We show that an M X N user MIMO X network with A antennas at each node hasAMN/(M+N-1) degrees of freedom (DoF), thus resolving in this case a discrepancybetween the spatial scale invariance conjecture (scaling the number of antennasat each node by a constant factor will scale the total DoF by the same factor)and a decomposability property of overconstrained wireless networks. While thebest previously-known general DoF outer bound is consistent with the spatialinvariance conjecture, the best previously-known general DoF inner bound,inspired by the K user MIMO interference channel, was based on thedecomposition of every transmitter and receiver into multiple single antennanodes, transforming the network into an AM X AN user SISO X network. While sucha decomposition is DoF optimal for the K user MIMO interference channel, a gapremained between the best inner and outer bound for the MIMO X channel. Here weclose this gap with the new insight that the MIMO X network is only one-sideddecomposable, i.e., either all the transmitters or all the receivers (but notboth) can be decomposed by splitting multiple antenna nodes into multiplesingle antenna nodes without loss of DoF. The result is extended to SIMO andMISO X networks as well and in each case the DoF results satisfy the spatialscale invariance property. In addition, the feasibility of linear interferencealignment is investigated based only on spatial beamforming without symbolextensions. Similar to MIMO interference networks, we show that when theproblem is improper, it is infeasible.
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