四元数矩阵重构鲁棒波束形成算法

极化敏感阵列的四元数信号模型保持了偶极子阵元分量之间固有的正交性,因而四元数MVDR（Q-MVDR）算法具有比传统复数域MVDR算法更优的性能,但在强期望信号和导向矢量失配的情况下,Q-MVDR算法性能严重下降,甚至会出现期望信号相消现象.针对此问题,提出一种基于四元数矩阵重构的鲁棒波束形成算法.首先建立极化敏感阵列的四元数模型,将协方差矩阵重构方法扩展到四元数域,利用子空间方法得到干扰信号的导向矢量估计,并采用Capon谱估计方法获得干扰信号的功率,重构出干扰噪声协方差矩阵；然后根据信号子空间与噪声子空间的正交性,以及期望信号导向矢量与信号子空间属于同一子空间的特性,将权矢量投影到四元数信号子空间,对期望信号导向矢量失配误差进行修正；最后通过仿真实验验证了算法的有效性.仿真结果表明,在强期望信号和期望信号导向矢量失配时,与传统算法相比,本文算法有效避免期望信号相消引起的性能下降,增强了算法的鲁棒性,可以达到接近最优值的输出信干噪比(SINR).

Robust beamforming algorithm based on quaternion matrix reconstruction

The quaternion MVDR (Q-MVDR) algorithm has better performance than the traditional complex-domain MVDR algorithm due to the inherent orthogonality between the dipole element components in quaternion signal model of the polarization sensitive array. However, when it comes to the situation where strong desired signal and steering vector are mismatched, the performance of Q-MVDR will be degraded significantly, which can even aggravate the signal self-nulling effect. To address this problem, a robust beamforming algorithm based on quaternion matrix reconstruction was proposed. First, a quaternion signal model of polarization sensitive array was established, and the covariance matrix reconstruction method was extended to the quaternion domain. The steering vector and power of interference signals were obtained by subspace method, and the Capon spectral estimator was adopted to reconstruct the interference-plus-noise covariance matrix. Then, according to the orthogonality of signal subspace and noise subspace, as well as the characteristics that the desired signal vector and signal subspace belong to the same subspace, an improved version of steering vector mismatch correction method was introduced, which utilized the projection technique of weight vector to eigenspace signal subspace. Finally, the effectiveness of the algorithm was verified by numerical simulations. Simulation results show that the proposed technique had better robustness than traditional Q-MVDR algorithm in effectively avoiding the performance degradation caused by signal self-nulling effect, and it is able to provide similar SINR close to the optimal value in both strong desired signal and steering vector mismatch cases.