[Paper Review] Interference Alignment with Incomplete CSIT Sharing

Paul de Kerret, David Gesbert|arXiv (Cornell University)|Nov 22, 2012

Advanced MIMO Systems Optimization4 citations

TL;DR

This paper investigates interference alignment (IA) feasibility in K-user MIMO interference channels with incomplete channel state information at transmitters (CSIT), where each transmitter knows only a subset of the global channel matrix. It proposes a CSIT allocation policy that preserves IA feasibility even in tightly-feasible antenna configurations with minimal CSIT, and develops a heuristic algorithm for super-feasible settings to reduce feedback overhead while maintaining degrees of freedom gain.

ABSTRACT

In this work, we study the impact of having only incomplete channel state information at the transmitters (CSIT) over the feasibility of interference alignment (IA) in a K-user MIMO interference channel (IC). Incompleteness of CSIT refers to the perfect knowledge at each transmitter (TX) of only a sub-matrix of the global channel matrix, where the sub-matrix is specific to each TX. This paper investigates the notion of IA feasibility for CSIT configurations being as incomplete as possible, as this leads to feedback overhead reductions in practice. We distinguish between antenna configurations where (i) removing a single antenna makes IA unfeasible, referred to as tightly-feasible settings, and (ii) cases where extra antennas are available, referred to as super-feasible settings. We show conditions for which IA is feasible in strictly incomplete CSIT scenarios, even in tightly-feasible settings. For such cases, we provide a CSIT allocation policy preserving IA feasibility while reducing significantly the amount of CSIT required. For super-feasible settings, we develop a heuristic CSIT allocation algorithm which exploits the additional antennas to further reduce the size of the CSIT allocation. As a byproduct of our approach, a simple and intuitive algorithm for testing feasibility of single stream IA is provided.

Motivation & Objective

• To analyze the feasibility of interference alignment (IA) when transmitters have only partial knowledge of the global channel state information (CSIT), specifically sub-matrices of the channel matrix.
• To identify conditions under which IA remains feasible even with strictly incomplete CSIT, particularly in tightly-feasible antenna configurations where removing one antenna breaks feasibility.
• To develop a CSIT allocation policy that minimizes feedback overhead while preserving IA feasibility in such incomplete CSIT scenarios.
• To extend the approach to super-feasible settings—where extra antennas are available—by designing a heuristic CSIT allocation algorithm to further reduce required CSIT.
• To provide a simple, intuitive feasibility test for single-stream IA based on the proposed framework.

Proposed method

• Introduces a novel CSIT framework where each transmitter receives only a subset of the global channel coefficients, specific to its own role in the interference network.
• Classifies antenna configurations into tightly-feasible (removal of one antenna breaks IA feasibility) and super-feasible (extra antennas available) settings.
• Uses algebraic geometry and variable/equation counting (via N_var and N_eq) to derive necessary and sufficient conditions for IA feasibility under incomplete CSIT.
• Proposes a CSIT allocation policy that ensures beamformer coherency across transmitters by allowing each transmitter to reconstruct the required interference alignment beamformers from its partial CSIT.
• Applies a sub-IC decomposition approach: fixes beamformers in a tightly-feasible sub-IC and proves that IA feasibility is preserved in the full network.
• Develops a heuristic CSIT allocation algorithm for super-feasible settings that leverages redundant antennas to minimize the size of the required CSIT.

Experimental results

Research questions

• RQ1 Under what conditions is interference alignment still feasible when transmitters have only partial knowledge of the global channel matrix?
• RQ2 Can IA feasibility be preserved in tightly-feasible antenna configurations with minimal CSIT sharing?
• RQ3 How can CSIT be allocated across transmitters to minimize feedback overhead while maintaining IA feasibility?
• RQ4 What is the impact of extra antennas (super-feasible settings) on reducing the required CSIT size for IA?
• RQ5 Can a simple and intuitive feasibility test for single-stream IA be derived from the proposed CSIT allocation framework?

Key findings

• IA remains feasible even in tightly-feasible settings when CSIT is incomplete, provided that each transmitter is allocated a sub-matrix of the global channel matrix that enables coherent beamformer design.
• A CSIT allocation policy is proposed that preserves IA feasibility while significantly reducing feedback overhead, particularly in tightly-feasible configurations.
• For super-feasible settings, a heuristic CSIT allocation algorithm is developed that exploits redundant antennas to further reduce the size of the required CSIT.
• The proposed framework enables a simple and intuitive feasibility test for single-stream IA by analyzing sub-ICs and beamformer coherency across transmitters.
• Theoretical analysis confirms that fixing beamformers in a tightly-feasible sub-IC does not compromise IA feasibility in the full interference channel.
• The results demonstrate that full CSIT is not necessary for IA feasibility, and that minimal, strategically allocated CSIT can maintain optimal degrees of freedom in MIMO interference channels.