A theoretical limit for the ML performance of MIMO systems based on lattices

We employ the theory of multidimensional lattice constellations in order to evaluate the maximum-likelihood (ML) performance of a general multiple-input multiple-output MIMO system. We show that the lattice representation of the equivalent system model enables a mapping of the received signal set to a single point in a multidimensional constellation, with the generator matrix being equal to the equivalent channel matrix. With the aid of this geometrical interpretation, we derive a performance limit for a general MIMO system in terms of the symbol error probability, which can be written in closed form for various designs. Application of the proposed analysis to popular MIMO schemes reveals the tractability of the approach and validates that designs exploiting the available degrees of freedom in a better way approach the proposed performance limit.