Capacity Analysis of Power Beacon-Assisted Energy Harvesting MIMO System Over $\kappa -\mu$ Shadowed Fading Channels

In this paper, novel ergodic capacity (EC) performance evaluation results of a power beacon (PB)-assisted multi-input multi-output (MIMO) wireless powered communication network are presented. In the considered system, the energy harvesting node harvests energy from the radio-frequency signals sent by the dedicated PB and uses this energy to communicate with the destination node. To accurately model the combined effect of multi-path fading and shadowing, it is assumed that the energy transfer link is subject to $\kappa$ - $\mu$ shadowed fading. Performance evaluation results are presented for two cases, depending upon the availability of channel state information (CSI) at the PB, namely, $no$ CSI and $full$ CSI. In the former case, equal power allocation is assumed, whereas, in the later case, energy beamforming is employed to increase energy transfer efficiency. For the performance evaluation of EC under $full$ CSI, a closed-form approximation for the probability density function of the maximum eigenvalue of a $\kappa$ - $\mu$ shadowed distributed random matrix is derived. For both $no$ CSI and $full$ CSI cases, lower and upper bounds on the achievable EC are derived in closed-form. Moreover, in order to obtain further insights on the impact of key parameters on the system performance, asymptotic EC expressions which become very tight at low- and high-signal-to-noise ratio regimes, are obtained. Using the proposed EC lower bound as well as these asymptotic results, simple closed-form expressions for the optimal time split that maximize the achievable EC are derived. Numerically evaluated results accompanied with Monte-Carlo simulations are further presented to corroborate the theoretical analysis.