On the ergodic capacities of decode-and-forward MIMO relay network with simultaneous wireless information and power transfer

In this article, simultaneous wireless information and power transfer (SWIPT) has been studied for point-to-point decode-and-forward (DF) based multiple-input-multiple-output (MIMO) relay network with an energy-constrained relay. This relay is capable of harvesting energy from the wireless signals received from the source terminal. In particular, three different SWIPT schemes, that is, time switching, power splitting, and antenna switching are considered for EH at relay. New closed-form approximations for the sum ergodic capacity of a DF MIMO relay network have been derived with spatial multiplexing at source, zero-forcing receivers at relay and destination. Based on the sum capacity approximations, optimal splitting coefficients for aforementioned SWIPT schemes that maximize the sum capacity are presented. Moreover, the impact of system parameters on these optimal coefficients has been studied. In addition to this, first optimization problems for the number of antennas at relay have been formulated and then these problems are transformed into concave form by relaxing constraints to be defined over positive real numbers instead of taking only discrete values. New closed-form solutions for the optimum number of antennas at relay have been derived. Furthermore, new closed-form approximations for the ergodic capacities in the presence of an external co-channel interference are also presented. Numerical results show that approximations for the sum capacity match well with the exact ones obtained through Monte-Carlo simulations, particularly when the channel hardening effect kicks in, that is, for large degrees of freedom. Finally, the solutions for the optimization problems have also been validated by the numerical examples.