Cognitive radio can improve the spectrum efficiency by fusing with technologies such as multi-input multi-output (MIMO)

orthogonal frequency division multiplexing (OFDM)

ultra wideband (UWB)

cooperative communication

etc.Cognitive MIMO is a fusion technology of cognitive radio and MIMO

which has advantages of interference suppression

anti-multipath fading

spatial diversity

and multiplexing.However

there is intercoupling among its precoding matrices because of the interference temperature constraint in underlay sharing mode

which makes it difficult for the cognitive MIMO in the underlay interference network to obtain optimal transmitting performance.Consequently

an optimal interference align algorithm for cognitive MIMO interference network is proposed to obtain the optimized interference network transmitting performance

in which the iteration relationship between the optimal transmitting and receiving matrices is derived by interactively and alternately using transmitting precoding and receiving interference subspace matrix

and the derivation process is based on Rayleigh-Ritz theorem and convex optimization theory.In order to remove the interference temperature constraint

the Lagrange partial of dual-decomposition was exploited

and the sub-gradient projection method was adopted to update the Lagrange variable

which overcame the shortcoming of decreasing transmitting rate caused by ignorance of the matrix rank constraint in the existing semi-definite relaxation algorithms.The validity of this algorithm is verified by theoretical analysis and numeric simulations

and results also indicate that the proposed algorithm is capable of maximizing the cognitive MIMO interference network available transmitting rate.