  In this paper, we study the performance of regularized channel inversion
(RCI) precoding in large MISO broadcast channels with confidential messages
(BCC). We obtain a deterministic approximation for the achievable secrecy
sum-rate which is almost surely exact as the number of transmit antennas $M$
and the number of users $K$ grow to infinity in a fixed ratio $\beta=K/M$. We
derive the optimal regularization parameter $\xi$ and the optimal network load
$\beta$ that maximize the per-antenna secrecy sum-rate. We then propose a
linear precoder based on RCI and power reduction (RCI-PR) that significantly
increases the high-SNR secrecy sum-rate for $1<\beta<2$. Our proposed precoder
achieves a per-user secrecy rate which has the same high-SNR scaling factor as
both the following upper bounds: (i) the rate of the optimum RCI precoder
without secrecy requirements, and (ii) the secrecy capacity of a single-user
system without interference. Furthermore, we obtain a deterministic
approximation for the secrecy sum-rate achievable by RCI precoding in the
presence of channel state information (CSI) error. We also analyze the
performance of our proposed RCI-PR precoder with CSI error, and we determine
how the error must scale with the SNR in order to maintain a given rate gap to
the case with perfect CSI.
