Stochastic misalignment model for magneto-inductive SISO and MIMO links

Magneto-inductive (MI) systems for wireless communications or power transfer usually suffer from coil mis-alignment, because of mobility or deployment. The impact on performance is hard to analyze because mutual inductance is an involved function of geometry. We focus on links whose coil separation exceeds coil dimensions, which is characteristic for communications links and becoming increasingly desired for wireless powering. In this regime, the dipole approximation allows for an accurate closed-form description of misalignment. In order to analyze fully unaligned links, we propose a stochastic misalignment model that assumes uniformly random coil orientation(s). To this effect, we derive the probability density function (PDF) of mutual inductance for practically relevant setups, comprising single coils and collocated coil arrays. This gives rise to a misalignment comparison of beamforming, coil selection, and single-input single-output (SISO) links. The PDFs lead to the expected attenuation due to misalignment. We relate misalignment to communications performance by means of a basic circuit. A byproduct of the stochastic model is the maximum likelihood range estimate for a noiseless mutual inductance measurement under unknown arrangement.