Modeling multipath channel as FIR

haowang73

Question：
Why multipath channel can modelled as Finite Impulse Response (FIR) filters (what is the relationship between FIR filters and multipath channel)? and how to model it as FIR filters?

Answer：
If the receiver in the multipath channel receives signals from a single source, generally each path in the multipath is delayed one from another and generally each path has different attenuation. A FIR filter has as input a single sequence and the output is a set of signals that have been delayed and weighted (attenuated if you will). I hope the resemblance is clear enough now. For more than one source you would probably use one FIR filter per source. So, a FIR filter can be defined (perhaps a very sparse filter - i.e. one with many zero coefficients) that has an output that is the same as a (perhaps simplified) multiple-path environment.  This implies that the simulating filter have a unit delay that is adequate to resolve the paths as well as may be desired.  In general, delay is not known for a path to within the propagation time of a single wavelength - so resolution down to sub-wavelength times is most often unecessary. If antennas or arrays are involved then the output of the filter needs to take into account the attenuation at each angle of arrival due to the receive beam pattern.  At short range, the transmitter beam pattern may also be important.  Or, maybe I should really say that at long range maybe the transmitter beam pattern could be neglected.  It depends on the geometry. Things get more complicated and depart from the FIR filter model when the paths are dynamic and introduce Doppler shifts, etc.Fred