15 Feb 2001Property of R. Struzak1 Radio Link Fundamentals Probability of Interference Prof. R. Struzak United Nations Educational, Scientific and Cultural Organization & International Atomic Energy Agency The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste-Miramare, Italy, tel , fax , School on Data and Multimedia Communications Using Terrestrial and Satellite Radio Links, 12 February - 2 March 2001, |

15 Feb 2001Property of R. Struzak2 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 These materials may not be published, copied to or issued from another Web server without the author's express permission.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

15 Feb 2001Property of R. Struzak3 Definition

15 Feb 2001Property of R. Struzak4 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

15 Feb 2001Property of R. Struzak5 Events Involved

15 Feb 2001Property of R. Struzak6 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.

15 Feb 2001Property of R. Struzak7 Interference means "A and B and C and D*” where D* is the negation or opposite of D

15 Feb 2001Property of R. Struzak8 Probability

15 Feb 2001Property of R. Struzak9 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)

15 Feb 2001Property of R. Struzak10 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

15 Feb 2001Property of R. Struzak11 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)

15 Feb 2001Property of R. Struzak12 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.

15 Feb 2001Property of R. Struzak13 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.

15 Feb 2001Property of R. Struzak14 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.

15 Feb 2001Property of R. Struzak15 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.

15 Feb 2001Property of R. Struzak16 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.

15 Feb 2001Property of R. Struzak17 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.

15 Feb 2001Property of R. Struzak18 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.

15 Feb 2001Property of R. Struzak19 Continuous operation

15 Feb 2001Property of R. Struzak20 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) = 1 and the probability of interference depends entirely on the factor in square brackets in eq. (2).

15 Feb 2001Property of R. Struzak21 Independent operation

15 Feb 2001Property of R. Struzak22 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

15 Feb 2001Property of R. Struzak23 High-reliability systems

15 Feb 2001Property of R. Struzak24 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)

15 Feb 2001Property of R. Struzak25 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)

15 Feb 2001Property of R. Struzak26 Probability of Interference During a Transmission

15 Feb 2001Property of R. Struzak27 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.

15 Feb 2001Property of R. Struzak28 If both the wanted transmission and the unwanted energy are present all the time, this probability is one.

15 Feb 2001Property of R. Struzak29 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

15 Feb 2001Property of R. Struzak30 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)

15 Feb 2001Property of R. Struzak31 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.