1 Introduction to Fading Channels, part 1 Dr. Essam Sourour Alexandria University, Faculty of Engineering, Dept. Of Electrical Engineering

2 Characterization of Fading Channels Large Scale Fading Short Scale Fading Fading Counter Measures Section Overview

3 Two main effects: –Large Scale –Small Scale Large Scale Fading –Depends on environment and topology –Path Loss, Shadowing Small Scale Fading –Faster Changes –Depends on signal parameters Characterization

4 Small Scale and Large Scale Fading Characterization, cont.

5 For Open Areas use Line of Sight (LOS): Path Loss L (in dB) in far field: Loss(dB)  20 log d Loss with distance follows 20 dB/Octave Line of Sight (LOS)

6 Loss(dB)  40 log d Loss with distance follows 40 dB/Octave In General, with many rays Loss(dB)  10  log d The loss exponent  depends on environment 2~3Obstructed in factories3 ~ 5Shadowed Urban 4~6Obstructed in building2.7~3.5Urban 1.6~1.8In-building LOS2Free Space  Environment  Path Loss with Distance

7 Most famous model: Okumura-Hata Okumura made extensive measurements Hata transformed Okumura’s plots to an empirical model Valid for MHz Model takes the effect of –Transmitter height h b in m –receiver height h m in m –frequency f c in MHz –Distance d in km –different environments Hata Propagation Model

8 Hata’s Model

COST 231 Extension to Hata The European Cooperative for Scientific and Technical Research (COST) extended Hata model to 2GHz 9 Valid for 1.5 Ghz<f c <2 GHz, 30 m<h b <200 m and 1 m<h m <10 m

Indoor Propagation Loss (ITU-R P Simple ITU model for WPAN: L(dB) = 20 log(f ) + N log(d) + L f (n) − 28 N =Distance Power Loss Coefficient f =Frequency (MHz) d =Distance (m) between nodes (d > 1) L f =Floor Penetration Loss Factor (dB) n =Number of Floors Penetrated (n > 0) 10

Indoor Model Parameters 11

12 In addition, indoor obstacles add more losses Extensive measurements made. Tables available in literature For example: –Concrete wall, 8 to 15 dB –Concrete floor, 10 dB –Foil insulation, 3.9 dB Indoor Effects

13 Surrounding Environment varies, even at same distance from Tx Path Loss is random, with an average that depends on distance and frequency Distribution, in dB, found to be Gaussian Denoted by Log-Normal Shadowing Over and above loss due to distance Shadowing Loss

14 L(dB)| d = L(dB)| do + 10  log (d/d o ) + X  X  is Gaussian with zero mean and standard deviation   depends on environment, increases with more variations Outdoor:  = 5 ~ 12 dB, typical 8 dB Hence, L(dB) is Gaussian with mean given by any of the distance-based relations, and standard deviation  Shadowing Loss, Cont.

Indoor Shadowing 15 Indoor shadowing standard deviation for ITU-R P model

Total Effect In all previous models the received power at distance Where The value of , K and K do depends on frequency and environment 16

Cell Coverage Area 17 Coverage may be defined as the percentage of the area of the cell that receive power > P min C=covered area inside cell / cell area C  1

Coverage calculation, 1 Received power P rec (x) at any distance r is Gaussian, with: –Mean  dB (r) which depends on r, given by any of the previous relations (LOS, two paths, Hata, or COST-231) –Standard deviation  that depends on location Define F(r) as the probability P rec (x) exceeds P min 18

Coverage calculation, 2 On the average, the part of the area dA with received power > P min is : F (r) dA The total area (yellow part) in the cell with received power > P min is : Hence, the coverage C is given by: 19

Coverage calculation, 3 F(r) can be written as: Using integral (2.58) in textbook, we get 20

Coverage calculation, 4 Note that, without shadowing, the received power at cell border is given by: If we transmit enough power P t such that P rec (at R)=P min, then a=0 and Q(a)=0.5 In this case: Also, if there is no shadowing,  =0, b=  and C=1 21

Homework Please solve the following problems from Chapter 2 of the textbook: Problems: 1, 13, 14, 15, 17, 19, 21, 23, 24, 25 You may use any of the models in the lecture but specify in your answer which propagation model you are using. 22