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
i
antennas (i ∈ [1, …, K]), the base station has Σ
i=1
^K
M
i
antennas and the relay is equipped with N
R
antennas. To study the capacity of this network, the degree of freedom (DOF) is characterized to be 2 Σ
i=1
^K
M
i
if N
R
≥ Σ
i=1
^K
M
i
. 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.