# Where in the signal chain is Channel Equalization applied?

I am reading about channel equalization and I am somewhat confused on where in the signal chain channel equalization is normally applied and if it's before or after a correlator detector or matched filter.

My confusion is that if equalization occurs before matched filtering/correlator detection, then a training sequence used to estimate the channel will need to be based upon the output of the ADC, not of the matched filter. So if a pseudo-random sequence is used as a pilot tone it won't consist of symbols but of some other modulation type.

If the equalization is based upon the symbol rate output of the matched filter how are fractional delays handled?

• This really does depend on what you're doing. Often, you can model an equalizer as an LTI system (e.g. a filter); and then, you can use the commutation property of convolution to prove it doesn't matter where you do what. The interesting question is where you get your channel state information from; but that's not necessarily the place where you apply your equalization! Nov 7, 2018 at 16:47
• I see, but in terms of estimating the channel(for example using a training sequence) does the pilot sequence consist of a sequence of symbols or something else? I have a read a few papers on this but no one actually talks about where in the signal chain this is applied. Nov 7, 2018 at 16:51
• It consists of something of known properties. Often it's easiest to use symbols, because, hey, you already have a transmitter for these, but sometimes the symbols might have disadvantegous properties (e.g. not DC-free enough, no possibility to make white in spectrum), so that you use something else. Nov 7, 2018 at 16:59
• As in everything you do in engineering, it depends; you take a problem and you solve it. The solution to the problem (here: estimating a channel) depends on your problem's specifics. Nov 7, 2018 at 17:00
• Ok so if you're using symbols you apply your LS criteria using the output of the correlator? Again it's not clear at all where this is actually applied. Nov 7, 2018 at 17:03