Fundamental Limits of Wideband Localization— Part I: A General Framework

By Yuan Shen, Moe Z. Win. IEEE Transactions on Information Theory, 2010

870 citations recorded by the source corpus.

The availability of position information is of great importance in many commercial, public safety, and military applications. The coming years will see the emergence of location-aware networks with submeter accuracy, relying on accurate range measurements provided by wide bandwidth transmissions. In this two-part paper, we determine the fundamental limits of localization accuracy of wideband wireless networks in harsh multipath environments. We first develop a general framework to characterize the localization accuracy of a given node here and then extend our analysis to cooperative location-aware networks in Part II. In this paper, we characterize localization accuracy in terms of a performance measure called the squared position error bound (SPEB), and introduce the notion of equivalent Fisher information (EFI) to derive the SPEB in a succinct expression. This methodology provides insights into the essence of the localization problem by unifying localization information from individual anchors and that from a priori knowledge of the agent's position in a canonical form. Our analysis begins with the received waveforms themselves rather than utilizing only the signal metrics extracted from these waveforms, such as time-of-arrival and received signal strength. Hence, our framework exploits all the information inherent in the received waveforms, and the resulting SPEB serves as a fundamental limit of localization accuracy.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/a89f3f1038752542d8cbad9835b396874c6c0036

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Citations in the corpus

A Tutorial on Environment-Aware Communications via Channel Knowledge Map for 6G (2023, background): “For example, if the local wireless environment information (such as buildings and their dielectric properties) is available, ray tracing could be applied offline to generate wireless channel knowledge that is highly related to the static wireless environment, and such knowledge could provide an…”
The Integrated Sensing and Communication Revolution for 6G: Vision, Techniques, and Applications (2024, neutral): “…error bound (SPEB) can be applied to measure the sensing performance in ISAC systems, which is given by The notation J e ( p ) denotes the equivalent Fisher information matrix (EFIM) for p , which is obtained by calculating the Schur complement of submatrix in the original FIM J ( s ) [73].”
A Survey on Fundamental Limits of Integrated Sensing and Communication (2021, methodology): “where Jp (p1) denotes the additional information from the prior position knowledge [78].”
Radar-Assisted Predictive Beamforming for Vehicular Links: Communication Served by Sensing (2020, positive): “One can see in both ﬁgures that the real RMSEs are tightly lower-bounded by the predicted RMSEs (which are also predicted PCRBs according to Theorem 1) in general 2 , which proves the correctness of our theoretical derivation in Sec.”
A Theoretical Foundation of Network Localization and Navigation (2018, methodology): “with spatial consistency among agents according to [171]; then delays and amplitudes are generated using QuaDRiGa [172] according to the Urban Micro B1 for channels between anchor k and the agents with LOS states, where anchor k serves as the transmitter and the agents as the receivers; finally, the”
Reconfigurable Intelligent Surfaces: A signal processing perspective with wireless applications (2021, neutral): “Using RIS configurations with temporal balance and balanced power allocation across subcarriers and an RIS phase reference in the center of the RIS, the FIM of the geometric parameters [ , , ] d b 1 az x z RIS x is a diagonal matrix with entries (see [35, eqs.”
Reconfigurable Intelligent Surfaces for Localization: Position and Orientation Error Bounds (2020, methodology): “estimation error from any unbiased estimator, and it can be represented with the inverse of the Fisher information matrix (FIM) [58], [59].”
Beyond Massive MIMO: The Potential of Positioning With Large Intelligent Surfaces (2017, background): “The CRLB for terminal-positioning has been analyzed thoroughly in the literature for traditional antenna-array systems such as in [21]–[30], and the positioning performance has been evaluated based on various metrics such as AoA [23], timeof-arrival (ToA) [27], time-difference-of-arrival (TDoA) [25]”
WiFi-based indoor positioning (2015, background): “By exploiting and detecting phase difference among antennas [4], the direction of an incoming signal can be calculated.”
Indoor Tracking: Theory, Methods, and Technologies (2015, background): “Theoretical performance bounds on ML position estimates can be found in [40] and [41].”
High-Accuracy Localization for Assisted Living: 5G systems will turn multipath channels from foe to friend (2016, methodology): “we evoke the matrix inversion lemma to account for the nuisance parameters { } k a and a parameter transformation to convert the delays { } k x to the position vector p [30].”
Massive MIMO is a Reality - What is Next? Five Promising Research Directions for Antenna Arrays (2019, background): “…4G, Fisher information analysis reveals that the measurement variance is inversely proportional to the SNR and the square of the signal bandwidth, while the resolution (the difference in arrival time between two paths that can still be distinguished) is limited to the inverse of the bandwidth [86].”
Fundamental Limits of Wideband Localization— Part II: Cooperative Networks (2010, methodology): “The impact of these phenomena has been investigated for non-cooperative localization [7], [ 8], [29]–[31].”