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Bandwidth efficiency in m - ary psk

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In M-ary psk
Rb=Rs*log M log with base 2
Rb- bit rate
Rs - symbol rate
then bandwidth required for passband signal is B=Rs
and bandwidth effeciency = Rb/B=log M log with base 2.
Is the above formula for bandwidth efficiency correct ?
But in simon haykin it is given that bandwidth efficiency is (log M )/2 log with base 2
 

Hi erece,

occuped bandwidth depends of the spectral shaping of the transmission.
Minimum bandwidth is B=Rs, so maximum spectral efficiency is log2(M).
Usually, bandwidth is wider, for example using raised cosine shaping B=Rs*(1+alpha).
Sometimes, unshaped transmission (rectangular pulses in time domain) assumes a required bandwidth B=2*Rs; in that case result is log2(M)/2.
regards

Z
 

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