Beyond Massive-MIMO: The Potential of Positioning with Large Intelligent Surfaces

Abstract: We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (LIS), which is a newly proposed concept beyond massive-MIMO where future man-made structures are electronically active with integrated electronics and wireless communication making the entire environment \lq\lq{}intelligent\rq\rq{}. In a first step, we derive Fisher-information and Cram\'{e}r-Rao lower bounds (CRLBs) in closed-form for positioning a terminal located perpendicular to the center of the LIS, whose location we refer to as being on the central perpendicular line (CPL) of the LIS. For a terminal that is not on the CPL, closed-form expressions of the Fisher-information and CRLB seem out of reach, and we alternatively find approximations of them which are shown to be accurate. Under mild conditions, we show that the CRLB for all three Cartesian dimensions ($x$, $y$ and $z$) decreases quadratically in the surface-area of the LIS, except for a terminal exactly on the CPL where the CRLB for the $z$-dimension (distance from the LIS) decreases linearly in the same. In a second step, we analyze the CRLB for positioning when there is an unknown phase $\varphi$ presented in the analog circuits of the LIS. We then show that the CRLBs are dramatically increased for all three dimensions but decrease in the third-order of the surface-area. Moreover, with an infinitely large LIS the CRLB for the $z$-dimension with an unknown $\varphi$ is 6 dB higher than the case without phase uncertainty, and the CRLB for estimating $\varphi$ converges to a constant that is independent of the wavelength $\lambda$. At last, we extensively discuss the impact of centralized and distributed deployments of LIS, and show that a distributed deployment of LIS can enlarge the coverage for terminal-positioning and improve the overall positioning performance.

• The paper derives closed-form and approximate CRLBs showing that positioning accuracy improves quadratically with surface area and linearly with distance along the CPL.
• The study reveals that unknown phase uncertainty increases the CRLB by 6 dB for the z-dimension, highlighting the need for robust calibration techniques.
• The analysis compares centralized and distributed LIS deployments, demonstrating that distributed setups enhance coverage and precision for positioning systems.

Positioning with Large Intelligent Surfaces: Potential and Challenges

The paper "Beyond Massive-MIMO: The Potential of Positioning with Large Intelligent Surfaces" by Sha Hu, Fredrik Rusek, and Ove Edfors introduces an innovative approach to wireless communication and positioning through the concept of Large Intelligent Surfaces (LIS). This work extends the massive multiple-input multiple-output (MIMO) systems by embedding wireless communication capabilities into entire environments, turning them "intelligent." The authors explore the theoretical underpinnings of this concept by deriving closed-form expressions and approximations for positioning accuracy using the Fisher-information and Cramér-Rao lower bounds (CRLB).

Core Contributions

The paper provides a comprehensive investigation into the positioning capabilities of LIS, offering the following key contributions:

• CRLB Derivation: The authors derive closed-form CRLBs for a terminal positioned along the Central Perpendicular Line (CPL) of the LIS, and approximate CRLBs for terminals positioned elsewhere. They highlight that the bounds decrease quadratically with respect to the LIS surface area for lateral positioning on the ($x$ and $y$ dimensions) and linearly for distance ($z$ dimension) when on the CPL.
• Impact of Phase Uncertainty: The research analyzes the CRLB with an unknown phase $\varphi$ in the LIS analog circuitry. This phase uncertainty significantly increases the CRLB, meaning positioning accuracy deteriorates as a result. The study reveals that the CRLB for the $z$-dimension with unknown phase is 6 dB higher than with a known phase, indicating substantial sensitivities to such uncertainties.
• Deployment Strategies: The effect of deploying LISs as centralized singular units versus distributed multiple units is discussed. The results demonstrate that distributed deployments improve coverage and positioning accuracy, especially for terminals significantly distant from the CPL.

Implications and Future Directions

The theoretical findings in this work imply that LIS can offer considerable enhancements in spatial positioning precision, a critical component in applications like autonomous navigation, urban planning, and Internet of Things (IoT) ecosystems. The quadratic improvement in accuracy with surface area surpasses traditional sensors, compensating for larger wavelengths involved.

In the face of unknown phase uncertainties, the research underscores the need for more robust calibration techniques and signal processing strategies that can mitigate their adverse effects. This is pivotal for practical deployment, considering the non-idealities of real-world hardware.

The exploration into centralized versus distributed LIS deployments showcases a potentially transformative approach for infrastructure design, capable of supporting expansive positioning networks with greater resilience and lower average error margins. Future work in this domain could focus on practical implementations, calibration solutions, phased-array technologies, and advanced signal processing methodologies to leverage the full theoretical potential of LIS.

Conclusion

This paper advances the foundational understanding of large intelligent surfaces in wireless communication and positioning, offering significant theoretical insights into their capabilities and limitations. By rigorously deriving and analyzing CRLBs, accounting for practical challenges like phase uncertainty, and considering innovative deployment strategies, the research provides a vital stepping stone toward future wireless systems that integrate seamlessly with physical environments. Further experimental validation and algorithmic developments will be essential in adapting these concepts for real-world applications, potentially shaping the future of smart and autonomous systems.