# Flexible Null Broadening Robust Beamforming Based on JADE
###### Abstract  
In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain-phase errors of the array. Firstly, the actual steering vector with gain-phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain-phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method. beamforming; null broadening; JADE; CMT; gain-phase error Article  
Flexible Null Broadening Robust Beamforming Based on JADE  
in [11; 12]. [PERSON] [13] proposed a null broadening beamforming based on a first- and second-order iterative, and explained that the second-order requires fewer iterations than the first-order. Another method is the traditional null broadening technology, which was first proposed by [PERSON] and [PERSON] [14; 15]. [PERSON] constructs a new interference-plus-noise covariance matrix by setting N equal intensity discrete virtual interferences near a real interference location, which achieves null broadening. [PERSON] takes advantage of the fact that the frequency diffusion of the incident signal can be equivalent to the expansion of the spatial angle, which achieves null broadening by the virtual frequency band to modify the covariance matrix. Because the noise item is not affected, the [PERSON] method is better than the [PERSON] method. After summarizing the [PERSON] and [PERSON] methods, [PERSON] proposed the covariance matrix tapers (CMT), which achieved null broadening by performing a Hadamard product on the sampling covariance matrix and the taper matrix [16]. The wide null can be generated in the interference angle without prior information of interference. However, the null will be shallow, and degree of freedom (DOF) will be lost when the null is broadened. The loss of degrees of freedom occur when there are non-dynamic and dynamic interferences at the same time. The CMT will broaden all the interferences corresponding to the nulls. Each broadened null will consume at least two DOFs, which will waste the DOF in non-dynamic interference. In order to tackle this problem, [PERSON] proposed a flexible method to broaden the null, which uses the relationship between each eigenvector and each interference to widen different widths for different interferences and reduce the loss of DOF as much as possible [17]. However, due to eigenvalue decomposition and the ranking of eigenvalues, this algorithm cannot distinguish between different interference information by the size of eigenvalues when the power of multiple interferences is similar, which will cause the disorder of the broadening position. The common points of the above literature are based on the ideal array condition. In the presence of gain-phase errors, the interference suppression ability of the algorithm will drop sharply. Blind source separation (BSS) is a technique that can separate and recover relatively independent source signals from unknown multi-source hybrid systems [18].