The Channel Between Randomly Oriented Dipoles: Statistics and Outage in the Near and Far Field

TL;DR

This paper analyzes the statistical behavior and outage performance of wireless channels modeled by randomly oriented dipoles, revealing how antenna orientation randomness affects communication reliability and power transfer efficiency.

Contribution

It provides a closed-form statistical description of dipole-based channels with random orientations and characterizes outage probabilities and diversity exponents in various propagation regimes.

Findings

Outage probability scales as SNR^{-1/2} in high SNR regimes.

Diversity exponent is 1/2 in general, improving to 1 at the near-far-field transition.

Polarization diversity enhances channel robustness in the transition region.

Abstract

We consider the class of wireless links whose propagation characteristics are described by a dipole model. This comprises free-space links between dipole antennas and magneto-inductive links between coils, with important communication and power transfer applications. A dipole model describes the channel coefficient as a function of link distance and antenna orientations. In many use cases the orientations are random, causing a random fading channel. This paper presents a closed-form description of the channel statistics and the resulting outage performance for the case of i.i.d. uniformly distributed antenna orientations in 3D space. For reception in AWGN after active transmission, we show that the high-SNR outage probability scales like $p_\mathrm{e} \propto \mathrm{SNR}^{-1/2}$ in the near- or far-field region, i.e. the diversity exponent is just 1/2 (even 1/4 with backscatter or load modulation). The diversity exponent improves to 1 in the near-far-field transition due to polarization diversity. Analogous statements are made for the power transfer efficiency and outage capacity.