Transmitter Optimization in Slow Fading MISO Wiretap Channel

In this paper, we consider the transmitter optimization problem in slow fading multiple-input-single-output (MISO) wiretap channel. The source transmits a secret message intended for $K$ users in the presence of $J$ non-colluding eavesdroppers, and operates under a total power constraint. The channels between the source and all users and eavesdroppers are assumed to be slow fading, and only statistical channel state information (CSI) is known at the source. For a given code rate and secrecy rate pair of the wiretap code, denoted by $(R_{D}, R_{s})$, we define the non-outage event as the joint event of the link information rates to $K$ users be greater than or equal to $R_{D}$ and the link information rates to $J$ eavesdroppers be less than or equal to $(R_{D} - R_{s})$. We minimize the transmit power subject to the total power constraint and satisfying the probability of the non-outage event to be greater than or equal to a desired threshold $(1-\epsilon)$.