discussion 1

EE359 Discussion Session 1Signal Propagation Models

September 30, 2014

EE359 Discussion 1 September 30, 2014 1 / 20

Outline

1 Signal representation and propagation models

2 Other models for path loss

3 System design considerations


Outline





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.


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


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


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


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


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)


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)


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


Outline





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)


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


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


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


Outline





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


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


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


Homework 1

Problem 5: Make sure you convert to/from linear and dB scale


Signal representation and propagation modelsOther models for path lossSystem design considerations

discussion 1

Documents

2014ee359 discussion

mentionedee359 discussion

mediumee359 discussion

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baseband signal convenient

nx varnx varnx

path lossenergy

attenuation eidi