To implement coherent detection, a local oscillator (LO) that is exactly synchronized to the carrier must be provided at the receiver. A BPSK signal is a double sideband suppressed carrier (DSBSC) type of signal e(t) = p(t) cosω0t, and therefore, the carrier is not directly available in the BPSK signal. The carrier can be recovered using a squaring loop, as shown in Fig. Consider first the situation where the input is a BPSK signal. The frequency multiplier is a nonlinear circuit, which squares the signal.
Squaring e(t) results in
with p(t)= ±1, the square is just 1. The bandpass filter following the frequency multiplier is tuned to the carrier second harmonic, which provides one of the inputs to the phase detector of the phase-locked loop. The voltage-controlled oscillator (VCO) in the phase-locked loop (PLL) operates at the carrier frequency. The second frequency multiplier provides the second harmonic of this as the other input to the phase detector. The phase difference between these two inputs generates a bias voltage that brings the frequency of the VCO into synchronism with the carrier frequency as derived from the BPSK signal.