Aalto University School of Electrical Engineering ELEC ......Aalto University School of Electrical...

Aalto University School of Electrical Engineering

ELEC-E4750 Radiowave Propagation and Scattering Session 10: Cellular links (3)

ELEC-E4750 24.11.2016

1



Schedule

2

Wk Date Location New topics, lectures and deadlines

43 Tue. 25 Oct. R037/TU3 1194-1195 Thu. 27 Oct.

44 Tue. 01 Nov. Topic 7: wireless and cellular systems Thu. 03 Nov. Clicker lecture 7

45 Tue. 08 Nov. Topic 8: cellular links (1) Thu. 10 Nov. Clicker lecture 8

46Tue. 15 Nov. Topic 9: cellular links (2) Thu. 17 Nov. Clicker lecture 9; threshold deadline of

topics 5-8

47 Tue. 22 Nov. Topic 10: cellular links (3) Thu. 24 Nov. Clicker lecture 10

•  Suzan leads on 25 and 27 Oct. •  Usman is away for 25.9-01.11. •  Jan, Usman and Suzan lead on 24 Nov.


Books, Topics and Exercises §  Books

§  Main books §  S. Saunders, Antennas and Propagation for Wireless Communication Systems, Chapters 3, 5,

6-8, 10, 12 15, Wiley. §  H. L. Bertoni, Radio propagation for modern wireless systems, Chapters 2-6, Prentice Hall. §  A. . Molisch, Wireless Communications, Chapters 1 and 8, Wiley. §  John A. Richards, Radio wave propagation, an introduction or the non-specialist, Chapter 3,

Springer. §  Hardcover or paperback copies of both books are available in AaltoELEC and main

library. §  Supplemental books:

§  D. M. Pozar, Microwave Engineering, Chapter 1, Wiley.

§  Topic 9: Cellular links (2) (Ch. 12, Ch. 2) §  Exercise 1: Physical propagation modeling in microcells §  Exercise 2: Pathloss and small-scale fading

§  Topic 10: Cellular links (3) (Ch. 10, Ch. 5) §  Exercise 1: Small-scale fading models §  Exercise 2: Characterization of small-scale fading (simulations)

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Contact Sessions for Topic 10•  Goals of the present exercise problems are to

–  Acquire the physical understanding of small-scale fading (problem 1) –  Be able to characterize small-scale fading mathematically (problem

2) •  During the contact sessions, you are

–  solving the exercise problems by referring to relevant parts of the course books.

•  A limited number of course books are available in the room. –  encouraged to discuss with other students and teachers. –  asked to contact teachers once your solutions are ready.

•  If you prepare exercise solutions in an electronic format (recommended), upload the solution to MyCourses first and then contact teachers.

–  asked to propose points for your ready solutions to the teachers. –  not given exercise points without discussing with teachers.

•  The discussions MUST happen in the contact sessions. –  reminded that the threshold deadline topic 9-12 exercises and the

deadline of all exercises returns is December 15th.



Empirical Pathloss Estimation

5

pathloss

Shadowing

Small-scale fading



Rayleigh Fading•  Many propagation paths with

similar power

6 f (x + jy) = 1

2πσ 2 exp −x2 + y2

2σ 2

"

#$

%

&'

f (x) = 12πσ

exp −x2

2σ 2

"

#$

%

&'

Figs from Saunders,

Ch. 10.



PDF of Rayleigh fading

7

f (x) = 12πσ 2

exp −x2

2σ 2

⎛

⎝⎜

⎞

⎠⎟

f (y) = 12πσ 2

exp −y2

2σ 2

⎛

⎝⎜

⎞

⎠⎟

PDF(r) = rσ 2 exp −

r2

2σ 2

⎛

⎝⎜

⎞

⎠⎟

Fig from Saunders,

Ch. 10.

Aalto University School of Electrical Engineering A. B. C. D.

0%

67%

33%

0%

Q1a:WhichstatementisincorrectaboutRayleighfadingofreceivedfieldstrength?A.  Wecanobserveitinrichsca1ering

environments.B.  Theircomplexamplitudeslooklike

whiteGaussiannoise.C.  Wecanpredictwhereinspacewe

seelargeandsmallamplitudes.D.  Correspondingphaseisuniformly

distributedover0to2π.


0% 0%

100%

0%

Q1b:WhichstatementisincorrectaboutRayleighfadingofreceivedfieldstrength?A.  Wecanobserveitinrichsca1ering

environments.B.  Theircomplexamplitudeslooklike

whiteGaussiannoise.C.  Wecanpredictwhereinspacewe

seelargeandsmallamplitudes.D.  Correspondingphaseisuniformly

distributedover0to2π.



