Robust Near-Field 3D Localization of an Unaligned Single-Coil Agent Using Unobtrusive Anchors

The magnetic near-field provides a suitable means for indoor localization, due to its insensitivity to the environment and strong spatial gradients. We consider indoor localization setups consisting of flat coils, allowing for convenient integration of the agent coil into a mobile device (e.g., a smart phone or wristband) and flush mounting of the anchor coils to walls. In order to study such setups systematically, we first express the Cram\'er-Rao lower bound (CRLB) on the position error for unknown orientation and evaluate its distribution within a square room of variable size, using 15 x 10cm anchor coils and a commercial NFC antenna at the agent. Thereby, we find cm-accuracy being achievable in a room of 10 x 10 x 3 meters with 12 flat wall-mounted anchors and with 10mW used for the generation of magnetic fields. Practically achieving such estimation performance is, however, difficult because of the non-convex 5D likelihood function. To that end, we propose a fast and accurate weighted least squares (WLS) algorithm which is insensitive to initialization. This is enabled by effectively eliminating the orientation nuisance parameter in a rigorous fashion and scaling the individual anchor observations, leading to a smoothed 3D cost function. Using WLS estimates to initialize a maximum-likelihood (ML) solver yields accuracy near the theoretical limit in up to 98% of cases, thus enabling robust indoor localization with unobtrusive infrastructure, with a computational efficiency suitable for real-time processing.Comment: 7 pages, to be presented at IEEE PIMRC 201

Magneto-inductive Passive Relaying in Arbitrarily Arranged Networks

We consider a wireless sensor network that uses inductive near-field coupling for wireless powering or communication, or for both. The severely limited range of an inductively coupled source-destination pair can be improved using resonant relay devices, which are purely passive in nature. Utilization of such magneto-inductive relays has only been studied for regular network topologies, allowing simplified assumptions on the mutual antenna couplings. In this work we present an analysis of magneto-inductive passive relaying in arbitrarily arranged networks. We find that the resulting channel has characteristics similar to multipath fading: the channel power gain is governed by a non-coherent sum of phasors, resulting in increased frequency selectivity. We propose and study two strategies to increase the channel power gain of random relay networks: i) deactivation of individual relays by open-circuit switching and ii) frequency tuning. The presented results show that both methods improve the utilization of available passive relays, leading to reliable and significant performance gains.Comment: 6 pages, 9 figures. To be presented at the IEEE International Conference on Communications (ICC), Paris, France, May 201

Practical Accuracy Limits of Radiation-Aware Magneto-Inductive 3D Localization

The key motivation for the low-frequency magnetic localization approach is that magnetic near-fields are well predictable by a free-space model, which should enable accurate localization. Yet, limited accuracy has been reported for practical systems and it is unclear whether the inaccuracies are caused by field distortion due to nearby conductors, unconsidered radiative propagation, or measurement noise. Hence, we investigate the practical performance limits by means of a calibrated magnetoinductive system which localizes an active single-coil agent with arbitrary orientation, using 4 mW transmit power at 500 kHz. The system uses eight single-coil anchors around a 3m x 3m area in an office room. We base the location estimation on a complex baseband model which comprises both reactive and radiative propagation. The link coefficients, which serve as input data for location estimation, are measured with a multiport network analyzer while the agent is moved with a positioner device. This establishes a reliable ground truth for calibration and evaluation. The system achieves a median position error of 3.2 cm and a 90th percentile of 8.3 cm. After investigating the model error we conjecture that field distortion due to conducting building structures is the main cause of the performance bottleneck. The results are complemented with predictions on the achievable accuracy in more suitable circumstances using the Cram\'er-Rao lower bound.Comment: To appear at the IEEE ICC 2019 Workshops. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Pairwise Distance and Position Estimators From Differences in UWB Channels to Observers

We consider the problem of obtaining relative location information between two wireless nodes from the differences in their ultra-wideband (UWB) channels to observer nodes. Our approach focuses on the delays of multipath components (MPCs) extracted from the observed channels. For the two different cases of known and unknown MPC association between these channels, we present estimators for the distance and for the relative position vector between the two nodes. The position estimators require both MPC directions and MPC delays as input. All presented estimators exhibit very desirable technological properties: they do not require line-of-sight conditions, precise synchronization, or knowledge about the observer locations or about the environment. These advantages could enable low-cost wireless network localization in dynamic multipath environments. The exposition is complemented by a numerical evaluation of the estimation accuracy using random sampling, where especially the position estimators show the potential for great accuracy.Comment: To appear at the IEEE Global Communications Conference (GLOBECOM) Workshops 2021, Madrid, Spain. This work has been submitted to the IEEE for publication. Copyright may be transferred without notice. This is the short conference version of the full paper arXiv:2108.09703. v2 fixes a copy-and-paste error in (21). arXiv admin note: substantial text overlap with arXiv:2108.0970

