Figure 1.4: An additive white Gaussian noise (AWGN) channel.
Observe that for any channel with input X(t) and output Y (t), the noise could be defined to
be Z(t)= Y (t) − X(t). Thus there must be something more to an additive-noise channel model
than what is expressed in Figure 1.4. The additional required ingredient for noise to be called
additive is that its probabilistic characterization does not depend on the input.
In a somewhat more general model, called a linear Gaussian channel, the input waveform X(t)
is first filtered in a linear filter with impulse response h(t), and then independent white Gaussian
noise Z(t) is added, as shown in Figure 1.5, so that the channel output is
Y (t)= X(t) ∗ h(t)+ Z(t),
where “∗” denotes convolution. Note that Y at time t is a function of X over a range of times