Matched filtering of a phase encoded Sweep-Spread Carrier signal: evaluation of the methodical error

Implementation of the Sweep-Spread Carrier (S2C) signal in underwater telemetry provides an opportunity to get rid of the use of equalising filters in the S2C-receiver for elimination of signal distortions. Matched filter is considered to be the simplest and simultaneously the most effective solution for recovery of receiving S2C signals. However, for matched filtering of S2C signals, there is no theory that provide an evaluation of errors, which appear on filter output. The phase (the information parameter) is very sensitive to estimation errors. Thus, before implementation of matched filters, an accurate mathematical justification of the filtering must be carried out. In contrast to frequency-constant carrier, an antiderivative of the frequency-modulated oscillation cannot be described via elementary functions and, correspondingly, an integral of such oscillation function cannot be found in analytical way. In result, the calculation of such an important filter characteristic as the methodical error cannot be carried out analytically. Numerical integration is considered to be useful for evaluation of the error in a particular case only. An accurate error evaluation in general form is possible only if appropriate mathematical expressions are developed. The paper introduces a derivation of mathematical formulas allowing the accurate estimation of a maximum value for the methodical error during matched filtering of a phase manipulated sweep-spread carrier signal.