On the MISO compound wiretap channel

We study the secure degrees of freedom (d.o.f.) of the MISO compound wiretap channel. The transmitter has M antennas, whereas the legitimate receiver and the eavesdropper each have one antenna and the channel vectors take one of finitely many values. If the number of states of either the legitimate receiver or the eavesdropper channel is less than M, then then we achieve full 1 d.o.f. If however the number of states of both the legitimate receiver and the eavesdropper channel are at-least equal to M, then we establish that the d.o.f. is strictly less than 1. Our upper bound is, to our knowledge, the first bound which is strictly tighter than the ¿pairwise upper bound¿. Lower bounds that combine ideas based on time-sharing, noise transmission, signal alignment and multi-level coding schemes are also provided.