and \eqref{Lemma1_2}, and using the fact that $\gamma \geq 1$, we have} \\
\nonumber
 d_{min}^2(\gamma ,\theta) \leq \min \lbrace d_{min}^2(\mathcal{S}),\gamma ^2 d_{min}^2(\mathcal{S})\rbrace =d_{min}^2(\mathcal{S}). \end{aligned}$$ ]{}

In the following lemma, it is proved that in order to study the distance profile in $ \mathcal{S}_{\text{eff}} $ it is sufficient to consider $\theta \in \left[ 0,\pi /M\right] $ when both users use $M$-PSK signal sets. Distance profiles for other values of $\theta$ can be obtained from $\theta \in [0, \pi/M] $. We use the term wedge $[\theta_1, \theta _2]$ to denote the region $\gamma \geq 1$ and $\theta \in [\theta_1, \theta_2]$ on the $ (\Gamma , \Theta) $ plane. The lines $ \theta= \theta_1 $ and $ \theta= \theta _2 $ for $ \gamma \geq 1 $ and the arc $ \gamma=1 $ for $ \theta \in [\theta _1, \theta _2] $ form the boundary of the wedge $ [\theta _1 , \theta _2] $.

\[lemmaangle\] To study the distance profile in $ \mathcal{S}_{\text{eff}} $ when both the users use $M$-PSK constellations, it is sufficient to consider the case $ 0 \leq \theta \leq \pi /M $. All other cases can be obtained from this.

The proof is in two steps. First we 