# Simulating multipath channel

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

• 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. Oct 29, 2019 at 21:05
• 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. Oct 29, 2019 at 21:08

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).