Performance Analysis of Binary Antipodal Signals with Matched Filters 2.11 2001/06/28 2005/09/20 11:32:46.378 GMT-5 Behnaam Aazhang aaz@ece.rice.edu Dinesh Rajan dinesh@ece.rice.edu Mohammad Jaber Borran mohammad@ece.rice.edu Roy Ha rha@rice.edu Shawn Stewart mrshawn@alumni.rice.edu Behnaam Aazhang aaz@ece.rice.edu analysis antipodal binary symbol bit-error bit-error probability correlator error matched filter orthogonal receiver signal Bit-error analysis for an antipodal signal set by using a matched filter receiver.

Matched Filter receiver Recall r t s m t N t where m 1 or m 2 and s 1 t s 2 t (see ).

Y 1 T E s ν 1 Y 2 T E s ν 2 since s 1 t s 2 t then ν 1 is 0 N 0 2 E s . Furthermore ν 2 ν 1 . Given ν 1 then ν 2 is deterministic and equals ν 1 . Then Y 2 T Y 1 T if s 1 t is transmitted. If s 2 T is transmitted Y 1 T E s ν 1 Y 2 T E s ν 2 ν 1 is 0 N 0 2 E s and ν 2 ν 1 . The receiver can be simplified to (see )

If s 1 t is transmitted Y 1 T E s ν 1 . If s 2 t is transmitted Y 1 T E s ν 1 . P e 12 s 1 t Y 1 T 0 12 s 2 t Y 1 T 0 12 y 0 1 2 N 0 2 E s y E s 2 N 0 E s 12 y 0 1 2 N 0 2 E s y E s 2 N 0 E s Q E s N 0 2 E s Q 2 E s N 0 This is the exact bit-error rate of a correlation receiver. For a bit-error analysis for orthogonal signals using a matched filter receiver, refer here.