# How exactly to implement the fractional part of a 'fractional equalizer'?

I have written my own LSE equalizer (that works on the bit level), and literature I have read says that 'fractional' based ones are much better. So how exactly does one get 'fractional' bits? Is it as simple as resampling the softbit decisions to 2x, 4x or whatever of their bit rate and applying the equalizer like that?

Thanks

The only difference with a fractionally-spaced equalizer (FSE) is the sample rate that it runs at: instead of the one sample per symbol that you see with a "standard" equalizer, an FSE operates at some multiple of the symbol rate. Typical values I've seen before are $T/2$- and $T/4$-spaced equalizers, which operate at twice and four times the symbol rate, respectively.
• As the name indicates, you want the samples to be spaced (for example) $T/2$ (i.e. half of a symbol time). If you have 20 samples per symbol and the ideal peak is at sample index 13, then you would feed samples 3, 13, 23 (i.e. the 3rd sample from the next symbol interval), 33 (the 13th sample from the next symbol interval), and so on into the filter. If you have a timing tracking loop that follows the peak over time, you would adjust the sample that you pass to the filter accordingly. You just want to ensure the right amount of time spacing between samples. – Jason R Nov 7 '11 at 15:06
• You would fill the expected training sequence with what you would expect to see out of your receiver in the ideal case. So, whatever the ideal matched filter would output $T/2$ before and after the symbol centers would be what you would put in. – Jason R Nov 7 '11 at 15:47