On the SDoF for Multiple Full-Duplex MIMO Users Pair-Wise Communications

This paper explores the pair-wise secure degree of freedom (SDoF) of a network with multiple full-duplex multiple-input multiple-output nodes, where the nodes communicate with each other while being wiretapped by a multi-antenna eavesdropper. This paper aims to fill the gap in the theoretical analysis of the optimal pair-wise SDoF of multiple full-duplex node systems from an information theory perspective when the channel state information remains unknown to each node at the beginning of the coherence interval. To this end, we first derive an upper bound of the achievable SDoF of the system using the optimal signal structure of the pair-wise secrecy rate. Then, by demonstrating that the upper bound is achievable using Gaussian signals, the optimal SDoF of the system is derived. The numerical results verify that the obtained optimal pair-wise SDoF extends the existing research with two legitimate nodes and increases the optimal SDoF by adjusting the number of out-of-pair transmit antennas appropriately.