On the maximum sum-rate of cognitive MIMO interference channels

In this paper, we address the problem of maximizing the ergodic sum-rate of an N-user cognitive MIMO Interference Channel (IC) formed by unlicensed (or secondary) users. We assume that N secondary users coexist in the same area and try to access the same set of frequency bands. In such a setup, we define a cognitive MIMO IC as an extension of a classical IC where each user has multiple antennas and multiple frequency bands for transmission. We further assume a typical cognitive radio scenario where the structure of interference signals is not known and interference cancelation is not possible. Therefore, interference is treated as Gaussian noise in this work. The problem of ergodic sum-rate maximization reduces to the problem of finding the optimal power allocation for each user over each spatial channel in each frequency band. This problem belongs to the class of non-linear non-convex optimization problems and is hence challenging to solve analytically. We extend a reformulation and linearization (RLT) based branch and bound (BB) method to solve this problem. BB/RLT was recently proposed to solve the sum-rate maximization problem of a single band MIMO IC with the guaranteed convergence to the global optimum. It should be noted that we are proposing an optimal power control scheme to perform power control simultaneously over spatial and spectral dimensions without any explicit interference cancelation or Interference Alignment (IA). We also present some interesting comparisons between the sum-rates achievable by the proposed scheme and those by IA.