how can an FIR filter equalizer another FIR filter?

Question

I am adapting a blind adaptive channel equalizer using CMA. Both the channel and the equalizer are modeled as LTI FIR filters. But how can the equalizer be (approximate) the inverse of the channel if it also FIR?

I am adapting a blind adaptive channel equalizer using CMA. Both the channel and the equalizer are LTI FIR filters. For perfect equalization the equalizer is the inverse of the channel but the inverse of an FIR filter is an IIR filter. I know that I can use an FIR filter to equalize an FIR channel but what I don't know is why? What says that an FIR filter can approximate the inverse of another FIR filter? Is there some theory out there because I have not come across any yet.

Answer 1

While you may want an IIR implementation for an exact answer, a FIR with enough taps can probably provide a good approximation. There is some discussion of inversion of FIR filters in the link below that you may find interesting or helpful.

Answer 2

I don't understand your question, sorry. You use a finite impulse response filter to approximate your channel response ; why would you not be able to use a second FIR to modify the transfer function / impulse response of the channel filter? Are you worried about the delay?