Small_Scale_Fading_Class_Notes_slides.pptx

class notes

1. Small Scale Fading ArunKumar Jayaprakasam Scope : Chapter 5 (till 5.7) of “Wireless Communications: Principles and Practice” by Theodore S. Rappaport

2. Agenda Introduction Time Dispersion Delay Spread and Coherence Bandwidth Frequency Dispersion Doppler Spread and Coherence Time Types of Fading Stochastic Models Rayleigh Ricean Some Techniques for Channel Measurement

3. Introduction and Time Dispersion

4. Scales of Mobile Signal Variation

5. Small-Scale Fading Rapid fluctuations of radio signal amplitude , phase, or delays Occurs or short time period or short travel distance Large-scale path loss effects can be ignored Caused by arrival of two or more waves from the source combining at the receiver Resultant detected signal varies widely in amplitudes and phase Bandwidth of transmitted signal is important factor

6. Experimental record of received signal envelope in an urban area

7. Multipathradio propagation in urban areas

8. Determining the impulse response of a channel Transmit a narrowband pulse into the channel Measure replicas of the pulse that traverse different paths between transmitter and receiver

9. Parameters of Mobile Multipath Channels Time Dispersion Parameters Grossly quantifies the multipath channel Determined from Power Delay Profile (average over different time, a function of delay) Parameters include Mean Access Delay RMS Delay Spread Excess Delay Spread (X dB) Coherence Bandwidth Doppler Spread and Coherence Time

10. Power Delay Profiles Power delay profiles are generally represented as plots of relative received power as a function of excess delay with respect to a fixed time delay reference. Power delay profiles are found by averaging instantaneous power delay profile measurements over a local area. Are measured by channel sounding techniques Plots of relative received power as a function of excess delay They are found by averaging intantenous power delay measurements over a local area Local area: no greater than 6m outdoor Local area: no greater than 2m indoor Samples taken at l /4 meters approximately For 450MHz – 6 GHz frequency range.

11. Impulse Response Model of a Multipath Channel

12. PDP Outdoor

13. PDP Indoor

14. Time Dispersion Parameters The mean excess delay, rms delay spread, and excess delay spread (X dB) are multipath channel parameters that can be determined form a power delay profile. The mean excess delay is the first moment of the power delay profile and is defined as The rms delay spread is the square root of the second central moment of the power delay profile, where Typical values of rms delay spread are on the order of microseconds in outdoor mobile radio channel and on the order of nanoseconds in indoor radio channel

15. Maximum Excess Delay (X dB) Maximum Excess Delay (X dB): Defined as the time delay value after which the multipath energy falls to X dB below the maximum multipath energy (not necesarily belongingto the first arriving component). It is also called excess delay spread . The maximum excess delay is defined as (  x -  ), where  is the first arriving signal and  x is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal. The value of  x is sometimes called the excess delay spread of a power delay profile. In practice, values depend on the choice of noise threshold used to process P(  ). The noise threshold is used to differentiate between multipath components and thermal noise. Noise Thresholds The values of time dispersion parameters also depend on the noise threshold (the level of power below which the signal is considered as noise). If noise threshold is set too low, then the noise will be processed as multipath and thus causing the parameters to be higher.

16. RMS Delay Spread

17. Effect of delay spread

18. Comparison of the BER for a fading and non-fading channel

19. Effect on error rate

20. Coherent bandwidth Analogous to the delay spread parameters in the time domain, coherence bandwidth is used to characterize the channel in the frequency domain. Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered flat. Two sinusoids with frequency separation greater than B c are affected quite differently by the channel. Receiver f 1 f 2 Multipath Channel Frequency Separation: |f 1 -f 2 |

21. Coherent Bandwidth Frequency correlation between two sinusoids: 0 <= C r 1 , r 2 <= 1. Coherence bandwidth is the range of frequencies over which two frequency components have a strong potential for amplitude correlation.  is rms delay spread If correlation is above 0.9, then If correlation is above 0.5, then This is called 50% coherence bandwidth

22. Example For a multipath channel, s is given as 1.37 m s. The 50% coherence bandwidth is given as: 1/5 s = 146kHz . This means that, for a good transmission from a transmitter to a receiver, the range of transmission frequency (channel bandwidth) should not exceed 146kHz, so that all frequencies in this band experience the same channel characteristics. Equalizers are need ed in order to use transmission frequencies that are separated larger than this value. This coherence bandwidth is enough for a n AMPS channel (30kHz band needed for a channel), but is not enough for a GSM channel (200kHz needed per channel).

