Robust Adaptive Beamforming Based On Response Ripple Constraint Of The Uncertain Set

In the field of array signal processing, adaptive beamforming is a ubiquitous task with wide applications. The traditional data-dependent beamforming methods are supposed to maintain the signal of interest(SOI) to be unit while suppress the interferers.However, in practical scenarios, due to the imperfection of array and environment knowledge, the performance of traditional beamforming methods will degrade severely since the SOI will be treated as a interference to be suppressed.In order to increase the robustness against such imperfections, many robust adaptive beamforming methods are proposed. Among these methods, diagonal loading(DL)is a popular robust beamforming method in which an additional constraint on the Euclidean norm of the weight vector is imposed to the objective of the Capon beamformer.In essence, the DL method is equivalent to inject an artificial white noise in the input data to reduce the input signal-to-noise ratio(SNR) which will reduce the sensitivity to the steering vector error of SOI. In addition, in order to overcome the drawbacks of the traditional DL method and determine the loading level, the uncertainty set of steering vector is considered in many literatures.In this paper, we have made the following three main contributions:1) We show that the magnitude response ripple constraint over the steering vector uncertainty set can be transformed to a norm constraint on the weight vector, in which the maximum norm value is related to the radius of the steering vector uncertainty set and the number of array sensors.2) In order to suppress the interferences, we develop a new robust linearly-constrainedminimum-variance beamformer(LCMV) which can be viewed as a combination of the LCMV beamformer and the norm-constrained Capon beamformer(NCCB). And we formulate a closed-form solution for the corresponding optimization problem.3) In the absence of a priori knowledge for the interferences, we propose a novel robust beamformer in which the sidelobe control is taken into consideration. The solution of the corresponding optimization problem can be obtained by CVX software package with carefully selected parameters.The proposed method is compared to other existing methods. Under the same scenarios, simulation results are also provided to demonstrate that our proposed algorithms are more robust than other tested methods.