1(signal Level which will cause specified Threshold degradation)==>Then based on Ifl , exact threshold degradation is calculated.
Thus You see,for cases where Ifl ≈Obj,final/actual Threshold degradation for that case will be also ≈ to defined Threshold degradation.
Correlation Options:When an interference path is the same as the main path, the interference case is defined as correlated. In this case it is expected that fading on the
interfering main paths will occur at the same time. In the case of multipath fading, the actual fade depths on the two paths will depend on the type of correlation. If the interfering
transmitter antenna heights are the same as the main transmitter heights, then the two paths are completely correlated. In this case it is common practice to ignore the case,
particularly if automatic transmit power control is employed. The main path will increase power in response to the fade; however the interfering transmitter may not change.
A partially correlated situation exists when the interfering transmitter antenna heights are different than the main transmitter antenna height. In this case, an additional loss in the order
of 5 to 10 dB is added to the interfering signal.Although the same correlation options are used for both mulipath and rain, the definition of correlation is actually whether the interfering
and main paths are in the same rain cell.
Rain will attenuate the desired & interfering signals equally if the polarizations are the same for both signals.The pol of the interfering signal is indeterminate offboresight & can be
conisdered to be circular at discrimination angles >90degree.Therefore the fading could be considered as completely correlated & the case could be ignored.
Adjacent Channel fade correlation:From Multipath point, freq difference between the desired signal & adjacent channel interferer is small enough to offer some multipath fade
correlation.This correlation combined with filter improvement is usually sufficient to clear the case. So we generally keep this also ignored inPl4.0 Correlation window.From Rain
point,interfering & desired paths are completely correlated & the interference can be ignored.
Ignore Diversity Antenna:This option ignores all receive frequencies associated with a space diversity receive only antenna. In the initial frequency analysis, this option will
reduce the number of cases by 50%. If the main and diversity antenna gains are different, then the final analysis should consider the diversity antennas.

16. I hope this been informative for you & would like to Thanks You..!
Index