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Small scale fading

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Chap 5 (small scale fading)
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Small scale fading

  1. 1. Wireless Communications Principles and Practice 2nd Edition T.S. Rappaport Chapter 5: Mobile Radio Propagation: Small-Scale Fading and Multipath
  2. 2. Introduction  Reflection, Diffraction and Scattering of waves  Most cellular systems operate in urban area, where no direct line-of-site path between Rx and Tx  Presence of high rise buildings causes severe diffraction loss  Due to multiple reflections, em waves travel along different paths of varying lengths
  3. 3.  Propagation models focused on predicting average received signal strength at a given distance from transmitter  Models predicting mean signal strength for an arbitrary T-R separation distance are large scale models  Models that characterize rapid fluctuations of received signal strength over very short distances or short time intervals are small scale models
  4. 4. Co-channel and Adjacent Channel Interference, Propagation
  5. 5. Small-scale and large-scale fading Figure 4.1 Small-scale and large-scale fading.
  6. 6. Small-Scale Fading and Multipath  Rapid fluctuations of the amplitude, phase or multipath delays of a radio signal over a short period of time or travel distance is known as small-scale fading  Large- scale path loss effects may be ignored
  7. 7.  Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times  Multipath waves combine at the receiver antenna to give a resultant signal which can widely vary in amplitude and phase
  8. 8.  This depends on the distribution of the intensity and relative propagation time of the waves and the bandwidth of the transmitted signal  Multipath in the radio channel creates small-scale fading effects
  9. 9. Three most important fading effects  Rapid changes in signal strength over a small travel distance or time interval  Random frequency modulation due to varying Doppler shifts on different multipath signals  Time dispersion (echoes) caused by multipath propagation delays
  10. 10.  In Built-up urban areas, fading occurs because there is no single line-of- sight path MS and BTS antennas  Mobile antennas are well below the height of surrounding structures  Even if LOS exists, there are reflections from ground and surrounding structures
  11. 11.  Multipath signals add vectorially at receiver antenna and cause the signal received by the mobile to distort or fade  Even when the mobile is stationary, fading may occur because of moving objects in radio channel
  12. 12.  Due to constructive and destructive effects of multipath waves, receiver moving at high speed can pass through several fades in a small period of time  More serious case is that of a deep fade in received signal  Due to relative motion between mobile and base station ,Doppler shift in frequency takes place
  13. 13. Factors influencing Small-Scale fading  Multipath propagation: Presence of reflecting objects and scatterers in the channel creates constantly changing environment  Random phase and amplitudes of different multipath signals induce small- scale fading and or distortion
  14. 14.  Speed of the mobile: Relative motion results in random frequency modulation due to different Doppler shifts on each multipath component  Speed of surrounding objects: If objects in radio channel are in motion, a time varying Doppler shift is induced
  15. 15.  If surrounding objects move at a greater rate than the mobile, this effect dominates the small-scale fading  Motion of surrounding objects may be ignored otherwise and only speed of the mobile needs to be considered  Coherence time defines staticness of the channel
  16. 16.  Transmission bandwidth of the signal: If the transmitted radio signal bandwidth is greater than bandwidth of multipath channel ,received signal will be distorted but small- scale fading will be insignificant  In the other case, signal will not be distorted in time but signal will change rapidly  Coherence bandwidth is a measure of max. freq. difference for which signals are strongly correlated in amplitude
  17. 17. Doppler Shift Geomerty
  18. 18.  Difference in path lengths traveled by the wave from source S to mobile at points X and Y is ∆l=d cosθ =v∆t cos θ  Phase change in received signal due to difference in path lengths is  ∆Φ=(2π∆l)/λ = (2π v∆t cos θ) /λ  Doppler shift is given by  fd =(1/ 2π)*(∆Ф/∆t)= (v cos θ) /λ
  19. 19. Example 5.1  Solved the problem with all the students participating in the process
  20. 20. Impulse Response Model of a Multipath Channel  The small-scale variations of a mobile radio signal can be directly related to the impulse response of the mobile radio channel  Impulse response is a wideband channel characterization and contains all information necessary to simulate or analyze any type of radio transmission through the channel
  21. 21.  Mobile radio channel may be modeled as a linear filter with time varying impulse response  Time variation is due to receiver motion in space  Filtering nature is caused by summation of amplitudes and delays of multiple arriving waves at any instant of time
  22. 22.  Consider the case where time variation is due strictly to receiver motion in space  Receiver moves along the ground at some constant velocity v  For a fixed position d, channel between T and R can be modeled as a linear time invariant system
  23. 23. Channel issues
  24. 24.  Due to different multipath waves which have propagation delays which vary over different spatial locations of the receiver, impulse response of the channel should be a function of the position of the receiver  Channel impulse response can be expressed as h (d, t).
