network coding in [@Akino], which was subsequently derived analytically in [@Vijay]. This quantized knowledge of the fade state is made available to the users to adapt their modulation scheme via rotation of constellations to compensate for the possibly bad channel conditions. MAC with limited channel state information at transmitter (CSIT) has been studied from an information theoretic point of view in [@Reza],[@Cemal]. In [@Wiese], it was shown that for a two-user discrete memoryless MAC with additional common message, finer CSIT results in increasing the capacity region. To the best of our knowledge, explicit modulation schemes with finite constellations and quantized fade state feedback has not been reported before.

The contributions and organization of this paper are as follows:

-   A quantization of the $ (\Gamma , \Theta) $ plane is derived, for the case when both users use $M$-PSK constellations at the input. We illustrate the quantization procedure by taking examples of the QPSK and 8-PSK case. (Section \[sec:chan\_quan\])

-   A modulation scheme is proposed for the users, which adapts according to the quantized feedback about the fade state that they receive from the destination, in order to satisfy a certain minimum distance guarantee $\delta$ in $\mathcal{S}_{\text{eff}}$ given in . 