Optimality of Orthogonal Access for One-dimensional Convex Cellular Networks

TL;DR

This paper proves that a simple orthogonal access scheme is optimal for maximizing sum degrees of freedom in one-dimensional convex cellular networks without channel state information at transmitters, but not in higher dimensions or non-convex cases.

Contribution

It establishes the optimality of greedy orthogonal access in one-dimensional convex cellular networks under topology-only knowledge, revealing a fundamental limitation in more complex scenarios.

Findings

Orthogonal access achieves sum degrees of freedom in 1D convex networks.

Optimality does not extend to 2D or non-convex networks.

Results establish capacity for related index coding problems.

Abstract

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.