Closed-Form Approximations of Range Mutual Information for Integrated Sensing and Communication Systems.

Area of Science:

• Electrical Engineering
• Information Theory
• Signal Processing

Background:

• Sensing mutual information (SMI) is a key metric for integrated sensing and communication (ISAC).
• Conventional SMI evaluation in ISAC focuses on amplitude and phase, neglecting range information.
• An explicit evaluation of range mutual information (RMI) is needed for comprehensive ISAC performance assessment.

Purpose of the Study:

• To develop a novel closed-form approximation for RMI in ISAC systems.
• To derive the posterior probability density function (PDF) of the target range.
• To analyze RMI under high signal-to-noise ratio (SNR) in both sensing-unconstrained and constrained scenarios.

Main Methods:

• Derivation of the posterior PDF of target range using signal autocorrelation and cross-correlation.
• Approximation of the range PDF as Gaussian and truncated Gaussian distributions under high SNR.
• Derivation of closed-form RMI approximations incorporating an entropy correction term for constrained scenarios.
• Utilizing maximum likelihood estimation (MLE) for range estimation performance evaluation.

Main Results:

• The posterior range PDF is formulated as a function of signal correlations.
• Under high SNR, the range PDF approximates Gaussian (unconstrained) or truncated Gaussian (constrained) distributions.
• Closed-form RMI approximations are derived for both scenarios.
• In the unconstrained scenario, RMI is proportional to delay interval, bandwidth, and SNR.
• The constrained scenario RMI approximation includes an entropy correction term.

Conclusions:

• The proposed closed-form RMI approximations accurately reflect ISAC performance.
• The derived RMI metrics enhance the evaluation of sensing capabilities in ISAC.
• Simulation results validate the theoretical RMI approximations and their effectiveness.