Abstract
In a full-duplex bidirectional interference network with $2K$ transceivers, there are $K$ communication pairs: each user transmits a message to and receives a message from one intended user and interferes with and experiences interference from all other users. All nodes may interact, or adapt inputs to past received signals, and may thus co-operate with each other. We derive a new outer bound, and use interference alignment to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is $K$ : full-duplex operation doubles the DoF, but interaction and co-operation does not further increase the DoF. We next characterize the DoF of a full-duplex bidirectional interference network with a MIMO full-duplex relay. If the relay is noncausal/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 full-duplex bidirectional interference network beyond $K$ , as if no relay or interaction is present.
Highlights
In wireless communications, current two-way systems often employ either time or frequency division to achieve two-way or bidirectional communication
3) we show a result which is in sharp contrast to the previous point: if the relay is causal instead of noncausal, meaning that at time k it may only forward a signal which depends on the received signals up to and including time k−1, we derive a novel outer bound which shows that the degrees of freedom (DoF) of the K-pair-user full-duplex bi-directional interference network with a causal MIMO relay is K
In [26], the authors identified the DoF of the full-duplex 2-pair and 3-pair two-way multi-antenna relay MIMO interference channel, in which again there is no interference between users who only communicate through the relay
Summary
Current two-way systems often employ either time or frequency division to achieve two-way or bidirectional communication. In this work we seek to understand the potential of full duplex systems, with and without multi-antennas relays, in wireless environments with possibly significant amounts of interference (motivated by for example extreme densification of networks). We currently understand the theoretical limits of a point-topoint, full-duplex Gaussian two-way channel where two users wish to exchange messages over in-band Gaussian channels in each direction: the capacity region is equal to two independent Gaussian noise channels operating in parallel [9]. In general finding the full capacity region of the full-duplex TWIC is a difficult task, though progress has been made for several classes of deterministic channel models [11], and capacity is known to within a constant gap in certain parameter regimes and adaptation constraints [11], [12], [16]. We ask whether the same is true for the more general, full-duplex bi-directional interference network with and without a MIMO relay node
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