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Joint Communication and Parameter Estimation in MIMO Channels

Gökhan Yılmaz, Franz Lampel, Hamdi Joudeh, Giuseppe Caire

TL;DR

This work provides an information-theoretic foundation for joint communication and sensing (JCAS) in a MIMO setting where the sensing parameter is a fixed random vector drawn from a known prior. It derives a capacity–MSE function $C(\Delta)$ that captures the fundamental trade-off between reliable data rate and sensing accuracy, showing that Gaussian inputs with an optimally chosen covariance $\mathbf{Q}$ achieve all optimal points and that almost-constant covariance codes enable achievability. A Bayesian ECRB-based framework precisely characterizes the asymptotic sensing performance via $\mathrm{tr}(\mathbb{E}[\mathbf{J}(\bm{\uptheta}|\mathbf{Q})^{-1}])$, and a convex optimization yields the trade-off curve under a power constraint $\operatorname{tr}(\mathbf{Q}) \le P$. The paper also provides a BCRB-based upper bound and illustrates the theory with DoA estimation and OFDM case studies, highlighting when trade-offs are active or degenerate. Overall, this work offers rigorous benchmarks and optimal signaling principles for practical JCAS system design with fixed sensing parameters, informing beamforming and subcarrier power allocation strategies in real-world deployments.

Abstract

We study a joint communication and sensing setting comprising a transmitter, a receiver, and a sensor, all equipped with multiple antennas. The transmitter sends an encoded signal over the channel with the dual purpose of communicating an information message to the receiver, and enabling the sensor to estimate a target parameter vector by generating back-scattered signals. We assume that the transmitter and sensor are co-located, or fully connected, giving the latter access to the transmitted signal. The target parameter vector is randomly drawn from a continuous distribution, yet remains fixed throughout the transmission block. We establish the fundamental performance trade-off between the communication and sensing tasks, captured in terms of a capacity-MSE function. In doing so, we identify optimal coding schemes for this multi-antenna joint communication and sensing setting. Moreover, we particularize our result to two practically-inspired scenarios where we showcase optimal schemes and trade-offs.

Joint Communication and Parameter Estimation in MIMO Channels

TL;DR

This work provides an information-theoretic foundation for joint communication and sensing (JCAS) in a MIMO setting where the sensing parameter is a fixed random vector drawn from a known prior. It derives a capacity–MSE function that captures the fundamental trade-off between reliable data rate and sensing accuracy, showing that Gaussian inputs with an optimally chosen covariance achieve all optimal points and that almost-constant covariance codes enable achievability. A Bayesian ECRB-based framework precisely characterizes the asymptotic sensing performance via , and a convex optimization yields the trade-off curve under a power constraint . The paper also provides a BCRB-based upper bound and illustrates the theory with DoA estimation and OFDM case studies, highlighting when trade-offs are active or degenerate. Overall, this work offers rigorous benchmarks and optimal signaling principles for practical JCAS system design with fixed sensing parameters, informing beamforming and subcarrier power allocation strategies in real-world deployments.

Abstract

We study a joint communication and sensing setting comprising a transmitter, a receiver, and a sensor, all equipped with multiple antennas. The transmitter sends an encoded signal over the channel with the dual purpose of communicating an information message to the receiver, and enabling the sensor to estimate a target parameter vector by generating back-scattered signals. We assume that the transmitter and sensor are co-located, or fully connected, giving the latter access to the transmitted signal. The target parameter vector is randomly drawn from a continuous distribution, yet remains fixed throughout the transmission block. We establish the fundamental performance trade-off between the communication and sensing tasks, captured in terms of a capacity-MSE function. In doing so, we identify optimal coding schemes for this multi-antenna joint communication and sensing setting. Moreover, we particularize our result to two practically-inspired scenarios where we showcase optimal schemes and trade-offs.

Paper Structure

This paper contains 30 sections, 5 theorems, 84 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Signal model
  4. Encoding, decoding, and estimation
  5. Encoding
  6. Decoding
  7. Estimation
  8. Asymptotic rate-MSE trade-off
  9. Main Result
  10. Preliminaries
  11. Result and insights
  12. Trade-off
  13. Almost-constant covariance codes
  14. Analytical properties
  15. BCRB-based bound
  16. ...and 15 more sections

Key Result

Lemma 1

$\operatorname{tr}\left( \mathbbmss{E} \left[ \bm{J}(\bm{\uptheta}|\bm{Q})^{-1} \right] \right)$ is monotonically non-increasing and convex in $\bm{Q} \in \mathbb{S}_{+}^M$.

Figures (4)

  • Figure 1: The considered MIMO JCAS system model.
  • Figure 2: Capacity–MSE trade-off with a uniform prior in JCAS with DoA estimation.
  • Figure 3: Capacity-MSE trade-off with a non-uniform prior in JCAS with DoA estimation.
  • Figure 4: Capacity–MSE trade-off in JCAS with OFDM.

Theorems & Definitions (11)

  • Remark 1
  • Definition 1
  • Remark 2
  • Lemma 1
  • Theorem 1
  • Remark 3
  • Lemma 2
  • Lemma 3: Extended Feinstein’s lemma polyanskiy2025
  • Lemma 4
  • Remark 4
  • ...and 1 more