notes13 - ECE 562 Fall 2010 Signaling on Bandlimited...

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Unformatted text preview: ECE 562 Fall 2010 Signaling on Bandlimited Channels We restrict our attention to linear modulation schemes. The information bearing signal s ( t ) is given by s ( t ) = X n =0 s m n g ( t- nT ) with T = T s , the symbol period, and g being a unit energy pulse shaping signal. The signal s ( t ) is passed through the channel, modeled as a linear time-invariant system with (baseband) bandwidth W and impulse response h ( t ) and additive WGN w ( t ). The received signal is given by r ( t ) = X n =0 s m n b ( t- nT ) + w ( t ) where b ( t ) = g ? h ( t ). Now the signal space at the receiver S = span { b ( t- nT ) ,n = 0 , 1 ,... } and while g is usually chosen so that g ( t- nT ) g ( t- `T ) for ` 6 = n , b does not necessarily inherit this property (unless the channel is ideal). Nevertheless, we can obtain sufficient statistics for detecting the symbols by projecting r ( t ) on to b ( t- nT ), n = 0 , 1 ,... to get h r ( t ) ,b ( t- nT ) i = Z - r ( t ) b * ( t- nT ) dt = r ? g R ( nT ) if...
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notes13 - ECE 562 Fall 2010 Signaling on Bandlimited...

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