On the degrees-of-freedom of the MIMO three-way channel with intermittent connectivity

Abstract

The degrees-of-freedom (DoF) of the multi-antenna three-way channel (3WC) with an intermittent node is studied. Special attention is given to the impact of adaptation. A nonadaptive transmission scheme based on interference alignment, zero-forcing, and erasure-channel treatment is proposed, and its corresponding DoF region is derived. Then, it is shown that this scheme achieves the sum-DoF of the intermittent channel, in addition to the DoF region of the nonintermittent one. Thus, adaptation is not necessary from those perspectives. To the contrary, it is shown that adaptation is necessary for achieving the DoF region of the intermittent case. This is shown by deriving an outer bound for the intermittent channel with nonadaptive encoding, and giving a counterexample of an adaptive scheme which achieves DoF tuples outside this bound. This highlights the importance of cooperation in this intermittent network. I. INTRODUCTIONMulti-way, full-duplex, and device-to-device (D2D) communications are important techniques that are expected to gain more prominence in future communication systems. Multiway communication refers to communication between multiple nodes each acting as a source, a destination, and possibly a relay. Full-duplex operation is defined as when these three functionalities take place over the same time/frequency resources, and D2D communication refers to direct communication between users without or with limited base-station intervention. Those techniques attracted and continue to attract research attention [1]- [5].Consider a setup where three nodes (D2D users e.g.) communicate with each other in a multi-way fashion. This setup can be modeled as a three-way channel (3WC), an extension of Shannon's two-way channel [6] which has been studied in [7]- [9]. Therein, it is assumed that the nodes are always connected. This assumption is not always valid in practice since a node might have intermittent connectivity, e.g. due to shadowing, or if a D2D node causes strong interference to a cellular user, in which case it is not permitted to use its band [10].The impact of intermittency on the performance of various networks was studied in [11]-[14] for instance. In this paper, we study the impact of intermittency on the multiple-input multiple-output (MIMO) 3WC. We consider a full-duplex MIMO 3WC with full message-exchange, where each node has an independent message to each of the other two nodes. The permanent nodes have only causal knowledge of the A. Chaaban and M.-S. Alouini are with the Division of Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE) at King Abdullah

Degrees-of-Freedom of the MIMO Three-Way Channel With Node-Intermittency

“…The respective remaining cases follow by renaming. Preliminary work [1] fixed node 1 to be intermittent and further assumed a relation on the numbers of antennas, which is not w.l.o.g. We fix node 1 to be intermittent, but allow for any combination of numbers of antennas, which is approach a) and w.l.o.g.…”

“…We try to achieve d = (0.5, 0, 0.5, 4, 0, 4). To transmit on average half a symbol per channel access full-duplex over the intermittent 1 ↔ 2, we use a rate 1 2 EC over one available ZF dimension in each direction (a = 0). All of them create interference at node 1, but this four-dimensional interference subspace can be aligned with the two-dimensional interference subspace caused by 2 → 3 (γ 1 = 2).…”

UAV-aided Multi-Way Communications

“…The (sum) degreesof-freedom (DoF), i.e., the sum-capacity scaling over the signal-to-noise ratio (SNR) of the MIMO multi-way channel ( Fig. 1) was studied in a previous work [12].…”