Robust Array Signal Processing Using L1-Kernel-Based Principal Component Analysis

In this paper, we present a set of efficient dimensionality reduction methods for array signal processing using
$\ell_{1}-$
Kernel-based multiplication-free PCA (
$\ell_{1}$
-MF-PCA) techniques. Our proposed
$\ell_{1}$
-MF-PCA methods utilize
$\ell_{1}$
-norm kernels, which enhance the robustness of the approach compared to classical
$\ell_{2}$
-PCA. Additionally, we demonstrate that the
$\ell_{1}-$
MF-PCA methods are energy-efficient, reducing the number of multiplication operations significantly. Multiplication operations are known to be costly in terms of energy consumption in many processors. Furthermore, we extend the
$\ell_{1}$
-MF - PCA methods into the complex-valued versions for the direction of arrival (DOA) estimation task. We experimentally show that the proposed methods are robust to outliers and outperform traditional approaches in terms of accuracy and efficiency. Our results demonstrate the potential of the proposed
$\ell_{1}$
-MF - PCA methods for array signal processing applications, particularly in energy-constrained settings.