Cramér-Rao Lower Bounds for Positioning with Large Intelligent Surfaces

Hu, Sha; Rusek, Fredrik; Edfors, Ove

doi:10.1109/vtcfall.2017.8288263

Cited by 20 publications

(37 citation statements)

References 8 publications

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“…Signal model (4), which has also been discussed in [2, Proposition 1], is more accurate than what is usually considered in traditional large antenna-array systems [20], where in the latter case terminals are assumed to be in the far-field and a planar-wave approximation is used in (2) and the term cos φ(x, y) is approximated by 1.…”

Section: A Narrow-band Received Signal Model At the Lismentioning

confidence: 99%

Beyond Massive MIMO: The Potential of Data Transmission With Large Intelligent Surfaces

Rusek

Edfors

2018

IEEE Trans. Signal Process.

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790

568

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In this paper, we consider the potential of data-transmission in a system with a massive number of radiating and sensing elements, thought of as a contiguous surface of electromagnetically active material. We refer to this as a large intelligent surface (LIS). The "LIS" is a newly proposed concept, which conceptually goes beyond contemporary massive MIMO technology, that arises from our vision of a future where man-made structures are electronically active with integrated electronics and wireless communication making the entire environment "intelligent".We firstly consider capacities of single-antenna autonomous terminals communicating to the LIS where the entire surface is used as a receiving antenna array. Under the condition that the surfacearea is sufficiently large, the received signal after a matched-filtering (MF) operation can be closely approximated by a sinc-function-like intersymbol interference (ISI) channel. Secondly, we analyze the capacity per square meter (m 2 ) deployed surface,Ĉ, that is achievable for a fixed transmit power per volume-unit,P ; the volume-unit can be m, m 2 , and m 3 depending on the scenario under investigation. As terminal-density increases, the limit ofĈ achieved when the wavelength λ approaches zero isP /(2N 0 )[nats/s/Hz/volume-unit], where N 0 is the spatial power spectral density (PSD) of the additive white Gaussian noise (AWGN). Moreover, we also show that the number of independent signal dimensions per m deployed surface is 2/λ for one-dimensional terminal-deployment, and π/λ 2 per m 2 for two and three dimensional terminal-deployments. Thirdly, we consider implementations of the LIS in the form of a grid of conventional antenna elements and show that, the sampling lattice that minimizes the surface-area of the LIS and simultaneously obtains one signal space dimension for every spent antenna is the hexagonal lattice. Lastly, we extensively discuss the design of the state-of-the-art low-complexity channel shortening (CS) demodulator for data-transmission with the LIS.The authors are with the P 2N 0 [nats/s/Hz/volume-unit], whereP is the transmit power per volume-unit and N 0 is the spatial power spectral density (PSD) of additive white Gaussian noise (AWGN). In particular, we show

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Section: A Narrow-band Received Signal Model At the Lismentioning

confidence: 99%

Beyond Massive MIMO: The Potential of Data Transmission With Large Intelligent Surfaces

Rusek

Edfors

2018

IEEE Trans. Signal Process.

Self Cite

790

568

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“…Furthermore, the CRLB for estimating ϕ is usually significantly large and about 4π 2 λ 2 times of the CRLB for the z-dimension. Moreover, for an infinitely large LIS, the CRLB for the z-dimension with unknown ϕ is 6 dB higher than with known ϕ, and the CRLB for estimating ϕ converges to a constant 1 .…”

mentioning

confidence: 96%

“…Then, we also extensively discuss the impact of deployments with a single centralized LIS 1 Note that, all CRLBs and their limits considered in this paper can be linearly scaled down by the signal-to-noise ratio (SNR) as a natural result. and multiple distributed smaller LISs constrained to the same total surface-area.…”

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confidence: 99%

Beyond Massive MIMO: The Potential of Positioning With Large Intelligent Surfaces

Rusek

Edfors

2018

IEEE Trans. Signal Process.

