Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge

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

Nematic cells with defect-patterned alignment layers

Using Monte Carlo simulations of the Lebwohl--Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. We find that the nematic order depends crucially on the ratio of the height of the cell $H$ to $a$. When $H/a \gtrsim 0.9$ the system is very well--ordered and the frustration induced by the lattice of defects is relieved by a network of half--integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When $H/a \lesssim 0.9$ the system is disordered and the half--integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures and study the switching behavior in the presence of an electric field

Cellular Interference Alignment

Interference alignment promises that, in Gaussian interference channels, each link can support half of a degree of freedom (DoF) per pair of transmit-receive antennas. However, in general, this result requires to precode the data bearing signals over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels, in the case of time-frequency invariant channels. In this work we consider a wireless cellular system scenario where the promised optimal DoFs are achieved with linear precoding in one-shot (i.e., over a single time-frequency slot). We focus on the uplink of a symmetric cellular system, where each cell is split into three sectors with orthogonal intra-sector multiple access. In our model, interference is "local", i.e., it is due to transmitters in neighboring cells only. We consider a message-passing backhaul network architecture, in which nearby sectors can exchange already decoded messages and propose an alignment solution that can achieve the optimal DoFs. To avoid signaling schemes relying on the strength of interference, we further introduce the notion of \emph{topologically robust} schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Towards this end, we design an alignment scheme which is topologically robust and still achieves the same optimum DoFs

Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling

In this work, we prove that a positive secure degree of freedom is achievable for a large class of Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wire-tap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.Comment: 6 pages, Submitted to IEEE Globecom, March 200