Blind MIMO wiretap channel with delayed CSIT

We study the Gaussian MIMO wiretap channel where a transmitter wishes to communicate a secure message to a legitimate receiver in the presence of eavesdroppers, while the eavesdroppers should not be able to decode the secure message. Each node in the network is equipped with arbitrary number of antennas. Furthermore, channels are time varying, and the transmitter has no channel state information (CSIT) of its channels to the eavesdroppers; and it only has access to delayed CSIT of the channel to the legitimate receiver. We completely characterize the secure degrees of freedom (SDoF) of such network, when restricted to linear encoding schemes. In particular, we strictly improve the state-of-the-art achievable schemes for this network. Furthermore, we develop a tight converse result by presenting a lemma, which states that once the transmitter(s) in a network have no CSIT of a certain receiver, and receivers have the same number of antennas, the least amount of alignment will occur at that receiver, meaning that transmit signals will occupy the maximal signal dimensions at that receiver.