$ M $-PSK constellations at the input, for some $ \mathcal{C} \in \bar{\mathcal{C}} $ the corresponding region $ \mathcal{R}(\mathcal{C}) $ can be a null set, because the associated class distance function $ d_{\mathcal{C}}(\gamma, \theta) $ does not give the minimum distance in $ \mathcal{S}_{\text{eff}} $ for any value of $ (\gamma, \theta) $ in $ \lbrace (\Gamma, \Theta) \setminus \mathcal{H} \rbrace $. There is always a distance class $\mathcal{C} \in \bar{\mathcal{C}} $ for which the associated class distance function is $ d_{\mathcal{C}(\gamma, \theta)} = d_{min}(\mathcal{S}) $. We denote this particular distance class as $ \mathcal{C}_{d_{min}(\mathcal{S})} $. From Lemma \[lem:uppermin\], the value of this class distance function is the upper bound for the minimum distance in $ \mathcal{S}_{\text{eff}} $. For example when both users use QPSK signal sets at the input, then from Table \[tab:qpskex\], $ \mathcal{C}_{d_{min}(\mathcal{S})} = \mathcal{C}_1 $ and the associated class distance function is $ d_{\mathcal{C}_1}(\gamma, \theta)= d_{min}(\mathcal{S})= \sqrt{2} $.

The procedure to obtain the quantization of the $(\Gamma,\Theta)$ plane, when both users use $M$-PSK constellations at the input, is as follows:

1.  Obtain the $N_W$ singular fade states in $ \mathcal{H}_W $ *i.e.*, lying in the wedge $[0, \pi /M]$. Each of these singular fade state is 