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Digital Transmission over Baseband Channels

Module by: Behnaam Aazhang. E-mail the author

Summary: I have no idea whatsoever.

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

Consider modulated signals x t = s m ⁢t x t s m t for 0≤t≤T 0 t T for some m∈12…M m 1 2 … M . The channel output is then

r t =∫−∞∞ x τ ⁢g⁢t−τdτ+ N t =∫−∞∞ S m ⁢τ⁢g⁢t−τdτ+ N t r t τ x τ g t τ N t τ S m τ g t τ N t
(1)

The signal contribution in the frequency domain is

∀f: S m ˜ ⁢f= S m ⁢f⁢G⁢f f S m ˜ f S m f G f
(2)

The optimum matched filter should match to the filtered signal:

∀f: H m opt ⁢f= S m ⁢f¯⁢G⁢f¯⁢e(−i)⁢2⁢π⁢f⁢t f H m opt f S m f G f 2 f t
(3)
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 ˜ =∫−∞∞| S m ˜ ⁢f|2df E s ˜ f S m ˜ f 2
(4)
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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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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