Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Stochastic Fundamental Limits in a Downlink Integrated Sensing and Communication Network

Marziyeh Soltani, Mahtab Mirmohseni, Rahim Tafazolli

TL;DR

The central limit theorem provides a viable approach for deriving PDFs of the signal-to-noise ratio for users and the CRB for the target and it is demonstrated that the central limit theorem provides a viable approach for deriving these PDFs.

Abstract

This paper aims to analyze the stochastic performance of a multiple input multiple output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario, where a base station (BS) transmits a dual-functional radar-communication (DFRC) signal matrix, serving the purpose of transmitting communication data to the user while simultaneously sensing the angular location of a target. The channel between the BS and the user is modeled as a random channel with Rayleigh fading distribution, and the azimuth angle of the target is assumed to follow a uniform distribution. Due to the randomness inherent in the network, the challenge is to consider suitable performance metrics for this randomness. To address this issue, for users, we employ the user's rate outage probability (OP) and ergodic rate, while for target, we propose using the OP of the Cramér-Rao lower bound (CRLB) for the angle of arrival and the ergodic CRLB. We have obtained the expressions of these metrics for scenarios where the BS employs two different beamforming methods. Our approach to deriving these metrics involves computing the probability density function (PDF) of the signal-to-noise ratio for users and the CRLB for the target. We have demonstrated that the central limit theorem provides a viable approach for deriving these PDFs. In our numerical results, we demonstrate the trade-off between sensing and communication (S \& C) by characterizing the region of S \& C metrics and by obtaining the Pareto optimal boundary points, confirmed with simulations.

On Stochastic Fundamental Limits in a Downlink Integrated Sensing and Communication Network

TL;DR

The central limit theorem provides a viable approach for deriving PDFs of the signal-to-noise ratio for users and the CRB for the target and it is demonstrated that the central limit theorem provides a viable approach for deriving these PDFs.

Abstract

This paper aims to analyze the stochastic performance of a multiple input multiple output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario, where a base station (BS) transmits a dual-functional radar-communication (DFRC) signal matrix, serving the purpose of transmitting communication data to the user while simultaneously sensing the angular location of a target. The channel between the BS and the user is modeled as a random channel with Rayleigh fading distribution, and the azimuth angle of the target is assumed to follow a uniform distribution. Due to the randomness inherent in the network, the challenge is to consider suitable performance metrics for this randomness. To address this issue, for users, we employ the user's rate outage probability (OP) and ergodic rate, while for target, we propose using the OP of the Cramér-Rao lower bound (CRLB) for the angle of arrival and the ergodic CRLB. We have obtained the expressions of these metrics for scenarios where the BS employs two different beamforming methods. Our approach to deriving these metrics involves computing the probability density function (PDF) of the signal-to-noise ratio for users and the CRLB for the target. We have demonstrated that the central limit theorem provides a viable approach for deriving these PDFs. In our numerical results, we demonstrate the trade-off between sensing and communication (S \& C) by characterizing the region of S \& C metrics and by obtaining the Pareto optimal boundary points, confirmed with simulations.
Paper Structure (25 sections, 10 theorems, 52 equations, 5 figures)

This paper contains 25 sections, 10 theorems, 52 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Subspace Joint Beamforming (SJB)
  4. Linear Beamforming (LB)
  5. Problem Formulation
  6. SJB performance analysis
  7. OP of the user
  8. OP of the target
  9. User Ergodic Rate and Target Ergodic CRB
  10. LB Performance Analysis
  11. OP of the user
  12. OP of the Target
  13. Upper Bound
  14. Lower Bound
  15. Approximation
  16. ...and 10 more sections

Key Result

Lemma 1

The optimal solution of optimization lies in the span of $\{\mathbf{a}, \mathbf{h}\}$.

Figures (5)

  • Figure 1: System model: (A) subspace joint beamforming (SJB), (B) linear beamforming (LB).
  • Figure 2: OP of the target versus $\epsilon(dB)$
  • Figure 3: OP of the user versus $\gamma$
  • Figure 4: OP of the target versus OP of the user
  • Figure 5: Communication channel model

Theorems & Definitions (13)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • proof
  • Lemma 6
  • Lemma 7
  • proof
  • Lemma 8
  • ...and 3 more