  This paper studies a multi-hop decode-and-forward (DF) simultaneous wireless
information and power transfer (SWIPT) system where a source sends data to a
destination with the aid of multi-hop relays which do not depend on an external
energy source. To this end, we apply power splitting (PS) based SWIPT relaying
protocol so that the relays can harvest energy from the received signals from
the previous hop to reliably forward the information of the source to the
destination. We aim to solve two optimization problems relevant to our system
model. First, we minimize the transmit power at the source under the individual
quality-of-service (QoS) threshold constraints of the relays and the
destination nodes by optimizing PS ratios at the relays. The second is to
maximize the minimum system achievable rate by optimizing the PS ratio at each
relay. Based on convex optimization techniques, the globally optimal PS ratio
solution is obtained in closed-form for both problems. By setting the QoS
threshold constraint the same for each node for the source transmit power
problem, we discovered that either the minimum source transmit power or the
maximum system throughput can be found using the same approach. Numerical
results demonstrate the superiority of the proposed optimal SWIPT PS design
over conventional fixed PS ratio schemes.
