Cube lattice decoder

An insight to the ℓ₁ lattice decoder for flat-fading multiple antenna wireless communications systems is presented in this paper. In particular, we show that by formulating the problem as a bounded error subset selection, the equivalent decoder finds the nearest lattice point to the received signal in the ℓ₁ sense. The search for the nearest lattice point is bounded inside a hypercube centered at the received vector; where the dimensions and orientation of the hypercube depends on the channel conditions. The search for the nearest codeword to the received vector is achieved by modeling the problem as a Mixed Integer Linear Program. The proposed decoder achieves near-optimum performance while its complexity is invariant with the operating signal to noise ratio.