the point $ e^{j\frac{(m-1)2 \pi}{M}} + \gamma e^{j \theta}  e^{j\frac{(n-1)2 \pi}{M}} $ in $ \mathcal{S}_{\text{eff}} $. For each distance class $ \mathcal{C} $, among all the pairs $ (i,j) \in \mathcal{C} $ choose the one with the minimum value of $ i+j $ to be the representative in $ \mathcal{C} $. If more than one pair has the same value of $ i+j $ choose the one with the lowest value of $ i $ as the class representative. When the users $ M $-PSK signal set at input, there are $ \frac{M^2(M^2-1)}{2} $ pairwise distances in $ \mathcal{S}_{\text{eff}} $. These pairwise distances are thus partitioned into distance classes.

Fig. \[fig:qpskeff\], shows $ \mathcal{S}_{\text{eff}} $ when both users use QPSK constellations for $(\gamma, \theta)=(2,14^\circ)$. There are 120 pairwise distances and 20 distance classes. These are listed in Table \[tab:qpskex\], along with the corresponding class distance functions, and the class representatives.

   $ k $   $ \mathcal{C}_k $                                                 $ d_{\mathcal{C}_k}(\gamma, \theta) $                                Class representative
  -------- ----------------------------------------------------------------- -------------------------------------------------------------------- ----------------------
   $ 1 $   $(1,2),(1,4),(2,3),(3,4),(5,6),(6,7),(7,8),(5,8),$                $ \sqrt{2} $                                                         $ (1,2) $
           $(9,10),(10,11),(11,12),(9,12),(13,14),(14,15),(15,16),(13,16)$                                                                        
   $ 2 $   $(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16)$          $ 2 $                                                                $(1,3)$
   $ 3 $   $(1,6),(1,16),(2,15),(4,7),(6,11),(5,12),(11,16),(10,13)$         $ 2 \gamma ^2 +2+ 4 \gamma \cos \theta $                             $ 