ECE 414 Tutorial 3

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Transcript of ECE 414 Tutorial 3

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ECE 414 Tutorial 3 l
l delay power spectral density l mean delay spread l rms delay spread
l delay spread à ISI/ frequency selective?
Autocorrelation function of h(τ,t)
l time-frequency correlation function
à ISI/frequency selective?
l time-frequency correlation function
l Let Δf=0 à time correlation function , which measures how fast the channel changes with time à Fast or slow fading
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l is the FT of w.r.t. Δt
l Let Δf=0 à Doppler power spectral density , the FT of
l Side note:
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l RMS Doppler spread:
ECE 414 Tutorial 3 l Example 1
profileintensity multipath above theexhibiting channel For the
1) calculate the mean delay spread, τ
2) calculate the RMS delay spread, τσ
3) would this channel be suitable for AMPS (30kHz) or GSM (200kHz) without the user of equalizer?
0 1 5 20 )(usτ
0 dB10−
us d d
f kHz T τσ
Δ ≈ = =
For AMPS, 30 ( ) frequency non-selectives cW kHz f= << Δ ⇒ For GSM, 200 ( ) frequency selectives cW kHz f= >> Δ ⇒
AMPS: no ISI, no equalizer needed⇒ neededequalizer ISI, :GSM
Here, the delay components are (0,1,5,20). What happens to the delay spread if the four component are (0,1,5,10) ? Question :
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channel Verify the
[ ] 1 2 1 2
where and are constants, is a random variable uniformly distributed in , , and ( ) is a random process independent of , with [ ( )] and [ ( ) ( )] ( - ), is a WSSUS channel?
n
θ
Ω
Refer to Tutorial 1
ECE 414 Tutorial 3 l Example 3 (P2-7)
l The time variant transfer function of a WSSUS channel is given by
a. Does the channel exhibit frequency-selective fading or flat fading? Explain.
b. Derive the channel impulse response h(τ,t). c. Given that the transmitted signal is x(t), derive the
received signal r(t) in the absence of background noise. From the relation between x(t) and r(t), find the mean delay ( ) and delay spread ( ) of the channel.
( , ) ( )exp( ( )).H f t t j tα θ=
τ τσ
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ECE 414 Tutorial 3 l Example 4 (P2-10)
l A WSSUS channel: Multipath delay spread Tm = 1s, Doppler spread Bd = 0.02Hz, Channel bandwidth Ws = 5Hz, Symbol duration Ts = 10s.
a. Determine the coherence bandwidth and the coherence
time. b. Does this channel exhibit frequency selective fading?
Explain. c. Does this channel exhibit slow or fast fading? Explain.
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slow (Δt)c>>Ts