+ 1 $ bits, for the $M$-PSK case.'
author:
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title: 'An Adaptive Modulation Scheme for Two-user Fading MAC with Quantized Fade State Feedback'
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INTRODUCTION
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A multiple access channel (MAC) consists of multiple users transmitting independent information to a common destination. There is no cooperation among the users. The capacity region for a discrete memoryless MAC is well known [@Cover] [@Gallager]. For a two-user MAC with additive white Gaussian noise (AWGN) the capacity achieving input is the continuous Gaussian alphabet. The two-user Gaussian MAC with finite input constellations like $M$-QAM, $M$-PSK was studied in [@HarshanCR] [@HarshanCPA]. It was shown that relative rotation between input constellations [@HarshanCR], or a constellation power allocation scheme [@HarshanCPA] may be employed to maximize the constellation constrained (CC) capacity regions. Trellis based coding schemes were also suggested to achieve any rate pair within the CC capacity region.

In this paper, a two-user MAC with quasi-static fading is considered, as shown in Fig. \[fig:mac\]. The two users transmit information to a common destination. The random variables $h_1$ and $h_2$ are the channel gains for User-1 and User-2 respectively and $h_1$,$h_2$ $\sim \mathcal{CN}(0,1)$, where $ \mathcal{CN}(0,s) $ denotes the circular symmetric complex Gaussian random variable with 