41st IEEE CDC Las Vegas, Nevada December 9th 2002

1. 41st IEEE CDC Las Vegas, Nevada December 9th 2002 Workshop M-5: Wireless Communication Channels: Modeling, Analysis, Simulations and Applications Organizers: Charalambos D. Charalambous Nickie Menemenlis

2. Wireless Communication Channels Schedule • 08:00-08:45 Introduction to Wireless Communication Channels (C.D. Charalambous) • 8:45-9:15 Statistical Analysis of Wireless Fading Channels (C.D. Charalambous) • 9:15-9:25 Break • 9:25 -10:10 Stochastic Differential Equations in Modeling Log-Normal Shadowing (N. Menemenlis) • 10:10-10:55 Stochastic Differential Equations in Modeling Short-Term Fading (N. Menemenlis) • 10:55-11:00 Break • 11:00-12:00 Applications (C.D. Charalambous) • Additional information can be found at: • http://www.site.uottawa.ca/~chadcha/CDC2002

3. Introduction to Wireless Communication Channels • Shannon’s communication channel • Impulse response of wireless fading channels • Large-scale and small scale propagation models • Log-Normal shadowing channel • Short-term fading channel • Autocorrelation functions and power spectral densities • Assumption: WSSUS • Time spreading • Time variations • Channel classification • Channel simulations

4. Chapter 1: Shannon’s Wireless Communication System Channel code word Message Signal Modulated Transmitted Signal Source Source Encoder Channel Encoder Mod- ulator Wireless Channel User Source Decoder Channel Decoder Demod- ulator Received Signal Estimate of Message signal Estimate of channel code word

5. Chapter 1: Large and Small Scale Propagation Models Area 1 Area 2 Short-term fading Log-normal shadowing Transmitter

6. Chapter 1: Impulse Response Characterization Time variations property t2 t(t2) t1 t(t1) Time spreading property t0 t(t0) • Impulse response: Time-spreading : multipath • and time-variations: time-varying environment

7. Chapter 1: Multipath Fading Components • Complex low-pass representation of impulse response

8. Chapter 1: Band-pass Representation of Impulse Response • Band-pass representation of impulse response:

9. Chapter 1: Representation of Additive Noise Channel • Low-pass and band-pass representation of received signal:

10. Chapter 1: Large and Small Scale Propagation Models • Large scale propagation models: • T-R separation distances are large • Main propagation mechanism: reflections • Attenuation of signal strength due to power loss along distance traveled: shadowing • Distribution of power loss in dBs: Log-Normal • Log-Normal shadowing model • Fluctuations around a slowly • varying mean

11. Chapter 1: Large and Small Scale Propagation Models • Small scale propagation: • T-R separation distances are small • Heavily populated, urban areas • Main propagation mechanism: scattering • Multiple copies of transmitted signal arriving at the transmitted via different paths and at different time-delays, add vectotrially at the receiver: fading • Distribution of signal attenuation • coefficient: Rayleigh, Ricean. • Short-term fading model • Rapid and severe signal • fluctuations around a slowly • varying mean

12. Chapter 1: Log-Normal Shadowing Model

13. Chapter 1: Log-Normal Shadowing Model

14. Chapter 1: Log-Normal Shadowing Model • Power path-loss in dB’s, x, and Distributions: x : normal and attenuation coefficient, r, vs d r=ekx : log-normal

15. Chapter 1: Short-Term Fading Model z z0 nth incoming wave En=:{rn,fn,an,bn}; n=1,…, N O’(x0 ,y0 ,z0) bn O an x x0 y0 g O’’ v y direction of motion of mobile on x-y plane • 3-Dimensional Model [Clarke 68, Aulin 79]

16. Chapter 1: Short-Term Fading Model • 3-D Model [Clarke 68, Aulin 79] • Transmitted signal: Re{ejwct} • Total field at mobile, or receiving location, O’(x0, y0, z0)

17. Chapter 1: Short-Term Fading Model • 3-D Model [Clarke 68, Aulin 79] • Total field at receiving location when mobile moves • O’(x0, y0, z0) => (x0+vtcosg, y0 +vtsing, z0), v: velocity of mobile

18. Chapter 1: Short-Term Fading Model • 3-D Model [Clarke 68, Aulin 79] • Statistical characterization of {I(t), Q(t)}

19. Chapter 1: Short-Term Fading Model • Statistical characterization of rn

20. Chapter 1: Short-Term Fading Model • Autocorrelation functions

21. Chapter 1: Short-Term Fading Model

22. Chapter 1: Time Delays of Paths • Complex low-pass representation of impulse response: • Typically the time delays are modeled using exponential distribution, implying that the number of paths is a Poisson counting process • In reality this representation is not very accurate.

