Performance Analysis of Binary Orthogonal Signals with Correlation 2.11 2001/06/28 2005/09/20 11:47:31.968 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 orthogonal binary signal set by using a correlator-type receiver. Orthogonal signals with equally likely bits, r t s m t N t for 0 t T , m 1 , m 2 , and s 1 s 2 0 .

Correlation (correlator-type) receiver r t r r 1 r 2 s m η (see )

Decide s 1 t was transmitted if r 1 r 2 . P e m ̂ m b ̂ b P e 12 s 1 t  transmitted r R 2 12 s 2 t  transmitted r R 1 12 r 2 R 2 r 1 f r s 1 t r 12 r 2 R 1 r 1 f r s 2 t r 12 r 2 R 2 r 1 1 2 N 0 2 r 1 E s 2 N 0 1 N 0 r 2 2 N 0 12 r 2 R 1 r 1 1 2 N 0 2 r 1 2 N 0 1 N 0 r 2 E s 2 N 0 Alternatively, if s 1 t is transmitted we decide on the wrong signal if r 2 r 1 or η 2 η 1 E s or when η 2 η 1 E s . P e 12 η ′ E s 1 2 N 0 η ′ 2 2 N 0 12 s 2 t  transmitted r 1 r 2 Q E s N 0 Note that the distance between s 1 and s 2 is d 1 2 2 E s . The average bit error probability P e Q d 1 2 2 N 0 as we had for the antipodal case. Note also that the bit-error probability is the same as for the matched filter receiver.