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Cooperative Radar and Communications Signaling: The Estimation and Information Theory Odd Couple
Daniel W. Bliss
TL;DR
Radar and communications are usually treated as interfering systems despite shared spectral constraints. The paper develops MUDR and joint estimation–information bounds for a radar-relay receiver observing both signals, showing how their interaction can potentially enhance both systems under certain conditions.
Problem
Radar and communications systems commonly treat one another as interference, motivating analysis of whether joint operation can improve both systems under constrained spectrum.
Method
The paper develops MUDR, which jointly decodes communications and estimates the radar channel, and formulates inner and outer performance bounds in communication and estimation rates.
Results
An achievable inner bound based on water-filling is developed and illustrated for a joint radar–communications system.
Takeaways & Limitations
The radar-relay scenario indicates that cooperative radar and communications performance can potentially be enhanced by their interaction under theoretical constraints.
Abstract
from arXiv · showhide
We investigate cooperative radar and communications signaling. While each system typically considers the other system a source of interference, by considering the radar and communications operations to be a single joint system, the performance of both systems can, under certain conditions, be improved by the existence of the other. As an initial demonstration, we focus on the radar as relay scenario and present an approach denoted multiuser detection radar (MUDR). A novel joint estimation and information theoretic bound formulation is constructed for a receiver that observes communications and radar return in the same frequency allocation. The joint performance bound is presented in terms of the communication rate and the estimation rate of the system.
I. INTRODUCTION
The paper frames radar–communications coexistence as a joint system rather than mutual interference, using multiple-access bounds to study simultaneous radar estimation and communications reception.
- Limited spectral resources increasingly force radar and communications systems into coexistence, which are typically separated temporally, spectrally, or spatially.
- Prior coexistence approaches include cognitive sensing, cooperative sensing, signal sharing, waveform shaping, passive radar, and communications systems that modulate radar waveforms.
- MUDR jointly decodes communications and estimates the radar channel, allowing interactions to potentially enhance both systems under theoretical constraints.
- The preliminary radar-relay scenario uses a communications waveform for radar, with simultaneous reception of the radar return and communications signal as the principal performance constraint.
- A. Multiple-Access Communications Analogy: The multiple-access analogy models two independent transmitters communicating with one receiver and represents achievable rates through bounds whose region is shown as a pentagon.
- A. Multiple-Access Communications Analogy: The analogy motivates joint radar–communications bounds but is not directly applicable because radar returns are not drawn from a countable dictionary.
B. Joint Radar-Communications Notation
The notation section introduces a consolidated overview of the symbols used to describe the joint radar–communications system.
- Table I provides an overview of the important notation employed in discussing the joint radar–communications topic.
C. Joint Radar-Communications Channel Model
The channel model combines radar returns, communications signals, thermal noise, target-range dynamics, and estimation assumptions to support joint analysis.
- The model estimates target range while assuming known target cross-section, well-separated targets, Gaussian returns before pulse compression, and predictable range variation.
- For N targets, the observed radar return is modeled as a target-dependent signal plus complex Gaussian noise.
- Range and delay are related through propagation, with c denoting the speed of light; the discussion focuses on range rather than amplitude estimation.
- The tracked-target model uses an expected radar return with Gaussian process variation in the next observation’s range.
- A prediction function parameterized by the pulse repetition interval and other parameters describes target evolution between updates.
- The receiver observes the communications signal and radar return together, and small delay variations permit a derivative-based waveform approximation.
D. Radar-Prediction-Suppressed Observed Signal
The communications receiver mitigates radar interference by subtracting a predicted radar return, while prediction error contributes to the residual interference-plus-noise signal.
- The receiver subtracts the predicted radar return to mitigate unnecessary interference for communications.
- For small delay-process variations, the difference between correct and predicted waveforms can be approximated using a derivative.
- The observed communications signal includes the communications waveform and additive noise after radar-return suppression.
- The communications receiver treats residual radar interference together with noise as its effective interference-plus-noise term.
- For a flat radar power spectral shape, the scaling constant satisfies γ^2 = (2π)^2/12.
E. Radar Estimation Information Rate
The paper defines an estimation information rate for radar delay estimation using parameter and uncertainty entropies, with uncertainty characterized through Cramer-Rao analysis under Gaussian assumptions.