  25. 25.  x (t) is transmitted signal  y(d,t) received signal at position d can be expressed as a convolution of x(t) with h(d,t)  y(d,t)=x(t)©h(d,t)=∫x(τ)h(d, t- τ)d τ  For a causal system h(d,t)=0 for t<0  d=vt ,the position of receiver
  26. 26.  y(vt,t) =∫x(τ)h( vt,t-τ)d τ  Since v is constant, y(vt,t) is just function of t.  Mobile radio channel can be modeled as a linear time varying channel ,where the channel changes with time and distance  Since v may be assumed constant over a short time interval ,we may let x(t) represent transmitted bandpass waveform
  27. 27.  Impulse response h (t,τ)completely characterizes the channel and is a function of both t and τ  Variable t represents time variations due to motion , variable τ represents channel multipath delay for a fixed value of t
  28. 28.  If multipath channel is assumed to be bandlimited channel, h(t,τ) may be represented by a complex baseband impulse response hb(t,τ)  Received signal in Multipath channel consists of a series of attenuated ,time delayed ,phase shifted replicas of the transmitted signal, the baseband impulse response of a multipath channel can be expressed by
  29. 29.  hb(t,τ)=Σai(t,τ)exp[j(2πfcτ,i(t)+φi(t,τ))]§ (τ-τi(t))  Ai and Ti are real amplitudes and excess delays respectively of the ith multipath component at time t  Phase term represents the phase shift due to free space propagation of ith multipath component
  30. 30. Complex Baseband model for RF systems
  31. 31. Time-varying impulse response
  32. 32. Measured impulse responses
  33. 33. Relationship between bandwidth and received power  In actual wireless communication systems, the impulse response of a multipath channel is measured in the field using channel sounding techniques  Illustrate how the small scale fading behaves quite differently for two signals with different bandwidths in identical multipath channel
  34. 34.  Received local ensemble average power of wideband and narrowband signals are equivalent  Pulse is wideband signal and CW signal is a narrowband signal  Received power is computed for both the cases
  35. 35. Small Scale Multipath measurements  Three techniques  Direct pulse measurements, spread spectrum sliding correlator measurement and swept frequency measurements
  36. 36. Channel Sounder: Pulse type
  37. 37.  Allows engineers to determine rapidly the power delay profile of any channel  The system transmits a repetitive pulse of width Tbb and uses a receiver with a wide bandpass filter.  BW=2/ Tbb Hz  Signal is amplified ,detected with an envelope detector and displayed and stored on high speed oscilloscope
  38. 38.  This gives immediate measurement of the square of the channel impulse response convolved with the probing pulse  If oscilloscope is set on average mode, this system can provide a local average power delay profile
  39. 39. Channel Sounder: PN Type
  40. 40. Spread Spectrum Sliding Correlator Channel Sounding  A carrier is spread over a large bandwidth by mixing it with a binary pseudo-noise sequence having a chip duration Tc and chip rate Rc equal to 1/Tc  The power spectrum envelope is given by [sin π(f-fc)Tc] / π(f-fc)Tc] 2
  41. 41.  Null-to-null RF bandwidth is BW=2Rc  Spread spectrum signal is received, filtered and despread using a PN sequence generator identical to that used at the transmitter  Two PN sequences are identical but chip clock rate is higher at Tx than that at Rx
  42. 42.  Mixing the chip sequences in this fashion implements a sliding correlator  When faster chip clock catches up with PN code of slower chip clock, two will be virtually identically aligned , giving maximal correlation  When the two sequences are not maximally correlated ,mixing the incoming signal with unsynchronized receiver chip sequence will spread the signal into the bandwidth at least as large as receiver’s PN sequence.
  43. 43.  Narrowband filter following correlator can reject almost all of the incoming power  Processing gain= 2Rc/Rbb= 2Tbb/Tc  Tbb is period of baseband signal  When incoming signal is correlated with received sequence, the signal is despread ,envelope detected and displayed on an oscilloscope
  44. 44.  Different multipath signals have different time delays, they will maximally correlate with receiver PN sequence at different times  After envelope detection, channel impulse response convolved with the pulse shape of a single chip is displayed on the oscilloscope
  45. 45.  Time resolution ∆τ of multipath components using spread spectrum system with sliding correlator is 2Tc=2/Rc  The system can resolve two multipath components as long as they are equal to or greater than two chip durations apart(2Tc seconds)
  46. 46.  The sliding correlation process gives equivalent time measurements that are updated every time the two sequences are maximally correlated  Time between maximal correlations ∆T is given by Tc =γ l /Rc  Tc = chip period (seconds)  Rc=chip rate (Hz)
  47. 47.  γ =slide factor and l=sequence length in chips  Slide factor is defined as ratio between transmitter chip clock rate and difference between transmitter and receiver chip clock rates  γ =α/(α-β) alpha is Tx chip clock rate and beta is Rx chip clock rate
  48. 48.  Since incoming spread spectrum signal is mixed with a receiver PN sequence that is slower than transmitted sequence, the signal is essentially down-converted to a low-frequency narrowband signal.  Processing gain is realized using a narrowband filter.
