On the DoF of Two-Way <inline-formula> <tex-math notation="LaTeX">$2\times 2\times 2$</tex-math> </inline-formula> MIMO Relay Networks

Abstract

This paper studies the degrees of freedom (DoF) of two-way $2\times 2\times 2$ MIMO interference networks, a class of two-way four-unicast networks. We first provide upper and lower bounds on the sum DoF of general two-way $2\times 2\times 2$ MIMO interference networks with any number of antennas in each node. We then investigate the special case where all user nodes have $M$ antennas and relay nodes have $N$ antennas, and provide the simplified bounds on the sum DoF. We show that our proposed achievable rate for this special case is higher than the achievable rates recently proposed in [1] . Moreover, for this special case, we obtain the exact DoF $=4M$ when $N \geq 2M$ , and DoF $=4N$ when $M \leq 2N$ .