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

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:

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

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

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

Chapter 1: Wireless Communication System v(t) noise n(t) u(t) r(t) Channel 1... user 1 user M Co-Channel Interference - Forward Channel Channel 1 Channel M Transmitter Receiver Reverse Channel

Chapter 1: Impulse Response Characterization  (t 0 ) t0t0 t2t2  (t 2 ) t1t1  (t 1 ) Time spreading property Time variations property Impulse response: Time-spreading : multipath and time-variations: time-varying environment

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

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

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

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 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

Chapter 1: Log-Normal Shadowing Model Transmitter  n,1 Receiver  k,1  or  d  n,3  n,2  k,2  k,3  k,4 one subpath LOS path k path n d(t) v mR (t) nn

Chapter 1: Log-Normal Shadowing Model

Power path-loss in dB’s, x, andDistributions: x : normal and attenuation coefficient, r, vs d r=e kx : log-normal

Chapter 1: Short-Term Fading Model nn nn x z y nth incoming wave E n =:{r n,  n,  n,  n }; n=1,…, N O O’(x 0,y 0,z 0 )  direction of motion of mobile on x-y plane v x0x0 z0z0 y0y0 O’’ 3-Dimensional Model [Clarke 68, Aulin 79]

Chapter 1: Short-Term Fading Model 3-D Model [Clarke 68, Aulin 79] Transmitted signal: Re{e j  c t } Total field at mobile, or receiving location, O ’( x 0, y 0, z 0 )

Chapter 1: Short-Term Fading Model 3-D Model [Clarke 68, Aulin 79] Total field at receiving location when mobile moves O ’( x 0, y 0, z 0 ) => ( x 0 +vtcos , y 0 +vtsin , z 0 ), v: velocity of mobile

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

Chapter 1: Short-Term Fading Model Statistical characterization of r n

Autocorrelation functions Chapter 1: Short-Term Fading Model

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.

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 Chapter 1: Channel Autocorrelation Functions

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

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

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

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

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

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

 c (  t;  ) S c ( ;  ) S c ( ;  f) Scattering Function FF FtFt FF FtFt WSSUS Channel Power Delay Profile Power Delay Spectrum   c (  ) TmTm ff BcBc |  c (  f)| FF  t=0 tt TcTc |  c (  t)|  f=0  t=0 BdBd S c ( )  f=0 FtFt Doppler Power Spectrum tt |  c (  t;  f)| ff S c (  ) 

Chapter 1: Channel Classification Based on Time-Spreading Flat Fading 1.B S < B C  T m < T s 2.Rayleigh, Ricean distrib. 3.Spectral chara. of transmitted signal preserved Frequency Selective 1.B S > B C  T m > T s 2.Intersymbol Interference 3.Spectral chara. of transmitted signal not preserved 4.Multipath components resolved Signal Channel freq. BSBS BCBC BCBC BSBS Channel Signal

Chapter 1: Channel Classification Based on Time-Variations Fast Fading 1.High Doppler Spread 2.1/B d  T C < T s Slow Fading 1.Low Doppler Spread 2.1/B d  T C > T s Signal freq. BDBD BSBS BSBS BDBD Doppler Signal Doppler

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

Flat Fading  (t): Rayleigh or Ricean Chapter 1: Flat Fading Channel Simulations

Frequency Selective Chapter 1: Frequency Selective Channel Simulations

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

M. Gudamson. Correlation model for shadow fading in mobile radio systems. Electronics Letters, 27(23): , D. Giancristofaro. Correlation model for shadow fading in mobile radio channels. Electronics Letters, 32(11): , 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): , E. Biglieri, J. Proakis, S. Shamai. Fading channels: Information-theoretic and communication aspects. IEEE Transactions on Information Theory, 44(6): , October W.C.Jakes. Microwave mobile communications, New York, Wiley- Interscience, K. Pahlavan, A.H. Levesque. Wireless Information Networks, New York, Wiley-Interscience, J.G. Proakis. Digital Communications, Mc-Graw-Hill, New-York, T.S. Rappaport. Wireless Communications, Prentice Hall, Chapter 1: References