The paper focuses on the two-way relay channel (TWRC) and the multi-way wireless network with three terminals, where all three want to exchange or share data and have to do that with the help of a relay. This paper shows how it is possible to significantly decrease the number of time slots required to exchange messages between terminals in networks based on time-division multiple access (TDMA), by taking into consideration new techniques at the physical (PHY) layer. The paper considers a PHY

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... er where physical-layer network coding (PLNC), multiple-input multiple-output (MIMO), and in-band "full-duplex" (IBFD) with loopback interference cancellation are all integrated, so that it is possible to significantly increase the overall throughput of the network. This is entirely attained by transferring the burden from the time domain to the spatial domain, via spatial multiplexing and by simultaneously resorting to non-orthogonal multiple access, which is the consequence of using both PLCN and IBFD. For the TWRC, it is shown that, if a massive MIMO relay is used, a simple lattice-based PLNC can be directly applied and, with typical IBFD interference cancellation amounts, a TWRC can effectively use only one time slot instead of the four needed when adopting the traditional TDMA exchange. In the case of the Y-network (i.e., with three terminals), a technique is presented that allows all the information exchange between terminals to be cut from the six time slots required in TDMA to only one time slot, provided that the information packets are not too short. The error performance of these systems is measured by means of simulation using MIMO Rayleigh fading channels.