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 communica-tion,etc.Cognitive MIMO is a fusion technology of cognitive radio and MIMO,which has advantages of interference sup-pression,anti-multipath fading,spatial diversity,and multiplexing.However,there is intercoupling among its precoding matri-ces 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 interfer-ence 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 de-rived by interactively and alternately using transmitting precoding and receiving interference subspace matrix,and the deriva-tion process is based on Rayleigh-Ritz theorem and convex optimization theory.In order to remove the interference tempera-ture constraint,the Lagrange partial of dual-decomposition was exploited,and the sub-gradient projection method was adopt-ed 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 the-oretical analysis and numeric simulations,and results also indicate that the proposed algorithm is capable of maximizing the cognitive MIMO interference network available transmitting rate.%认知无线电通过与 MIMO （Multi-Input Multi-Output）、OFDM（Orthogonal Frequency Division Multiple-xing）、超宽带、协作通信等技术融合来改善频谱利用率。而认知MIMO是认知无线电和MIMO技术的融合，虽然具有干扰抑制、抗多径衰落、空间分集和复用等优势，但是由于underlay共享方式中干扰温度约束的存在，导致发送预编码矩阵之间相互耦合，因此该技术在underlay干扰网络中难以获得最优的传输性能。针对该问题，通过交替迭代的方式，结合Rayleigh-Ritz定理和凸优化理论，推导了最优收发矩阵之间的迭代关系，提出一种最优干扰对齐算法。该算法利用Lagrange部分对偶方式来去除干扰温度约束，并采用次梯度投影法更新Lagrange变量，克服了已有半正定松弛算法因忽略矩阵秩约束而导致速率性能下降的缺陷。理论分析和数值仿真验证了算法的有效性，结果表明所提算法可实现网络可达速率和的最大化。
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