Reweighted Nuclear Norm Approach for Interference Alignment

Managing uncoordinated interference becomes a substantial problem for heterogeneous networks, since the unplanned interferences from the femtos cannot be coordinately aligned with that from the macro/pico base stations (BSs). Due to the uncoordinated interference, perfect interference alignment (IA) may be not attained. In order to achieve linear capacity scaling by IA, we follow the rank-constrained rank minimization (RCRM) framework which minimizes the rank of the interference subspace with full rank constraint on the direct signal space. Considering that the sum of log function can obtain low-rank solutions to linear matrix inequality (LMI) problems for positive semidefinite matrices, we introduce sum of log function as an approximation surrogate of the rank function. To minimize the concave function, we implement a Majorization-Minimization (MM) algorithm and develop a reweighted nuclear norm minimization algorithm with a weight matrix introduced. Moreover, considering the practical available signal-to-noise ratio (SNR), a mixed approach is developed to further improve the achievable sum rate in low-to-moderate SNR region. Simulation results show that the proposed algorithm considerably improves the sum rate performance and achieves the highest multiplexing gain than the recently developed IA approaches for various interference channels.