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A very simple LMS-based adaptive notch filter implemented in FPGAs can be used for carrier recovery of a QPSK signal and for direct detection of a BPSK signal. The key aspect of our paper lies in the alternative approach in the realization of carrier frequency detection or synchronization circuit. The carrier frequency after detection is used in the conventional QPSK detector. Also the demodulator has a simple hardware realization that does not require a reference signal.