Unique-Word Detection in TDMA: Acquisition and Retention

Establishing frame and burst synchronism in TDMA requires detection of a known, approximately periodic signal corrupted by noise. This paper presents a Markovian modeling approach to analyzing the performance of a sync detector that repeatedly compares the output of an
n
-bit binary correlator to an acceptance/rejection threshold. The detector is defined to be in one of two modes of operation: INITIAL ACQUISITION, during which it seeks to identify the start of a frame; and RETENTION, in which periodic detection of the frame (and burst) is essential for TDMA operations. During acquisition, the
n
-bit sync word is assumed embedded in random data, and bit errors are assumed uncorrelated. The acquisition models permit ready computation of acquisition-time statistics and the probability of false acquisition. The retention models identify paths by which synchronism can be lost, their probability of occurrence, and a resulting mean time to loss of synchronism. Unlike the acquisition models, account is taken of the deterministic data pattern immediately preceding the sync word, and sources of timing error that alter the sync word's ideally periodic arrival. The models presented in this paper allow the detector's key performance indexes to be assessed as a function of its external environment: bit-error rate, timing uncertainty, and data pattern preceding the sync word; and internal parameters: sync word pattern, correlation detection threshold, detection aperture widths, number of consecutive detections before acquisition can be declared, and the number of tolerable consecutive sync word misses before synchronism is declared lost.