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EE359 Discussion Session 1Signal Propagation Models
September 30, 2014
EE359 Discussion 1 September 30, 2014 1 / 20
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Outline
1 Signal representation and propagation models
2 Other models for path loss
3 System design considerations
EE359 Discussion 1 September 30, 2014 2 / 20
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Outline
1 Signal representation and propagation models
2 Other models for path loss
3 System design considerations
EE359 Discussion 1 September 30, 2014 3 / 20
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Baseband versus passband
Passband
sp(t) = sI(t) cos(2pifct) sQ(t) sin(2pifct)
Baseband
sb(t) = sI(t) + jsQ(t)
Baseband passbandsp(t) = Re
(sb(t)e
j2pifct)
Passband baseband (under narrowband assumption T 1fc
)
sI(t) 2T
T0sp(t) cos(2pifct)dt, sQ(t) 2
T
T0sp(t) sin(2pifct)dt.
EE359 Discussion 1 September 30, 2014 4 / 20
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When to use baseband and passband?
Baseband signal convenient for DSP (digital signal processing) andmathematical analysis
Passband signal (EM wave of frequency fc) is what is transmittedand received through medium
EE359 Discussion 1 September 30, 2014 5 / 20
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dB versus linear
Power often measured in dB
If P is in linear units (e.g. watts), then the same quantity in dB unitsis defined as
10 log10(P )
ThusP (dB) = 10 log10(P (in watts))
For this session, we use the linear units unless otherwise mentioned
EE359 Discussion 1 September 30, 2014 6 / 20
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Point to point wireless channel
Main effects1 Path loss
I Due to diffraction/finite area of antennasI Large scale effects ( Km)
2 Signal attenuation or shadowingI Due to absorption/scattering/reflectionI Medium scale effects ( tens of metres)
3 Fading (we will revisit this later)I Due to phase cancellation/reinforcement due to multipath combiningI Small scale ( cm)
Pt PrO1 O2
Figure: Representative wireless channel
EE359 Discussion 1 September 30, 2014 7 / 20
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Effect 1: Path loss
Energy spreads due to finite area of transmitters (diffraction)
Finiteness with respect to the wavelength
Wavelength dependence is due to this diffraction effect
Free space path loss (wavelength )
Line of sight: PrPt =(
4pid
)2GtGr where G represent gains
Valid in far field with no reflectors e.g. satellite communications
Pt Pr
d
Figure: Free space path loss
EE359 Discussion 1 September 30, 2014 8 / 20
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Effect 2: Signal attenuation or shadowing
Power of EM wave suffers attenuation eidi when it passes throughobject i of thickness diLog of power satisfies logPr = logPt
i idi
One way to model is by approximating sum as a gaussian randomvariable nx at location x (log normal shadowing)
Account for spatial density of scatterers by modeling dependencebetween spatially close points, e.g.
cov(nx, nx+)var(nx) var(nx+)
= e||||/Xc
Pt PrO1
1Pt
O2
12Pt
Figure: Shadowing (randomness comes from random number of objects)
EE359 Discussion 1 September 30, 2014 9 / 20
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Effect 2: Signal attenuation or shadowing
Power of EM wave suffers attenuation eidi when it passes throughobject i of thickness diLog of power satisfies logPr = logPt
i idi
One way to model is by approximating sum as a gaussian randomvariable nx at location x (log normal shadowing)
Account for spatial density of scatterers by modeling dependencebetween spatially close points, e.g.
