Lattice-reduction-aided preequalization over algebraic signal constellations

Lattice-reduction-aided (LRA) equalization techniques have become very popular in multiple-input/multiple-output (MIMO) multiuser communication as they obtain the full diversity order of the MIMO channel. For joint transmitter-side LRA preequalization or precoding on the broadcast channel, the signal constellation is required to be periodically extendable, which is typically achieved by employing square QAM constellations. However, recent enhancements of the LRA philosophy- named integer-forcing equalization-additionally demand the data symbols to be representable as elements of a finite field over the grid the signal points are drawn from. This significantly constraints the choice of the constellation, especially when considering the complex baseband and complex-valued constellations. To overcome the lack of flexibility, in this paper, we present constellations with algebraic properties for use in LRA preequalization directly enabling the desired finite-field property. In particular, fields of Gaussian primes (integer lattice) and Eisenstein primes (hexagonal lattice) are studied and compared to conventional constellations. The respective transmitter- and receiver-side operations are detailed and the adaptation of the channel matrix factorization is proposed. Numerical simulations cover the performance of such schemes.