distance distribution of the input constellation. In our case, the distance distribution of $ \mathcal{S}_{\text{sum}} $ decides the error performance at the destination. For any value of $  (\gamma,\theta) $, $d^{'2}_{(s_1,s_2)_{\text{sum}}\leftrightarrow (s'_1, s'_2)_{\text{sum}}}$ denotes the distance between the two points $(s_1,s_2)_{\text{sum}}$ and $(s'_1,s'_2)_{\text{sum}}$, where $ (s_1,s_2)_{\text{sum}} $, $(s'_1,s'_2)_{\text{sum}}$ $\in \mathcal{S}_{\text{sum}}$ refer to the points $ \sqrt{P}h_1(s_1+\gamma e^{j \theta} s_2) $ and $\sqrt{P}h_1(s'_1+\gamma e^{j \theta} s'_2)$ respectively with $ s_1,s_2,s'_1,s'_2 \in \mathcal{S} $. It is given by $$\begin{aligned}
\nonumber
d ^{'2}_{(s_1,s_2)_{\text{sum}}\leftrightarrow (s'_1, s'_2)_{\text{sum}}} &= P \vert h_1\vert ^2\vert(s_1-s'_1 )+ \gamma e^{j\theta } (s_2-s'_2) \vert ^2 \\
\label{eqn:sumdistance}
&= P \vert h_1 \vert ^2 d^2_{(s_1,s_2)\leftrightarrow (s'_1, s'_2)},\end{aligned}$$ where , $d^2_{(s_1,s_2)\leftrightarrow (s'_1, s'_2)}$ denotes the distance between the points $(s_1,s_2)$ and $(s'_1,s'_2)$, where $ (s_1,s_2), (s'_1,s'_2) $ refers to the points $ s_1+\gamma e^{j \theta} s_2 $ and $s'_1+\gamma e^{j \theta} s'_2$ in $ \mathcal{S}_{\text{eff}}  $. Since $ P \vert h_1 \vert ^2  $ simply scales the distances in $ \mathcal{S}_{\text{eff}} $ we can focus only on $$\begin{aligned}
\label{eqn:dist}
d^2_{(s_1,s_2)\leftrightarrow (s'_1, s'_2)}= \vert(s_1-s'_1 )+ \gamma e^{j\theta } (s_2-s'_2) \vert ^2\end{aligned}$$ as the quantity of interest.

It is clear from that for certain values of $ (\gamma, \theta) $ the distance between points $(s_1,s_2)$ 