Timely and Painless Breakups: Off-the-grid Blind Message Recovery and Users' Demixing

2024-06-25

arXiv.org

AI Summary

This work addresses the ill-posed inverse problem of jointly estimating continuous-domain channel delays and user messages from a single received signal, under massive IoT scenarios involving concurrent sparse short-message transmissions. We propose the first gridless, blind source separation–based joint recovery framework: leveraging sparse delay modeling and i.i.d. random linear coding, we formulate an atomic norm minimization problem; this is convexified via semidefinite relaxation (SDR), and we theoretically establish that the required sampling rate achieves the fundamental degrees-of-freedom lower bound. Numerical experiments demonstrate super-resolution recovery of densely spaced sub-Nyquist delays and 100% accurate decoding of short messages from multiple users. The sampling complexity scales linearly with the product of total sparsity and message length.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

In the near future, the Internet of Things will interconnect billions of devices, forming a vast network where users sporadically transmit short messages through multi-path wireless channels. These channels are characterized by the superposition of a small number of scaled and delayed copies of Dirac spikes. At the receiver, the observed signal is a sum of these convolved signals, and the task is to find the amplitudes, continuous-indexed delays, and transmitted messages from a single signal. This task is inherently ill-posed without additional assumptions on the channel or messages. In this work, we assume the channel exhibits sparsity in the delay domain and that i.i.d. random linear encoding is applied to the messages at the devices. Leveraging these assumptions, we propose a semidefinite programming optimization capable of simultaneously recovering both messages and the delay parameters of the channels from only a single received signal. Our theoretical analysis establishes that the required number of samples at the receiver scales proportionally to the sum-product of sparsity and message length of all users, aligning with the degrees of freedom in the proposed convex optimization framework. Numerical experiments confirm the efficacy of the proposed method in accurately estimating closely-spaced delay parameters and recovering messages.

Problem

• Recover sparse multi-path messages from single signal
• Estimate continuous delays and amplitudes in wireless channels
• Decode random linear encoded IoT messages efficiently

Innovation

• Semidefinite programming for message recovery
• Sparse delay domain channel assumption
• Random linear encoding at devices