MISO broadcast channels with confidential messages and alternating CSIT

We study the two-user multiple-input single-output (MISO) broadcast channel with confidential messages under the assumption of alternating channel state information at the transmitter (CSIT). We consider two alternating states: PD and DP which occur for an equal fraction of time. In state PD, the CSIT of the channel to the first receiver is available perfectly without delay (P) while that of the second receiver is available with a delay of one channel use (D); in state DP, the roles of the receivers are reversed. We characterize the exact secure degrees of freedom (s.d.o.f.) region of this system, and show as a corollary that the sum s.d.o.f. is 3/2. We observe that this sum s.d.o.f. is the same as what can be achieved by the states PP and DD occurring for equal fraction of time. Though the s.d.o.f. of the system in the states PD and DP is not known individually, we are able to establish the s.d.o.f. region when the two states alternate and occur for an equal fraction of the time.