The Radio Channel COS - PowerPoint Presentation

1. The Radio ChannelCOS 463: Wireless NetworksLecture 14Kyle Jamieson[Parts adapted from I. Darwazeh, A. Goldsmith, T. Rappaport, P. Steenkiste]

2. The radio channel is what limits most communications systems – the main challenge!Understanding its properties is therefore key to understanding radio systems’ designThere is variation in many different propertiesCarrier frequency, environment (e.g. indoors, outdoors, satellite, space)Many different models covering many different scenarios2Radio Channel: Motivation

3. A channel model describes what happensGives channel output power for a particular input power“Black Box” – no explanation of mechanismRequires appropriate statistical parameters (e.g. loss, fading)A propagation model describes how it happensHow signal gets from transmitter to receiverHow energy is redistributed in time and frequencyCan inform channel model parameters3Channel and Propagation Models

4. Large scale channel modelFriis Free space modelHow much power delivered from omnidirectional transmitter to omnidirectional receiver, in free space?Small-scale channel models4Today

5. Deliver Watts to an omnidirectional transmitting antennaSo then power density (Watts per unit area) at range d is W/m2Independent of wavelength (frequency) 5Transmitting in Free Space Total spherical surface area:  unit area 

6. Effective aperture : fraction of incident power density p captured and received: Larger antennas at greater λ capture more powerTherefore, power received is the product of the power density and effective aperture: 6Idealized Receive Antenna

7. Antennas don’t radiate power equally in all directionsSpecific to the antenna designModel these gains in the directions of interest between transmitter, receiver:Transmit antenna gain GtReceive antenna gain Gr7Antenna Gain

8. Power received is the product of the power received by idealized antennas, times transmit and receive antenna gains: 8Friis Free Space Channel Model

9. Large scale channel modelsSmall-scale channel modelsMulti-path propagationMotion and channel coherence time9Today

10. Small-scale models: Characterize the channel over at most a few wavelengths or a few seconds10Small-scale versus large-scale modeling

11. Receiver gets multiple copies of signalEach copy follows different path, with different path lengthCopies can either strengthen or weaken each otherDepends on whether they are in or out of phaseEnables communication even when transmitter and receiver are not in “line of sight”Allows radio waves effectively to propagate around obstacles, thereby increasing the radio coverage areaTransmitter, receiver, or environment object movement on the order of λ significantly affects the outcomee.g. 2.4 GHz  λ = 12 cm, 900 MHz  ≈ 1 ft11Multipath Radio Propagation

12. Radio Propagation MechanismsReflectionScatteringDiffractionRefractionPropagation wave changes direction when impinging on different mediumReflectionPropagation wave impinges on large object (compared to λ)ScatteringObjects smaller than λ (i.e. foliage, street signs etc.)DiffractionTransmission path obstructed by surface with sharp irregular edgesWaves bend around obstacle, even when line of sight does not existRefraction

13. Large scale channel modelsSmall-scale channel modelsMulti-path propagationFrequency-domain viewTime-domain viewMotion and channel coherence time13Today

14. Suppose transmitter is distance d (propagation time delay τ = d / c) away from receiver (where c is the speed of light)Radio frequency transmitted signal: Carrier frequency fc corresponds to radio wavelength λBaseband transmitted signal in one symbol period: How to model the effect of the channel? Sinusoidal carrier, line of sight only14ReceiverTransmitterd, τλ

15. Represent channel’s amplitude attenuation with a real number aModels, e.g. attenuation due to two refractions and partial reflection as the signal passes through an indoor wallSinusoidal carrier, line of sight only:Signal Attenuation15ReceiverTransmittera, d, τ

16. Received signal travels distance dOne wavelength corresponds to a 360˚ (2π radian) phase shiftRepresent path’s phase shift with an angle (real number) θ = 2π⋅ d / λ “Abstract away” distance and wavelength into (one) phase shift θSinusoidal carrier, line of sight only:Signal Phase Shift16ReceiverTransmittera, θλ

17. Wireless channel h attenuates by a, phase-shifts by θTherefore, Received baseband signal: (no noise) Sinusoidal carrier, line of sight only:Channel Model17ReceiverTransmittera, θIQxyRotate by θScale by axy

18. What if reflections (e.g., indoor walls) introduce a second path?Wireless channel becomes the superposition of the direct path’s channel h1 and the reflection path’s channel h2Line-of-sight plus reflecting path: Motivation18ReceiverTransmitterh1 (a1, θ1)h2 (a2, θ2)

19. Channel is now  Line-of-sight plus reflecting path:Channel Model19ReceiverTransmitterh1 (a1, θ1)h2 (a2, θ2)h1h2IQh2h

20. Phase difference between paths Depends on wavelength and path length differenceSo, depends on wavelength (frequency) as well as channel attenuation Line-of-sight plus reflecting path:Channel Model20ReceiverTransmitterh1 (a1, θ1)h2 (a2, θ2)h1h2IQΔθ

21. Interference between reflected and line-of-sight radio waves results in frequency dependent fadingCoherence bandwidth Bc: Frequency range over which the channel is roughly the same (“flat”)Reflections cause frequency selectivity

22. One 2.4 GHz Wi-Fi channel is centered at 2412 MHz and spans a 20 MHz bandwidthObserve: Frequency-selective fading22Practical Frequency-Selective Fading[D. Halperin]Recall, phase shift for kth path Received phase difference between paths depends on wavelengthChannel spans 2402–2422 MHzLowest wavelength (2402 MHz): 12.49 cmHighest wavelength (2422 MHz): 12.39 cmJust one millimeter wavelength differenceAlmost the same. Contradiction?  

