A Study On The Adaptive Beamforming Algorithms Based On The Noncircular Signals

Adaptive beamformer is a sonsor array which constructs the efficient filter for spatial signals and exacts information that we are interested in. Adaptive beamforming has attracted widespread attention around the world and widely used in many fields such as communication, radar, biomedical engineering, sonar and astronomy. Although the conventional adaptive beamformer has been shown to be optimal for circular signals, it becomes suboptimal for noncircular (NC) signals. Optimal widely-linear filters are of great value in many practical situations if the signals share the second-order NC properties. Consequently, a widely-linear (WL) beamformer which utilizes the noncircularity of the received signals is proposed in the literature.Conventional adaptive array assumes the signals are circular and usually we can find a linear and time invariant complex filter, such that its output optimizes an second-order criterion under certain constraints. But in practice, NC signals such as the BPSK, offset-QPSK, PAM and ASK-modulated signals, have been widely used in many modern communication systems. As a result, the conventional adaptive beamformer which has been shown to be optimal for circular signals becomes suboptimal. Unlike the conventional beamformer, the optimal WL beamformer has been proposed to gain the optimal outputs for the noncircular signals. However, its performance may considerably degrade for the finite number of training samples. To circumvent this issue, an eigenspace-based WL beamformer for NC signals is proposed in this paper, which utilizes the eigenstructure of the augmented correlation matrix to improve the performance of the WL beamformer.For the continuous adaptive beamformer, the least mean squares (LMS) based beamformer enjoys a great popularity for its simplicity. It directly give a solution to update the weight vector at each iteration. However, it is difficult to choose a reasonable value for the constant step size which controls the convergence rate of the weight vector and also determines the final excess mean square errors. In order to circumvent this problem, this paper has devised shrinkage linear LMS (SL-LMS) for adaptive beamforming, which is able to improve the convergence speed of the weight vector and provide much better steady-state behavior. The step size of the SL-LMS algorithm is adjusted according to the relationship between the noise-free a posterior error and the noise-free a priori error. As a result, the SL-LMS algorithm can adaptively adjust the step size to provide faster convergence and less misadjustment than the LMS algorithm. Like the widely-linear based adaptive beamforming methods such as the WL-CLMS algorithm, the proposed shrinkage WL LMS (SWL-CLMS) algorithm takes advantage of the NC properties of the desired signal. As a result, the augmented array aperture provides considerable improvement in the output SINR and the estimation accuracy of the weight vector. Moreover, by minimizing the square of the instantaneous augmented noise-free a posterior error, we get the SWL-CLMS algorithm which can efficiently sense the approximately optimal step size to provide a much faster convergence speed. Numerous simulation results illustrate that the proposed algorithms provide much better performance than the existing approaches.