- The estimation information rate treats delay estimation as an information channel based on parameter entropy and estimation-uncertainty entropy.
- When targets are well separated, each target estimation can be modeled as an independent information channel.
- Delay-estimation uncertainty is obtained for each target using the complex Slepian-Bangs formulation of the Cramer-Rao bound under circularly symmetric Gaussian noise.
- The process would theoretically remove all clutter.
- The resulting estimation-error entropy is formulated under a Gaussian estimation-error assumption.
- Process and estimation uncertainties are combined through their entropy under Gaussian assumptions for both uncertainties.
2) Radar Random Process Entropy:
The mutual-information rate is bounded in bits per pulse repetition interval using the integration period and duty factor, with the bound relying on Cramer-Rao-level estimation performance.
- The mutual information rate is approximately bounded in bits per pulse repetition interval T_pri, with integration period related by T = δT_pri.
- The rate bound assumes the estimator achieves Cramer-Rao performance.
- If the estimation-error variance is larger, the resulting rate bound is lower.
III. INNER RATE BOUNDS
The inner-bound analysis seeks achievable communication and estimation rates for a joint radar-communications receiver, including regimes where one signal can be decoded or isolated without contamination.
- The analysis searches for achievable inner bounds using an idealized receiver, with fundamental performance lying between inner and outer bounds.
- When R_est ≈ 0, communications operates according to the isolated communications-system bound.
- At sufficiently low R_com for a given transmit power, the communications signal can be decoded and completely subtracted, enabling uncontaminated radar-parameter estimation.
- In the corresponding regime, the estimation-rate bound R_est is given by Equation (19).
- The two vertices correspond to estimation and communications rates, and achievable rates lie within the triangle connecting them.
A. Water-filling
The water-filling inner bound divides bandwidth into communications-only and mixed-use channels, allocating communications power between them while maintaining waveform integration as α varies. The approach has a self-consistency boundary when the radar subband becomes too small.
- A. Water-filling: Water-filling splits the total bandwidth into communications-only and mixed-use sub-bands, then allocates communications power between the two channels.The mixed-use channel operates at the successive-interference-cancellation rate vertex.
- A. Water-filling: The critical point separates exclusive use of the communications-only channel from use of both effective channels for communications.Below the transition, no communications power is allocated to the mixed-use channel; above it, both channels are used.
- A. Water-filling: The resulting construction provides communications and radar estimation inner bounds based on the allocated powers and the two-channel operating scheme.The communications-only rate, mixed-use communications rate, and corresponding radar estimation rate are specified as separate inner-bound components.
- A. Water-filling: Holding waveform integration κ = (1 − α) TB constant while varying α determines the radar estimation rate under the bandwidth split.For sufficiently large α, the formulation becomes self-inconsistent because T > Trpi.
B. Examples
The example compares several inner and outer performance bounds for joint communications and radar estimation. The water-filling bound exceeds the linearly interpolated bound in the displayed example, although convexity is not guaranteed generally.
- B. Examples: The example assumes communications reception through an antenna sidelobe, so radar and communications receive gains are not identical.The plotted parameters are listed in Table II.
- B. Examples: The best-case performance under SIC occurs at the vertex where the SIC and outer-bound lines intersect.The vertex is determined by the joint solution of the relevant equations.
- B. Examples: The water-filling bound exceeds the linearly interpolated bound in the example, but water-filling is not guaranteed to be convex or larger in general.The overall inner bound is produced by the convex hull of all contributing inner bounds.
- B. Examples: Figure 2 compares outer bounds, the SIC communications bound, a linear interpolation, and the water-filling inner bound.The outer bounds are red, SIC is green dashed, interpolation is gray dashed, and water-filling is blue.
IV. CONCLUSION
The paper develops a novel approach for joint radar and communications performance bounds using a water-filling achievable inner bound and presents an example. It frames the work as an initial investigation with opportunities for improved bounds and broader scenarios.
- IV. CONCLUSION: The paper develops a novel approach for producing joint radar and communications performance bounds.It presents an achievable inner bound based on water-filling and an example application.
- IV. CONCLUSION: The authors characterize the work as an initial investigation with potential improvements to the inner bounds and extensions to additional scenarios.The conclusion identifies both bound refinement and scenario expansion as future directions.