Data Communication, Lecture91 PAM and QAM

Data Communication, Lecture92 Homework 1: exercises 1, 2, 3, 4, 9 from chapter1 deadline: 85/2/19

Data Communication, Lecture93

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Data Communication, Lecture911

Data Communication, Lecture912

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Data Communication, Lecture915

Data Communication, Lecture916 Constellation Performance Measures

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Data Communication, Lecture918 coding gain (or loss ), of a particular constellation with data symbols { x i }, i=0,...,M−1 with respect to another constellation with data symbols {~ x i } is defined as where both constellations are used to transmit ¯b bits of information per dimension.

Data Communication, Lecture919

Data Communication, Lecture920 The Filtered (One-Shot) AWGN Channel

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Data Communication, Lecture922 Note that: The set of N functions {Φ n (t)} n=1,...,N is not necessarily orthonormal. For the channel to convey any and all constellations of M messages for the signal set {x i (t)}, the basis set {Φ n (t)} must be linearly independent.

Data Communication, Lecture923

Data Communication, Lecture924

Data Communication, Lecture925 Additive Self-Correlated Noise

Data Communication, Lecture926 In practice, additive noise is often Gaussian, but its power spectral density is not flat. Engineers often call this type of noise “self- correlated” or “colored”.

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Data Communication, Lecture929 Example: QPSK with correlated Noise One can compute that:

Data Communication, Lecture930

Data Communication, Lecture931

Data Communication, Lecture932 Thus, the optimum detector for this channel with self-correlated Gaussian noise has larger minimum distance than for the white noise case, illustrating the important fact that having correlated noise is sometimes advantageous.