Summary
This paper looks at how well we can detect if targets are present and estimate their details at the same time using sensing data. The authors use concepts from information theory, like entropy and mutual information, to understand the fundamental limits of this joint task. They show that detection and estimation accuracy combine neatly when measured in certain units called entropy volume. In essence, each bit of sensing information cuts down the uncertainty about targets by half, and compressing data between steps loses some of this information. Their results are demonstrated with a simple example involving a single target’s presence and range.
What this means in practice
- •For radar system engineers: Determine fundamental limits on how accurately radar can simultaneously detect targets and estimate their parameters using integrated sensing data.
- •For sensor fusion developers: Optimize data processing pipelines to minimize information loss when compressing intermediate sensing data between detection and estimation stages.
Tested on simulated data.
Abstract
The development of integrated sensing and communication calls for a unified theoretical foundation for sensing. This paper models target-presence patterns and continuous physical parameters as a mixed discrete-continuous state $Ξ$ on a branched reference measure, and treats posterior entropy volume and joint mutual information as two complementary representations of the same limit. Entropy volume carries physical units, can be compared with engineering scales such as resolution cells, and remains meaningful when the number of active targets varies; mutual information is dimensionless, invariant to coordinates and units, and additive through the chain rule. We define entropy number, entropy volume, and mixed entropy volume for discrete, continuous, and mixed states, respectively. The maximum-entropy principle for the uniform distribution on a support of fixed measure explains the measure-theoretic meaning of the exponential entropy scale, while the main limit follows from a mixed asymptotic equipartition property and a posterior probability-volume inequality through conditional typical sets. For asymptotically reliable high-probability sensing regions, the minimum achievable first-order posterior mixed entropy volume equals the prior mixed entropy volume multiplied by $2^{-I(Ξ;Y)}$, where $I(Ξ;Y)=I(V;Y)+I(X_V;Y\mid V)$. Thus, detection and estimation contributions multiply in the volume domain and add in the bit domain, and one sensing bit halves the posterior effective measure. We further prove that posterior-preserving cascades attain the direct-inference limit, while arbitrary intermediate compression incurs the exact information loss $I(Ξ;Y\mid Z)$. Numerical results for a single-target presence-range model illustrate the information composition, posterior entropy-volume contraction, and cascade-interface loss.