Aalto University School of Electrical Engineering. ELEC-E4750 Radiowave Propagation and Scattering Session 10: Cellular links (3)

Transcription

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

2 Schedule Wk Date Location New topics, lectures and deadlines Tue. 25 Oct. R037/TU Thu. 27 Oct. Tue. 01 Nov. Thu. 03 Nov. Clicker lecture 7 Topic 7: wireless and cellular systems Tue. 08 Nov. Topic 8: cellular links (1) Thu. 10 Nov. Clicker lecture 8 Tue. 15 Nov. Topic 9: cellular links (2) Thu. 17 Nov. Clicker lecture 9; threshold deadline of topics 5-8 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 Jan, Usman and Suzan lead on 24 Nov. 2

3 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) 3

4 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 15 th.

5 Empirical Pathloss Estimation Small-scale fading pathloss Shadowing 5

6 Rayleigh Fading f (x) = 1 " x2 exp$ 2πσ # 2σ 2 % ' & Many propagation paths with similar power Figs from Saunders, Ch. 10. f (x + jy) = 1 2πσ exp " x2 + y 2 $ 2 # 2σ 2 % ' & 6

7 PDF of Rayleigh fading Fig from Saunders, Ch. 10. f (x) = 1 2πσ exp x 2 2 2σ 2 f (y) = 1 2πσ exp y 2 2 2σ 2 PDF(r) = r r2 exp 2 σ 2σ 2 7

8 Q1a: Which statement is incorrect about Rayleigh fading of received field strength? A. We can observe it in rich sca1ering environments. B. Their complex amplitudes look like white Gaussian noise. C. We can predict where in space we see large and small amplitudes. D. Corresponding phase is uniformly distributed over 0 to 2π. 33 % 67 % 0 % 0 % A. B. C. D.

9 Q1b: Which statement is incorrect about Rayleigh fading of received field strength? A. We can observe it in rich sca1ering environments. B. Their complex amplitudes look like white Gaussian noise. C. We can predict where in space we see large and small amplitudes. D. Corresponding phase is uniformly distributed over 0 to 2π. 100 % 0 % 0 % 0 % A. B. C. D.

10 Rice Fading Rayleigh fading + dominant propagation path, e.g., LOS Figs from Saunders, Ch s =1 φ = π 2 Imaginary f (x + jy) = πσ exp " (x scosφ)2 + (y ssinφ) 2 $ 2 # 2σ Real % ' &

11 Q2a: The two standing wave curves represent Rayleigh and Rice fading. Which one is Rice Fading? A. Curve A. B. Curve B. 10 A B 78 % 0 Gain [db] Distance [6] A B 22 % A. B.

12 Q2b: The two standing wave curves represent Rayleigh and Rice fading. Which one is Rice Fading? A. Curve A. B. Curve B. 10 A B 100 % 0 Gain [db] Distance [6] A B 0 % A. B.

13 Cumulative Distribution Function (CDF) 10 CDF(r') = prob(x r') = 10 0 r' PDF(r) dr Gain [db] Distance [6] Cumulative probability Gain [db] 13

14 Q3: Derive the CDF of Rayleigh fading from the PDF on the paper you have. You can discuss with your peers. CDF(r') = r' PDF(r) dr PDF(r) = r r2 exp 2 σ 2σ 2 Probability PDF of Rayleigh distribution Envelope [db] 14

15 Q4a: The two CDF curves represent Rayleigh and Rice fading. Which one is Rice Fading? A. Curve A. B. Curve B. Cumulative probability A B Gain [db] 44 % 56 % A. B.

16 Q4a: The two CDF curves represent Rayleigh and Rice fading. Which one is Rice Fading? A. Curve A. B. Curve B. Cumulative probability A B Gain [db] 0 % 100 % A. B.

17 Empirical Pathloss Estimation Small-scale fading pathloss Shadowing 17

18 Shadowing Figs from Saunders, Ch

19 Empirical Modeling of Shadowing Fig from Saunders, Ch

20 Shadowing: Physical Interpretation and Modeling Caused by obstacles in propagation path between mobile and base station. A = A1 A2 A N L = 10 log 10 A = L1 + L2 + + L N Central limit theorem à Normal distribution in the log-domain. 20

21 Q5a: Pathloss (P), shadowing (S), and small-scale fading (F). Which statement is correct? A. Typical dynamic range of the received signal is P > S >> F. B. What we call standing wave is equivalent to F. C. Typical spajal range of S is inversely proporjonal to the radio frequency. D. The central limit theorem defines the signal distribujons of P, S and F. 33 % 22 % 22 % 22 % A. B. C. D.

22 Q5b: Pathloss (P), shadowing (S), and small-scale fading (F). Which statement is correct? A. Typical dynamic range of the received signal is P > S >> F. B. What we call standing wave is equivalent to F. C. Typical spajal range of S is inversely proporjonal to the radio frequency. D. The central limit theorem defines the signal distribujons of P, S and F. 100 % 0 % 0 % 0 % A. B. C. D.

23 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 15 th.