Fundamental limits of wireless two-way full-duplex communication networks

Most wireless communication networks are two-way, where nodes act as both sources and destinations of messages. This allows for "adaptation" at or "interaction" between the nodes -- a node's channel inputs may be functions of its message(s) and previously received signals allowing for potentially larger rates than those achievable in feedback-free one-way channels where inputs are functions of messages only. However, examples exist of channels where adaptation is not beneficial from a capacity perspective; we ask whether analogous results hold for several multi-user two-way networks. We first consider deterministic two-way channel models: the binary modulo-2 addition channel and a generalization of this, and the linear deterministic channel which models Gaussian channels at high SNR. For these deterministic models we obtain the capacity region for the two-way multiple access/broadcast channel, the two-way Z channel and the two-way interference channel (under certain "partial" adaptation constraints in some regimes). We permit all nodes to adapt their channel inputs to past outputs (except for portions of the linear high-SNR two-way interference channel where we only permit 2 of the 4 nodes to fully adapt). However, we show that the two-way fully or partially adaptive capacity region consists of two parallel "one-way" regions operating simultaneously in opposite directions, i.e. adaptation is useless. We next consider two noisy channel models: first, the Gaussian two-way MAC/BC, where we show that adaptation can at most increase the sum-rate by 1/2 bit in each direction. Next, for the two-way interference channel, partial adaptation is shown to be useless when the interference is very strong. In the strong and weak interference regimes, we show that the non-adaptive Han and Kobayashi scheme utilized in parallel in both directions achieves to within a constant gap for the symmetric rate of the fully (for some regimes) or partially (for the remaining regimes) adaptive models. Then we generalize the two-way interference channel to the K-pair-user two-way interference channel (TWIC) and show that for symmetric scenarios and certain interference regimes, non-interactive schemes again achieve to within a constant gap for the fully adaptive Gaussian model. Furthermore, we investigate the degrees of freedom (DoF, also known as the multiplexing gain) of the K-pair-user TWIC with and without a MIMO relay, where we emphasize all nodes operate in full-duplex mode. We first derive a new outer bound (allows interaction) to demonstrate that the optimal DoF of the K-pair-user TWIC is K: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. We next employ a MIMO relay in the K-pair-user TWIC. If the relay is non-causal/instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k-1), we show that a full-duplex MIMO relay cannot increase the DoF of the K-pair-user TWIC beyond K, as if no relay or interaction is present. We comment on reducing the number of antennas at the instantaneous relay.