1. 1 مقدمه بخش کانال فيدينگ

2. 2 References Wireless Communications: Principles and Practice, Chapters 3 and 4, T. Rappaport, Prentice Hall, 1996. Principles of Mobile Communication, Chapter 2, G. Stüber, Kluwer Academic Publishers, 1996. Slides for EE535, K. Chugg, 1999. Spread Spectrum Systems, Chapter 7, R. Dixon, Wiley, 1985 (there is a newer edition). Wideband CDMA for Third Generation Mobile Communications, Chapter 4, T. Ojanpera, R. Prasad, Artech, House 1998. Propagation Measurements and Models for Wireless Communications Channels, Andersen, Rappaport, Yoshida, IEEE Communications, January 1995.

3. 3 Radio Propagation Effects Transmitter d Receiver hbhb hmhm Diffracted Signal Reflected Signal Direct Signal Building

4. 4 Propagation Mechanisms Reflection –Propagation wave impinges on an object which is large as compared to wavelength - e.g., the surface of the Earth, buildings, walls, etc. –Surface large relative to wavelength of signal –May have phase shift from original –May cancel out original or increase it Diffraction –Radio path between transmitter and receiver obstructed by surface with sharp irregular edges –Waves bend around the obstacle, even when LOS (line of sight) does not exist –Edge of impenetrable body that is large relative to wavelength –May receive signal even if no line of sight (LOS) to transmitter

5. 5 … Propagation Mechanisms Scattering - Objects smaller than the wavelength of the propagation wave e.g. foliage, street signs, lamp posts –Obstacle size on order of wavelength Lamp posts etc. If LOS, diffracted and scattered signals not significant –Reflected signals may be If no LOS, diffraction and scattering are primary means of reception

6. 6 Essential Definitions Reflection: A change in the direction of a signal without penetrating the object. Occurs when the path of a signal is obstructed. The dimensions of the obstructing object is larger than the wavelength of the signal Diffraction: An object with large dimension blocks the path of a wave. Scattering: An object in the path of a wave causes it to spread or scatter in different directions. Occurs when the dimensions of the object are comparable to the wavelength of the signal.

7. 7 Reflection, Diffraction, Scattering

8. 8 Types of Waves Transmitter Receiver Earth Sky wave Space wave Ground wave Troposphere ( 0 - 12 km) Stratosphere ( 12 - 50 km) Mesosphere ( 50 - 80 km) Ionosphere ( 80 - 720 km)

9. 9 Propagation mechanisms A: free space B: reflection C: diffraction D: scattering A: free space B: reflection C: diffraction D: scattering reflection: object is large compared to wavelength scattering: object is small or its surface irregular

10. 10 Refraction Perfect conductors reflect with no attenuation Dielectrics reflect a fraction of incident energy –“Grazing angles” reflect max* –Steep angles transmit max*  rr tt Reflection induces 180  phase shift *The exact fraction depends on the materials and frequencies involved

11. 11 Diffraction Diffraction occurs when waves hit the edge of an obstacle –“Secondary” waves propagated into the shadowed region –Excess path length results in a phase shift –Fresnel zones relate phase shifts to the positions of obstacles T R 1st Fresnel zone Obstruction

12. 12 Scattering Rough surfaces –critical height for bumps is f(,incident angle)critical height –scattering loss factor modeled with Gaussian distribution. Nearby metal objects (street signs, etc.) –Usually modelled statistically Large distant objects –Analytical model: Radar Cross Section (RCS)RCS

13. 13 Free Space 2a Free space power flux density (W/m 2 ) –power radiated over surface area of sphere –where G t is transmitter antenna gain By covering some of this area, receiver’s antenna “catches” some of this flux

14. 14 Free Space 2b Fraunhofer distance: d > 2D 2 / Antenna gain and antenna aperture –A e is the antenna aperture, intuitively the area of the antenna perpendicular to the flux –G r is the antenna gain for a receiver. It is related to A e. –Received power (P r ) = Power flux density (P d ) * A e

15. 15 Free Space 2c –where L is a system loss factor –P t is the transmitter power –G t and G r are antenna gains – is the carrier wavelength

16. 16 Free Space Assumes far-field (Fraunhofer region) –d >> D and d >>, where D is the largest linear dimension of antenna is the carrier wavelength No interference, no obstructions

17. 17 Free Space Propagation Model Received power at distance d is –where P t is the transmitter power in Watts –a constant factor K depends on antenna gain, a system loss factor, and the carrier wavelengthconstant factor

18. 18 2-Ray Ground Reflection For d >> h r h t,For d >> h r h t –low angle of incidence allows the earth to act as a reflector –the reflected signal is 180  out of phase –P r  1/d 4 (  =4) R T htht hrhr Phase shift!

