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# notes5 - ECE 562 Fall 2011 September 7 2011 Digital...

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ECE 562 Fall 2011 September 7, 2011 Digital Modulation After possible source and error control encoding, we have a sequence { m n } of message symbols to be transmitted on the channel. The message symbols are assumed to come from a finite alphabet, say { 0 , 1 , . . . , M 1 } . In the simplest case of binary signaling, M = 2. Each symbol in the sequence is assigned to one of M waveforms { s 0 ( t ) , . . . , s M - 1 ( t ) } . Memoryless modulation versus modulation with memory. If the symbol to waveform mapping is fixed from one interval to the next, i.e., m mapsto→ s m ( t ), then the modulation is memoryless. If the mapping from symbol to waveform in the n -th symbol interval depends on previously transmitted symbols (or waveforms) then the modulation is said to have memory. For memoryless modulation, to send the sequence { m n } of symbols at the rate of 1 /T s symbols per second, we transmit the signal s ( t ) = summationdisplay n s m n ( t nT s ) . (1) Linear versus nonlinear modulation. A digital modulation scheme is said to be linear if we can write the mapping from the sequence of symbols { m n } to the transmitted signal s ( t ) as concatenation of a mapping from the sequence { m n } to a complex sequence { c n } , followed by a linear

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