  In this paper, we consider a robust lattice alignment design for K-user
quasi-static MIMO interference channels with imperfect channel knowledge. With
random Gaussian inputs, the conventional interference alignment (IA) method has
the feasibility problem when the channel is quasi-static. On the other hand,
structured lattices can create structured interference as opposed to the random
interference caused by random Gaussian symbols. The structured interference
space can be exploited to transmit the desired signals over the gaps. However,
the existing alignment methods on the lattice codes for quasi-static channels
either require infinite SNR or symmetric interference channel coefficients.
Furthermore, perfect channel state information (CSI) is required for these
alignment methods, which is difficult to achieve in practice. In this paper, we
propose a robust lattice alignment method for quasi-static MIMO interference
channels with imperfect CSI at all SNR regimes, and a two-stage decoding
algorithm to decode the desired signal from the structured interference space.
We derive the achievable data rate based on the proposed robust lattice
alignment method, where the design of the precoders, decorrelators, scaling
coefficients and interference quantization coefficients is jointly formulated
as a mixed integer and continuous optimization problem. The effect of imperfect
CSI is also accommodated in the optimization formulation, and hence the derived
solution is robust to imperfect CSI. We also design a low complex iterative
optimization algorithm for our robust lattice alignment method by using the
existing iterative IA algorithm that was designed for the conventional IA
method. Numerical results verify the advantages of the proposed robust lattice
alignment method.
