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Common data for Questions 74 and 75: Two 4-ary signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the symbols in both constellations are equiprobable. Let $N_0/2$ denote the power spectral density of white Gaussian noise. The ratio of the average energy of Constellation 1 to the average energy of Constellation 2 is

1. 4a²
2. 4
3. 2
4. 8

Correct answer: 4

Solution

With an orthonormal basis, symbol energy is the sum of squares of its coordinates. From the given constellation geometry, the average energy of Constellation 1 is four times that of Constellation 2. Hence the required ratio is 4.

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