Question

The constellation diagram of two 8-ary signalling schemes are shown in the figure. If all the symbols in the constellation are equiprobable and the average energy of constellation 1 and constellation 2 is equal then the relation between 'R' and 'd' is :

• A. R = 1.73 d
• B. R = d
• C. R = 1.22 d
• D. R = 1.5d

Answer 1

The correct option is C R = 1.22 d

Average energy of constellation 1,

$E_1={\sum }_{t=1}^g{E}_{St}{P}_i$

$=R^2$

Average energy of constellation 2,

$E_2={\sum }_{t=1}^g{E}_{st}{P}_i$



$E_2=d^2\left(\frac{1}{8}\right)\times 4+2d^2\left(\frac{1}{8}\right)\times 4$

$E_2=\frac{3d^2}{2}$

Since $E_1=E_2\Rightarrow R^2=\frac{3d^2}{2}$

$\Rightarrow R=1.22d$