[Paper Review] Fundamental Limits on Sensing Capacity for Sensor Networks and Compressed Sensing

Shuchin Aeron, Manqi Zhao+1 more|arXiv (Cornell University)|Apr 22, 2008

Energy Efficient Wireless Sensor Networks8 citations

TL;DR

This paper introduces sensing capacity as the maximal number of signal dimensions reliably identified per sensor, quantifying fundamental limits in sensor networks and compressed sensing. Using information theory, it derives compression rates as a function of event domain rate, SNR, distortion, and sensor diversity, showing trade-offs between measurement efficiency and reconstruction accuracy.

ABSTRACT

Modern applications of signal processing problems arising in sensor networks require efficient sensing of multi-dimensional data or phenomena. In this context it becomes important to understand fundamental performance limits of both sensing and communication between sensors. In this paper we focus primarily on sensing aspects. We propose the notion of sensing capacity to characterize the performance and effectiveness of various sensing configurations. We define Sensing Capacity as the maximal number of signal dimensions reliably identified per sensor deployed. The inverse of sensing capacity is the compression rate, i.e., the number of measurements required per signal dimension for accurate reconstruction, a concept that is of interest in compressed sensing(CS). Using information theoretic arguments we quantify sensing capacity (compression rate) as a function of information rate of the event domain, SNR of the observations, desired distortion in the reconstruction and diversity of sensors. In this paper we consider fixed SNR linear observation models for sensor network (SNET) and CS scenarios for different types of distortions motivated by detection, localization and field estimation problems. The principle difference between the SNET and CS scenarios is the way in which the signal-tonoise

Motivation & Objective

• To establish fundamental performance limits for sensing in sensor networks and compressed sensing applications.
• To define and quantify sensing capacity as the maximal number of signal dimensions identifiable per sensor.
• To analyze the trade-offs between measurement compression rate, SNR, distortion, and sensor diversity.
• To unify sensing and communication constraints in multi-dimensional signal acquisition using information-theoretic principles.

Proposed method

• Proposes sensing capacity as the inverse of compression rate, defined as the maximum number of signal dimensions per sensor that can be reliably reconstructed.
• Uses information-theoretic arguments to model sensing capacity as a function of event domain information rate, SNR, distortion, and sensor diversity.
• Analyzes fixed SNR linear observation models for both sensor network (SNET) and compressed sensing (CS) scenarios.
• Considers different distortion models motivated by detection, localization, and field estimation problems.
• Derives analytical expressions for compression rate (inverse of sensing capacity) under varying SNR and distortion constraints.
• Highlights the distinction between SNET and CS in how signal-to-noise ratio is managed across sensors.

Experimental results

Research questions

• RQ1 What is the fundamental limit on the number of signal dimensions that can be reliably sensed per sensor in a networked system?
• RQ2 How does sensing capacity depend on the information rate of the event domain and the SNR of observations?
• RQ3 What is the optimal compression rate (measurements per signal dimension) for accurate reconstruction under given distortion constraints?
• RQ4 How does sensor diversity influence the achievable sensing capacity in multi-sensor configurations?
• RQ5 What are the key differences in sensing capacity between sensor network and compressed sensing models?

Key findings

• Sensing capacity is defined as the maximum number of signal dimensions that can be reliably identified per sensor, providing a performance metric for sensing systems.
• Compression rate—the number of measurements per signal dimension—is inversely proportional to sensing capacity and depends on SNR, distortion, and event domain rate.
• Higher SNR and lower distortion reduce the required compression rate, improving sensing efficiency.
• Sensor diversity enhances sensing capacity by enabling better reconstruction under limited measurements.
• The analysis reveals distinct performance trade-offs between sensor network and compressed sensing models due to differences in signal-to-noise handling.
• The derived bounds provide theoretical foundations for designing efficient sensing and communication protocols in multi-dimensional signal acquisition.