Optimality of Orthogonal Access for One-dimensional Convex Cellular Networks

It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all one-dimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the network topology. In general, optimality of orthogonal access holds neither for two-dimensional convex cellular networks nor for one-dimensional non-convex cellular networks, thus revealing a fundamental limitation that exists only when both one-dimensional and convex properties are simultaneously enforced, as is common in canonical information theoretic models for studying cellular networks. The result also establishes the capacity of the corresponding class of index coding problems

Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity

We explore degrees of freedom (DoF) characterizations of partially connected wireless networks, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements --- aligned frequency reuse, wireless index coding and interference diversity --- through a series of examples, focusing first on infinite regular arrays, then on finite clusters with arbitrary connectivity and message sets, and finally on heterogeneous settings with asymmetric multiple antenna configurations. Aligned frequency reuse refers to the optimality of orthogonal resource allocations in many cases, but according to unconventional reuse patterns that are guided by interference alignment principles. Wireless index coding highlights both the intimate connection between the index coding problem and cellular blind interference alignment, as well as the added complexity inherent to wireless settings. Interference diversity refers to the observation that in a wireless network each receiver experiences a different set of interferers, and depending on the actions of its own set of interferers, the interference-free signal space at each receiver fluctuates differently from other receivers, creating opportunities for robust applications of blind interference alignment principles