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4.13 Performance analysis of binary antipodal signals with matched

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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 1
Y 2 T E s 2
since s 1 t s 2 t then 1 is 0 N 0 2 E s . Furthermore 2 1 . Given 1 then 2 is deterministic and equals 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 1
Y 2 T E s 2
1 is 0 N 0 2 E s and 2 1 .

The receiver can be simplified to (see )

If s 1 t is transmitted Y 1 T E s 1 .

If s 2 t is transmitted Y 1 T E s 1 .

P e 1 2 s 1 t Y 1 T 0 1 2 s 2 t Y 1 T 0 1 2 y ∞ 0 1 2 N 0 2 E s y E s 2 N 0 E s 1 2 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 matchedfilter receiver, refer here .
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Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
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