Degrees of freedom of asymmetrical multi-way relay networks

In this paper, we introduce an asymmetrical multi-way relay channel where a base station conveys independent symbols to K different users while receiving independent symbols from the users. In this network, user i Shas M<inf>i</inf> antennas (i ∈ [1, …, K]), the base station has Σ<inf>i=1</inf><sup>K</sup> M<inf>i</inf> antennas and the relay is equipped with N<inf>R</inf> antennas. To study the capacity of this network, the degree of freedom (DOF) is characterized to be 2 Σ<inf>i=1</inf><sup>K</sup> M<inf>i</inf> if N<inf>R</inf> ≥ Σ<inf>i=1</inf><sup>K</sup> M<inf>i</inf>. The DOF implies that the number of symbols any transmitter can deliver and receive is equivalent to its number of antennas. The DOF is achievable with a proposed joint multiple access and broadcast precoding design using the signal space alignment concept.

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