Layered Interference Alignment: Achieving the Total DoF of MIMO X Channels

Abstract

The $K\times 2$ and $2\times K$, Multiple-Input Multiple-Output (MIMO) X channel with constant channel coefficients available at all transmitters and receivers is considered. A new alignment scheme, named \emph{layered interference alignment}, is proposed in which both vector and real interference alignment are exploited, in conjunction with joint processing at receiver sides. Data streams with fractional multiplexing gains are sent in the desired directions to align the interfering signals at receivers. To decode the intended messages at receivers, a joint processing/simultaneous decoding technique, which exploits the availability of several receive antennas, is proposed. This analysis is subsequently backed up by metrical results for systems of linear forms. In particular, for such linear forms, Khintchine--Groshev type theorems are proved over real and complex numbers. It is observed that $K\times 2$ and $2\times K$, X channels with $M$ antennas at all transmitters/receivers enjoy duality in Degrees of Freedom (DoF). It is shown that incorporating the layered interference alignment is essential to characterize the total DoF of $\frac{2KM}{K+1}$ in the $K\times 2$ and $2\times K$, $M$ antenna X channels.

26 pages, 4 figures. Preliminary version. Any comments and suggestions for improvement are most welcome

References in corpus (3)

• Interference Alignment and the Degrees of Freedom for the K User Interference Channel
• Ubiquity and a general logarithm law for geodesics
• On the Degrees-of-Freedom of the K-User Gaussian Interference Channel

Cited by in corpus (1)

• Systems of small linear forms and Diophantine approximation on manifolds