# EE359 – Lecture 7 Outline Multipath Intensity Profile Doppler Power Spectrum Shannon Capacity Capacity of Flat-Fading Channels Fading Statistics Known.

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EE359 – Lecture 7 Outline Multipath Intensity Profile Doppler Power Spectrum Shannon Capacity Capacity of Flat-Fading Channels Fading Statistics Known Fading Known at RX

Review of Last Lecture Signal envelope distributions: CLT approx.  Rayleigh distribution (power exponential) When LOS present, Ricean distribution used Measurements support Nakagami distribution Average Fade Duration: Rayleigh fading AFD Wideband Channels Individual multipath components resolvable True when time difference between multipath components exceeds signal bandwidth R t1t1 t2t2 t3t3

Characterizing Wideband Channels Wideband channels introduce time-distortion (  ) and time-variation (Doppler,  ) Wideband channels c(  t) characterized by scattering function from A c (  1,  2,  t)=A c ( ,  t)  Narrowband  Wideband   s( ,  )= F  t [A c ( ,  t)] Characterizes delay spread & Doppler

Multipath Intensity Profile Defined as A c ( ,  t=0)= A c (  ) Determines average (T M ) and rms (   ) delay spread Approximate max delay of significant m.p. Coherence bandwidth B c =1/T M Maximum frequency over which A c (  f)=F[A c (  )]>0 A c (  f)=0 implies signals separated in frequency by  f will be uncorrelated after passing through channel  Ac()Ac() TMTM  f A c (f) 0 Bc

Doppler Power Spectrum S c (  )=F[A c ( ,  t)]= F[A c (  t)] Doppler spread B d is maximum doppler for which S c (  )=>0. Coherence time T c =1/B d Maximum time over which A c (  t)>0 A c (  t)=0 implies signals separated in time by  t will be uncorrelated after passing through channel  Sc()Sc() BdBd

Shannon Capacity Defined as the maximum MI of channel Maximum error-free data rate a channel can support. Theoretical limit (not achievable) Channel characteristic Not dependent on design techniques

Capacity of Flat-Fading Channels Capacity defines theoretical rate limit Maximum error free rate a channel can support Depends on what is known about channel Fading Statistics Known Hard to find capacity Fading Known at Receiver Only