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 N ≥ (K + 1)M - 1, i.e., user limited regime. On the other hand, for N <; (K + 1) 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 [1, (N - M + 1)/M], 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.