23. Frequency Dispersion

24. 11/26/2016 24 Doppler shift S = signal source v = velocity d = distance Y-X on mobiles path of movement t = d/v l = dcos 1 = vtcos  1 if S is far away, assume  1 ≈  2  = (4.1) phase shift: f d = (4.2) Doppler shift = relative frequency change during t d Y X l  2  1 S v

25. e.g. f c = 1850 MHz   = c/ f c = 0.162m v = 60mph = 28.62 m/s a. mobile moving directly towards transmitter:  = o  cos  = 1 f d = v/  = 160Hz f = f c + f d = 1850.00016MHz b. mobile moving directly away from transmitter  = 180 o  cos  = -1 f d = - v/  = -160Hz f = f c + f d = 1849.99984MHz c. mobile moving  to angle of signal’s arrival  = 90 o  cos  = 0 f d = 0 11/26/2016 25 S v S v

26. Mobility Moving receive antenna Transmit antenna Movement

27. Mobility Phase offset due to Doppler effect Doppler

28. Reflection Simple reflection and superposition Transmit antenna r d 180 degrees phase change

29. Reflection Superposition of two sinusoids Constructive if phase difference is multiple of 360 degrees Destructive superposition if 180 Coherence Distance

30. Reflecting Wall Moving Antenna

31. Coherence Time Delay spread and Coherence bandwidth describe the time dispersive nature of the channel in a local area. They don’t offer information about the time varying nature of the channel caused by relative motion of transmitter and receiver. Doppler Spread and Coherence time are parameters which describe the time varying nature of the channel in a small-scale region.

32. Doppler Spread Measure of spectral broadening caused by motion, the time rate of change of the mobile radio channel, and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. We know how to compute Doppler shift: f d Doppler spread, B D , is defined as the maximum Doppler shift: f m = v/ l If the baseband signal bandwidth is much less than B D then effect of Doppler spread is negligible at the receiver.

33. Coherence Time Coherence time is the time duration over which the channel impulse response is essentially invariant. If the symbol period of the baseband signal (reciprocal of the baseband signal bandwidth) is greater the coherence time, than the signal will distort, since channel will change during the transmission of the signal . Coherence time (T C ) is defined as: T S T C D t=t 2 - t 1 t 1 t 2 f 1 f 2

34. Coherence Time Coherence time is also defined as: Coherence time definition implies that two signal s arriving with a time separation greater than T C are affected differently by the channel. Coherence time Tc is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersive- ness of the channel in the time domain. If the coherence time is defined as the time over which the time correlation function is above 0.5, then the coherence time is approximately, where

35. Types of Small Scale Fading

36. Types of Small-scale Fading Small-scale Fading (Based on Doppler Spread) Fast Fading High Doppler Spread Coherence Time < Symbol Period Channel variations faster than baseband signal variations Slow Fading Low Doppler Spread Coherence Time > Symbol Period Channel variations smaller than baseband signal variations

37. Flat Fading (Frequency Flat Fading) Occurs when symbol period of the transmitted signal is much larger than the Delay Spread of the channel Bandwidth of the applied signal is narrow. If B s  B c , and T s     Flat fading May cause deep fades. require 20 or 30 dB more power to achieve low BER during times of deep fades. Increase the transmit power to combat this situation. The spectral characteristics of the transmitted signals are preserved at the receiver, however the strength of the received signal changes with time. Flat fading channels are known as amplitude varying channels or narrow-band channels. Radio channel has a constant gain and linear phase response over a bandwidth which is greater than the bandwidth of the transmitted signal. It is the most common type of fading described in the technical literature.