Rice Fading•  Rayleigh fading + dominant

propagation path, e.g., LOS

10

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

Real

Imaginary

f (x + jy) = 12πσ 2 exp −

(x − scosφ)2 + (y− ssinφ)2

2σ 2

"

#$

%

&'

s =1

φ =π2

Figs from Saunders,

Ch. 10.

Aalto University School of Electrical Engineering A. B.

22%

78%

Q2a:ThetwostandingwavecurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A.  CurveA.B.  CurveB.

-10 -5 0 5 10Distance [6]

-30

-20

-10

0

10

Gai

n [d

B]

AB

A B


0%

100%

-10 -5 0 5 10Distance [6]

-30

-20

-10

0

10

Gai

n [d

B]

AB

Q2b:ThetwostandingwavecurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A.  CurveA.B.  CurveB.

A B



Cumulative Distribution Function (CDF)

13

CDF(r ') = prob(x ≤ r ') = PDF(r)−∞

r '∫ dr

-20 -10 0 10Gain [dB]

10-2

10-1

100

Cum

ulat

ive

prob

abilit

y-10 -5 0 5 10

Distance [6]

-30

-20

-10

0

10

Gai

n [d

B]



Q3: Derive the CDF of Rayleigh fading from the PDF on the paper you have. You can discuss with your peers.

14

CDF(r ') = PDF(r)−∞

r '∫ dr

PDF(r) = rσ 2 exp −

r2

2σ 2

⎛

⎝⎜

⎞

⎠⎟

-30 -20 -10 0 10Envelope [dB]

0

0.1

0.2

0.3

0.4

0.5

Prob

abilit

y

PDF of Rayleigh

distribution


56%

44%

-20 -10 0 10Gain [dB]

10-2

10-1

100

Cum

ulat

ive

prob

abilit

yQ4a:ThetwoCDFcurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A.  CurveA.B.  CurveB.

A

B


100%

0%-20 -10 0 10

Gain [dB]10-2

10-1

100

Cum

ulat

ive

prob

abilit

yQ4a:ThetwoCDFcurvesrepresentRayleighandRicefading.WhichoneisRiceFading?A.  CurveA.B.  CurveB.

A

B



Empirical Pathloss Estimation

17

pathloss

Shadowing

Small-scale fading



Shadowing

18

Figs from Saunders,

Ch. 9.



Empirical Modeling of Shadowing

19

Fig from Saunders,

Ch. 9.


Shadowing: Physical Interpretation and Modeling •  Caused by obstacles in propagation path between mobile

and base station.

20

NAAAA ×××= …21

NLLLAL +++== …2110log10Central limit theorem à Normal distribution in the log-domain.


33%

22%22%22%

Q5a:Pathloss(P),shadowing(S),andsmall-scalefading(F).Whichstatementiscorrect?A.  Typicaldynamicrangeofthe

receivedsignalisP>S>>F.B.  Whatwecallstandingwaveis

equivalenttoF.C.  TypicalspaJalrangeofSis

inverselyproporJonaltotheradiofrequency.

D.  ThecentrallimittheoremdefinesthesignaldistribuJonsofP,SandF.


0% 0%0%

100%

Q5b:Pathloss(P),shadowing(S),andsmall-scalefading(F).Whichstatementiscorrect?A.  Typicaldynamicrangeofthe

receivedsignalisP>S>>F.B.  Whatwecallstandingwaveis

equivalenttoF.C.  TypicalspaJalrangeofSis

inverselyproporJonaltotheradiofrequency.

D.  ThecentrallimittheoremdefinesthesignaldistribuJonsofP,SandF.



Contact Sessions for Topic 10•  Goals of the present exercise problems are to

–  Acquire the physical understanding of small-scale fading (problem 1) –  Be able to characterize small-scale fading mathematically (problem

2) •  During the contact sessions, you are

–  solving the exercise problems by referring to relevant parts of the course books.

•  A limited number of course books are available in the room. –  encouraged to discuss with other students and teachers. –  asked to contact teachers once your solutions are ready.

•  If you prepare exercise solutions in an electronic format (recommended), upload the solution to MyCourses first and then contact teachers.

–  asked to propose points for your ready solutions to the teachers. –  not given exercise points without discussing with teachers.

•  The discussions MUST happen in the contact sessions. –  reminded that the threshold deadline topic 9-12 exercises and the

deadline of all exercises returns is December 15th.

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