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.
The ratio of the average energy of Constellation $1$ to the average energy of Constellation $2$ is
- $4 a^{2}$
- $4$
- $2$
- $8$