Orbital Angular Momentum: From State Disentanglement Towards the Secrecy Outage Probability

Abstract

How are we able to fix it so as to theoretically go over it, if the optimality and efficiency of the orbital angular momentum (OAM) multiplexing technique in a multi-input multi-output (MIMO) system fails in practice -- something that technically causes a considerable reduction in the maximum achievable value of the transceiver's degree-of-freedom? Is the aforementioned challenging issue theoretically interpretable? This paper considers the above mentioned challenge in the reconfigurable intelligent surface based systems -- as an exemplified system model -- and consequently proposes a Mendelain randomaisation (MR) technique through which we can further overcome the aforementioned challenge. Towards such end and in this paper, we take into account a Markov chain $\mathcal{G}-\circ -\mathcal{X}-\circ -\mathcal{Y}-\circ -\mathcal{V}$ while $\mathcal{G}$, $\mathcal{X}$, $\mathcal{Y}$ and $\mathcal{V}$ respectively denote transmit design parameters, quality of goods, error floor in data detection and non-orthogonality set in the OAM implementation -- arisen from other non-optimalities, disturbances and inefficiencies such as the atmospheric Kolmogorov turbulence. Furthermore, we consider a not-necessarily-Gaussian randomisation method according to which the resultant probability distribution function (PDF) is 2-D in relation to a definable outage probability in the design problem in relation to $\mathcal{Y}$ -- that is, in terms of ${\beta }_{\mathcal{X}}\theta$ while the randomisation is applied to $\theta$ as the control input which should be optimally derived as the graph-theoretically associating parameter between $\mathcal{X}$ and $\mathcal{Y}$, and ${\beta }_{\mathcal{X}}$ is the the associating parameter between $\mathcal{G}$ and the exposure $\mathcal{X}$.