On the Secure Degrees of Freedom for Two-User MIMO Interference Channel With a Cooperative Jammer

Abstract

We investigate the secure degrees of freedom (SDoF) for the two-user multiple-input multiple-output (MIMO) interference channel with a cooperative jammer, where each transmitter is equipped with $M$ antennas, each receiver is equipped with $N$ antennas, and the jammer is equipped with $K$ antennas. For each one of the four regions of parameters $(M,N)$ , i.e., $1\leq \frac {N}{M} , $\frac {N}{M} \geq 2$ , $\frac {1}{2}\le \frac {N}{M} , and $\frac {N}{M} , we provide both upper and lower bounds on the SDoF of the system which depend on the value of $K$ . In particular, the upper bound is the union of three upper bounds that are based on the DoF of the MIMO interference channel, the SDoF of the MIMO wiretap channel with a jammer, and the Secrecy Penalty Lemma and the Role of A Helper Lemma for the interference channel, respectively. For the lower bound, we provide achievability schemes that make use of signal alignment, zero forcing, cooperative jamming, and multi-slot transmission. Our results indicate that the SDoF of the system under consideration improves with respect to the no jammer case in all regimes, especially when $N>2M$ . Moreover, we quantify the SDoF gap of the network and reveal it as a function of the number of the antennas. For large $K$ , the upper and lower bounds coincide in all regimes, and the exact SDoF can be achieved.