  This paper first considers a multicell network deployment where the base
station (BS) of each cell communicates with its cell-edge user with the
assistance of an amplify-and-forward (AF) relay node. Equipped with a power
splitter and a wireless energy harvester, the self-sustaining relay scavenges
radio frequency (RF) energy from the received signals to process and forward
the information. Our aim is to develop a resource allocation scheme that
jointly optimizes (i) BS transmit powers, (ii) received power splitting factors
for energy harvesting and information processing at the relays, and (iii) relay
transmit powers. In the face of strong intercell interference and limited radio
resources, we formulate three highly-nonconvex problems with the objectives of
sum-rate maximization, max-min throughput fairness and sum-power minimization.
To solve such challenging problems, we propose to apply the successive convex
approximation (SCA) approach and devise iterative algorithms based on geometric
programming and difference-of-convex-functions programming. The proposed
algorithms transform the nonconvex problems into a sequence of convex problems,
each of which is solved very efficiently by the interior-point method. We prove
that our algorithms converge to the locally optimal solutions that satisfy the
Karush-Kuhn-Tucker conditions of the original nonconvex problems. We then
extend our results to the case of decode-and-forward (DF) relaying with
variable timeslot durations. We show that our resource allocation solutions in
this case offer better throughput than that of the AF counterpart with equal
timeslot durations, albeit at a higher computational complexity. Numerical
results confirm that the proposed joint optimization solutions substantially
improve the network performance, compared with cases where the radio resource
parameters are individually optimized.
