Transient probability response of cycle slip occurrence in the PSK-TDMA carrier recovery

The class of carrier recovery which is often employed in PSK-TDMA systems is 'frequency multiplier/narrow-band filter/frequency divider'. Cycle slips occur when a signal extracted from the narrow-band filter is embedded in some noise. In the PSK-TDMA systems, a transmitted signal S is of the burst form while received noise N is in the steady state. A preceding burst signal I is often allocated immediately before the burst signal S. In this paper, the transient occurrence probability of the cycle slips is analytically derived, assuming that the products of the multiplier, which are a burst signal (S x S) and a preceding burst signal (I x I) as well as a steady-state noise (N x N), a burst noise (S x N) and a preceding burst noise (I x N), are coexistent at the narrow-band filter output. Also, the transient cycle slip occurrence probability is numerically calculated using the results of the analysis.