38. Flat Fading (Frequency Flat Fading) h(t, t) s(t) r(t) T S t T S + t t << T S Occurs when: B S << B C and T S >> s t B C : Coherence bandwidth B S : Signal bandwidth T S : Symbol period s t : Delay Spread

39. Frequency Selective Fading Occurs when channel multipath delay spread is greater than the symbol period. Symbols face time dispersion Channel induces Intersymbol Interference (ISI) Bandwidth of the signal s(t) is wider than the channel impulse response. Radio channel has a constant gain and linear phase response over a bandwidth which is smaller than the bandwidth of the transmitted signal. Frequency selective fading is due to time dispersion of the transmitted symbols within the channel. Thus the channel induces inter-symbol-interference. Statistical impulse response model and computer generated impulse responses are used for analyzing frequency selective small-scale fading. Frequency selective fading channels are known as wideband channels since the BW of the signal is wider than the BW of the channel impulse response. As time varies, the channel varies in gain and amplitude across the spectrum of s(t), resulting in time varying distortion in the received signal r(t). If B s  B c , and 0.1T s     Frequency selective fading

40. Frequency Selective Fading h(t, t) s(t) r(t) T S t T S + t t >> T S T S Causes distortion of the received baseband signal Causes Inter-Symbol Interference (ISI) Occurs when: B S > B C and T S < s t As a rule of thumb: T S < s t

41. Fast Fading Due to Doppler Spread Rate of change of the channel characteristics is larger than the Rate of change of the transmitted signal The channel changes during a symbol period. The channel changes because of receiver motion. Coherence time of the channel is smaller than the symbol period of the transmitter signal It causes frequency dispersion due to Doppler spread and leads to distortion. Note that, when a channel is specified as a fast or slow fading channel, it does not specify whether the channel is flat or frequency selective A flat, fast fading channel  the amplitude of the delta function varies faster than the rate of change of the transmitted baseband signal. A frequency selective, fast fading channel  the amplitudes, phases, and time delays of any one of the multipath components varies faster than the rate of change of the transmitted baseband signal. Occurs when: B S < B D and T S > T C B S : Bandwidth of the signal B D : Doppler Spread T S : Symbol Period T C : Coherence Time

42. Slow Fading Due to Doppler Spread Rate of change of the channel characteristics is much smaller than the rate of change of the transmitted signal Occurs when: B S >> B D and T S << T C B S : Bandwidth of the signal B D : Doppler Spread T S : Symbol Period T C : Coherence Bandwidth

43. Different Types of Fading With Respect To SYMBOL PERIOD Transmitted Symbol Period Symbol Period of Transmitting Signal T S T S T C s t Flat Slow Fading Flat Fast Fading Frequency Selective Slow Fading Frequency Selective Fast Fading

44. Different Types of Fading With Respect To BASEBAND SIGNAL BANDWIDTH Transmitted Baseband Signal Bandwidth B S B D Flat Fast Fading Frequency Selective Slow Fading Frequency Selective Fast Fading B S Transmitted Baseband Signal Bandwidth Flat Slow Fading B C

45. Fading Stochastic Models

46. Fading Distributions Describes how the received signal amplitude changes with time. Remember that the received signal is combination of multiple signals arriving from different directions, phases and amplitudes. With the received signal we mean the baseband signal, namely the envelope of the received signal (i.e. r(t)). It is a statistical characterization of the multipath fading. Two distributions Rayleigh Fading Ricean Fading

47. Rayleigh Distributions Describes the received signal envelope distribution for channels, where all the components are non-LOS: i.e. there is no line-of–sight (LOS ) component.

48. Ricean Distributions Describes the received signal envelope distribution for channels where one of the multipath components is LOS component. i.e. there is one LOS component.

49. Rayleigh Fading

50. Rayleigh Fading

51. Rayleigh Fading Distribution The Rayleigh distribution is commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. The envelope of the sum of two quadrature Gaussian noise signals obeys a Rayleigh distribution.  is the rms value of the received voltage before envelope detection, and  2 is the time-average power of the received signal before envelope detection.

52. Rayleigh PDF s 2s 3s 4s 5s 0.6065/s mean = 1.2533 s median = 1.177 s variance = 0.4292 s 2

53. A typical Rayleigh fading envelope at 900MHz.

54. Ricean Distribution When there is a stationary (non-fading) LOS signal present, then the envelope distribution is Ricean . The Ricean distribution degenerates to Rayleigh when the dominant component fades away.

55. CDF Cumulative distribution for three small-scale fading measurements and their fit to Rayleigh, Ricean, and log-normal distributions.

