15 Feb 2001Property of R Struzak1 Radio Link Fundamentals Coverage (Selected Issues) Prof. Ryszard 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 These materials may not be published, copied to or issued from another Web server without the author's express permission.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 Summary Slide Potential Coverage Potential Interference Actual Coverage Coverage Loss Antenna Directivity

15 Feb 2001Property of R Struzak4 Radio Link and Interferer TRc I Ds Di

15 Feb 2001Property of R Struzak5 Simplest Scenario The transmitter (T), receiver (Rc), and interferer (I) are –isotropic, –at fixed positions, –operating at the same time at the same frequency X Z Y AI Rc T Ds Di

15 Feb 2001Property of R Struzak6 Propagation Model Free-space

15 Feb 2001Property of R Struzak7 Normal Operation Conditions Minimum quality assured (e.g. BER) The signal power (Ps) available at the receiver should be Prmin or greater –White, isotropic noise The minimum signal-to-interference power ratio at the receiver input (SIR) should be SIRmin or greater –Other noise

15 Feb 2001Property of R Struzak8 Potential Coverage No interference from other transmitters/ sources of radio waves White, isotropic noise exists! Criterion: S/N or Prmin

15 Feb 2001Property of R Struzak9 Potential Coverage Sphere centred at the transmitter (0, 0, 0) R T

15 Feb 2001Property of R Struzak10

15 Feb 2001Property of R Struzak11 Potential Coverage (cont) With no interferer, communication is possible if the receiver is located on the surface of, or inside, the potential coverage sphere –At the surface of the sphere Ps = Psmin –Inside the sphere Ps > Psmin Outside the sphere no communication is possible because Ps < Psmin

15 Feb 2001Property of R Struzak12 Potential Interference A single interferer Isotropic white noise ignored Criterion: S/I

15 Feb 2001Property of R Struzak13 Potential Interference

15 Feb 2001Property of R Struzak14 Potential Interference (cont.1) If SIR = SIR min then

15 Feb 2001Property of R Struzak15 Potential Interference (cont.2)

15 Feb 2001Property of R Struzak16 Potential Interference (cont.3)

15 Feb 2001Property of R Struzak17 Potential Interference (cont. 4)

15 Feb 2001Property of R Struzak18 Potential Interference (cont. 5)

15 Feb 2001Property of R Struzak19 Potential Interference (cont. 6) B Ri A T I Z Y X

15 Feb 2001Property of R Struzak20 Interference Cone, Q > 1 Z Y X T Interferer inside the sphere

15 Feb 2001Property of R Struzak21 Interference Cone (cont.) Q>1 Z Y X T B  /2 d Ri

15 Feb 2001Property of R Struzak22 Interference Cone, Q < 1 I X Wanted transmitter inside the sphere

15 Feb 2001Property of R Struzak23 Transmitter Domination (Q > 1) The interferer is inside the sphere; the transmitter is outside –SIR = SIRmin at the surface of the sphere –SIR < SIRmin inside the sphere –SIR > SIRmin outside the sphere The receiver must be outside the sphere for normal operation Note: The sphere is on the right side of plane x = (A/2)

15 Feb 2001Property of R Struzak24 The Balance (Q = 1) The sphere degenerates into plane x = A/2 that creates two half-spaces The transmitter is on the left half-space where SIR > SIRmin The interferer is on the right half-space where SIR < SIRmin The receiver must be on the left side of the plane x = A/2 for normal operation

15 Feb 2001Property of R Struzak25 Interferer Dominance (Q < 1) The interferer is outside the sphere; the transmitter is inside (jamming) –SIR = SIRmin at the surface of the sphere –SIR > SIRmin inside the sphere –SIR < SIRmin outside the sphere The receiver must be inside the sphere for normal operation Note: The sphere is on the left side of plane x = (A/2)

15 Feb 2001Property of R Struzak26 Actual Coverage: Q>1 As long as d > 0, the actual and the potential coverage regions coincide. No coverage loss. d = B – (Rs + Ri) Sphere of potential coverage Sphere of potential interference

15 Feb 2001Property of R Struzak27 Actual Coverage: Q>1 (cont) Coverage lost Potential Interference Sphere Potential Coverage Sphere Z = 0

15 Feb 2001Property of R Struzak28 Actual Coverage: Q>1 (cont.2) Coverage lost Potential Interference Sphere Potential Coverage Sphere Z = 0 Actual Coverage Region

15 Feb 2001Property of R Struzak29 Actual Coverage: Q<1 Potential Interference Sphere Potential Coverage Sphere Actual Coverage Region Z = 0 Lost coverage

15 Feb 2001Property of R Struzak30 Coverage loss Coverage Loss = = Potential Coverage – Actual coverage –Volume, –Surface, –Population, etc Relative Coverage Loss = % of the potential coverage lost

15 Feb 2001Property of R Struzak31 Coverage loss (cont) If Q>1 and if the whole sphere of potential interference is contained within the sphere of potential coverage, then Relative Coverage Loss (Volume) = = (Ri/Rs) 3 Relative Coverage Loss (Equatorial plane) = = (Ri/Rs) 2

15 Feb 2001Property of R Struzak32 Summary With isotropic transmitter, receiver and interferer, the coverage depends on: Transmitter power Pt Weighted ratio of the transmitter power to interferer power Q = P/(Pi SIR) Continued

15 Feb 2001Property of R Struzak33 Summary (cont) Distance between the transmitter and interferer, A. If the number of transmitters over a given area increases, the distance between them decreases

15 Feb 2001Property of R Struzak34 Antenna Directivity Directive antenna can eliminate (or attenuate) radiation coming from a limited number of discrete interferers It cannot eliminate isotropic noise

15 Feb 2001Property of R Struzak35 Antenna Directivity Receiving antenna gain = G within apical angle  and is null elsewhere

15 Feb 2001Property of R Struzak36 Directive Antenna Effectiveness Effective Limiting case Not effective T T T II I

15 Feb 2001Property of R Struzak37 Relations between angles TI  Receiver       R R R  h

15 Feb 2001Property of R Struzak38 Effectiveness Circle TI  Receiver  R R h A

15 Feb 2001Property of R Struzak39 Effectiveness on a Plane T  TI Rc

15 Feb 2001Property of R Struzak40 3D Effectiveness ` B R h X Y Z Vectors h and R lie in plane z = ay The plane turns around axis OX The tip of vector h encircles point B The tip of vector R encircles the tip of vector h O

15 Feb 2001Property of R Struzak41 3D Effectiveness (cont. 1) Parametric equation

15 Feb 2001Property of R Struzak42 3D Effectiveness (cont. 2)

15 Feb 2001Property of R Struzak43 3D Effectiveness (cont. 3)

15 Feb 2001Property of R Struzak44 3D Effectiveness (cont. 4)

15 Feb 2001Property of R Struzak45 3D Effectiveness (cont. 5) Cross-section in plane x = B Cross-section in plane z = ay (h + R) 2R

15 Feb 2001Property of R Struzak46 Propagation Model Different propagation mechanism for the wanted and the interfering signals Variability and random factors Probabilistic approach