  In this paper, a joint beamforming design for max-min fair simultaneous
wireless information and power transfer (SWIPT) is investigated in a green
cloud radio access network (Cloud-RAN) with millimeter wave (mmWave) wireless
fronthaul. To achieve a balanced user experience for separately located data
receivers (DRs) and energy receivers (ERs) in the network, joint transmit
beamforming vectors are optimized to maximize the minimum data rate among all
the DRs, while satisfying each ER with sufficient RF energy at the same time.
Then, a two-step iterative algorithm is proposed to solve the original
non-convex optimization problem with the fronthaul capacity constraint in an
$l_0$-norm form. Specifically, the $l_0$-norm constraint can be approximated by
the reweighted $l_1$-norm, from which the optimal max-min data rate and the
corresponding joint beamforming vector can be derived via semidefinite
relaxation (SDR) and bi-section search. Finally, extensive numerical
simulations are performed to verify the superiority of the proposed joint
beamforming design to other separate beamforming strategies.
