Change Detection with Sparse Signals using Quantum Designs

TL;DR

This paper introduces new change detection methods for sparse signals using quantum-inspired sensing matrices, demonstrating improved performance in massive access scenarios with unknown parameters.

Contribution

It proposes two approaches for change detection with unknown parameters and designs sensing matrices using quantum information theory, notably SIC POVM, for enhanced detection performance.

Findings

SIC POVM design enables exact computation of post-change pdfs.

Proposed methods outperform conventional codes in massive access.

Performance varies with SNR and decision statistic choice.

Abstract

We consider the change detection problem where the pre-change observation vectors are purely noise and the post-change observation vectors are noise-corrupted compressive measurements of sparse signals with a common support, measured using a sensing matrix. In general, post-change distribution of the observations depends on parameters such as the support and variances of the sparse signal. When these parameters are unknown, we propose two approaches. In the first approach, we approximate the post-change pdf based on the known parameters such as mutual coherence of the sensing matrix and bounds on the signal variances. In the second approach, we parameterize the post-change pdf with an unknown parameter and try to adaptively estimate this parameter using a stochastic gradient descent method. In both these approaches, we employ CUSUM algorithm with various decision statistics such as the energy of the observations, correlation values with columns of the sensing matrix and the maximum value of such correlations. We study the performance of these approaches and offer insights on the relevance of different decision statistics in different SNR regimes. We also address the problem of designing sensing matrices with small coherence by using designs from quantum information theory. One such design, called SIC POVM, also has an additional structure which allows exact computation of the post-change pdfs of some decision statistics even when the support set of the sparse signal is unknown. We apply our detection algorithms with SIC POVM based sequences to a massive random access problem and show their superior performance over conventional Gold codes.