Research On Robust Adaptive Algorithms For Beamforming

Adaptive beamforming technology is a spatial filtering technique in array signal processing.By adjusting the weighting coefficients of the antenna array,the output signals from each array element are weighted and summed,so that the antenna array achieves maximum gain in the direction of the desired signal,while suppressing interference from other signals and noise,and achieving directional reception of the desired signal.The adaptive beamforming algorithm,as the core of adaptive beamforming technology,directly determines the main performance of the beamformer.Due to its low computational complexity,ease of implementation,and stable performance,the adaptive filtering algorithm has become widely used in adaptive beamforming algorithms.Among the many existing adaptive filtering algorithms,most of them can achieve good convergence performance in Gaussian scenarios.However,in practice,many environmental noises contain non-Gaussian impulse noise.In this scenario,the performance of adaptive filtering algorithms based on Gaussian noise assumptions will decrease significantly or even diverge.In addition,the step-size,as an important parameter of the adaptive filtering algorithm,directly affects the convergence performance of the algorithm.Within the stable range,the larger the step-size,the faster the convergence speed of the algorithm,but the larger the steady-state misadjustment;and vice versa.Therefore,when selecting the step-size parameter,the trade-off between the convergence speed and the steady-state misadjustment of the algorithm needs to be considered.To suppress the interference of non-Gaussian impulse noise on the algorithm and solve the trade-off problem caused by the fixed step-size,this paper proposes two variable step-size adaptive filtering algorithms to combat impulsive noise,and applies them to adaptive beamforming to enhance the robustness and convergence performance of the adaptive beamformer.The main work of this paper are summarized as follows:1)Although the normalized least mean m-estimate(NLMM)algorithm shows good robustness in non-Gaussian impulsive noise scenarios,but the trade-off between convergence speed and steady-state misadjustment caused by a fixed step-size is still a problem.To solve this problem,this paper proposes a new combination step-size NLMM(CSS-NLMM)algorithm,which adjusts the weight of large and small step-sizes in CCS by mixing factors,achieving fast convergence speed and low steady-state misadjustment.At the same time,the proposed CSS strategy is directly extended to other robust NLMS algorithms to obtain CSS-MCC-NLMS and CSS-NLMP algorithms.In addition,based on the mixed Gaussian model,this paper analyzes the theoretical performance of the CSS-NLMM algorithm and obtains a verifiable steady-state and transient model.2)To address the trade-off problem caused by the fixed step-size of the NLMM algorithm,this paper also proposes a switching step-size NLMM(SSS-NLMM)algorithm,which selects the best step-size for each iteration by comparing the mean square deviation(MSD)trend of different step-size NLMM algorithms.Moreover,to improve the convergence performance of the algorithm in different transition stages,this paper introduces a feedback mechanism for the minimum MSD trend,so that the SSS-NLMM algorithm can achieve fast convergence and low steady-state misadjustment.3)The proposed CSS-NLMM and SSS-NLMM algorithms are applied to beamforming to obtain new adaptive beamforming algorithms,namely,complex-valued CSS-NLMM(CSS-CNLMM)and complex-valued SSS-NLMM(SSS-CNLMM)algorithms,enhancing the robustness and convergence performance of the adaptive beamformer,and making the output signal-to-noise ratio of the beamformer approach the optimal value quickly under the condition of small impulsive repetition frequency.When the input signal is non-circular,a widely-linear beamforming model is studied,and widely-linear CSS-CNLMM(WL-CSS-CNLMM)and widely-linear SSS-CNLMM(WL-SSS-CNLMM)algorithms are proposed,which fully utilize the non-circular characteristics of the signal and significantly improve the output signal-to-noise ratio of the adaptive beamformer.