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 four symbols in both the constellations are equiprobable. Let $\frac{N_{0}}{2}$ 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?
- Probability of symbol error for Constellation $1$ is lower
- Probability of symbol error for Constellation $1$ is higher
- Probability of symbol error is equal for both the constellations
- The value of $N_{0}$ will determine which of the two constellations has a lower probability of symbol error