Harmonic Retrieval with $L_1$-Tucker Tensor Decomposition

TL;DR

This paper introduces an $L_1$-based tensor decomposition approach for harmonic retrieval that is robust to outliers, improving signal recovery in noisy environments with complex data.

Contribution

It develops new $L_1$-PCA algorithms for third-order complex tensors and applies them to a novel HR model with outlier resistance, along with a new subcarrier recovery method.

Findings

Proposed method is robust to outliers in harmonic retrieval.

Simulation results show improved performance over existing tensor algorithms.

Method effectively recovers signals in noisy, outlier-prone scenarios.

Abstract

Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have developed a number of approaches to recover the original signals. Most of them rely on classical singular value decomposition, which are vulnerable to unexpected outliers. In this paper, we present new decomposition algorithms of third-order complex-valued tensors with $L_1$-principle component analysis ($L_1$-PCA) of complex data and apply them to a novel random access HR model in presence of outliers. We also develop a novel subcarrier recovery method for the proposed model. Simulations are designed to compare our proposed method with some existing tensor-based algorithms for HR. The results demonstrate the outlier-insensitivity of the proposed method.