Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO with Stochastic Geometry

Abstract: Cell-Free (CF) Massive MIMO is an alternative topology for future wireless networks, where a large number of single-antenna access points (APs) are distributed over the coverage area. There are no cells but all users are jointly served by the APs using network MIMO methods. Prior works have claimed that CF Massive MIMO inherits the basic properties of cellular Massive MIMO, namely channel hardening and favorable propagation. In this paper, we evaluate if one can rely on these properties when having a realistic stochastic AP deployment. Our results show that channel hardening only appears in special cases, for example, when the pathloss exponent is small. However, by using 5--10 antennas per AP, instead of one, we can substantially improve the hardening. Only spatially well-separated users will exhibit favorable propagation, but when adding more antennas and/or reducing the pathloss exponent, it becomes more likely for favorable propagation to occur. The conclusion is that we cannot rely on channel hardening and favorable propagation when analyzing and designing CF Massive MIMO networks, but we need to use achievable rate expressions and resource allocation schemes that work well also in the absence of these properties. Some options are reviewed in this paper.

• The paper reveals that channel hardening is not inherent in cell-free massive MIMO and requires multiple antennas per AP (5–10) for significant presence.
• Favorable propagation, which minimizes inter-user interference, is limited in cell-free systems and requires users to be spatially well-separated.
• Achieving efficient cell-free massive MIMO performance requires optimizing antennas per AP and considering deployment strategies that account for stochastic channel behavior.

An Analytical Examination of Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO

The paper "Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO with Stochastic Geometry" by Zheng Chen and Emil Björnson investigates the extent to which channel hardening and favorable propagation, two pivotal properties inherent to conventional massive MIMO, are applicable to cell-free massive MIMO networks. Unlike traditional structured cellular networks, cell-free massive MIMO systems employ a vast array of single-antenna access points (APs) distributed over a geographical area without defined cell boundaries. This distributed nature is what prompts the necessity to rigorously evaluate channel behavior using stochastic geometry.

Key Findings

1. Deficiency in Channel Hardening: The study reveals that channel hardening, wherein the multi-antenna fading channels are transformed into deterministic scalar channels, is not inherently present in cell-free massive MIMO. Through comprehensive analytical modeling using a Poisson Point Process to represent stochastic AP distribution, they conclude that cell-free networks inherently lack the predictability in channel behavior seen in traditional massive MIMO settings. It was observed that significant channel hardening can be achieved only by increasing the number of antennas per AP (5–10 antennas), as merely increasing the number of APs does not suffice.
2. Limited Favorable Propagation: Favorable propagation, characterized by orthogonal channel vectors that minimize inter-user interference, does not naturally manifest in cell-free systems without conditions being met. The work highlights that spatially well-separated users are crucial for favorable propagation to be observed, underscoring the importance of geographic dispersion among users.

Implications

The implications of these findings have both theoretical and practical bearings. Theoretically, the results argue against depending on classic Massive MIMO models as the baseline for cell-free designs, necessitating new theoretical frameworks for understanding the channel characteristics specific to these systems. Practically, these findings suggest that the deployment strategies for achieving efficient cell-free massive MIMO performance should focus on optimizing the number of antennas per AP rather than simply increasing AP density.

Moreover, the paper evaluates achievable rate expressions in the absence of channel hardening, speculating on the adequacy of existing lower bounds typically predicated on this assumption. The authors recommend deploying downlink pilots for channel estimation at the terminals due to the weak presence of channel hardening, in contradiction to systems with a naturally tight lower bound on achievable rates.

Prospects for Future AI Developments

As the industry continues to advance towards ubiquitous 5G and beyond, the insights from this study pave the way for a shift in how large-scale distributed antenna systems should be engineered. It points towards a focus on improving spatial parameters, increasing antenna density with multiple-antenna APs, and implementing algorithms that can exploit non-uniform user distribution and pathloss variations. Future research should also seek to develop sophisticated signal processing techniques that can inherently account for the non-uniform nature of AP-user placements and leverage machine learning for adaptive resource management tailored to the specific stochastic properties of cell-free systems.

In conclusion, this paper provides a critical evaluation of key assumptions in cell-free massive MIMO theory, utilizing stochastic geometry to elucidate limitations and potentials, thereby refining the path forward for theoreticians and practitioners aiming to leverage the advantages of this cellular architecture.