19. 19 Ground Reflection 1.5 The power at the receiver in this model is –derivation calculates E field; –P r = |E| 2 A e ; A e is ant. aperture The “breakpoint” at which the model changes from 1/d 2 to 1/d 4 is  2  h t h r / –where h r and h t are the receiver and transmitter antenna heights

20. 20 Ground Reflection 2 Intuition: ground blocks 1st Fresnel zoneFresnel –Reflection causes an instantaneous 180  phase shift –Additional phase offset due to excess path length –If the resulting phase is still close to 180 , the gound ray will destructively interfere with the LOS ray. R T htht hrhr p1p1 p0p0 180 

21. 21 Hilly Terrain Propagation can be LOS or result of diffraction over one or more ridges LOS propagation modelled with ground reflection: diffraction loss But if there is no LOS, diffraction can actually help!

22. 22 Hilly Terrain Propagation can be LOS or result of diffraction over one or more ridges But if there is no LOS, diffraction can actually help!

23. 23 Fresnel Zones Bounded by elliptical loci of constant delay Alternate zones differ in phase by 180  –Line of sight (LOS) corresponds to 1st zone –If LOS is partially blocked, 2nd zone can destructively interfere (diffraction loss) Fresnel zones are ellipses with the T&R at the foci; L 1 = L 2 + Path 1 Path 2

24. 24 Fresnel Zones –The Fresnel zones are propagation break points –At the first Fresnel zone (n=1) no reflections of waves can take place and –The distance to this point is: –Until this point, the propagation is assumed to be free space and rays travel is direct (point to point) with no reflections –Free space and terrestrial propagation models are used for design of microcells and also for in building coverage or solutions –when the distance is less than the first Fresnel zone, none of the models is adequate and empirical design is used

25. 25 What is Radio? Radio Xmitter induces E&M fields –Electrostatic field components  1/d 3 –Induction field components  1/d 2 –Radiation field components  1/d Radiation field has E and B component –Field strength at distance d = E  B  1/d 2 –Surface area of sphere centered at transmitter

26. 26 General Intuition Two main factors affecting signal at receiver –Distance (or delay)  Path attenuation –Multipath  Phase differences Green signal travels 1/2 farther than Yellow to reach receiver, who sees Red. For 2.4 GHz, (wavelength) =12.5cm.

27. 27 Objective Invent models to predict what the field looks like at the receiver. –Attenuation, absorption, reflection, diffraction... –Motion of receiver and environment… –Natural and man-made radio interference... –What does the field look like at the receiver?

28. 28 Models are Specialized Different scales –Large scale (averaged over meters) –Small scale (order of wavelength) Different environmental characteristics –Outdoor, indoor, land, sea, space, etc. Different application areas –macrocell (2km), microcell(500m), picocell

29. 29 Radio Propagation Mechanisms Free Space propagation Refraction –Conductors & Dielectric materials (refraction) Diffraction –Fresnel zones Scattering –“Clutter” is small relative to wavelength

30. 30 Fading - Multipath Propagation Multipath –Signals on transmission take many paths to arrive at a receiver (multipath) –The strongest component arrives from the direct path Multipath Effects cause –time variations due to multiple delays –random frequency modulations due to Doppler shifts –random changes in signal strengths over short periods –Multipath delay causes the signal to appear noise- like in amplitude

31. 31 Effects of Multipath Propagation Signals may cancel out due to phase differences Intersymbol Interference (ISI) –Sending narrow pulse at given frequency between fixed antenna and mobile unit –Channel may deliver multiple copies at different times –Delayed pulses act as noise making recovery of bit information difficult –Timing changes as mobile unit moves Harder to design signal processing to filter out multipath effects

32. 32 Fading is rapid fluctuations of the amplitude of a radio signal over a short period of time or travel distance. Fading is caused by interference between two or more versions of transmitted signal, which arrives at the receiver at slightly different times. These multipath waves combine at the receiver antenna to give a resultant signal, which can vary in delay, in amplitude and phase.

