The objective of this research is to develop time-varying signal processing methods for rapidly varying non-stationary signals based on time-varying autoregressive (TVAR) modeling, and to apply such methods to frequency-modulated (FM) interference rejection in direct-sequence spread spectrum (DSSS) communications.

For fast varying non-stationary signal processing, such as the task to reject an FM interference that could chirp over the entire DSSS bandwidth in a symbol interval, an explicit description of the variation is necessary to form a time-varying filter. This is realized using the TVAR model, which is an autoregressive model whose coefficients are time-varying with the variation modeled as a linear combination of a set of known functions of time. In DSSS communications, when the strength of an interference - which could be a hostile jammer or overlaid communication signal - possibly exceeds the inherent spread spectrum processing gain, interference rejection is necessary to secure a usable bit-error-rate.

The contributions of this research include: a) revealed the advantageous performance of TVAR model based instantaneous frequency estimation (TVAR-IF), which is expected to change the prevailing opinion that regards TVAR-IF as a poor estimator; b) proposed a time-varying Prony method to improve TVAR-IF at low SNR; c) proposed to use TVAR-IF for time-varying FIR notch filter based FM jammer suppression in DSSS communications; d) developed TVAR model based time-varying optimum filters, including the TVAR based Kalman filter (TVAR-KF) and the TVAR based Wiener filter (TVAR-WF); e) developed a TVAR-WF based formulation of FM interference soft-cancellation in DSSS communications; and f) proposed a TVAR based linear prediction error (TVAR-LPE) filter for soft-cancellation of FM interference in DSSS communications.

For the interference rejection problem, our TVAR-IF controlled notch filter yields high processing gain close to that using the known IF and much higher than that using the WVD based IF estimate. Furthermore, unlike the IF based notch filter approaches, the proposed soft-cancellation methods utilize the full spectral information captured by the TVAR model. Our soft-cancellation approaches, including TVAR-WF and TVAR-LPE, maintain at least the DSSS system performance expected when no filtering is used, even under estimated conditions. The latter is in contrast to the notch filter based approaches, which may cause deterioration of overall system performance at low jammer-to-signal ratios.