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ECE 562
Fall 2011
August 30, 2011
Complex Baseband Representation
Channel Model for PointtoPoint Communications
Pointtopoint communications systems are well modeled using a bandpass additive noise channel
model of the form shown in Figure 1.
˜
s
(
t
)
˜
h
(
t
)
˜
y
(
t
)
n
(
t
)
˜
r
(
t
)
−
f
c
f
c
f

˜
S
(
f
)

Figure 1: Real bandpass channel model for pointtopoint communications
◦
The message bearing signal ˜
s
(
t
) is a realvalued bandpass signal whose spectrum is concentrated
in the vicinity of some carrier frequency
f
c
.
◦
Distortions introduced by the channel are characterized by a linear
time invariant
system with
impulse response
˜
h
(
t
), and frequency response
˜
H
(
f
) concentrated around
f
c
. The channel re
sponse
˜
h
(
t
) may or may not be known at the receiver. In the simplest case, the response
˜
h
(
t
)
corresponds to a an ideal bandpass ±lter with bandwidth corresponding to that of the signal ˜
s
(
t
).
◦
The additive noise process
n
(
t
) is usually idealized by
White Gaussian Noise
(WGN).
◦
The received signal ˜
r
(
t
) is a realvalued bandpass process as well.
In the following we convert the bandpass channel model into a more convenient and equivalent
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This document was uploaded on 02/08/2012.
 Fall '09

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