A Robust Beamforming Algorithm for Sparse Array Based on Atomic Norm Minimization

doi:10.12382/bgxb.2023.0618

Abstract

Abstract:

Aiming at the performance degradation of the beamforming algorithm when some mismatches are present in the signal model. A robust beamforming algorithm based on atomic norm minimization (ANM) is proposed to improve the beamforming performance of sparse array during the mismatch of signal model. The proposed algorithm is used to construct an ANM-based noise reduction model and transform it into an equivalent semi-definite programming problem according to the covariance matrix structure of sparse array. Meanwhile, the dual problem of this model is derived to improve the computational efficiency, and the received data and covariance matrix of the array after noise reduction are obtained. The spatial spectrum is proved to be unambiguous based on the structural properties of a coprime array, and the directions of arrival of the incident signals are obtained directly by using the multiple signal classification algorithm for the resulting covariance matrix. The received data of a uniform linear array with the same aperture as the coprime array is obtained using the virtual filling technique, and the array output is ultimately obtained. Simulated results verify the feasibility and accuracy of the proposed algorithm, which improves the output signal to interference plus noise ratio by at least 1.5dB compared to the other tested algorithms.

Key words: robust beamforming, sparse array, atomic norm minimization, dual problem

CLC Number:

TN827⁺.2

LÜ Yan, CAO Fei, JIN Wei, HE Chuan, YANG Jian, ZHANG Hui. A Robust Beamforming Algorithm for Sparse Array Based on Atomic Norm Minimization[J]. Acta Armamentarii, 2024, 45(8): 2737-2748.

Figures/Tables 11

Fig.1 The structure of coprime array

Fig.2 Schematic diagram of the equivalent ULA

Table 1 Steps of the proposed algorithm

步骤	内容
1	获取K快拍的阵列接收信号X,求解式(28)利用对偶性得到式(27)的最优解,记为Y^和 $Z 1 $ ;
2	利用MUSIC算法得到 $Z 1 *$ 的空间谱,获得入射信号的$\operatorname{DOA}\left\{\hat{\theta}_{1}, \hat{\theta}_{2}, \cdots, \hat{\theta}_{Q}\right\}$;
3	根据式(36)得到空间间隙位置的虚拟阵元接收数据$\hat{\boldsymbol{Y}}^{}$,并将其和Y^进行重排;
4	结合式(37)计算阵列权值矢量 $w ˜$ ,最终获得阵列的输出 $y ˜$ 。

Table 1 Steps of the proposed algorithm

步骤	内容
1	获取K快拍的阵列接收信号X,求解式(28)利用对偶性得到式(27)的最优解,记为Y^和 $Z 1 $ ;
2	利用MUSIC算法得到 $Z 1 *$ 的空间谱,获得入射信号的$\operatorname{DOA}\left\{\hat{\theta}_{1}, \hat{\theta}_{2}, \cdots, \hat{\theta}_{Q}\right\}$;
3	根据式(36)得到空间间隙位置的虚拟阵元接收数据$\hat{\boldsymbol{Y}}^{}$,并将其和Y^进行重排;
4	结合式(37)计算阵列权值矢量 $w ˜$ ,最终获得阵列的输出 $y ˜$ 。

Fig.3 MUSIC spatial spectrum

Fig.4 DOA estimated results

Fig.5 Comparison of noise reduction performances

Fig.6 Test results of Experiment 3.2

Fig.7 Test results of Experiment 3.3

Fig.8 Test results of Experiment 3.4

Fig.9 Comparison of beam patterns

Fig.10 Running times of different algorithms

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