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

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.