# Symbol Timing recovery for modulation producing ISI

I am interested in understanding why the common timing recovery algorithms function for modulation schemes which produce ISI.

For example, suppose you are receiving at the output of a matched filter a raised cosine pulse and you are interested in timing recovery. For simplicity lets assume BPSK(though I would be interested in QAM). Besides the ideal sampling times there will be ISI.

Most of the common symbol timing recovery algorithms seem to use symmetry in the received signal, either balancing the measured value at the left and right sides of the ideal sampling instant or use zero crossings.

In the case of a sequence of raised cosine pulses, these features no longer exist as the signals overlap.

How do timing recovery algorithms work in this case?

In general the ISI is never severe enough for the symbol timing recovery algorithm not to work, but it does degrade its achievable performance on the $$P_{be}$$ vs. $$\dfrac{E_b}{N_0}$$ curve. In other words, for the same error rate, you need better SNR to make up for the ISI.
• The timing error signal might temporarily leave that region due to noise or ISI, and that's why one filters the error signal. Chasing the unfiltered error signal sample by sample will lead to a very jittery symbol clock estimate and poor clock tracking stability; which is precisely why one doesn't use a PID filter with only a proportional term, for this task. The output of the integral branch of the filter provides an estimate of the average symbol clock period. An nonlinear implementation detail is that the integral branch is constrained to stay within$\pm x\%$ of the expected clock period – Andy Walls Nov 17 '18 at 17:38