Degrees of freedom of MIMO cognitive interference channel with user cooperation

In multiple-input multiple-output cognitive interference channels, secondary users share frequency bands with primary users. The different frequency authorities of the secondary users and the primary users complicate the determination of the upper bound (UB) of the degrees of freedom (DoF). This study focuses on the (K+1)-user interference channel from the perspective of the solvability of multivariable quadratic equations. The UB of the spatial DoF based on coordinated beamforming is derived from Bezout's theory, where the relationship between the UB and user count is non-linear. A joint interference aligned algorithm based on user cooperation is proposed. The algorithm is theoretically proved to be globally convergent and the DoF is analyzed to be insensitive to the convergent error, which means the proposed algorithm can achieve the UB of DoF through limited iterations. Theoretical analysis and simulation results show that extra DoF can be obtained by the secondary users by cooperating with the primary users. Furthermore, a user coordinated interference aligned algorithm is proposed to verify the availability of DoF. Global convergence has been proved, which means the proposed algorithm is capable of analyzing the UB of DoF under ideal conditions. However, algorithm maybe not convergent due to rounded error and limited iterative times. A further study on error of convergence is given to illustrate that the DoF is insensitive to convergence errors. So the upper bound can be achieved in limited iteration rounds.