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I am working on modelling some FM transmitted signals, and I'm trying to figure out how to model the effects of multipath channels. The most obvious method is to delay the signal by some integral number of samples and then add it to itself (with some attenuation factor). But, this is obviously not very realistic, since 1 sample's worth of time is a long time for a radio wave (at least at a reasonable sample rate). It would be nice to be able to delay the signal by a fraction of a sample. However, I don't know how to do this... Can anyone enlighten me? I am fairly new to the DSP field, I'm sure this isn't a particularly challenging task.

Also, is this actually a good method for modelling multipath effects?

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  • $\begingroup$ Search for fractional delay filtering. See e.g. here. $\endgroup$ – Matt L. Nov 1 '14 at 9:39
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One approach is to upsample the signal, then delay it, then downsample (or, if feasible, you can do the rest of the processing at the higher sampling rate).

This general approach to modeling multipath is correct. However, you need to make sure that your model is realistic and/or useful for your purpose. A few things to consider:

  • If you add delayed/attenuated replicas of the signal to itself, then you're assuming you have line-of-sight between the transmit and receive antennas. The effect is different when you don't have line-of-sight.

  • The number of paths is important too. A channel with many paths is easier to understand theoretically, because you can make certain assumptions about the overall channel gain (e.g. that it's a Gaussian random variable).

  • The maximum delay is important too. A very large delay introduces very destructive effects on the received signal. Many, very small delays can be modeled as a single gain factor.

  • In a static environment, the channel is also static. If the antennas and/or obstacles in the environment are in movement, then the channel is dynamic, in the sense that the number of paths, and the gain of each, vary with time.

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