Influence of multi-path fading on MIMO/OAM communications

Summary form only given. Modern wireless communications systems exploit spatial multiplexing to increase channel capacity. This is alternately referred to as multiple-input multiple-output (MIMO) communications [1] or, in the case in which the spatial structure exploits angular symmetry, the use of orbital angular momentum (OAM) states [2]. In both cases the creation of correlated spatial basis functions produce orthogonal, robust and non-interfering (strong) channels. Recent studies have explored the ability of selected antenna configurations to produce radio vortices carrying orbital angular momentum, including but not limited to circular phased antenna arrays [3] and current ring resonators [4]. The former study shows that conventional circular antenna arrays can be optimized to generate OAM states. The latter study shows that electromagnetic field generators based on circular ring resonators, whose perimeters are integer times of equivalent wavelength, have attractive potential for producing radio vortices carrying OAM. The starting point of wireless communication studies involving OAM is the transmission of electromagnetic fields in free-space. In this work, we include the effect of multi-path fading in free-space communications between antenna arrays capable of generating OAM states. The focus of our study is on the impedance matrix relating currents and voltages in the elements of a transmitting and receiving antenna array. We assume that the electromagnetic field fluctuations driving the multi-path fading are statistically equivalent to those produced by multiple reflections and scattering within a cavity with irregular geometry and distributed wall losses. These are modelled with the so-called random coupling model (RCM) [5], a statistical model that combines: i) random plane wave superpositions to describe the cavity eigenfunction distribution, with ii) random matrix theory (RMT) to describe cavity eigenvalue distribution. Here, the model is developed to assess the robustness of OAM wireless links in the presence of multi-path interference. For a wireless link between circular antenna arrays, we obtain a free-space radiation impedance matrix for the p-th communications channel created by the discrete circular current density, with radiation reactance X and radiation resistance R matrices that have a block diagonal structure, and whose elements can be calculated in closed-form. This matrix can be used in the RCM to capture interference from the environment through the following relation Z
_RCM
= jX + R
^1/2
ξR
^1/2
where the normalized statistical impedance matrix ξ, given by a sum over eigenmodes with properties i) and ii), encodes the reaction of the reflecting walls and objects to a source radiating waves in the environment. The impedance model can be used to quantify the cross-talk between communication channels operating in real life wireless environments.