**Introduction**

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,

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where and

_{ }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

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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:

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If the channel is noisy, some of the demodulated bits will be in error.