\theta'}\vert ^2.\end{aligned}$$ From , these $ L $ class distance functions differ only in the constant coefficient $ \vert s_{2,i}-s'_{2,i}\vert ^2  $. From Definition \[def:distclass\], all these coefficients are different. Let $$\begin{aligned}
\nonumber
l'= \text{arg} \, \min_{1\leq i \leq L} \vert s_{2,i}-s'_{2,i}\vert ^2.\end{aligned}$$ Now, from , $ d_{\mathcal{C}_{l'}}(\gamma, \theta) $ is minimum among all $ d_{\mathcal{C}_i}(\gamma, \theta) $ for all values of $ (\gamma , \theta) \neq (\gamma' , \theta')$.

\[rd\] The region corresponding to distance class $ \mathcal{C} $, $ \mathcal{R}(\mathcal{C}) $ denotes the region in the complex plane $ \lbrace (\Gamma, \Theta)/ \mathcal{H} \rbrace $ for which the class distance function $ d_{\mathcal{C}}(\gamma, \theta) $ gives the minimum distance in $ \mathcal{S}_{\text{eff}}$, *i.e.*, $$\begin{aligned}
\nonumber
\mathcal{R}(\mathcal{C}) = \lbrace &(\gamma ,\theta ) \in \lbrace (\Gamma , \Theta) / \mathcal{H} \rbrace \vert \\
\nonumber
&d_{\mathcal{C}}(\gamma ,\theta) \leq d_{\mathcal{C'}}(\gamma , \theta)\: \text{for all}\: \mathcal{C'} \neq \mathcal{C} \in \bar{\mathcal{C}} \rbrace .\end{aligned}$$

When both the users use $ M $-PSK constellations at the input, $ \mathcal{R}_W (\mathcal{C}) $ denotes the portion of the region $ \mathcal{R}(\mathcal{C}) $ lying in the wedge $ [0, \pi/M] $, *i.e.*, $$\begin{aligned}
\nonumber
\mathcal{R}_W(\mathcal{C}) = \mathcal{R}(\mathcal{C}) \cap \, \text{wedge}\, [0, \pi/M].\end{aligned}$$

Note that, when both the users use 