一种加权稀疏约束稳健Capon波束形成方法

为了克服标准Capon波束形成器旁瓣级高以及存在角度失配时性能急剧下降等缺点, 在稀疏约束Capon波束形成器的基础上, 提出了一种加权稀疏约束Capon波束形成器. 该方法利用波束响应的稀疏分布特性, 在标准Capon波束形成优化模型中加入旁瓣区域波束响应稀疏约束(l₁ 范数约束), 使旁瓣区域波束响应向量中非零元素的个数最小化; 通过阵列采样数据协方差矩阵特征分解得到信号子空间及噪声子空间, 利用信号子空间与噪声子空间的正交特性, 构造加权矩阵对稀疏约束进行加权, 使得稀疏重构时波束响应向量中不同角度对应的元素得到不同程度的约束. 该方法有效地抑制了Capon波束形成器的高旁瓣级, 加深了干扰方位零陷, 提高了阵列输出信干噪比. 由于稀疏约束, 波束响应向主瓣集中, 期望信号方向附近的波束响应都较大, 从而也提高了阵列抗导向矢量角度失配的能力. 数值仿真和水池实验验证了所提方法的有效性.

Robust Capon beamforming with weighted sparse constraint

Adaptive beamforming is widely used in the fields such as radar, sonar, wireless communication to estimate the parameters of the signal of interest (SOI) at the output of a sensor array by data-adaptive spatial filtering and interference suppression. The standard Capon beamformer (SCB) is a typical adaptive beamforming approach which provides a superior performance by minimizing the array output power while simultaneously maintaining the array response under the assumption of distortionless direction of arrival (DOA). However, the advantages in performance of SCB are obtainable only when the number of snapshots available for the sample covariance matrix estimation is large enough and the direction of the SOI is known accurately. When applied to practical situations where the aforementioned two requirements are not satisfied, SCB will suffer high sidelobe levels and performance degradation in the parameter estimates due to lack of measurements and mismatch in the steering vector.A sparsity-constrained Capon beamformer (SCCB) arises to alleviate these problems. Unlike SCB, the constraint in SCCB is composed of two parts: the original array output power constraint part and the sparse constraint part (?1 norm constraint, encouraging sparse distribution in the array responses). However, if the sparse constraint in SCCB is set too large compared with the array output power constraint part, the responses in the directions of interferences will be influenced, and a tradeoff between the ability to reduce the sidelobe levels and the ability to reject the interferences must be made. Thus, based on the SCCB, a new robust Capon beamformer utilizing a weighted sparse constraint is proposed in this paper. In the proposed method, the sparse constraint part is replaced by a weighted sparse constraint, which is applied only to the sidelobe regions of the beampattern. By doing so, the number of the non-zero elements in the sidelobe response is minimized, resulting in an enhanced mainlobe region and suppressed sidelobe ones.In sparse recovery, the sparse constraint (the l₁ norm constraint) does not necessarily enforce democratic penalization, which means that larger coefficients are penalized more heavily than smaller coefficients. Based on such a consideration, a weighting matrix can be constructed to put larger weights in the interferences directions to discourage their responses, and put smaller weights to maintain the responses in the remaining parts of the sidelobe regions. In this paper, the weighting matrix is obtained by utilizing the orthogonality between the signal subspace and the noise subspace. Since the steering vectors corresponding to the interferences and the SOI span the same space as the signal subspace, the inner products between the steering vectors in the interference directions and the noise subspace will produce zeroes ideally. By taking the reciprocals of these inner products, large values will yield in the interference directions while small values are obtained in other directions in the sidelobe regions. Using these values as the weights to the sparse constraint, a beampattern with deeper nulls, lower sidelobes, and better robustness to steering vector mismatch is obtainable as compared with SCB and SCCB. Besides, the output SINR is also effectively improved. Numerical simulations and a water-tank experiment are conducted to demonstrate the effectiveness of the proposed method.