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United Nations Educational, Scientific and Cultural Organization & International Atomic Energy Agency
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste-Miramare, Italy, tel. +39 40 2240111, fax +39 40 224163, School on Data and
Multimedia Communications Using Terrestrial and Satellite Radio Links, 12 February - 2 March 2001,
[email protected] | www.ictp.trieste.it/~radionet/2001_school/Timetable.html
Radio Link Fundamentals
Probability of Interference
Prof. R. Struzak
[email protected]
15 Feb 2001
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• Note: These materials may be used for study,
research, and education in not-for-profit
applications. If you link to or cite these materials,
please credit the author, Ryszard Struzak. These
materials may not be published, copied to or
issued from another Web server without the
author's express permission. Copyright © 2001
Ryszard Struzak. All commercial rights are
reserved. If you have comments or suggestions,
please contact the author at
[email protected].
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Definition
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Interference: the effect of unwanted
energy upon reception in a radio
communication system manifested by:
– performance degradation,
– misrepresentation,
– or loss of information
which would not happen in the absence of
that unwanted energy
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Events Involved
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• A: The desired transmitter is transmitting".
• B: The wanted signal is satisfactorily
received in the absence of unwanted energy
• C: Another equipment is producing unwanted
energy
• D: The wanted signal is satisfactorily
received in the presence of the unwanted
energy
All these statements refer to the same (small)
time period.
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•
Interference means
"A and B and C and D*”
• where
D* is the negation or opposite of D
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Probability
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• Let P(x) = the probability of x
• P(x I y) = the probability of x, given y
• Then, the probability of interference
during the small time period is
P(I) = P(A and B and C and D*)
(1)
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• An equivalent form:
P(l) = [P(B| A) - P(D| A and C)] P(A and C)
(2)
• P(I) in (2) can be interpreted as a fraction of time:
No. of interference seconds during a time period
divided
by No. of seconds in the time period
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• Probability of interference during the time
that the wanted transmitter is transmitting
P'(I) = P(B and C and D*| A)
(3)
or
P'(I) = [P(B| A) - P(D| A and C)] P(C| A)
(4)
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• P(I) in (4) can be interpreted as a fraction of
time: No. of interference seconds
divided by
No. of seconds the wanted transmitter is
transmitting during the time period.
• P(I) in (4) is larger than P(I) in (2) unless
the wanted transmitter is on all the time.
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• P(B| A) is the probability that a wanted
signal will be correctly received when there
is no interference
• Often expressed as the probability
that S/ N > R, where S is the signal power,
N is the noise power, and R is the signal-tonoise ratio required for satisfactory service.
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• P(B| A) is related to the reliability, and is
often computed when the system is
designed.
• It can be computed if system parameters
(for example, transmitter and receiver
location, power, required S/ N) are known
using statistical data on transmission loss
and on radio noise.
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•
Many systems (e.g. satellite or microwave relay
point-to-point) are designed so that P(B| A) ~ 1.
• In other services, such as long-distance
ionospheric point-to-point services, or mobile
services near the edge of the coverage area, P(B|
A) may be quite small. In this case, the
probability of interference will be small regardless
of the other probabilities.
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• P(D| A and C) is the probability that the wanted
signal will be correctly received even when the
unwanted energy is present.
– It can be computed if there is sufficient information
about the location, frequency, power etc., of the source
of unwanted energy.
• Assumption: P(DI A and C) <= P(BI A)
– If the signal can be received satisfactorily in the
presence of unwanted energy, then it can surely be
received satisfactorily in the absence of the unwanted
energy. P(I) cannot be negative.
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P(A and C) is the probability that the wanted
transmitter and the source of unwanted energy are
on simultaneously.
– In some situations, the wanted transmitter and source of
unwanted energy may be operated independently. For
example, they may be on adjacent channels.
– In this case, (A and C) = P(A)P(C),
where P(A) is the fraction of time that the wanted
transmitter is emitting, and P(C) is the fraction of time
that the unwanted source is on.
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In other situations, the operation may be
highly dependent. For example, the
transmitters may be co-channel base
stations in a well-designed and disciplined
mobile service. In this case, P(A and C) is
small.
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Continuous operation
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If the two transmitters both operate continuously
(e.g. one might be part of a microwave point-topoint service, and the other a satellite sharing the
same frequency band), then
P(A and C) = 1
and the probability of interference depends
entirely on the factor in square brackets in eq. (2).
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Independent operation
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• If the two transmitters operate
independently, P(C| A) = P(C)
• If the two transmitters are co-channel
stations in a disciplined land mobile service,
P(C| A) is small
• If the unwanted transmitter is on all the
time, P(C| A) = 1
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High-reliability systems
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High reliability means P(B| A) ~ 1
Now {1 - P(DI A and C) ~ P(D*I A and C)} (5)
which is the probability that the wanted signal is not
received in the presence of unwanted energy.
Then P(I) = P(D*| A and C) P(A and C)
Equation (4) becomes
P'(I) = P(D*| A and C) P(C| A)
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(6)
(7)
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If in addition, both transmitters operate
continuously, or at least on the same
schedule, so that P(A and C) = P(CI A) = 1,
then:
P(I) = P(D*P(I) = P(D*| A and C) = P'(I)
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(8)
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Probability of Interference
During a Transmission
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• Equations (2) and (4) give the probability that
interference will occur at an instant of time. A
more conservative view is that interference occurs
if any part of a transmission is lost; that is, if the
unwanted energy causes loss of information
anytime during the wanted transmission.
– This is particularly applicable to digital transmission
systems.
– In this case, we replace the factor P(C| A) in equation
(4) with the probability that the wanted and unwanted
transmissions overlap.
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• If both the wanted transmission and the
unwanted energy are present all the time,
this probability is one.
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• If they are not present all the time, but one or both
transmit intermittently, then
P(overlap) = 1 - (1-NTua) exp[-TwN / (1-NTua)]
(9)
o
Tw: the length of a transmission by the wanted
transmitter;
N : the average number of unwanted emissions per unit time
o Tua: the average length of an unwanted emission.
Assumption: Poisson distribution
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• Substituting it into (2), the probability of
interference [P(intrf)] at some time during a
transmission of length Tw is:
• P(intrf | Tw) = [P(B| A) - P(D| A and C)] x
{1-(1-NTua) exp[- TwN /(1 - NTua)]} (10)
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• Notice that NTua is the fraction of time that
the unwanted energy is present.
• If the unwanted energy is present all the
time so that NTua = 1, then P(overlap) = 1.
• If NTw and NTua are both much smaller
than 1 (both operations are very
intermittent) then
P(overlap) ~ NTw + NTua.
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