Wireless-Powered Distributed Spatial Modulation With Energy Recycling and Finite-Energy Storage

The distributed spatial modulation (DSM) protocol, which allows relays to forward the source's data while simultaneously allowing the relays to transmit their own data, has been proposed by Narayanan et al. In this paper, we introduce two new protocols for enabling the DSM, consisting of single-antenna network nodes, with simultaneous wireless information and power transfer capability: power splitting-based DSM (PS-DSM) and energy recycling-based DSM (ER-DSM). More specifically, the PS-DSM relies on power splitters at the relay nodes to harvest energy transmitted from the source. On the other hand, the ER-DSM, by exploiting the inactive cooperating relays in DSM-based protocols, recycles part of the transmitted energy in the network, without relying on power splitters or time switches at the relays to harvest energy. This leads to an increase in the average harvested energy at the relays with reduced hardware complexity. Both the PS-DSM and the ER-DSM also retain all the original features of DSM. Due to its particular operating principle and specific advantages, we select the ER-DSM as the candidate for further mathematical analysis. More specifically, by considering a multi-state battery model, we propose an analytical framework based on a Markov chain formulation for modeling the charging/discharging behavior of the batteries at the relay nodes in the ER-DSM. Furthermore, based on the derived Markov chain model, we introduce a mathematical framework for computing the error probability of the ER-DSM, by explicitly taking into account, the effect of finite-sized batteries. The frameworks are substantiated with the aid of Monte Carlo simulations for various system setups.