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4.14 Performance analysis of orthogonal binary signals with matched

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Bit-error analysis for an orthogonal binary signal set by using a matched filter receiver.

r t Y Y 1 T Y 2 T

If s 1 t is transmitted

Y 1 T ∞ ∞ s 1 h 1 opt T 1 T ∞ ∞ s 1 s 1 1 T E s 1 T
Y 2 T ∞ ∞ s 1 s 2 2 T 2 T

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

H0

Y E s 0 1 2

H1

Y 0 E s 1 2
where 1 and 2 are independent are Gaussian with zero mean and variance N 0 2 E s . The analysis is identical to the correlator example .
P e Q E s N 0
Note that the maximum likelihood detector decides based oncomparing Y 1 and Y 2 . If Y 1 Y 2 then s 1 was sent; otherwise s 2 was transmitted. For a similar analysis for binary antipodal signals, refer here . See or .

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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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