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 LectureNakagami Fading DistributionWideband Multipath ChannelsScattering FunctionMultipath Intensity ProfileDoppler Power Spectrum

Review of Last Lecture

For fn~U[0,2p], rI(t),rQ(t) zero mean, WSS, with

Uniform AoAs in Narrowband ModelIn-phase/quad comps have zero cross

correlation and

PSD is maximum at the maximum Doppler frequency

PSD used to generate simulation values

)2()()( 0 p Drrr fJPAAQI

Decorrelates over roughly half a wavelength

p /cos),(]2[cos)( nDrDrr vfAfEPAnQnnI

)(]2[sin)( ,, p QInnQI rrDrrr AfEPA

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 ChannelsIndividual multipath components

resolvableTrue when time difference

between components exceeds signal bandwidth

uB/1 uB/1

1 2

Narrowband Wideband

Scattering FunctionTypically 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 Ac(1,2,t)=Ac(,t)

Statistical scattering function:

rs(,r)=Ft[Ac(,t)]

Multipath Intensity Profile

Defined as Ac(,t=0)= Ac()Determines average (TM ) and rms (s)

delay spread Approximate max delay of significant

m.p. Coherence bandwidth Bc=1/TM

Maximum frequency over which Ac(f)=F[Ac()]>0

Ac(f)=0 implies signals separated in frequency by f will be uncorrelated after passing through channel

Ac()TM

um BT /1

1 2 f

cu BB

Ac(f)0 Bc

Doppler Power Spectrum

Sc(r)=F[Ac(0,t)]= F[Ac(t)] Doppler spread Bd is maximum

doppler for which Sc (r)=>0.

Coherence time Tc=1/BdMaximum time over which Ac(t)>0Ac(t)=0 implies signals separated in

time by t will be uncorrelated after passing through channel

r

Sc(r)

Bd

Main Points

Fading distribution depends on environmentRayleigh, 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