23. Chapter 1: Channel Autocorrelation Functions • General expressions for the Autocorrelation function are introduced by Bello ’63 for a widely accepted Wide-Sense Stationary Uncorrelated Scattering (WSSUS) channel • WSS in the time-domain • US attenuation and phase shift of paths i and j are uncorrelated

24. Chapter 1: Channel Autocorrelation Functions • Time-spreading: Multipath characteristics of channel

25. Chapter 1: Channel Autocorrelation Functions • Time-spreading: Multipath characteristics of channel

26. Chapter 1: Channel Autocorrelation Functions • Time-spreading: Multipath characteristics of channel • Multi-path delay spread, Tm • Characterizes time dispersiveness of the channel, • Obtained from power delay-profile, Fc(t) • Indicates delay during which the power of the received signal is above a certain value. • Coherence bandwidth, Bcapprox. 1/ Tm • Indicates frequencies over which the channel can be considered flat • Two sinusoids separated by more than Bc: affected differently by the channel • Indicates frequency selectivity during transmission.

27. Chapter 1: Channel Autocorrelation Functions • Time variations of channel: Frequency-spreading

28. Chapter 1: Channel Autocorrelation Functions • Time variations of channel: Frequency-spreading

29. Chapter 1: Channel Autocorrelation Functions • Time variations of channel: Frequency-spreading • Doppler Spread, Bd • Characterizes frequency dispersiveness of the channel, or the spreading of transmitted frequency due to different Doppler shifts • Obtained from Doppler spectrum, Sc(l) • Indicates range of frequencies over which the received Doppler spectrum is above a certain value • Coherence time, Tcapprox. 1/ Bd • Time over which the channel is time-invariant • A large coherence time: Channel changes slowly

30. Chapter 1: Channel Autocorrelation Functions Fc(t ) Power Delay Profile |Fc(Df)| t Tm Ft Bc Df Dt=0 Power Delay Spectrum Fc( Dt;t ) Ft FDt |Fc(Dt;Df)| Dt=0 Scattering Function Df WSSUS Channel Sc( l;t ) Dt Sc(l; Df) Ft FDt Df=0 Df=0 Sc(l;t) |Fc(Dt)| Sc( l ) t Doppler Power Spectrum Tc Dt FDt l Bd l

31. Chapter 1: Channel Classification Based on Time-Spreading • Flat Fading • BS < BCTm < Ts • Rayleigh, Ricean distrib. • Spectral chara. of transmitted • signal preserved • Frequency Selective • BS > BC Tm > Ts • Intersymbol Interference • Spectral chara. of transmitted • signal not preserved • Multipath components resolved Channel Channel Signal Signal BC BS freq. freq. BS BC

32. Chapter 1: Channel Classification Based on Time-Variations • Fast Fading • High Doppler Spread • 1/Bd@ TC < Ts • Slow Fading • Low Doppler Spread • 1/Bd@ TC> Ts Signal Signal Doppler Doppler BD BS freq. freq. BS BD

33. Chapter 1: Channel Classification • Underspread channel: TmBd << 1 • Channel characteristics vary slowly (Bd small) or paths obtained within a short interval of time (Tm small). • Easy to extract channel parameters. • Overspread channel: TmBd >> 1 • Hard to extract parameters as channel characteristics vary fast and channel changes before all paths can be obtained.

34. Chapter 1: Flat Fading Channel Simulations • Flat Fading • a(t): Rayleigh or Ricean

35. Chapter 1: Frequency Selective Channel Simulations • Frequency Selective

36. Chapter 1: References • G.L. Turin. Communication through noisy, random-multipath channels. IRE Convention Record, pp. 154-166, 1956. • P. Bello. Characterization of random time-variant linear channels. IEEE Transactions in Communications, pp 360-393, 1963. • J.F. Ossanna. A model for mobile radio fading due to building reflections: Theoretical and experimental waveform power spectra. Bell Systems Technical Journal, 43:2935-2971, 1964. • R.H. Clarke. A statistical theory of mobile radio reception. Bell Systems Technical Journal, 47:957-1000, 1968. • M.J Gans. A power-spectral theory of propagation in the mobile-radio environment. IEEE Transactions on Vehicular Technology, VT-21(1):27-38, 1972. • H. Suzuki. A statistical model for urban radio propagation. IEEE Transactions in Communications, 25:673-680, 1977. • T. Aulin. A modified model for the fading signal at a mobile radio channel. IEEE Transactions on Vehicular Technology, VT-28(3):182-203, 1979. • A.D.Saleh, R.A.Valenzuela. A statistical model for indoor multi-path propagation. IEEE Journal on Selected Areas in Communications, 5(2):128-137, 1987.

37. Chapter 1: References • M. Gudamson. Correlation model for shadow fading in mobile radio systems. Electronics Letters, 27(23):2145-2146, 1991. • D. Giancristofaro. Correlation model for shadow fading in mobile radio channels. Electronics Letters, 32(11):956-958, 1996. • A.J. Coulson, G. Williamson, R.G. Vaughan. A statistical basis for log-normal shadowing effects in multipath fading channels. IEEE Transactions in Communications, 46(4):494-502, 1998. • E. Biglieri, J. Proakis, S. Shamai. Fading channels: Information-theoretic and communication aspects. IEEE Transactions on Information Theory, 44(6):2619-2692, October 1998. • W.C.Jakes. Microwave mobile communications, New York, Wiley-Interscience, 1974. • K. Pahlavan, A.H. Levesque. Wireless Information Networks, New York, Wiley-Interscience, 1995. • J.G. Proakis. Digital Communications, Mc-Graw-Hill, New-York, 1995. • T.S. Rappaport. Wireless Communications, Prentice Hall, 1996.