56. PDF Probability density function of Ricean distributions: K=-∞dB (Rayleigh) and K=6dB. For K>>1, the Ricean pdf is approximately Gaussian about the mean.

57. Small-scale fading mechanism Assume signals arrive from all angles in the horizontal plane 0<α<360 Signal amplitudes are equal, independent of α Assume further that there is no multipath delay: (flat fading assumption) Doppler shifts

58. Carrier Doppler spectrum Spectrum Empirical investigations show results that deviate from this model Power Model Power goes to infinity at fc +/-fm

59. Level Crossing Rate (LCR) Threshold (R) LCR is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified threshold level R in a positive going direction . It is given by:

60. Average Fade Duration Defined as the average period of time for which the received signal is b elow a specified level R. For Rayleigh distributed fading signal, it is given by:

61. Simulating 2-ray multipath a 1 and a 2 are independent Rayleigh fading  1 and  2 are uniformly distributed over [0,2)

62. Channel Measurement Techniques

63. 11/26/2016 63 Small Scale Path Measurements multipath structure used to determine small-scale fading effects Classification of Techniques for Wideband Channel Sounding (1) direct pulse (2) spread spectrum sliding correlator (3) swept frequency measurements

64. 11/26/2016 64 4.3.1: Direct RF Pulse System to measure channel impulse response simple & cheap channel sounding approach - quickly determine PDP fundamentally a wide-band pulsed bistatic radar transmit probing pulse, p(t) with time duration = T bb receiver uses wideband filter, BW = 2/ T bb Hz - envelope detector used to amplify & detect received signal T bb = minimum resolvable delay between MPCs e.g. let T bb = 1ns  BW = 2GHz & minimum resolvable delay = 1ns BW = 2/ T bb T bb T REP Detector Storage O-Scope Rx Tx Pulse Gen f c

65. 11/26/2016 65 4.3.2 Spread Spectrum (SS) Sliding Correlator Sounding probe signal is still wideband possible to detect transmitted signal using narrowband receiver, preceded by wideband mixer improved dynamic range compared to pulsed RF system SS : carrier  PN sequence  s preads signal over large bandwidth T c = chip duration R c = chip rate = T c -1 Tx PN Gen Tx Chip Clock R c =  (Hz) f c Rx PNGen Rx Chip Clock = β (Hz) correlation BW BW  2( - ) resolution  R c -1 ( rms pulse width) BW  2R c wideband filter Detector at f c Storage O-Scope narrowband System to Measure SS Channel Response

66. 11/26/2016 66 4.3.3 Frequency Domain Channel Sounding vector network analyzer controls synthesized frequency sweeper S-parameter test-set monitors channel frequency response sweeper scans specified frequency band (centered on a carrier ) Frequency Domain Channel Sounding System Rx Tx IFT Vector Network Analyzer with Swept Frequency Oscillator S-Parameter Test-Set h(t) = F -1 [ H(w) ] S 21 (w)  H(w) = Y(w)/X(w) Y(w) port 2 X(w) port 1

67. 11/26/2016 67 For each frequency step the S-parameter test-set transmits known signal on port 1 monitors received signal on port 2 Network Analyzer processes signal levels to determine complex response of the channel over the measured frequency give as S 21 (w )  H(w) - frequency domain representation of channel impulse response - IFT ( Inverse Fourier Transform ) used to convert back to time domain Works well for short ranges if carefully calibrated & synchronized

68. Thank You

69. Acknowledgements The contents of the slides have been taken from various sources for explanation purposes only. No copyright violation intended.

70. BACKUP

71. Rayleigh Fading Distribution The probability that the envelope of the received signal does not exceed a specified value of R is given by the CDF: r peak =  and p(  )=0.6065/ 

72. Ricean Fading Distribution When there is a dominant stationary signal component present, the small-scale fading envelope distribution is Ricean . The effect of a dominant signal arriving with many weaker multipath signals gives rise to the Ricean distribution. The Ricean distribution degenerates to a Rayleigh distribution when the dominant component fades away. The Ricean distribution is often described in terms of a parameter K which is defined as the ratio between the deterministic signal power and the variance of the multipath. K is known as the Ricean factor As A  0, K  -  dB, Ricean distribution degenerates to Rayleigh distribution.

73. Simulating Doppler fading Procedure