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316

204

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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 "intelligent". In a first step, we derive Fisher-information and Cramér-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 ϕ 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 ϕ is 6 dB higher than the case without phase uncertainty, and the CRLB for estimating ϕ converges to a constant that is independent of the wavelength λ. 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. Large intelligent surface (LIS), massive-MIMO, Fisher-information, Cramér-Rao lower bound (CRLB), terminal-positioning, central perpendicular line (CPL), arrive-of-angle (AoA), surface-area, phase-uncertainty. I. INTRODUCTION Wireless communication has evolved from few and geographically distant base stations to more recent concepts involving a high density of access points, possibly with many antenna elements on each. A Large Intelligent Surface (LIS) is a newly proposed concept in wireless communication that is envisioned in [2], where future man-made structures are electronically active with integrated electronics and wireless communication making the entire environment "intelligent". We foresee a practical implementation of LIS as a compact integration of a vast amount of tiny antenna-elements with reconfigurable processing networks. Antennas on the surface cooperate to transmit and sense signals, both for communication and other types of functionality. Machine learning [3] can bring intelligence in the systems both for autonomous operation of the system and for new functionality. One such application is depicted in Fig. 1, where three different terminals are communicating to LIS in an outdoor and indoor scenarios, respecti...

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“…Received signal strength (RSS) based positioning methods, in general, require high RSS values and coverage probability [76]. In particular, [77] derives the Cramér-Rao Bound for UE localization and positioning, whereas [4] studies the performance of LIS for positioning and localization and comparing the accuracy of distributed and centralized LIS systems. On the other hand, [14] examines the potential of mmWave MIMO system positioning with and without the aid of an LIS system.…”

Section: The Potential Of Positioning and Coverage In Lis Systemsmentioning

confidence: 99%

Intelligent Surfaces for 6G Wireless Networks: A Survey of Optimization and Performance Analysis Techniques

et al. 2020

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This paper surveys the optimization frameworks and performance analysis methods for large intelligent surfaces (LIS), which have been emerging as strong candidates to support the sixth-generation wireless physical platforms (6G). Due to their ability to adjust the behavior of interacting electromagnetic (EM) waves through intelligent manipulations of the reflections phase shifts, LIS have shown promising merits at improving the spectral efficiency of wireless networks. In this context, researchers have been recently exploring LIS technology in depth as a means to achieve programmable, virtualized, and distributed wireless network infrastructures. From a system level perspective, LIS have also been proven to be a lowcost, green, sustainable, and energy-efficient solution for 6G systems. This paper provides a unique blend that surveys the principles of operation of LIS, together with their optimization and performance analysis frameworks. The paper first introduces the LIS technology and its physical working principle. Then, it presents various optimization frameworks that aim to optimize specific objectives, namely, maximizing energy efficiency, sum-rate, secrecy-rate, and coverage. The paper afterwards discusses various relevant performance analysis works including capacity analysis, the impact of hardware impairments on capacity, uplink/downlink data rate analysis, and outage probability. The paper further presents the impact of adopting the LIS technology for positioning applications. Finally, we identify numerous exciting open challenges for LIS-aided 6G wireless networks, including resource allocation problems, hybrid radio frequency/visible light communication (RF-VLC) systems, health considerations, and localization. INDEX TERMS 6G technology, large intelligent surfaces (LIS), massive multiple-input multiple-output (mMIMO), millimetre waves (mmWave) communication, wireless communication.

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Cramér-Rao Lower Bounds for Positioning with Large Intelligent Surfaces

Cited by 20 publications

References 8 publications

Beyond Massive MIMO: The Potential of Data Transmission With Large Intelligent Surfaces

Beyond Massive MIMO: The Potential of Data Transmission With Large Intelligent Surfaces

Beyond Massive MIMO: The Potential of Positioning With Large Intelligent Surfaces

Intelligent Surfaces for 6G Wireless Networks: A Survey of Optimization and Performance Analysis Techniques

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