Solve the following problem:
Consider the four-phase and eight-phase signal constellations shown in Figure .
Determine the radii r1 and r2 of the circles such that the distance between two adjacent points in the two constellations is d. From this result, determine the additional transmitted energy required in the 8-PSK signal to achieve the same error probability as the four-phase signal at high SNR, where the probability of error is determined by errors in selecting adjacent points.