  49. 49.  The equivalent time measurements refer to the relative times of multipath components as they are displayed on the oscilloscope  Observed time scale on oscilloscope is related to actual propagation time scale by Actual propagation time=observed time/γ
  50. 50. Channel Sounder: Swept Freq. type
  51. 51.  Vector network analyzer controls a synthesized frequency sweeper  Sweeper scans a particular frequency band centered on the carrier by stepping through discrete frequencies  Number and spacings of frequency steps impact the time resolution of impulse measurements
  52. 52.  For each frequency step, the S parameter test set transmits a known signal at port 1 and monitors the received signal level at port 2.  These signal levels allow the analyzer to determine the complex response which is frequency domain representation of channel impulse response
  53. 53. Time Dispersion Parameters  Parameters which grossly quantify multipath channel  Excess delay, rms delay spread and excess delay spread are determined from a power delay profile(Graph of received signal power V/s excess delay)
  54. 54.  Time dispersive properties of wideband multipath channel are most commonly quantified by their excess delay( τ bar) and rms delay spread στ.  Mean access delay is Σ[P(τk) τk ]/ P(τk)  Rms delay spread is sqrt(tau square bar-tau bar square)
  55. 55.  These delays are measured relative to first detectable signal arriving at receiver at τ0 =0  Typical values are of the order of microseconds in outdoor mobile and nanoseconds in indoor radio channels
  56. 56. Measured power delay profiles
  57. 57. Indoor Power Delay Profile
  58. 58.  Maximum excess delay (X dB) of the power delay profile is defined to be the time delay during which multipath energy falls to X dB below the maximum.  In practice, values of rms delay spread, mean excess delay and excess delay spread depend on the choice of noise threshold
  59. 59. Typical RMS delay spreads
  60. 60. Coherence Bandwidth  It is a statistical measure of the range of frequencies over which channel can be considered flat.  Flat channel passes all spectral components with approximately equal gain and linear phase  It is the range of frequencies over which two frequency components have a strong potential for amplitude correlation
  61. 61.  Two sinusoids with frequency separation greater than Bc are affected quite differently by the channel.  If coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above 0.9, Bc =1/(50στ) approximately
  62. 62. Doppler Spread and Coherence Time  These parameters describe time varying describe the time varying nature of channel in small-scale region  Doppler spread BD is a measure of spectral broadening caused by time rate of change of mobile radio channel  Defined as range of frequencies over which received Doppler spectrum is non-zero
  63. 63.  Doppler spectrum is fc-fd to fc+fd  fd is function relative velocity of mobile and angle theta between direction of mobile and arrival of scattered waves  If baseband signal bandwidth is much greater than BD the effects of Doppler spread are negligible. This is slow fading channel
  64. 64. Coherence Time  Inversely proportional to Doppler Spread  Tc=1/Bd  Coherence time is statistical measure of the time duration over which channel impulse response is essentially invariant
  65. 65.  Coherence time is the time duration over which two received signals have a strong potential for amplitude correlation.  Tc=0.423/fm where fm =maximum Doppler shift =v/λ  Two signals arriving with a time separation greater than Tc are affected differently by the channel.
  66. 66. Two independent fading issues
  67. 67. Flat-fading (non-freq. Selective)
  68. 68. Frequency selective fading
  69. 69. Two independent fading issues
  70. 70. Rayleigh and Ricean Distributions  Rayleigh distribution is commonly used to describe statistical time varying nature of the received envelope of a flat fading signal or the envelope of an individual multipath component  Mean value of Rayleigh distribution is given by 1.2533 σ
  71. 71. Ricean Fading Distribution  When there is a dominant stationary signal component present, such as LOS propagation path, the small-scale fading envelope distribution is Ricean.  In such a situation, random multipath components arriving at different angles are superimposed on a stationary dominant signal.
  72. 72.  At the output of the envelope detector, this has effect of adding a dc component to the random multipath  The effect of a dominant signal arriving with many weaker multipath signals give rise to the Ricean distribution.  As dominant signal becomes weaker, the composite signal envelope is Rayleigh type.The Ricean distribution degenerates into a Rayleigh distribution when the dominant component fades away.
  73. 73. Rayleigh fading
  74. 74. Small-scale envelope distributions
  75. 75. Ricean and Rayleigh fading distributions
  76. 76. Small-scale fading mechanism
  77. 77. Doppler spectrum
  78. 78. Spectrum of Envelope of doppler faded signal
  79. 79. Simulating Doppler/Small-scale fading
  80. 80. Simulating Doppler fading
  81. 81. Simulating Doppler fading
  82. 82. Simulating multipath with Doppler-induced Rayleigh fading
  83. 83. Simulating 2-ray multipath
  84. 84. SIRCIM – Simulation of all indoor propagation Characteristics
  85. 85. SMRCIM – Simulation of all outdoor propagation Characteristics
  86. 86. SIRCIM and SMRCIM  Available from Wireless Valley Communications, Inc.  Source code in C is available  www. Wirelessvalley.com
  87. 87. Angular Spread model
  88. 88. Spatial distribution of Multipath
  89. 89. Angular Spread key to fading
  90. 90. Spatial orientation of multipath impacts the depths of fading
  91. 91. Angular Distribution of power
  92. 92. Angular Spread predicts correlation distances
  93. 93. Angular Spread predicts correlation distances