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Digital transmission over baseband channels

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Until this point, we have considered data transmissions over simple additive Gaussian channels that are not time or bandlimited. In this module we will consider channels that do have bandwidth constraints, and are limited to frequency range aroundzero (DC). The channel is best modified as g t is the impulse response of the baseband channel.

Consider modulated signals x t s m t for 0 t T for some m 1 2 M . The channel output is then

r t ∞ ∞ x g t N t ∞ ∞ S m g t N t

The signal contribution in the frequency domain is

f S m f S m f G f

The optimum matched filter should match to the filtered signal:

f H m opt f S m f G f 2 f t
This filter is indeed optimum ( i.e. , it maximizes signal-to-noise ratio); however, it requires knowledge of the channel impulse response.The signal energy is changed to
E s f ∞ ∞ S m f 2
The band limited nature of the channel and the stream of time limited modulated signal create aliasing which is referred to as intersymbol interference . We will investigate ISI for a general PAM signaling.
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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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