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Open Access Publications from the University of California

Degrees of Freedom of Rank-Deficient MIMO Interference Networks

  • Author(s): Krishnamurthy, Sundar Rajan
  • Ramakrishnan, Abinesh
  • Jafar, Syed Ali
  • et al.
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License

We characterize the degrees of freedom (DoF) of MIMO interference networks with rank-

deficient channel matrices. For the 2-user rank deficient MIMO interference channel, we prove

the optimality of previously known achievable DoF in the symmetric case and generalize the re-

sult to fully asymmetric settings. For the K-user rank deficient interference channel, we improve

the previously known achievable DoF and provide a tight outer bound to establish optimality

in symmetric settings. In particular, we show that for the K-user rank deficient interference

channel, when all nodes have M antennas, all direct channels have rank D0, all cross chan-

nels are of rank D, and the channels are otherwise generic, the optimal DoF value per user is

min(D0, M −min(M,(K−1)D)). For 2-user and 3-user rank deficient channels, achievable schemes2

are for both constant and time-varying channels, while for K-user rank deficient channels, we present schemes for time-varying channels and note that the insights would act as stepping stones for constant channels. Notably for interference channels, the rank-deficiency of direct channels does not help and the rank-deficiency of cross-channels does not hurt. The main technical challenge is to account for the spatial dependencies introduced by rank deficiencies in the interference alignment schemes that typically rely on the independence of channel coefficients.

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