On the Diversity-Multiplexing Tradeoff of Unconstrained Multiple-Access Channels

In this paper, the optimal diversity-multiplexing tradeoff (DMT) is investigated for the multiple-input multiple-output fading multiple-access channel with no power constraints (infinite constellations). For$K$ users ( $K>1$ ), $M$ transmit antennas for each user, and $N$ receive antennas, infinite constellations in general and lattices in particular are shown to attain the optimal DMT of finite constellations for $Nge (K+1) M-1$ , i.e., user limited regime. On the other hand, for $N< left ({K+1 }right )M-1$ , it is shown that infinite constellations cannot attain the optimal DMT.

This is in contrast to the point-to-point case in which the infinite constellations are DMT optimal for any $M$ and $N$ . In general, this paper shows that when the network is heavily loaded, i.e., $K>max left [{1,({N-M+1})/{M} }right ]$ , considering the shaping region in the decoding process plays a crucial role in pursuing the optimal DMT. By investigating the cases in which the infinite constellations are optimal and suboptimal, this paper also gives a geometrical interpretation to the DMT of infinite constellations in multiple-access channels.

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