On multi-user MISO wiretap channels with delayed CSIT

Abstract

The multiple-input single-output (MISO) wiretap channel with K legitimate single-antenna receivers, one single-antenna eavesdropper in presence of delayed channel state information at the transmitter (CSIT) is considered. The transmitter is equipped with (K+1) antennas and has independent messages intended for each one of the K legitimate receivers. While for the case of a single receiver wiretap channel, i.e., K = 1, the optimal secure degrees of freedom (SDoF) with delayed CSIT was recently characterized in [1] and shown to be 2/3, the extension to the multi-receiver case (K > 1) is far from straightforward. We present new results and insights for the simplest non-trivial extension of this problem, i.e., for the case of K = 2 receiver MISO wiretap channel with delayed CSIT. The contribution of this paper is two fold: a) an asymptotic achievable scheme is presented for the case of two legitimate receivers which achieves a sum-SDoF of 36/37 and b) a novel converse proof is presented which shows that the sum-SDoF is upper bounded by 16/15.