# Training Fractionally Spaced Channel Estimator and Equalizer

If you are attempting least squares channel estimation with a fractionally spaced channel estimator, do you want the training sequence to also be fractionally spaced or symbol spaced? It looks like you could do either.

• In fractionally-spaced equalizer (FSE) implementations that I've seen before, the filter decimates, so that for a spacing of $\frac{T}{N}$, only one sample is output for each $N$ inputs. In an LMS equalizer, for example, the training sequence is used as the desired output $d[n]$ when calculating the error signal $e[n] = d[n] - y[n]$, where $y[n]$ is the filter output. In this formulation, it looks like you would want a symbol-spaced training sequence in order for its sample rate to line up with the equalizer's output. – Jason R Feb 26 at 2:23
• Yes, but you could also estimate the channel taking into account mid-symbol values which are output by the correlator. In a sense this increases the information gained per training symbol, I'm not sure if this would screw something up or not? – FourierFlux Feb 26 at 18:58