Degrees of Freedom of Full-Duplex Cellular Networks: Effect of Self-Interference

It was recently shown that full-duplex (FD) operation at a base station (BS) can provide up to twice as many degrees of freedom (DoF) as a conventional half-duplex (HD) cellular network in the absence of self-interference. In practice, however, self-interference in an FD BS may not be eliminated completely due to imperfect cancellation, and it is not yet known whether FD operation can improve the sum DoF of cellular networks in the presence of residual self-interference. In this paper, we provide a complete characterization of the sum DoF in an FD-BS cellular network with self-interference, where the rank of the self-interference matrix is arbitrary. Specifically, we propose a self-interference cancellation scheme that maximizes the sum DoF, and we prove its optimality by deriving the matching upper bound. Our results show that even in the presence of residual self-interference, an FD-BS network can still outperform a conventional HD-BS network, and furthermore, the sum DoF coincides with that of an FD-BS network with no self-interference under certain conditions. We also derive an achievable sum rate under ergodic phase fading, showing that not only a sum-DoF gain but also a sum-rate gain can be obtained over the entire signal-to-noise ratio range even if residual self-interference exists.