15 Feb 2001 Property of R. Struzak 1 Radio Link Fundamentals Probability of Interference Prof. R. Struzak [email protected]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, smr1301@ ictp . trieste .it | www. ictp . trieste .it /~radionet/2001_school/Timetable.html
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15 Feb 2001Property of R. Struzak1 Radio Link Fundamentals Probability of Interference Prof. R. Struzak [email protected] United Nations Educational,
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15 Feb 2001 Property of R. Struzak 1
Radio Link FundamentalsProbability of Interference
United Nations Educational, Scientific and Cultural Organization & International Atomic Energy AgencyThe 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
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-to-noise 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-to-point service, and the other a satellite sharing the same frequency band), then
P(A and C) = 1and 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) (6)
Equation (4) becomes
P'(I) = P(D*| A and C) P(C| A) (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) (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