This paper studies a simultaneous wireless information and power transfer
(SWIPT)-aware fog computing network, where a multiple antenna fog function
integrated hybrid access point (F-HAP) transfers information and energy to
multiple heterogeneous single-antenna sensors and also helps some of them
fulfill computing tasks. By jointly optimizing energy and information
beamforming designs at the F-HAP, the bandwidth allocation and the computation
offloading distribution, an optimization problem is formulated to minimize the
required energy under communication and computation requirements, as well as
energy harvesting constraints. Two optimal designs, i.e., fixed offloading time
(FOT) and optimized offloading time (OOT) designs, are proposed. As both
designs get involved in solving non-convex problems, there are no known
solutions to them. Therefore, for the FOT design, the semidefinite relaxation
(SDR) is adopted to solve it. It is theoretically proved that the rank-one
constraints are always satisfied, so the global optimal solution is guaranteed.
For the OOT design, since its non-convexity is hard to deal with, a penalty
dual decomposition (PDD)-based algorithm is proposed, which is able to achieve
a suboptimal solution. The computational complexity for two designs are
analyzed. Numerical results show that the partial offloading mode is superior
to binary benchmark modes. It is also shown that if the system is with strong
enough computing capability, the OOT design is suggested to achieve lower
required energy; Otherwise, the FOT design is preferred to achieve a relatively
low computation complexity.