On the Secure Degrees of Freedom of Two-Way 2 × 2 × 2 MIMO Interference Channel

Abstract

We investigate the secure degrees of freedom (SDoF) for the two-way $2\times 2\times 2$ MIMO interference channel (IC) under three wiretap models, i.e., the confidential messages (CM) model, the untrusted relays (UR) model, and the combined CM and UR (CM-UR) model. For the general case of arbitrary antenna configuration under each wiretap model, we derive the upper bound on SDoF with Markov chain and secrecy constraints, and obtain the achievability schemes with designed interference neutralization, cooperative jamming, and interference alignment schemes. To gain insight on these bounds, we further consider the special case where each user node has $M$ antennas and each relay node has $N$ antennas, and highlight the modification process when achieving the maximum SDoF. For such special case, we show that the optimum SDoF of the CM model is achieved in the regimes $M\ge N$ and $M ; and for the UR model and CM-UR model, the optimum SDoF is achieved in the regimes $N\le ({M}/{2})$ , $N > 2M$ , and $N=M$ .