Cyclic Communication and the Inseparability of MIMO Multi-Way Relay Channels

Abstract

The K-user MIMO multi-way relay channel (Y-channel) consisting of K users with M antennas each and a common relay node with N antennas is studied in this paper. Each user wants to exchange messages with all the other users via the relay. A transmission strategy is proposed for this channel. The proposed strategy is based on two steps: channel diagonalization and cyclic communication. The channel diagonalization is applied by using zeroforcing beam-forming. After channel diagonalization, the channel is decomposed into parallel sub-channels. Cyclic communication is then applied, where signal-space alignment for network-coding is used over each sub-channel. The proposed strategy achieves the optimal DoF region of the channel if N ≤ M . To prove this, a new degrees-of-freedom outer bound is derived. As a by-product, we conclude that the MIMO Y-channel is not separable, i.e., independent coding on separate sub-channels is not enough, and one has to code jointly over several sub-channels.

Optimal Degrees of Freedom Region for the Asymmetric MIMO Y Channel

“…The achievability shall be proved in the next section. Remark 1 (Comparison to [13]): In the case with M 1 = M 2 = M 3 = M and N ≤ M , our result reduces to Theorem 1 in [13] with K = 3.…”

“…Note that PDE pattern have been introduced in [1], [2] and CDE pattern have been introduced in [12], [13].…”

Distributed User Scheduling for MIMO-Y Channel

“…Proof: Note that g (x 1 ,x 2 ) monotonically increases withx 1 andx 2 , we can check that [2] , g x [2] , x [3] = g x [3] , x [2] , and the proof is finished.…”

“…At each user S k , the received signal is given by (2), then the remaining signal after subtracting self-interference is given byỹ…”

“…The capacity and degrees-of-freedom of multi-way relay channel have been partially studied by [2]- [4] assuming specific system configurations and traffic patterns. The more general multi-group multi-way relay scenario is considered in [5] with a novel and efficient joint spatial and temporal signal processing.…”