Load Modulation for Backscatter Communication: Channel Capacity and Near-Capacity Schemes

In backscatter communication (BC), a passive tag transmits information by just affecting an external electromagnetic field through load modulation. Thereby, the feed current of the excited tag antenna is modulated by adapting the passive termination load. This paper studies the achievable information rates with a freely adaptable passive load. As a prerequisite, we unify monostatic, bistatic, and ambient BC with circuit-based system modeling. We present the crucial insight that channel capacity is described by existing results on peak-power-limited quadrature Gaussian channels, because the steady-state tag current phasor lies on a disk. Consequently, we derive the channel capacity for the case of an unmodulated external field, for general passive, purely reactive, or purely resistive tag loads. We find that modulating both resistance and reactance is important for very high rates. We discuss the capacity-achieving load statistics, rate asymptotics, technical conclusions, and rate losses from value-range-constrained loads (which are found to be small for moderate constraints). We then demonstrate that near-capacity rates can be attained by more practical schemes: (i) amplitude-and-phase-shift keying on the reflection coefficient and (ii) simple load circuits of a few switched resistors and capacitors. Finally, we draw conclusions for the ambient BC channel capacity in important special cases.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice. Included conference paper: arXiv:2201.0024

Magneto-Inductive Powering and Uplink of In-Body Microsensors: Feasibility and High-Density Effects

This paper studies magnetic induction for wireless powering and the data uplink of microsensors, in particular for future medical in-body applications. We consider an external massive coil array as power source (1 W) and data sink. For sensor devices at 12 cm distance from the array, e.g. beneath the human skin, we compute a minimum coil size of 150 um assuming 50 nW required chip activation power and operation at 750 MHz. A 275 um coil at the sensor allows for 1 Mbit/s uplink rate. Moreover, we study resonant sensor nodes in dense swarms, a key aspect of envisioned biomedical applications. In particular, we investigate the occurring passive relaying effect and cooperative transmit beamforming in the uplink. We show that the frequency- and location-dependent signal fluctuations in such swarms allow for significant performance gains when utilized with adaptive matching, spectrally-aware signaling and node cooperation. The work is based on a general magneto-inductive MIMO system model, which is introduced first.Comment: 6 pages, to appear at IEEE WCNC 2019. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Cooperative Magneto-Inductive Localization

Wireless localization is a key requirement for many applications. It concerns position estimation of mobile nodes (agents) relative to fixed nodes (anchors) from wireless channel measurements. Cooperative localization is an advanced concept that considers the joint estimation of multiple agent positions based on channel measurements of all agent-anchor links together with all agent-agent links. In this paper we present the first study of cooperative localization for magneto-inductive wireless sensor networks, which are of technological interest due to good material penetration and channel predictability. We demonstrate significant accuracy improvements (a factor of 3 for 10 cooperating agents) over the non-cooperative scheme. The evaluation uses the Cram\'er-Rao lower bound on the cooperative position estimation error, which is derived herein. To realize this accuracy, the maximum-likelihood estimate (MLE) must be computed by solving a high-dimensional least-squares problem, whereby convergence to local minima proves to be problematic. A proposed cooperative localization algorithm addresses this issue: first, preliminary estimates of the agent positions and orientations are computed, which then serve as initial values for a gradient search. In all our test cases, this method yields the MLE and the associated high accuracy (comprising the cooperation gain) from a single solver run. The preliminary estimates use novel closed-form MLE formulas of the distance, direction and orientation for single links between three-axis coils, which are given in detail.Comment: To appear at the IEEE PIMRC 2021 conference. This work has been submitted to the IEEE for publication. Copyright may be transferred without notic

Inter-Node Distance Estimation from Multipath Delay Differences of Channels to Observer Nodes

