Cooperative Communication for the Rank-Deficient MIMO Interference Channel With a Reconfigurable Intelligent Surface

We study cooperative communication with an active reconfigurable intelligent surface (RIS) for the
$K$
-user rank-deficient multiple-input multiple-output (MIMO) interference channel. Specifically, we assume that transmitters and receivers use
$M$
antennas each, and the channel matrix between each transmitter and each receiver has rank
$L_{2}$
whereas the channel matrix between each transmitter or each receiver and the RIS has rank
$L_{1}$
, where
$L_{1}, L_{2}\leq M$
. In the absence of the RIS, the multiplexing gain from MIMO is severely limited when
$L_{2}$
is small. We develop a novel cooperative transmission technique utilizing the RIS to overcome the channel rank deficiency and manage inter-user interference, and the key idea is to neutralize interfering links using signals reflected from the RIS or to reflect incident waves at the RIS to increase the rank of effective channel matrices, depending on the system configuration parameters. We analyze the achievable sum degrees of freedom (DoF) and sum rate, and derive an upper bound on the sum DoF, which is tight under certain conditions. The results show that using an active RIS can significantly improve both the sum rate and sum DoF compared to the network without the RIS, especially when
$L_{1}$
is small and/or
$L_{2}$
is large.