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Luigi Paura » 4.Digital Trasmission


Digital Trasmission over AWGN channel

Summary

  • Introduction
  • Geometric representation of M energy signals
  • Review of the digital memoryless modulation techniques

Geometric representation of signal waveforms

The Gram-Schmidt procedure allows us to represent a set of M signal waveforms of duration T with a set of N < M functions Ψk(t) of a basis with duration T (k=1,..,N)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)


Geometric representation of signal waveforms (next)

The r. v. ni e nk are uncorrelated and, since Gaussian are also statistically independent.
Given an arbitrary complete basis the componentsof a white signal are uncorrelated.
If the signal is Gaussian the components will be also indipendent.


Geometric representation of PAM signal waveforms

Since all the signals sm(t) are represented by a single basis function (namely, Ψ(t)), the PAM signalling is monodimensional (N=1).


Geometric representation of PAM signal waveforms (next)


Geometric representation of MPSK signal waveforms


Geometric representation of MPSK signal waveforms (next)


Geometric representation of MPSK signal waveforms (next)

The MPSK signalling can be obtained with two modulators PAM with carriers in quadrature.

The components must verify the requirement over the energy ⇒ They are not independent.


Geometric representation of MPSK signal waveforms (next)


QAM constellation


QAM constellation (next)


Orthogonal Signals


FSK Orthogonal Signals


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