This paper considers a K-user multiple-input multiple-output (MIMO) interference channel in which uncoordinated interference appears. Due to the uncoordinated interference, perfect interference alignment (IA) may be not attained, which indicates the interference subspaces can not be completely aligned. The rank constrained rank minimization (RCRM) framework has been recently developed to minimize the rank of the subspace spanned by interference signals with full rank constraint on the direct signal space. To solve this non-convex and intractable problem, we introduce a log-sum function as an approximation surrogate and develop a joint Frobenius norm and reweighted nuclear norm approach which jointly enhances the sum rate at low-to-moderate signal-to-noise ratio (SNR) and the achievable multiplexing gain per user in the high SNR regime. The optimum solutions are iteratively achieved with the convergence guaranteed. Simulation results are presented to validate the effectiveness of the proposed reweighted nuclear norm algorithm and its further development.
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