Fundamental Limits of Noncoherent Massive Random Access Networks

2025-09-25

AI Summary

This paper investigates the capacity limits of non-coherent massive random-access cellular networks, modeled as MIMO fading channels with infinitely many interfering cells, where users access randomly and only statistical channel knowledge is available at both transmitters and receivers. Adopting random coding and bursty signal design while treating interference as noise, we derive tight upper and lower bounds on the symmetric sum-rate capacity. Our key contribution is revealing that the decay rate of interference fading coefficients fundamentally governs capacity scaling: when the decay is no faster than exponential, capacity saturates with transmit power; when faster than double-exponential, capacity grows unbounded—challenging the classical “interference-limited” paradigm. These results demonstrate that, even without access coordination, certain channel attenuation characteristics enable infinite capacity, providing a theoretical foundation for ultra-massive low-Earth-orbit satellite networks and massive IoT deployments.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Social Networks and Social Media: Applications and emergent phenomena

Abstract

This paper studies the capacity of massive random-access cellular networks, modeled as a MIMO fading channel with an infinite number of interfering cells. To characterize the symmetric sum rate of the network, a random-coding argument is invoked together with the assumption that in all cells users draw their codebooks according to the same distribution. This can be viewed as a generalization of the assumption of Gaussian codebooks, often encountered in the literature. The network is further assumed to be noncoherent: the transmitters and receivers are cognizant of the statistics of the fading coefficients, but are ignorant of their realizations. Finally, it is assumed that the users access the network at random. For the considered channel model, rigorous bounds on the capacity are derived. The behavior of these bounds depends critically on the path loss from signals transmitted in interfering cells to the intended cell. In particular, if the fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly, then the capacity is bounded in the transmit power. This confirms that the saturation regime in interference-limited networks -- observed by Lozano, Heath, and Andrews ("Fundamental limits of cooperation", IEEE Trans. Inf. Theory, Sept. 2013) -- cannot be avoided by random user activity or by using channel inputs beyond the scale family. In contrast, if the fading coefficients decay faster than double-exponentially, then the capacity is unbounded in the transmit power. Proving an unbounded capacity is nontrivial even if the number of interfering cells is finite, since the condition that the users' codebooks follow the same distribution prevents interference-avoiding strategies such as time- or frequency-division multiple access. We obtain this result by using bursty signaling together with treating interference as noise.

Problem

• Characterizing capacity limits of massive random-access MIMO networks
• Analyzing symmetric sum rate under noncoherent fading conditions
• Determining capacity bounds dependence on interfering signal path loss

Innovation

• Noncoherent MIMO channel with infinite interfering cells
• Random coding with identical codebook distribution assumption
• Bursty signaling and treating interference as noise