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I'm trying to simulate a multipath channel to see how it would affect my signal. So considering my channel is LTI, I can model it as an FIR filter. I've been reading Telecommunication Breakdown and looking at some examples and there's one thing I don't quite understand in page 183 (Chapter 9: Stuff happens, Section 9.4: Other Impairments: "More What Ifs")

if cdi < 0.5, % channel ISI
    mc=[1 0 0 ] ; % distortion−free channel
elseif cdi<1.5 , % mild multipath channel
    mc=[1 zeros (1 ,M) 0.28 zeros (1, 2.3*M) 0.11 ] ;
el se % harsh multipath channel
    mc=[1 zeros (1, M) 0.28 zeros (1, 1.8*M) 0.44 ] ;
end

So cdi is a parameter to choose between distortion-free, mild or harsh multipath channel and mc is the resulting FIR filter. What I don't understand is:

  1. What's the point on inserting zeros in between?
  2. How does that make it mild or harsh?

Would you mind explaining that to me? Thanks

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  • $\begingroup$ Multipath channels are often modeled as FIR, but your logical step "LTI->can be modeled by FIR" is wrong. Could be an IIR, too. And physically, that's often closer to reality, but the FIR approximation happens to be good enough. $\endgroup$ – Marcus Müller Oct 29 '19 at 21:05
  • $\begingroup$ Re 2: There's no "point" to that. That's the channel model they're using. It follows from their modelling of the physical channel. $\endgroup$ – Marcus Müller Oct 29 '19 at 21:08
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  1. You put zeros in between to show delay between the channel taps. I don't know what $M$ is in your code but suppose $M=10$ and say your sample rate is 10 MHz. Then you can interpret mc = [1 zeros(1, M) 0.28 zeros(1, 2.3*M) 0.11]; as you get the first multipath component with zero delay (gain = 1), then 10 zeros later (which is equal to 1 microsecond) you get another multipath component (gain = 0.28), and finally after another 2.8 microseconds you receive the last multipath component (gain = 0.11).

  2. It looks like the "mild" vs "harsh" is just language that the author uses to let you know that mild happens to rarely cause errors where the harsh causes many errors.

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