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15 Feb 2001 Property of R Struzak 1
Radio Link FundamentalsCoverage (Selected Issues)
Prof. Ryszard 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, www.ictp.trieste.itSchool 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
15 Feb 2001 Property of R Struzak 2
• 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 These materials may not be published, copied to or issued from another Web server without the author's express permission.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].
15 Feb 2001 Property of R Struzak 3
Summary Slide
• Potential Coverage
• Potential Interference
• Actual Coverage
• Coverage Loss
• Antenna Directivity
15 Feb 2001 Property of R Struzak 4
Radio Link and Interferer
T Rc
I
Ds
Di
15 Feb 2001 Property of R Struzak 5
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 2001 Property of R Struzak 6
Propagation Model
• Free-space
2
4
DPP dtransmittereceived
15 Feb 2001 Property of R Struzak 7
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 2001 Property of R Struzak 8
Potential Coverage
• No interference from other transmitters/ sources of radio waves
• White, isotropic noise exists!
• Criterion: S/N or Prmin
15 Feb 2001 Property of R Struzak 9
Potential Coverage
• Sphere centred at the transmitter (0, 0, 0)R
trn
s
PP
Rmin4
T
15 Feb 2001 Property of R Struzak 10
15 Feb 2001 Property of R Struzak 11
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 2001 Property of R Struzak 12
Potential Interference
• A single interferer
• Isotropic white noise ignored
• Criterion: S/I
15 Feb 2001 Property of R Struzak 13
Potential Interference 2
Dt
Di
P
PSIR
i
t
minSIRP
PQ
i
t
minSIRQ
P
P
i
t
15 Feb 2001 Property of R Struzak 14
Potential Interference (cont.1)
• If SIR = SIRmin then
2
2
minmin
Di
DtQ
Dt
DiSIRQSIR
15 Feb 2001 Property of R Struzak 15
Potential Interference (cont.2)
0)(
)(
)(
222222
222
2222
2222
2222
zyAxQzyx
QzyAx
zyx
D
D
zyAxD
zyxD
i
t
i
t
15 Feb 2001 Property of R Struzak 16
Potential Interference (cont.3)
Q
AQQAzy
Q
QAxQ
Q
AQAQQAxQAzyxQ
QzQyQAQAxQxzyx
1)1()1(
12))(1(
2
22222
2
22222222
2222222
15 Feb 2001 Property of R Struzak 17
Potential Interference (cont. 4)
2
222
2
)1(1
1
Q
QAzy
Q
AQx
Q
15 Feb 2001 Property of R Struzak 18
Potential Interference (cont. 5)
1
1
2222
Q
AQRi
Q
QAB
RizyBx
15 Feb 2001 Property of R Struzak 19
Potential Interference (cont. 6)
B Ri
A
T
I
Z
Y
X
15 Feb 2001 Property of R Struzak 20
Interference Cone, Q > 1
Z
Y
XT
Interferer inside the sphere
15 Feb 2001 Property of R Struzak 21
Interference Cone (cont.)
Q>1
Z
Y
XT
B
/2
dRi 22
)2/cos(
RiBd
Bd
22)2/cos(
RiB
B
15 Feb 2001 Property of R Struzak 22
Interference Cone, Q < 1
I
X
Wanted transmitter inside the sphere
15 Feb 2001 Property of R Struzak 23
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 2001 Property of R Struzak 24
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 2001 Property of R Struzak 25
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 2001 Property of R Struzak 26
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 2001 Property of R Struzak 27
Actual Coverage: Q>1 (cont)
Coverage lost
Potential Interference Sphere
Potential Coverage Sphere
Z = 0
15 Feb 2001 Property of R Struzak 28
Actual Coverage: Q>1 (cont.2)
Coverage lost
Potential Interference Sphere
Potential Coverage Sphere
Z = 0
Actual Coverage Region
15 Feb 2001 Property of R Struzak 29
Actual Coverage: Q<1
Potential Interference Sphere
Potential Coverage Sphere
Actual Coverage Region
Z = 0
Lost coverage
15 Feb 2001 Property of R Struzak 30
Coverage loss
• Coverage Loss = = Potential Coverage – Actual coverage – Volume, – Surface, – Population, etc
• Relative Coverage Loss = % of the potential coverage lost
15 Feb 2001 Property of R Struzak 31
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 2001 Property of R Struzak 32
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 2001 Property of R Struzak 33
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 2001 Property of R Struzak 34
Antenna Directivity
• Directive antenna can eliminate (or attenuate) radiation coming from a limited number of discrete interferers
• It cannot eliminate isotropic noise
15 Feb 2001 Property of R Struzak 35
Antenna Directivity
• Receiving antenna gain = G within apical angle and is null elsewhere
15 Feb 2001 Property of R Struzak 36
Directive Antenna Effectiveness
Effective Limiting case Not effective
TTT
I I I
15 Feb 2001 Property of R Struzak 37
Relations between angles
T I
Receiver
R
R
R
h
2
2
22
22
15 Feb 2001 Property of R Struzak 38
Effectiveness Circle
T I
Receiver
R Rh
A
cot2
cos
sin2A
Rh
AR
15 Feb 2001 Property of R Struzak 39
Effectiveness on a Plane
T
T I
2
2
2
sin
2sin
2
)2sin(2
A
R
Surface
Rc
15 Feb 2001 Property of R Struzak 40
3D Effectiveness
`
B
R
hX
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 2001 Property of R Struzak 41
3D Effectiveness (cont. 1)
• Parametric equation
sincos
coscos
sin
Rhz
Rhy
RBx
15 Feb 2001 Property of R Struzak 42
3D Effectiveness (cont. 2)
R
x
R
x
hRhRhzy
RBxx
*1sin1cos
*sin
coscos2)cos(
sin*
2
22222
15 Feb 2001 Property of R Struzak 43
3D Effectiveness (cont. 3)
2222222
22222
22
2222
*2*
**2
*1
*12
RxRhhzyx
xRxRhh
R
xR
R
xhRhzx
15 Feb 2001 Property of R Struzak 44
3D Effectiveness (cont. 4)
322222
2
3
42
arcsin1arcsin2
hRhRh
R
hhR
Volume
15 Feb 2001 Property of R Struzak 45
3D Effectiveness (cont. 5)
Cross-section in plane x = B
Cross-section in plane z = ay
(h + R)
2R
15 Feb 2001 Property of R Struzak 46
Propagation Model
• Different propagation mechanism for the wanted and the interfering signals
• Variability and random factors
• Probabilistic approach