Estimation of phase error limits for PSK-modulated sweep-spread carrier signal

Sweep-spread carrier (S2C) communication method that has been recently developed especially for application in shallow water channels realizes frequency spread of a transmitted signal via its multiplication with a sequence of linear sweeps. This provides significant processing improvement on receiving side enabling clear separation of multipath arrivals by converting their time delays into their frequency reallocations. To provide a most effective and inexpensive filtering, a matched filter is considered to be a core part of the S2C demodulator, which uses a synchronous replica of the sweep-spread carrier signal as the reference signal for the matched filtering. However, if a frequency modulated carrier is applied for data transmission, the mechanism of evaluation of the information parameter (phase) have no strict mathematical justification. By use of frequency modulated carrier the output of matched filter contains the desired phase value, however, the methodical error of evaluation of filter output (its real and imaginary part) is unknown value, which cannot be found via estimation of define integral of correspondent oscillation function. The paper derives expression, which allows to evaluate the methodical error in analytical way in form of integrals of elementary oscillation functions.