On the Power Spectrum of a Biphase Modulated Signal in a Costas Demodulator

A study of the power spectrum of the phase/frequency error signal when a biphase modulated carrier signal imbedded in Additive White Gaussian Noise (AWGN) and shifted by an unknown frequency offset is received by a Costas' demodulator is presented. The Costast Loop is operated in one of two modes - the tracking mode or the acquisition mode. In the tracking mode we show that the spectrum of the error signal is quite similar to that of the unmodulated carrier case. In the acquisition mode it is shown that the error signal has significant power at twice the unknown frequency offset when Wideband Low Pass Filters (WBLPF) are used at the output of the phase detectors in the in-phase and quadrature phase arms.