Keywords: 
• 稳健Capon波束形成 /
• 加权稀疏约束 /
• 旁瓣抑制

Abstract: 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 interfer-ence 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 obtain-able 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 require-ments 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 ?1 norm constraint) does not necessarily enforce democratic penal-ization, which means that larger coeffcients are penalized more heavily than smaller coeffcients. 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.