7.2 Performance Characteristics of Digital Receivers
281
Fig. 7.9 Plot of the BER
(P e ) versus the factor Q
where the dashed line
represents the approximation
from Eq. (7.13)
Q =
b on
2σ on
=
1
2
S N R
which is one-half the signal-to-noise ratio. In this case, υ th = b on /2, so that the
optimum decision threshold is midway between the 0 and 1 signal levels.
Example 7.5 If the bit error rate is 10
−9 then from Eq. (7.13)
P e (Q) = 10
−9
=
1
2
1 − erf
Q
√
2
281
Fig. 7.9 Plot of the BER
(P e ) versus the factor Q
where the dashed line
represents the approximation
from Eq. (7.13)
Q =
b on
2σ on
=
1
2
S N R
which is one-half the signal-to-noise ratio. In this case, υ th = b on /2, so that the
optimum decision threshold is midway between the 0 and 1 signal levels.
Example 7.5 If the bit error rate is 10
−9 then from Eq. (7.13)
P e (Q) = 10
−9
=
1
2
1 − erf
Q
√
2