Multiple choice

Two 4-ray signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $\dfrac{N_0}{2}$ denote the power spectral density of white Gaussian noise.

If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?

  1. Probability of symbol error for constellation 1 is lower.

  2. Probability of symbol error for constellation 1 is higher.

  3. Probability of symbol error is equal for both the constellations.

  4. The value of 0 N will determine which of the two constellations has a lower probability of symbol error.
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A Correct answer
Explanation

Noise power is same for both which is $\dfrac{N_0}{2}$

Thus probability of error will be lower for the constellation 1 as it has higher signal energy.

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