ULA Fitting for Sparse Array Design

Sparse array (SA) geometries, such as coprime and nested arrays, can be regarded as a concatenation of two uniform linear arrays (ULAs). Such arrays lead to a significant increase of the number of degrees of freedom (DOF) when the second-order information is utilized, i.e., they provide long virtual difference coarray (DCA). Thus, the idea of this paper is based on the observation that SAs can be fitted through concatenation of sub-ULAs. A corresponding SA design principle, called ULA fitting, is then proposed. It aims to design SAs from sub-ULAs. Towards this goal, a polynomial model for arrays is used, and based on it, a DCA structure is analyzed if SA is composed of multiple sub-ULAs. SA design with low mutual coupling is considered. ULA fitting enables to transfer the SA design requirements, such as hole free, low mutual coupling and other requirements, into pseudo polynomial equation, and hence, find particular solutions. We mainly focus on designing SAs with low mutual coupling and large uniform DOF. Two examples of SAs with closed-form expressions are then developed based on ULA fitting. Numerical experiments verify the superiority of the proposed SAs in the presence of heavy mutual coupling.

Sparsity-Aware SSAF Algorithm with Individual Weighting Factors for Acoustic Echo Cancellation

In this paper, we propose and analyze the sparsity-aware sign subband adaptive filtering with individual weighting factors (S-IWF-SSAF) algorithm, and consider its application in acoustic echo cancellation (AEC). Furthermore, we design a joint optimization scheme of the step-size and the sparsity penalty parameter to enhance the S-IWF-SSAF performance in terms of convergence rate and steady-state error. A theoretical analysis shows that the S-IWF-SSAF algorithm outperforms the previous sign subband adaptive filtering with individual weighting factors (IWF-SSAF) algorithm in sparse scenarios. In particular, compared with the existing analysis on the IWF-SSAF algorithm, the proposed analysis does not require the assumptions of large number of subbands, long adaptive filter, and paraunitary analysis filter bank, and matches well the simulated results. Simulations in both system identification and AEC situations have demonstrated our theoretical analysis and the effectiveness of the proposed algorithms.

Asymmetric Correntropy for Robust Adaptive Filtering

In recent years, correntropy has been seccessfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this letter we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steadystate convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm.

Maximum Correntropy Criterion with Variable Center

Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at zero. However, zero-mean Gaussian function may not be a good choice for many practical applications. In this study, we propose an extended version of correntropy, whose center can locate at any position. Accordingly, we propose a new optimization criterion called maximum correntropy criterion with variable center (MCC-VC). We also propose an efficient approach to optimize the kernel width and center location in MCC-VC. Simulation results of regression with linear in parameters (LIP) models confirm the desirable performance of the new method.