  In this paper, we investigate the downlink secure beamforming (BF) design
problem of cloud radio access networks (C-RANs) relying on multicast fronthaul,
where millimeter-wave and microwave carriers are used for the access links and
fronthaul links, respectively. The base stations (BSs) jointly serve users
through cooperating hybrid analog/digital BF. We first develop an analog BF for
cooperating BSs. On this basis, we formulate a secrecy rate maximization (SRM)
problem subject both to a realistic limited fronthaul capacity and to the total
BS transmit power constraint. Due to the intractability of the non-convex
problem formulated, advanced convex approximated techniques, constrained
concave convex procedures and semi-definite programming (SDP) relaxation are
applied to transform it into a convex one. Subsequently, an iterative algorithm
of jointly optimizing multicast BF, cooperative digital BF and the artificial
noise (AN) covariance is proposed. Next, we construct the solution of the
original problem by exploiting both the primal and the dual optimal solution of
the SDP-relaxed problem. Furthermore, a per-BS transmit power constraint is
considered, necessitating the reformulation of the SRM problem, which can be
solved by an efficient iterative algorithm. We then eliminate the idealized
simplifying assumption of having perfect channel state information (CSI) for
the eavesdropper links and invoke realistic imperfect CSI. Furthermore, a
worst-case SRM problem is investigated. Finally, by combining the so-called
$\mathcal{S}$-Procedure and convex approximated techniques, we design an
efficient iterative algorithm to solve it. Simulation results are presented to
evaluate the secrecy rate and demonstrate the effectiveness of the proposed
algorithms.
