Homomorphic cyclostationary morphology matching for short-observation underwater acoustic pseudonoise-code period estimation

The short-observation condition in noncooperative underwater acoustic direct-sequence spread spectrum signals analysis makes conventional pseudonoise (PN)-code period estimation face problems such as degraded noise robustness and insufficient suppression of information-symbol-induced multiplicative interference (IMI). In this paper, a homomorphic cyclostationary morphology matching method is proposed to address these issues. Unlike conventional methods, the proposed method does not rely on spectral-line extraction and spacing estimation supported by long observations, but estimates the PN-code period by applying morphology matching to the homomorphically filtered received-signal autocorrelation. The received-signal autocorrelation is transformed into the homomorphic domain to convert the IMI into an additive structure. Candidate-period time synchronous averaging is then applied to average delay-domain values separated by each candidate period, enhancing the cyclostationary PN-code component and suppressing noise and IMI with less reliance on the number of available information symbols. A homomorphic cyclostationary morphology matching degree is further defined to quantify the morphology matching result, and the PN-code period is estimated by selecting the candidate period that maximizes this degree. Numerical simulations and experimental data demonstrate that the proposed method outperforms conventional methods under short-observation and low-signal-to-noise-ratio conditions.