cov(nx, nx+)var(nx) var(nx+)
= e||||/Xc(decorrelation distance)
Pt PrO1
1Pt
O2
12Pt
Figure: Shadowing (randomness comes from random number of objects)
EE359 Discussion 1 September 30, 2014 9 / 20
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Effect 3: Multipath combining or fading
Multipath not always bad (if resolvable); e.g. RAKE receivers
If not resolvable usually causes constructive or destructive interference
Variation of the order of wavelength since /2 shift causes pi phaseshift (thus causing cancellations /2 distance away from peaks)
Pt Pr
= pi
Figure: Multipath causing destructive interference
EE359 Discussion 1 September 30, 2014 10 / 20
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Outline
1 Signal representation and propagation models
2 Other models for path loss
3 System design considerations
EE359 Discussion 1 September 30, 2014 11 / 20
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Two ray model
ht hr
l
x x
Figure: Two ray model
PrPt
= c1|1l ej
x+x |2 where is phase difference between twocomponents
For low l, reflected component negligible hence close to free spacebehavior
For large l, l x+ x, 0, hence by Taylor series approximation,PrPr c1 |l x x
|2l4
Cutoff distance dc capturing change in rate of decay can be foundfrom plots or from heuristics (e.g. set the phase difference to be pi)
EE359 Discussion 1 September 30, 2014 12 / 20
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Ten ray models
Models rectilinear streets with buildings on both sides
Transmitters and receivers close to ground
Includes all rays undergoing up to three reflections
EE359 Discussion 1 September 30, 2014 13 / 20
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Empirical/ray tracing/simplified models
Ray-tracing modelsI Useful when geometric information availableI Useful for site planning
Empirical modelsI Usually fitted to be valid over large distance and frequency rangesI Usually captures effects not possible with simpler modelsI Okumura, hata, piecewise linear . . .
Simplified path loss modelsI Simple function of distance (far field)
PrPt
= K
(d0d
)I Useful for analytically modeling general power falloff
EE359 Discussion 1 September 30, 2014 14 / 20
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Homework 1
Disclaimer
Answer may vary depending on assumptions made
Feel free to ignore the suggestions/references
Problems 2, 4: two-ray, and simplified path loss models
Problem 3: Note that some reflected rays have much lower energyand wont really cause destructive interference
Problem 6: Explore validity of u(t) u(t ) in textbook derivation
EE359 Discussion 1 September 30, 2014 15 / 20
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Outline
1 Signal representation and propagation models
2 Other models for path loss
3 System design considerations
EE359 Discussion 1 September 30, 2014 16 / 20
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Outage
Received power needs to be above threshold (noise, rate, coding, . . . )
Outage event
Pr <
Given path loss (e.g. simplified) and shadowing models (e.g. log normal),one can compute outage probability (shadowing variance assumed to be 1)
Pout = 1Q(log() log(KPt) + log(d0/d))
where Q(x) , x
12piey2/2dy
Question
What will the above Pout look like in dB units ?
Check answer with Eq. 2.52 of text
EE359 Discussion 1 September 30, 2014 17 / 20
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Outage
Received power needs to be above threshold (noise, rate, coding, . . . )
Outage event
Pr <
Given path loss (e.g. simplified) and shadowing models (e.g. log normal),one can compute outage probability (shadowing variance assumed to be 1)
Pout = 1Q(log() log(KPt) + log(d0/d))
where Q(x) , x
12piey2/2dy
Question
What will the above Pout look like in dB units ?
Check answer with Eq. 2.52 of text
EE359 Discussion 1 September 30, 2014 17 / 20
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Constant received power contour
Contour with radial path loss
Same for direction dependent loss
Coverage hole due to random shadowing
Figure: Contour plots of received power for different effects
Without random fluctuations, contours of constant received powerwould be circular
With direction dependent gains the contours are amoeba like
With random shadowing they are amoeba like with holes
One objective of base station placement and power level selection (or siteplanning) is to minimize these coverage holes
EE359 Discussion 1 September 30, 2014 18 / 20
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Cell coverage area (C)
Definition
Expected fraction of locations within a cell where the received power isabove threshold
If A is the area of cell
C =1
AE
(A
1(Pr > )dA
)One measure of how strong chances of outage are for a power level
Can be computed analytically for log normal shadowing and circulargeometries
Note that we ignore out of cell interference which would be a morepertinent limiting factor
EE359 Discussion 1 September 30, 2014 19 / 20
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Homework 1
Problem 5: Make sure you convert to/from linear and dB scale
EE359 Discussion 1 September 30, 2014 20 / 20
Signal representation and propagation modelsOther models for path lossSystem design considerations
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