5. Assume that the signals in the following two-dimensional signal con- stellations are equally probable. Find the new signal coordinates in each case so that the average energy is minimized. Plot the signal constellations before and after energy minimization. (a) S₁ = (b) $₁ = $1 (c) $₁ = S1 = (3,1), S₂ (0.2), s₂ = (-1,3), s3 = (–4, −4), s4 = (−2,−4) (3,3), s₂ = (1, −2), s3 = (−1,1), s4 = (−3,2) = (2, 2), s3 = (−2, –4)

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5. Assume that the signals in the following two-dimensional signal con-
stellations are equally probable. Find the new signal coordinates in
each case so that the average energy is minimized. Plot the signal
constellations before and after energy minimization.
(a) $₁
=
=
(b) $1
(c) $₁ =
S1
(3,1), S₂
(0.2), s₂ = (−1,3), s3 = (–4, −4), s4 = (-2,-4)
(3, 3), S₂ = (1, -2), s3 = (−1, 1), S4 = (-3,2)
=
(2, 2), S3
: (-2,-4)
=
Transcribed Image Text:5. Assume that the signals in the following two-dimensional signal con- stellations are equally probable. Find the new signal coordinates in each case so that the average energy is minimized. Plot the signal constellations before and after energy minimization. (a) $₁ = = (b) $1 (c) $₁ = S1 (3,1), S₂ (0.2), s₂ = (−1,3), s3 = (–4, −4), s4 = (-2,-4) (3, 3), S₂ = (1, -2), s3 = (−1, 1), S4 = (-3,2) = (2, 2), S3 : (-2,-4) =
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