6.8 TIMING ERROR EFFECTS IN PULSED OPTICAL SYSTEMS
Pulsed communications are designed to use highly peaked, narrow width, laser pulses to carry data, but require accurate pulse or slot integrations for ideal decoding. These integrations must be clocked by auxiliary timing circuits that provide the start and stop markers for the integrators, so that the integration variables are produced only over the exact slot times. In deriving the expressions for the PE for these systems, we have been assuming perfect timing. In reality, if the timing is not accurate, the integrations occur over offset intervals, leading to false integation values that can degrade the decoding performance. In this section, we attempt to assess the timing error effects on the pulsed systems previously described.
Consider first the OOK system, in which we redraw the receiver decoder block diagram as in Figure 6.22, showing the timing subcircuit. This timing subsystem must provide the clocking for the bit integrations by continually monitoring the photodetector outputs. It operates in parallel with the decoder and must continually correct for any bit time shifting or drifting that may occur during transmission. Methods for achieving this timing are considered in Section 6.9.
Assume a timing error of Δ exists, so that the decoder bit integration interval is displaced from the true bit interval, as shown in Figure 6.23. If a signaling pulse arrives (a “1” bit was sent in that bit time) the offset decoder will integrate ...