The fade states which leads to violation of this minimum distance guarantee have been identified. Adaptation involves rotation of the constellation of one user relative to the other, without any change in transmit power, in order to effectively avoid these bad channel conditions. (Section \[sec:adapt\])

-   The procedure to obtain the optimal angles for rotation is stated for the $M$-PSK case. The optimal rotation angles are calculated in closed form for the QPSK and 8-PSK case. (Section \[sec:optimal\])

-   An upper bound on $\delta$, *i.e.*, the maximum value of the minimum distance in the effective constellation that can be guaranteed, is derived. (Section \[sec:upper\])

-   Simulation results are presented to show the extent to which the proposed strategy outperforms the conventional transmission scheme without adaptation. (Section \[sec:results\])

CHANNEL QUANTIZATION FOR $ M $-PSK SIGNAL SETS
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In this section we obtain a quantization of the $ (\Gamma, \Theta) $ plane into finite number of regions at the destination.

Distance Distribution in the effective constellation {#sec:quandist}
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Without loss of generality we assume that the average power constraint of each user is $ P=1 $. It is known that the error performance for an AWGN channel is determined by the Euclidean 