Fundamental Limits of Infinite Constellations in MIMO Fading Channels

The fundamental and natural connection between the infinite constellation (IC) dimension and the best diversity order it can achieve is investigated in this paper. In the first part of this paper, we develop an upper bound on the diversity order of ICs for any dimension and any number of transmit and receive antennas. By choosing the right dimensions, we prove in the second part of this paper that ICs in general and lattices in particular can achieve the optimal diversity-multiplexing tradeoff of finite constellations. This paper gives a framework for designing lattices for multiple-antenna channels using lattice decoding.