Lattice coding for MIMO systems in impulse noise

In this paper, we investigate signal space diversity (SSD) of lattice codes to mitigate the effect of impulse noise in wireless MIMO systems. A Middleton Class-A (MCA) model is one of the most accepted models for impulsive interference superimposed to additive white Gaussian noise (AWGN). To prove SSD for both Raleigh fading and impulse noise, we evaluate the pairwise-error probability (PEP) of optimum lattice decoding under perfect knowledge of noise states. However, due to the spatial coupling of impulse noise, the extension of the MCA model to MIMO systems leads to a correlated multivariate distribution. To maintain the full diversity advantages of lattice coding in MIMO systems, we investigate a diagonal design of lattice space-time (ST) coding for Rayleigh fading and correlated impulse noise. We also utilize a null space of the MIMO channel to extract noise states using a simple threshold detector. We show that the optimum lattice ST decoder can be realized by a noise-whitening transformation followed by a conventional sphere decoder. Finally, we evaluate the PEP of the optimum lattice ST decoding, which shows how impulse noise coupling limits the performance improvements of SSD with respect to the number of receive antennas.