EE359 – Lecture 6 Outline Announcements: HW due tomorrow 5pm Next 3 lectures rescheduled: 10/12 (Mon), 10/16 (Fri), 10/19 (Mon), all in Huang Eng. Center, room 18, 12-1:30pm. Next HW deadline will be extended to Monday 5pm (OH Mon). Review of Last Lecture Nakagami Fading Distribution Wideband Multipath Channels Scattering Function Multipath Intensity Profile Doppler Power Spectrum

Review of Last Lecture For  n ~U[0,2  ], r I (t),r Q (t) zero mean, WSS, with Uniform AoAs in Narrowband Model In-phase/quad comps have zero cross correlation and PSD is maximum at the maximum Doppler frequency l PSD used to generate simulation values Decorrelates over roughly half a wavelength

Signal Envelope Distribution CLT approx. for no dominant multipath component leads to Rayleigh distribution (power is exponential). When LOS component present, Ricean distribution is used Some measurements support Nakagami distribution Parameterized by m>.5, which approximates LOS power to multipath Similar to Ricean (m≈K, K≥1), but models “worse than Rayleigh” Yields closed form BER expressions

Wideband Channels Individual multipath components resolvable True when time difference between components exceeds signal bandwidth   NarrowbandWideband

Scattering Function Typically characterize c(t,t) by its statistics, since it is a random process Underlying process WSS and Gaussian, so only characterize mean (0) and correlation Autocorrelation is A c (  1,  2,  t)=A c ( ,  t) Statistical scattering function:   s( ,  )= F  t [A c ( ,  t)]

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 BcBc

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

Main Points Fading distribution depends on environment Rayleigh, Ricean, and Nakagami all common Scattering function characterizes rms delay and Doppler spread. Key parameters for system design. Delay spread defines maximum delay of significant multipath components. Inverse is coherence BW Doppler spread defines maximum nonzero doppler, its inverse is coherence time