A demodulation system for demodulating an input signal is provided. The input signal includes a carrier wave modulated with data symbols selected from a plurality of candidate complex symbol values. The system includes a carrier recovery module, operative to compensate for a carrier frequency of the carrier wave and output a demodulated data signal. The carrier recovery module includes: a first complex-signal conversion module, operative to convert the input signal into a complex-valued input signal; a voltage-controlled oscillator; a mixer, for mixing the complex-valued input signal and a complex-valued output signal of the voltage-controlled oscillator, and generating a mixer output signal; a low-pass filter, coupled to the mixer, operative to filter the carrier frequency from the mixer output signal, and output a signal corresponding to the demodulated data signal; and a folding module, operative to apply a folding algorithm to the output signal of the low-pass filter.