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Properties of the Mobile Radio Propagation Channel

Properties of the Mobile Radio Propagation Channel. Jean-Paul M.G. Linnartz Nat.Lab., Philips Research. Statistical Description of Multipath Fading. The basic Rayleigh / Ricean model gives the PDF of envelope But: how fast does the signal fade? How wide in bandwidth are fades?.

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Properties of the Mobile Radio Propagation Channel

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  1. Properties of the Mobile Radio Propagation Channel Jean-Paul M.G. Linnartz Nat.Lab., Philips Research

  2. Statistical Description of Multipath Fading The basic Rayleigh / Ricean model gives the PDF of envelope • But: how fast does the signal fade? • How wide in bandwidth are fades? Typical system engineering questions: • What is an appropriate packet duration, to avoid fades? • How much ISI will occur? • For frequency diversity, how far should one separate carriers? • How far should one separate antennas for diversity? • What is good a interleaving depth? • What bit rates work well? • Why can't I connect an ordinary modem to a cellular phone? The models discussed in the following sheets will provide insight in these issues Multipath fading

  3. The Mobile Radio Propagation Channel A wireless channel exhibits severe fluctuations for small displacements of the antenna or small carrier frequency offsets. Amplitude Frequency Time Channel Amplitude in dB versus location(= time*velocity) and frequency Multipath fading

  4. Time Domain Channel variations Delay spread Interpretation Fast Fading InterSymbol Interference Correlation Distance Channel equalization Frequency Doppler spectrum Frequency selective fading Domain Intercarrier Interference Coherence bandwidth Interpretation Some buzz words about Time Dispersion and Frequency Dispersion Time Dispersion Frequency Dispersion Multipath fading

  5. Fading is characterised by two distinct mechanisms • 1. Time dispersion • Time variations of the channel are caused by motion of the antenna • Channel changes every half a wavelength • Moving antenna gives Doppler spread • Fast fading requires short packet durations, thus high bit rates • Time dispersion poses requirements on synchronization and rate of convergence of channel estimation • Interleaving may help to avoid burst errors • 2. Frequency dispersion • Delayed reflections cause intersymbol interference • Channel Equalization may be needed. • Frequency selective fading • Multipath delay spreads require long symbol times • Frequency diversity or spread spectrum may help Multipath fading

  6. Time dispersion of narrowband signal (single frequency) • Transmit: cos(2p fc t) • Receive: I(t) cos(2p fc t) + Q(t) sin(2p fc t) • = R(t) cos(2p fc t + f) • I-Q phase trajectory • As a function of time, I(t) and Q(t) follow a random trajectory through the complex plane • Intuitive conclusion: • Deep amplitude fades coincide with large phase rotations Multipath fading

  7. Doppler shift • All reflected waves arrive from a different angle • All waves have a different Doppler shift The Doppler shift of a particular wave is Maximum Doppler shift: fD = fc v / c • Joint Signal Model • Infinite number of waves • Uniform distribution of angle of arrival f: fF(f) = 1/2p • First find distribution of angle of arrival the compute distribution of Doppler shifts • Line spectrum goes into continuous spectrum Doppler

  8. Doppler Spectrum If one transmits a sinusoid, … what are the frequency components in the received signal? • Power density spectrum versus received frequency • Probability density of Doppler shift versus received frequency • The Doppler spectrum has a characteristic U-shape. • Note the similarity with sampling a randomly-phased sinusoid • No components fall outside interval [fc- fD, fc+ fD] • Components of + fD or -fD appear relatively often • Fades are not entirely “memory-less” Doppler

  9. Autocorrelation of the signal We now know the Doppler spectrum. But how fast does the channel change? • Wiener-Kinchine Theorem: • Power density spectrum of a random signal is the Fourier Transform of its autocorrelation • Inverse Fourier Transform of Doppler spectrum gives autocorrelation of I(t) and Q(t) Autocorrelation

  10. ( ) 2 = p t C J 2 f 0 D Autocovariance of amplitude Autocorrelation

  11. How to handle fast multipath fading? Multipath fading

  12. Frequency Dispersion • Frequency dispersion is caused by the delay spread of the channel • Frequency dispersion has no relation to the velocity of the antenna Multipath fading

  13. Frequency Dispersion: Delay Profile Multipath fading

  14. Typical Delay Spreads Multipath fading

  15. Channel Parameters at 1800 MHz EnvironmentDelay SpreadAngle spreadMax. Doppler shift Macrocellular: Rural flat 0.5 ms 1 degree 200 Hz Macrocellular: Urban 5 ms 20 degrees 120 Hz Macrocellular: Hilly 20 ms 30 degrees 200 Hz Microcellular: Factory, Mall 0.3 ms 120 degrees 10 Hz Microcellular: Indoors, Office 0.1 ms 360 degrees 2..6 Hz Multipath fading

  16. Typical Delay Profiles Multipath fading

  17. How do systems handle delay spreads? Multipath fading

  18. Frequency and Time Dispersion Multipath fading

  19. Scatter Function of a Multipath Mobile Channel Gives power as function of · f Doppler Shift (derived from angle ) Excess Delay · Example of a scatter plot Horizontal axes: · x-axis: Excess delay time · y-axis: Doppler shift Vertical axis · z-axis: received power Multipath fading

  20. Scatter Function of a Multipath Mobile Channel Example of a scatter plot Excess Delay Doppler Shift derived from angle f Multipath fading

  21. Correlation of Fading vs. Frequency Separation Multipath fading

  22. Multipath fading

  23. Coherence Bandwidth Multipath fading

  24. Effects of fading on modulated radio signals

  25. Wideband Narrowband OFDM Time Time Time Frequency Frequency Frequency Effects of Multipath (I)

  26. DS-CDMA Frequency Hopping MC-CDMA + - + + - + - Time Time Time + - - - + - + - + - - + - + - + Frequency Frequency Frequency Effects of Multipath (II)

  27. Time Dispersion Revisited The duration of fades and the optimum packet length

  28. Time Dispersion Revisited: Duration of Fades Multipath fading

  29. Two-State Model Multipath fading

  30. Average Fade / Nonfade Duration Fade duration

  31. Average nonfade duration Fade duration

  32. How to handle long fades when the user is stationary? Fade duration

  33. Optimal Packet length Fade duration

  34. Optimal Packet length fc = 900 MHz 72 km/h (v=20 m/s) fade margin 10 dB Fade duration

  35. Derivation of Optimal Packet length Fade duration

  36. Average fade duration Fade duration

  37. Conclusion • The multipath channel is characterized by two effects: Time and Frequency Dispersion • Time Dispersion effects are proportional to speed and carrier frequency • System designer needs to anticipate for channel anomalies Multipath fading

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