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What is probability of error and Bandwidth requirement for BPSK?
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Error probability:

  • We know that BPSK signal is represented as follows:

Binary 1:x1(t)=2PscosωC t$

Binary 0: x2(t)=2PscosωCt

Therefore x2(t)=x1(t)

  • By using the matched filter for detection of BPSK signal.The expression for error probability of an optimum filter is,

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  • The expression for the signal to noise ration of matched filter is given by,

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  • Using the Rayleigh’s energy theorem,

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  • The limits of integration of the last term in equation (3) are 0 to T because x (t) is present only over one bit interval T. Substituting equation (3) into equation (2) we get,

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  • But x (t)=x1(t)x2(t)

and for BPSK x2(t)=x1(t)

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  • Substituting this value of x (t) into equation (4) we get,

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  • Substitute this into equation (5) to get

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  • The value of second term in the RHS in equation (6) is zero

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Bandwidth of BPSK:

  • From the frequency spectrum of BPSK signal ,it is clear that the bandwidth of a BPSK signal is given by,

BW= Highest frequency – Lowest frequency in main lobe =(fc+fb)(fcfb)

∴ BW=2 fb

Where fb=1/Tb

  • Thus the minimum bandwidth of BPSK signal is equal to twice the highest frequency contained in the baseband signal.
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