In phase shift keying (PSK), the phase of a carrier is changed according to the modulating waveform which is a digital signal. InBPSK, the transmitted signal is a sinusoid of fixed amplitude. It has one fixed phase when the data is at one level and when thedata is at the other level, phase is different by 180 degree. A Binary Phase Shift Keying(BPSK) signal can be defined as
where b(t) = +1 or -1, fc is the carrier frequency, and T is the bit duration. The signal has a power , so that , where A represents the peak value of sinusoidal carrier.
Thus the above equation can be written as
= , where E=PT is the energy contained in the bit duration.
Figure1. shows the BPSK signal for bit sequence 1001,
The received signal has the form = , where is the phase shift introduced by the channel. The signal b(t) is recovered in the demodulator. If synchronous demodulation is used, the waveform is required at the demodulator. Carrier recovery scheme in the demodulator is shown in Fig 2.
Figure2: BPSK modulator and demodulator
The recovered carrier is multiplied with the received signal to generate
Assuming that integral number of carrier cycles is present in bit duration voltage and the bit synchronizer in Fig 2 knows the end of a bit interval and beginning of the next, the output voltage at the output of the integrate and dump circuit is:
If the channel is noisy, some of the demodulated bits will be in error.