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This paper considers secure simultaneous wireless information and powertransfer (SWIPT) in cell-free massive multiple-input multiple-output (MIMO)systems. The system consists of a large number of randomly(Poisson-distributed) located access points (APs) serving multiple informationusers (IUs) and an information-untrusted dual-antenna active energy harvester(EH). The active EH uses one antenna to legitimately harvest energy and theother antenna to eavesdrop information. The APs are networked by a centralizedinfinite backhaul which allows the APs to synchronize and cooperate via acentral processing unit (CPU). Closed-form expressions for the averageharvested energy (AHE) and a tight lower bound on the ergodic secrecy rate(ESR) are derived. The obtained lower bound on the ESR takes into account theIUs' knowledge attained by downlink effective precoded-channel training. Sincethe transmit power constraint is per AP, the ESR is nonlinear in terms of thetransmit power elements of the APs and that imposes new challenges informulating a convex power control problem for the downlink transmission. Todeal with these nonlinearities, a new method of balancing the transmit poweramong the APs via relaxed semidefinite programming (SDP) which is proved to berank-one globally optimal is derived. A fair comparison between the proposedcell-free and the colocated massive MIMO systems shows that the cell-free MIMOoutperforms the colocated MIMO over the interval in which the AHE constraint islow and vice versa. Also, the cell-free MIMO is found to be more immune to theincrease in the active eavesdropping power than the colocated MIMO.

Optimal Downlink Transmission for Cell Free SWIPT Massive MIMO Systems with Active Eavesdropping