Massive MIMO has Unlimited Capacity (1705.00538v4)

Abstract: The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

• The paper demonstrates that Massive MIMO systems can overcome pilot contamination, enabling capacity to grow unbounded with an increasing number of antennas.
• The study employs rigorous mathematical analysis and realistic spatially correlated channel models to prove the asymptotic capacity gains.
• Numerical simulations confirm that even simplified covariance estimation techniques yield substantial improvements in spectral efficiency.

Massive MIMO Has Unlimited Capacity

The paper "Massive MIMO Has Unlimited Capacity" by Emil Bjornson, Jakob Hoydis, and Luca Sanguinetti rigorously addresses the longstanding assumption that pilot contamination imposes a fundamental limitation on the capacity of Massive MIMO (Multiple-Input Multiple-Output) systems. It challenges the conventionally held belief that pilot contamination creates a finite capacity limit as the number of base station antennas, $M$, tends to infinity.

Key Contributions

The paper's primary contribution is the demonstration that, under more sophisticated channel models and improved signal processing techniques, the capacity of Massive MIMO systems can indeed grow without bound as $M$ increases. This conclusion holds even in the presence of pilot contamination, provided certain conditions on the channel covariance matrices are met.

Main Results

1. Asymptotic Capacity: The authors prove that the capacity of Massive MIMO systems is not inherently limited by pilot contamination. This result is contingent upon the assumption that the channel covariance matrices of the UEs (user equipments), which share a pilot, are asymptotically linearly independent. This condition implies that minor modifications to conventional models result in substantial capacity enhancements.
2. Technical Approach: The work employs rigorous mathematical analysis to derive these results, focusing on precise modeling of spatial correlation and incorporating sophisticated signal processing techniques such as multicell MMSE (Minimum Mean Squared Error) combining and precoding.
3. Channel Models: The paper stresses the unrealistic nature of i.i.d. Rayleigh fading channel models used in prior studies. Instead, it incorporates spatially correlated channel responses, often observed in practical environments, to establish the potential for unlimited capacity.
4. Numerical Simulations: The theoretical findings are complemented by numerical simulations demonstrating unbounded capacity growth even with elementary empirical covariance estimation techniques that only utilize the diagonal elements of the covariance matrices.

Implications

1. Practical Insights: The paper fundamentally shifts the paradigm in Massive MIMO research, indicating that unlimited capacity is achievable without complex multicell cooperation or restrictive assumptions on channel orthogonality. This finding opens up new avenues in network architecture design, as system engineers can leverage these results to improve spectral efficiency under realistic conditions.
2. Theoretical Developments: On a theoretical front, the paper invigorates research into advanced signal processing techniques like MMSE which can effectively manage interference even in heavily contaminated spectrum environments. The role of linearly independent covariance matrices suggests areas for further exploration regarding robust modeling of channel conditions based on real-world data.
3. Future Work: Future investigations could focus on refining covariance estimation methods to further reduce complexity while maintaining performance benefits. Exploration into other facets of system design, such as energy efficiency and hardware impairments, under the new capacity paradigms might yield additional insights.
4. Generalization: While the primary results focus on asymptotic behavior, this research also provides insights relevant to finite $M$. It suggests that network designs should not impose static pilot sharing or reuse strategies that are overly conservative about pilot contamination.

Conclusion

This paper represents a significant advance in the understanding of Massive MIMO systems, challenging the constraints posed by pilot contamination and opening the door to unlimited capacity growth with increasing antennas. By leveraging well-founded mathematical reasoning and realistic modeling assumptions, it provides both a theoretical and practical framework for the future evolution of cellular networks, particularly in high-density environments. These insights reinforce the potential for Massive MIMO to serve as a cornerstone technology in next-generation wireless systems.