On Non-Integer Linear Degrees of Freedom of Constant Two-Cell MIMO Cellular Networks

The study of degrees of freedom (DoF) of multiuser channels has led to the development of important interference managing schemes, such as interference alignment (IA) and interference neutralization. However, while the integer DoF have been widely studied in literatures, non-integer DoF are much less addressed, especially for channels with less variety. In this paper, we study the non-integer DoF of the time-invariant multiple-input multiple-output (MIMO) interfering multiple access channel (IMAC) in the simple setting of two cells, $K$ users per cell, and $M$ antennas at all nodes. We provide the exact characterization of the maximum achievable sum DoF under the constraint of using linear interference alignment (IA) scheme with symbol extension. Our results indicate that the integer sum DoF characterization $2MK/(K+1)$ achieved by the Suh-Ho-Tse scheme can be extended to the non-integer case only when $K \leq M^2$ for the circularly-symmetric-signaling systems and $K \leq 2M^2$ for the asymmetric-complex-signaling systems. These results are further extended to the time-invariant parallel MIMO IMAC with independent subchannels.