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Performance of Communication Systems Corrupted by Noise Chap. 7
Substituting Eq. (7–86) for g s (t) + g n (t) gives
KR T (t) = K ƒ [A c + A c m(t) + x n (t)] + j[y n (t)] ƒ
(7–91)
The power is
[KR T (t)] 2 = K 2 A 2 c ec1 + m(t) + x 2
n(t)
d + c y 2
n(t)
d f
A c A c
(7–92)
For the case of large (SN) in , (y n >A c ) 2 1, so we have
[K R T (t)] 2 = (KA c ) 2 + K 2 A c 2 m 2 + K 2 x n
2
(7–93)
where (KA c ) 2 is the power of the AGC term, K 2 A 2 c m 2 is the power of the detected modulation
(signal), and K 2 2
x n is the power of the detected noise. Thus, for large ( S>N) in ,
a S N b out
= A c 2 m 2
x n
2
= A c 2 m 2
2N 0 B
(7–94)
Comparing this with Eq. (7–87), we see that for large (SN) in , the performance of the envelope
detector is identical to that of the product detector.
For small (SN) in , the performance of the envelope detector is much inferior to that of
the product detector. Referring to Eq. (7–91), we note that the detector output is
KR T (t) = K ƒ g T (t) ƒ = K ƒ A c [1 + m(t)] + R n (t)e ju n(t) ƒ
For (SN) in 6 1, as seen from Fig. 7–20, the magnitude of g T (t) can be approximated by
KR T (t) L K{A c [1 + m(t)] cos u n (t) + R n (t)}
(7–95)
Thus, for the case of a Gaussian noise channel, the output of the envelope detector consists of
Rayleigh distributed noise R n (t), plus a signal term that is multiplied by a random noise factor
cos u n (t). This multiplicative effect corrupts the signal to a much larger extent than the additive
Imaginary
g s (t)=A c [1+m(t)]
R T
R n
g T (t)
g T (t)=R n (t)e j¨(t)
R T
¨n (t)
Real
Figure 7–20 Vector diagram for AM, (S>N) in 1.