Performance Analysis of Antipodal Binary signals with Correlation 2.11 2001/06/27 2005/09/20 11:22:28.166 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 correlator-type receiver.

The bit-error probability for a correlation receiver with an antipodal signal set () can be found as follows: P e m ̂ m b ̂ b π 0 m 1 r 1 γ π 1 m 2 r 1 γ π 0 r γ f r 1 s 1 t r π 1 r γ f r 1 s 2 t r if π 0 π 1 12 , then the optimum threshold is γ 0 . f | r 1 s 1 t r E s N 0 2 f | r 1 s 2 t r E s N 0 2 If the two symbols are equally likely to be transmitted then π 0 π 1 12 and if the threshold is set to zero, then P e 12 r 0 1 2 π N 0 2 r E s 2 N 0 12 r 0 1 2 π N 0 2 r E s 2 N 0 P e 12 r ′ 2 E s N 0 1 2 π r ′ 2 2 12 r ″ 2 E s N 0 1 2 π r ″ 2 2 with r ′ r E s N 0 2 and r ″ r E s N 0 2 P e 1 2 Q 2 E s N 0 1 2 Q 2 E s N 0 Q 2 E s N 0 where Q b x b 1 2 π x 2 2 . Note that

P e Q d 1 2 2 N 0 where d 1 2 2 E s s 1 s 2 2 is the Euclidean distance between the two constellation points (). This is exactly the same bit-error probability as for the matched filter case. A similar bit-error analysis for matched filters can be found here. For the bit-error analysis for correlation receivers with an orthogonal signal set, refer here.