In order to avoid eavesdropping, beamforming can be used not only to induce artificial noise or jamming signal to an eavesdropper, but also transmit desired signals to a legitimate user (or sensor) from an access point (AP) equipped with an antenna array. In this paper, with proper power allocation, we show that beamforming under a rich scattering environment can guarantee a certain secrecy rate with an overwhelming probability. This approach becomes attractive for slow fading channels where the ergodic secrecy rate cannot be used to decide a target secrecy rate.