Abstract
This paper considers secure simultaneous wireless information and power transfer (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 information users (IUs) and an information-untrusted dual-antenna active energy harvester (EH). The active EH uses one antenna to legitimately harvest energy and the other antenna to eavesdrop information. The APs are networked by a centralized infinite backhaul which allows the APs to synchronize and cooperate via a central processing unit (CPU). Closed-form expressions for the average harvested 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 the IUs' knowledge attained by downlink effective precoded-channel training. Since the transmit power constraint is per AP, the ESR is nonlinear in terms of the transmit power elements of the APs and that imposes new challenges in formulating a convex power control problem for the downlink transmission. To deal with these nonlinearities, a new method of balancing the transmit power among the APs via relaxed semidefinite programming (SDP) which is proven to be rank-one globally optimal is derived. A fair comparison between the proposed cell-free and the colocated massive MIMO systems shows that the cell-free MIMO outperforms the colocated MIMO over the interval in which the AHE constraint is low and vice versa. Also, the cell-free MIMO is found to be more immune to the increase in the active eavesdropping power than the colocated MIMO.
Highlights
The main contributions of our work are: 1) To jointly improve the ergodic secrecy rate (ESR) and the average harvested energy (AHE), we propose optimized downlink transmissions of three different signals: information, AN and energy signals beamformed towards the information users (IUs), legitimate and illegitimate antennas of the energy harvester (EH), respectively; 2) We derive closed-form expressions for the AHE and a tight lower bound on the ESR
The derived expressions are deterministic at the central processing unit (CPU) and take into account the IUs’ knowledge attained by downlink effective precoded-channel training; 3) Knowing that the ESR is nonlinear in terms of the transmit power elements of the access points (APs), a new globally optimal iterative method for cooperatively balancing the transmit powers at the APs via relaxed semidefinite programming (SDP) is derived; 4) We provide a proof for the rank-one global optimality of our SDP solution (Theorem 3) and the convergence of our iterative SDP problem (Subsection IV-C2); 5) a fair performance comparison between the proposed cell-free and colocated massive multiple-input multiple-output (MIMO) systems is performed
The downlink simultaneous wireless information and power transfer (SWIPT) transmissions include: information, AN and energy signals beamformed towards the IUs, legitimate and illegitimate antennas of the EH, respectively
Summary
In contrast to multi-cell massive multiple-input multipleoutput (MIMO) systems in which the users in each cell (of a confined area) are served by an array of colocated antennas, cell-free massive MIMO is an architecture in which the users. Related Work: To the best of the authors’ knowledge, the secrecy performance in cell-free massive MIMO systems has only been studied in [15] where the focus was on maximizing the secrecy rate of a given IU when being attacked by an active EV under constraints on the individual rates of all IUs. We can compare the work in this paper to the work in [15] from two perspectives: 1) From system and signal design perspectives, our work considers the worst-case SWIPT problem by optimizing three different downlink signals: information, AN and energy signals beamformed towards the IUs, legitimate and illegitimate antennas of the dual-antenna EH, respectively; while the work in [15] considers the secrecy problem of a certain IU by optimizing the downlink information signals (no jamming or power transfer are considered); 2) From a problem-solving perspective, the employed lower bound on the secrecy rate in [15] imposes constraints on the domain of the linear programming (LP) optimization variables (the allocated power of the downlink information vectors) [15, (23)], i.e., the values of allocated power vectors are feasible on a sub-region of RN+ , where N is the total number of APs. Since the update in the proposed iterative algorithm does not include the power vector of the considered IU, the obtained solution is locally optimal, or at least, the globally optimal solution is not guaranteed.
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