23. 23Practical Frequency-Selective Fading[D. Halperin]Channel spans 2402–2422 MHzLowest wavelength (2402 MHz): 12.49 cmHighest wavelength (2422 MHz): 12.39 cmRecall, causes additive vs. destructive fadingFor Wi-Fi, so, e.g., , equals:160×12.49 cm wavelengths161×12.39 cm wavelengthsSo we move from e.g. constructive to destructive, to constructive fading from lowest to highest wavelength 

24. Forward channel (T to R) is Switch T and R roles, changing nothing else:Reverse channel (R to T) is The reverse radio channel is “reciprocal”Practical radio receiver circuitry induces differences between ,  24Radio Channels are “Reciprocal”Receiver RTransmitter Ta1,d1,τ1a2,d2,τ2

25. Approximate solutions to Maxwell’s electromagnetic equations by instead representing wavefronts as particles, traveling along raysApply geometric reflection, diffraction, scattering rulesCompute angle of reflection, angle of diffractionError is smallest when receiver is many λ from nearest scatterer, and all scatterers are large relative to λ25Putting it all Together: Ray TracingGood match to empirical data in rural areas, along city streets (radios close to ground), and indoorsCompletely site-specificChanges to site may invalidate model

26. Large scale channel modelsSmall-scale channel modelsMulti-path propagationFrequency-domain viewTime-domain viewMotion and channel coherence time26Today

27. What does the channel look like in time?27ReceiverTransmittera1,d1,τ1a2,d2,τ2Channel impulse response h(t)tτ1a1a1τ2a2Delay spread Td

28. Power received via the path with excess time delay is the value (height) of the discrete PDP component at P(τ) corresponds to |h(τ)|2 P(τ)t0Power delay profile (PDP)     

29. Given a PDP sampled at time steps :Mean excess delay : Expected value of Root mean squared (RMS) delay spread measures the spread of the power’s arrival in timeRMS delay spread is the variance of , where Maximum excess delay < X dB is the greatest delay at which the PDP is greater than X dB below the strongest arrival in the PDP 29Characterizing a power delay profile

30. Finite bandwidth of measurement normally results in continuous PDPPDP typically has a decaying exponential formEnvironmentRMS delay spreadIndoor cell10 – 50 nsSatellite mobile40 – 50 nsOpen area (rural)< 0.2 𝛍sSuburban macrocell< 1 𝛍sUrban macrocell1 – 3 𝛍sHilly macrocell3 – 10 𝛍sTypical RMS delay spreadsExample Indoor PDP Estimation

31. 31Indoor power delay profile

32. Slow down  sending data over a narrow bandwidth channelChannel is constant over its bandwidthMultipath is still present, so channel strength fluctuates over timeHow to model this fluctuation?32Flat FadingChannelNot shown above!

33. Random gain of kth arriving path: Therefore, the I and Q channel components are zero-mean Gaussian distributedSo is Rayleigh-distributed 33Rayleigh Fading Model Rayleigh PDFChannel impulse response h(t)tτ1a1τ2a2a3τ3

34. 34Rayleigh fading example

35. Large scale channel modelsSmall-scale channel modelsMulti-path propagationMotion and channel coherence time35Today

36. Suppose reflecting wall, fixed transmit antenna, no other objectsReceive antenna moving rightwards at velocity vTwo arriving signals at receiver antenna with a path length difference of 2(d − r(t))Stationary transmitter, moving receiver36Receiverantenna

37. Path length difference If  receive ≈ 0Destructive interferenceIf  receive ≈ 2Constructive interference 37How does fading in time arise?λ/2λsumReceiverantenna

38. In the preceding example, the reflected wave and direct wave travel in opposite directionsWhat happens if we move the reflecting wall to the left side of the transmitter?What is the nature of the multipath fading, both over time and over frequency?38Stretch Break and In-Class QuestionvTransmit antennaWallr(t)d

39. A change in path length difference of λ / 2 transitions from constructive to destructive interferenceReceiver movement of λ/4: coherence distanceDuration of time that transmitter, receiver, or objects in environment take to move a coherence distance: channel coherence time TcWalking speed (2 mph) @ 2.4 GHz: ≈ 15 millisecondsDriving speed (20 mph) @ 1.9 GHz: ≈ 2.5 millisecondsTrain/freeway speed (75 mph) @ 1.9 GHz: < 1 millisecond39Channel Coherence Time

40. Another perspective: Doppler EffectMovement by the transmitter, receiver, or objects in the environment creates a Doppler Shift 40v 

41. Doppler Shift of a path vradial is radial component of receiver’s velocity vector along the pathPositive with decreasing path length, negative with increasing path lengthSuppose v = 60 km/h, fc = 900 MHzDirect path , reflection path  Stationary transmitter, moving receiver:From a Doppler Perspective41Receiverantenna

42. Channel Doppler Spread Ds: maximum path Doppler shift, minus minimum path Doppler shiftSuppose v = 60 km/h, fc = 900 MHzDirect path , reflection path Doppler Spread: 100 HzResults in sinusoidal “envelope” at frequency Ds / 2: Stationary transmitter, moving receiver:From a Doppler Perspective42ReceiverantennaReceived signal5 ms

43. Sinusoidal “envelope” at frequency :Transition from 0 to peak in So qualitatively significant change in time Alternate definition of channel coherence time Channel Coherence Time:From a Doppler Perspective43Received signal 

44. Thursday Topic:Receiver Designs for the Wireless Channel44