We study the estimation of distance d between two wireless nodes by means of their wideband channels to a third node, called observer. The motivating principle is that the channel impulse responses are similar for small d and drift apart when d increases. Following this idea we propose specific distance estimators based on the differences of path delays of the extractable multipath components. In particular, we derive such estimators for rich multipath environments and various important cases: with and without clock synchronization as well as errors on the extracted path delays (e.g. due to limited bandwidth). The estimators readily support (and benefit from) the presence of multiple observers. We present an error analysis and, using ray tracing in an exemplary indoor environment, show that the estimators perform well in realistic conditions. We describe possible localization applications of the proposed scheme and highlight its major advantages: it requires neither precise synchronization nor line-of-sight connection. This could make wireless user tracking feasible in dynamic indoor settings.Comment: To appear at IEEE ICC 2019. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Magneto-Inductive Communication and Localization: Fundamental Limits with Arbitrary Node Arrangements

Wireless sensors are a key technology for many current or envisioned applications in industry and sectors such as biomedical engineering. In this context, magnetic induction has been proposed as a suitable propagation mechanism for wireless communication, power transfer and localization in applications that demand a small node size or operation in challenging media such as body tissue, fluids or soil. Magnetic induction furthermore allows for load modulation at passive tags as well as improving a link by placing passive resonant relay coils between transmitter and receiver. The existing research literature on these topics mostly addresses static links in well-defined arrangement, i.e. coaxial or coplanar coils. Likewise, most studies on passive relaying consider coil arrangements with equidistant spacing on a line or grid. These assumptions are incompatible with the reality of many sensor applications where the position and orientation of sensor nodes is determined by their movement or deployment. This thesis addresses these shortcomings by studying the effects and opportunities in wireless magnetic induction systems with arbitrary coil positions and orientations. As prerequisite, we introduce appropriate models for near- and far-field coupling between electrically small coils. Based thereon we present a general system model for magneto-inductive networks, applicable to both power transfer and communication with an arbitrary arrangement of transmitters, receivers and passive relays. The model accounts for strong coupling, noise correlation, matching circuits, frequency selectivity, and relevant communication-theoretic nuances. The next major part studies magnetic induction links between nodes with random coil orientations (uniform distribution in 3D). The resulting random coil coupling gives rise to a fading-type channel; the statistics are derived analytically and the communication-theoretic implications are investigated in detail. The study concerns near- and far-field propagation modes. We show that links between single-coil nodes exhibit catastrophic reliability: the asymptotic outage probability $\epsilon \propto \text{SNR}^{-1/2}$ for pure near-field or pure far-field propagation, i.e. the diversity order is 1/2 (even 1/4 for load modulation). The diversity order increases to 1 in the transition between near and far field. We furthermore study the channel statistics and implications for randomly oriented coil arrays with various spatial diversity schemes. A subsequent study of magneto-inductive passive relaying reveals that arbitrarily deployed passive relays give rise to another fading-type channel: the channel coefficient is governed by a non-coherent sum of phasors, resulting in frequency-selective fluctuations similar to multipath radio channels. We demonstrate reliable performance gains when these fluctuations are utilized with spectrally aware signaling (e.g. waterfilling) and that optimization of the relay loads offers further and significant gains. We proceed with an investigation of the performance limits of wireless-powered medical in-body sensors in terms of their magneto-inductive data transmission capabilities, either with a transmit amplifier or load modulation, in free space or conductive medium (muscle tissue). A large coil array is thereby assumed as power source and data sink. We employ previous insights to derive design criteria and study the interplay of high node density, passive relaying, channel knowledge and transmit cooperation in detail. A particular focus is put on the minimum sensor-side coil size that allows for reliable uplink transmission. The developed models are then used in a study of the fundamental limits of node localization based on observations of magneto-inductive channels to fixed anchor coils. In particular, we focus on the joint estimation of position and orientation of a single-coil node and derive the Cramér-Rao lower bound on the estimation error for the case of complex Gaussian observation errors. For the five-dimensional non-convex estimation problem we propose an alternating least-squares algorithm with adaptive weighting that beats the state of the art in terms of robustness and runtime. We then present a calibrated system implementation of this paradigm, operating at 500 kHz and comprising eight flat anchor coils around a 3m × 3m area. The agent is mounted on a positioner device to establish a reliable ground truth for calibration and evaluation; the system achieves a median position error of 3cm. We investigate the practical performance limits and dominant error source, which are not covered by existing literature. The thesis is complemented by a novel scheme for distance estimation between two wireless nodes based on knowledge of their wideband radio channels to one or multiple auxiliary observer nodes. By exploiting mathematical synergies with our theory of randomly oriented coils we utilize the random directions of multipath components for distance estimation in rich multipath propagation. In particular we derive closed-form distance estimation rules based on the differences of path delays of the extractable multipath components for various important cases. The scheme does not require precise clock synchronization, line of sight, or knowledge of the observer positions