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SYSC 4607 – Lecture 7 Outline

SYSC 4607 – Lecture 7 Outline. Review of Last Lecture Multipath Intensity (Power Delay) Profile Delay spread, Coherence BW Doppler Power Spectrum Doppler Spread, Coherence Time Capacity of Wireless Channels. Review of Last Lecture. Narrowband fading distribution depends on environment

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SYSC 4607 – Lecture 7 Outline

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  1. SYSC 4607 – Lecture 7 Outline • Review of Last Lecture • Multipath Intensity (Power Delay) Profile • Delay spread, Coherence BW • Doppler Power Spectrum • Doppler Spread, Coherence Time • Capacity of Wireless Channels

  2. Review of Last Lecture • Narrowband fading distribution depends on environment • Rayleigh, Rician, and Nakagami all common • Average fade duration determines how long a user is in continuous outage (e.g. for coding design) • Wideband models characterized by scattering function. • Scattering function gives the average power distribution w.r.t. multipath delay t and Doppler frequency ρ

  3. Scattering Function • Used to characterize c(t,t) statistically • Since underlying process Gaussian, need only characterize mean (0) and correlation • Autocorrelation for USWSS channel is Ac(t1,t2,Dt)=Ac(t,Dt) • Statistical scattering function: Sc(t,r)=FDt[Ac(t,Dt)]

  4. Power Delay Profile • Power delay profile (multipath intensity profile):Ac(t)=Ac(t,0) • Represents average power of impulse response associated with a given multipath delay t at a given location in space (variation in time, or equivalently space, is removed) • Distribution (pdf) of delay spread: • Mean and rms values of delay spread are commonly used measures of delay spread

  5. Delay Spread and Coherence Bandwidth Ac(t) • Delay spread (Tm ) approximates max delay of significant multipath components • Coherence bandwidth Bc=1/Tm • Maximum frequency over which AC(Df)=F[Ac(t)]>0 • AC(Df)=0 implies signals separated in frequency by Df will be uncorrelated after passing through channel Tm t Ac(f) f t

  6. Doppler Power Spectrum Sc(r) • Sc(r)=F[Ac(t=0,Dt)]= F[Ac(Dt)] • Doppler spread BD is maximum Doppler for which Sc (r) > 0. • Coherence time Tc=1/BD • Maximum time over which Ac(Dt)>0 • Ac(Dt)=0 implies signals separated in time by Dt will be uncorrelated after passing through channel r BD

  7. Capacity of Wireless Channels • Pioneered by Claude Shannon in 1948 • Shannon capacity is defined as the maximum Mutual Information of the channel (IT definition) • Capacity defines theoretical rate limit: Maximum error free rate a channel can support (Operational definition) • Theoretical limit (not achievable) • A property of channel (bandwidth, noise). Does not depend on design techniques

  8. Capacity of Flat-Fading Channels Depends on what is known about the channel • Unknown Fading: • Worst-case channel capacity • Fading Statistics Known • Hard to find capacity • Fading Known at Receiver Only

  9. Main Points • Multipath delay spread defines maximum delay of significant multipath components, its inverse is coherence bandwidth of channel • Doppler spread defines maximum nonzero Doppler, its inverse is coherence time • Fundamental capacity of flat-fading channels depends on what is known at TX and RX.

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