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

Gregor Dumphart

### Reference

PhD Thesis, ETH Zurich, Feb. 2020.

[BibTeX, LaTeX, and HTML Reference]

### Abstract

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 $\epsilon \propto \SNR^{-1/2}$ 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.