The effects of multipath delay spread on timing recovery

Equations for the recovered timing for a squaring timing recovery circuit under multipath radio propagation are derived. Both coherent and differential detections are studied. If delay spread is much smaller than the symbol duration, the recovered timing can be approximated by the centroid of the power delay profile, p(t). Two cases of timing loop bandwidth are considered. If the fading frequency is much lower than the bandwidth of the timing loop, the instantaneous sample of p(t) is used to generate the timing clock. If the fading frequency is much higher than the loop bandwidth, the ensemble average of p(t) over fading samples is used to recover the timing. A computer simulation is performed for a system operating in a frequency-selective, slowly fading environment. It is found that for root mean square (rms) delay spread less than or equal to 0.1 of the symbol duration, a squaring timing loop with either narrow or wide bandwidth can properly determine the timing detection. The main mechanism of the "irreducible bit error rate" in this case is the closure of the eye-pattern instead of timing error.