33. 33 Multipath effects –Rapid changes in signal strength over a small distance or time interval. –Random frequency modulation due to varying Doppler shift on different multipath signals. –Time dispersion (echoes) caused by multipath propagation delay.

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36. 36 Causes of fading In urban areas, fading occurs because the height of mobile is << height of surrounding structures, such as buildings and trees. Existence of several propagation paths between transmitter and receiver.

37. 37 Analysis methods of multipath channel Receive r dd Spatial position Transmitte r

38. 38 Convolution model for multipath propagation Received signal: y(t) = x(t) + A 1 x(t -  1 ) + A 2 x(t -  2 ) +... T R A 2 x(t-  2 ) A 1 x(t-  1 )

39. 39 Convolution Integral Convolution is defined by this integral: Indexes relevant portion of impulse response Scales past input signal

40. 40 Time varying system model for channel For a fixed position d, the channel between transmitter & receiver can be modulated as a linear time varying system (LTV system). Impulse response of the LTI system can be given as h(d,t). If x(t) is the transmitted signal, the received signal can be represented as: y(d,t) = x(t) * h(d,t) –* denotes convolution –h(d,t) is impulse response of the system

41. 41 y(d,t) = x(t) * h(d,t) t y(d,t) =  x(  ) h 1 (d,t -  ) d  -  Distance d = v.t where v is constant velocity of the receiver.

42. 42 t y(vt,t) =  x(  ) h 1 (vt,t -  ) d  -  This is a time varying system with impulse response of h(t,  )

43. 43 System definition Linear Time Varying (LTV) System h(t,  ) x(t)y(t)

44. 44 Signal definitions j 2  f c t x(t) = Re { c(t) e } l Transmitted signal C(t)

45. 45...Signal definitions j2  f c t y(t) = Re {r(t) e } j2  f c t h(t,  ) = Re {h b (t,  ) e } l Received signal l Impulse response

46. 46 Base band equivalent channel impulse response model h b (t,  ) c(t)r(t)

47. 47 r(t) = c(t) * h b (t,  ) Modeling of the base band impulse response model h b (t,  ) t3t3t3t3 t3t3t3t3 t2t2t2t2 t2t2t2t2 t1t1t1t1 t1t1t1t1 t0t0t0t0 t0t0t0t0   N-2  N-1  o  1  2 o  1  2 o  1  2 o  1  2  o  1  2 o  1  2 o  1  2 o  1  2 l Mathematicalmodel l Mathematical model

48. 48 Factors Influencing Fading Motion of the receiver: Doppler shift Transmission bandwidth of signal –Compare to BW of channel Multipath propagation –Receiver sees multiple instances of signal when waves follow different paths –Very sensitive to configuration of environment

49. 49 Effects of Multipath Signals Rapid change in signal strength due to phase cancellation Frequency modulation due to Doppler shifts from movement of receiver/environment Echoes caused by multipath propagation delay

50. 50 The Multipath Channel One approach to small-scale models is to model the “Multipath Channel” –Linear time-varying function h(t,  ) Basic idea: define a filter that encapsulates the effects of multipath interference –Measure or calculate the channel impulse response (response to a short pulse at f c ): h(t,  )   t

51. 51 Channel Sounding “Channel sounding” is a way to measure the channel responseChannel sounding –transmit impulse, and measure the response to find h(  ). –h(  ) can then be used to model the channel response to an arbitrary signal: y(t) = x(t)  h(  ). –Problem: models the channel at single point in time; can’t account for mobility or environmental changes h(t,  )   SKIP

52. 52 Characterizing Fading * From the impulse response we can characterize the channel: Characterizing distortion –Delay spread (  d ): how long does the channel ring from an impulse? –Coherence bandwidth (B c ): over what frequency range is the channel gain flat? –  d  1/B c In time domain, roughly corresponds to the “fidelity” of the response; sharper pulse requires wider bandtime domain

53. 53 WSSUS * Wide Sense Stationary (WSS) –Statistics are independent of small perturbations in time and position –I.e. fixed statistical parameters for stationary nodes Uncorrelated Scatter (US) –Separate paths are not correlated in phase or attenuation –I.e. multipath components can be independent RVs Statistics modeled as Gaussian RVs