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Sensing Mutual Information for Communication Signal with Deterministic Pilots and Random Data Payloads

Lei Xie, Hengtao He, Jun Tong, Fan Liu, Shenghui Song

TL;DR

This work tackles ISAC performance with practical hybrid waveforms that combine deterministic pilots and random data payloads. It derives a tractable, asymptotic expression for sensing mutual information (SMI) using random matrix theory and leverages it to formulate an ADMM-based precoding framework that maximizes SMI under transmit power and communication-rate constraints. The main contributions are the closed-form SMI approximation for hybrid signals and an efficient ADMM algorithm that yields a high-SMI precoder, validated by simulations showing accurate theory and superiority over benchmarks. The results enable improved sensing-communication trade-offs in real-world ISAC deployments, particularly for hybrid pilot-data signaling at mmWave frequencies.

Abstract

The recent emergence of the integrated sensing and communication (ISAC) framework has sparked significant interest in quantifying the sensing capabilities inherent in communication signals. However, existing literature has mainly focused on scenarios involving either purely random or purely deterministic waveforms. This overlooks a critical reality: operational communication standards invariably utilize a hybrid structure comprising both deterministic pilots for channel estimation and random payloads for data transmission. To bridge this gap, this paper investigates the sensing mutual information (SMI) and precoding design specifically for ISAC systems employing communication signals with both pilots and data payloads. First, by utilizing random matrix theory (RMT), we derive a tractable closed-form expression for the SMI that accurately accounts for the statistical properties of the hybrid signal. Building upon this theoretical foundation, we formulate a precoding optimization problem to maximize SMI with constraints on the transmit power and communication rate, which is solved via an efficient alternating direction method of multipliers framework. Simulation results validate the accuracy of the theoretical results and demonstrate the superiority of the proposed precoding design over conventional benchmarks.

Sensing Mutual Information for Communication Signal with Deterministic Pilots and Random Data Payloads

TL;DR

This work tackles ISAC performance with practical hybrid waveforms that combine deterministic pilots and random data payloads. It derives a tractable, asymptotic expression for sensing mutual information (SMI) using random matrix theory and leverages it to formulate an ADMM-based precoding framework that maximizes SMI under transmit power and communication-rate constraints. The main contributions are the closed-form SMI approximation for hybrid signals and an efficient ADMM algorithm that yields a high-SMI precoder, validated by simulations showing accurate theory and superiority over benchmarks. The results enable improved sensing-communication trade-offs in real-world ISAC deployments, particularly for hybrid pilot-data signaling at mmWave frequencies.

Abstract

The recent emergence of the integrated sensing and communication (ISAC) framework has sparked significant interest in quantifying the sensing capabilities inherent in communication signals. However, existing literature has mainly focused on scenarios involving either purely random or purely deterministic waveforms. This overlooks a critical reality: operational communication standards invariably utilize a hybrid structure comprising both deterministic pilots for channel estimation and random payloads for data transmission. To bridge this gap, this paper investigates the sensing mutual information (SMI) and precoding design specifically for ISAC systems employing communication signals with both pilots and data payloads. First, by utilizing random matrix theory (RMT), we derive a tractable closed-form expression for the SMI that accurately accounts for the statistical properties of the hybrid signal. Building upon this theoretical foundation, we formulate a precoding optimization problem to maximize SMI with constraints on the transmit power and communication rate, which is solved via an efficient alternating direction method of multipliers framework. Simulation results validate the accuracy of the theoretical results and demonstrate the superiority of the proposed precoding design over conventional benchmarks.
Paper Structure (8 sections, 3 theorems, 37 equations, 3 figures)

This paper contains 8 sections, 3 theorems, 37 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. SMI for communication signals with both deterministic pilots and random data payloads
  4. SMI-Oriented Precoding Design
  5. Updata $\mathbf{\Theta}^{(m+1)}$
  6. Update $\mathbf{\Omega}^{(m+1)}$
  7. Simulation Result
  8. Conclusions

Key Result

Proposition 1

Let $(\delta,\tilde{\delta})$ satisfy the following system of fixed-point equations: where $\rho = |\alpha|^2\sigma^{-2} \mathrm{tr}(\mathbf{R}_{r})$ and $d = \mathbf{a}_t^\mathrm{H} \mathbf{\Theta} \mathbf{a}_t$. In the asymptotic region where $L \to \infty$, the SMI is given by where the deterministic approximation $\bar{I}_s$ is defined as

Figures (3)

  • Figure 1: Illustration of the ISAC system.
  • Figure 2: SMI versus the number of time slots $L$.
  • Figure 3: SMI versus the communication rate $I_c$.

Theorems & Definitions (3)

  • Proposition 1
  • Lemma 1: 5429113
  • Proposition 2