A robust approach to optimum widely linear MVDR beamformer

Abstract

In many array processing, the received signals are nonstationary, or in particular, noncircular. Widely linear minimum variance distortionless response (WL MVDR) beamformers can exploit the noncircularity of received signals and improve the performance of the conventional MVDR beamformer. However, in the optimum WL MVDR beamformer, the array steering vector (ASV) and the signal noncircularity coefficient should be known a priori for the signal of interest. This requirement puts strict limitation to the implementation of this beamformer. We therefore in this paper propose a robust approach to the optimal WL MVDR beamformer that can deal with the uncertainties in the ASV and noncircularity coefficient. Two variants of the proposed approach are developed based on the treatment of the uncertainties. By doing so, the requirement on the exact information is relaxed while the performance improvement can still be obtained. Simulation studies are also provided to illustrate the performance of the proposed approach.

Third-Order Volterra MVDR Beamforming for Non-Gaussian and Potentially Non-Circular Interference Cancellation

“…Expression (18) describes the output of the MVDR beamformer which takes only into account the distribution of the total noise n(t), and thus its potential non-Gaussianity and non-circularity in particular. Choosing w f = (s H s) −1 s and comparing (18) and 15, we deduce that s MMSE (t) and s MVDR (t) have similar forms but where E[n(t)/x(t)] in (15), which contains information about the SOI distribution, has been replaced by E[n(t)/n s ⊥ (t)] in (18), which contains no information about the SOI distribution. If n(t) is Gaussian and circular, E[n(t)/n s ⊥ (t)] is a linear function of n s ⊥ (t) and the MVDR beamformer (18) is a linear function of x(t) corresponding to the Capon beamformer [2].…”

Widely linear minimum dispersion beamforming for sub-Gaussian noncircular signals

“…Besides, the gain and phase errors are drawn from two normal random generators with mean ¼ 1, standard deviation ¼ 0:05 and mean ¼ 1, standard deviation ¼ 0:025π, respectively. The proposed WL-QCMD beamformer is compared with the QCMD beamformer [13], worst-case-based beamformer [22], robust WL beamformer [19] and reconstruct-based WL beamformer [20]. Assume that ε a ¼ 0:3N ¼ 1:2 and ε γ ¼ 0:1.…”

“…So the ESVã γ cannot be known exactly, which will lead to the signal cancellation and performance degradation. Many robust WL beamformers are proposed to reduce errors [19][20][21]. The uncertainty set is used to gain the robustness against errors [19,21].…”

“…Many robust WL beamformers are proposed to reduce errors [19][20][21]. The uncertainty set is used to gain the robustness against errors [19,21]. In [20], the augmented interference-plus-noise covariance matrix is reconstructed to estimate the corrected ESV.…”

Blind Separation of Noncircular Sources Via Approximate Joint Diagonalization of Augmented Charrelation Matrices

“…This information is usually retrieved by exploiting the conjugate statistics of the sources (e.g., the conjugate power and the conjugate-covariance matrix) and can be used to boost the performance of sensor array signal processing. And a few examples are: (i) aperture extension for direction-of-arrival estimation [1,3,12,14,18], (ii) aperture extension for beamforming/filtering [5,29,31], (iii) aperture extension for ICA [20], (iv) improved detection performance [21,22], (v) enhanced model selection [17], and (vi) fully automatic calculation of regularization parameters in robust adaptive beamforming [32].…”