A New Outer Bound and the Noisy-Interference Sum-Rate Capacity for Gaussian Interference Channels (0712.1987v2)

Abstract: A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this paper. Specifically, it is shown that if the channel coefficients and power constraints satisfy a simple condition then single-user detection at each receiver is sum-rate optimal, i.e., treating the interference as noise incurs no loss in performance. This is the first concrete (finite signal-to-noise ratio) capacity result for the Gaussian interference channel with weak to moderate interference. Furthermore, for certain mixed (weak and strong) interference scenarios, the new outer bounds give a corner point of the capacity region.

• The paper introduces a novel outer bound for Gaussian interference channels using a tailored genie-aided approach and extremal inequalities.
• It establishes that under noisy interference conditions, treating interference as noise attains the sum-rate capacity at finite SNRs.
• The study provides practical insights into decoding strategies and network design for improved interference management in wireless systems.

A New Outer Bound and the Noisy-Interference Sum-Rate Capacity for Gaussian Interference Channels

The paper "A New Outer Bound and the Noisy-Interference Sum-Rate Capacity for Gaussian Interference Channels" by Xiaohu Shang, Gerhard Kramer, and Biao Chen addresses the intricate problem of characterizing the capacity of Gaussian interference channels (IC). This channel model is vital for understanding multi-user communication systems, particularly when signals from different transmitters mutually interfere. The authors propose a novel outer bound on the capacity region of such channels and present specific conditions under which the sum-rate capacity is obtained.

Key Contributions

The main contribution of the paper is the derivation of a new outer bound for the capacity region of Gaussian ICs through an inventive use of the genie-aided approach combined with recent developments in extremal inequalities. This bounding technique enables the determination of the sum-rate capacity under certain scenarios, specifically when interference can be classified as "noisy." The notion of noisy interference is defined by a condition involving channel gains and power constraints, which indicates that treating interference as noise does not degrade performance. This result provides the first concrete capacity characterization for Gaussian ICs with weak to moderate interference at finite signal-to-noise ratios (SNRs).

Significant Results

1. New Outer Bound: The paper presents an outer bound for Gaussian ICs, which is tighter than existing results. This bound is achieved without requiring each receiver to decode messages intended for the other receiver, simplifying practical implementations.
2. Sum-Rate Capacity for Noisy Interference: For scenarios where the product of the channel gains and the sum of power constraints satisfy a simple inequality, the sum-rate capacity can be achieved by treating interference as noise. This formulation yields a clear, analytical expression for capacity, enhancing our understanding of interference management.
3. Capacity Region Corner Points: In mixed interference scenarios, where one link exhibits strong interference while the other remains weak, the new outer bounds help identify corner points of the capacity region. These points correspond to optimal communication strategies in realistic asymmetric network settings.

Implications

The theoretical implications of this work lie in the refined understanding of capacity regions for interference-limited communication systems. Practically, it simplifies the design of communication protocols by legitimizing simple decoding strategies in cases of noisy interference, thus reducing the complexity of receiver implementations in wireless networks.

The conditions under which the new bounds provide tight results also propose a framework for assessing interference levels in ICs. By categorizing interference regimes, network designers can tailor modulation and coding schemes to spectral conditions, leading to enhanced throughput and efficiency. Furthermore, the extension of these bounds could serve future research in extending multi-user communication models, including those involving parallel interference channels like those in OFDM systems.

Future Directions

This work opens several avenues for further research in multi-user communications. One possible extension includes applying similar bounding techniques to multiple antenna systems or MIMO ICs, potentially revealing new insights into spatial interference mitigation. Additionally, integrating these findings into the design of power control and spectrum sharing algorithms could support the optimization of next-generation wireless networks.

In conclusion, the paper stands as a substantial contribution to the field, offering insights that clarify the impact of interference and inform practical communication strategies for Gaussian ICs.