notes11 - ECE 562 Fall 2010 Differential Phase Modulation...

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Unformatted text preview: ECE 562 Fall 2010 Differential Phase Modulation and Detection Consider MPSK signaling on an ideal AWGN channel with phase offset ( t ) that may change with time. Over N symbol intervals r ( t ) = N X n =1 E e j n g ( t- ( n- 1) T s ) e j ( t ) + w ( t ) . Suppose ( t ) changes slowly with time so that we can assume that it is constant over two consec- utive symbol intervals. For standard MPSK n = m n = 2 ( m n- 1) M , m n { 1 , 2 ,...,M } . We know that this scheme performs poorly if we cannot estimate at the receiver. But if ( t ) changes slowly, a differential modulation approach can be taken where the sequence { n } is generated from { m n } as n- n- 1 = m n = 2 ( m n- 1) M (with = 0) . Sufficient statistics for demodulation over the N-symbol interval are given by R n = h r ( t ) ,g ( t- ( n- 1) T s ) i , n = 1 , 2 ,...,N....
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notes11 - ECE 562 Fall 2010 Differential Phase Modulation...

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