[Paper Review] On Interference Alignment and the Deterministic Capacity for Cellular Channels with Weak Symmetric Cross Links

J. Buehler, Gerhard Wunder|arXiv (Cornell University)|Apr 1, 2011

Cooperative Communication and Network Coding7 references4 citations

TL;DR

This paper characterizes the capacity region of a two-cell cellular uplink with weak symmetric cross-links using a linear deterministic model. It proposes an interference alignment scheme that exploits channel gain differences between users in the same cell to align interference at the unintended receiver, achieving optimal sum rates by aligning interference in unused signal dimensions.

ABSTRACT

In this paper, we study the uplink of a cellular system using the linear deterministic approximation model, where there are two users transmitting to a receiver, mutually interfering with a third transmitter communicating with a second receiver. We give an achievable coding scheme and prove its optimality, i.e. characterize the capacity region. This scheme is a form of interference alignment which exploits the channel gain difference of the two-user cell.

Motivation & Objective

• To analyze the uplink capacity of a cellular system with two users in one cell and one in another, under weak symmetric cross-link interference.
• To develop an optimal transmission scheme that achieves the capacity region using interference alignment principles.
• To establish a theoretical foundation for interference management in cellular networks via deterministic channel modeling.
• To provide a rigorous outer bound that matches the achievable rate region, proving optimality of the proposed scheme.

Proposed method

• Models the cellular uplink using a linear deterministic channel where signal levels correspond to bit positions in binary vectors.
• Uses shift matrices to represent path loss and signal superposition via modulo-2 addition.
• Designs a coding scheme where transmitters in cell 1 align their interference at base station 2 by matching signal dimensions to unused parts of the intended signal.
• Applies interference alignment by aligning the interference from two users in cell 1 onto the lower bits of the signal space at base station 2.
• Derives an outer bound using Fano’s inequality and entropy inequalities, leveraging partial signal decomposition into upper and lower bit components.
• Proves optimality by showing the outer bound region coincides exactly with the achievable rate region.

Experimental results

Research questions

• RQ1 What is the capacity region of a two-cell cellular uplink with weak symmetric cross-links under a linear deterministic model?
• RQ2 How can interference from two co-channel users in one cell be aligned to minimize impact on a second base station?
• RQ3 Can interference alignment in a cellular setup outperform conventional interference avoidance in weak interference regimes?
• RQ4 Is the proposed coding scheme optimal, and can its optimality be proven via a matching outer bound?

Key findings

• The capacity region is fully characterized and proven to be optimal via a matching outer bound.
• The optimal scheme uses interference alignment by aligning the interference from two users in cell 1 onto the unused lower bits of the signal space at base station 2.
• The sum rate is maximized when interference is aligned in the part of the signal space not used by the intended transmitter in cell 2.
• The key insight is that the gain difference between the two users in cell 1 enables effective interference alignment even under weak symmetric cross-links.
• The outer bound derivation uses partial signal decomposition into upper and lower bit components, with entropy bounds applied to each.
• The result holds under the weak interference condition where the sum of interference gains is less than or equal to the smallest direct link gain.