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Joint and Robust Beamforming Framework for Integrated Sensing and Communication Systems

Jinseok Choi, Jeonghun Park, Namyoon Lee, Ahmed Alkhateeb

TL;DR

A joint communication and radar beamforming framework for maximizing a sum spectral efficiency (SE) while guaranteeing desired radar performance with imperfect channel state information (CSI) in multi-user and multi-target ISAC systems is presented.

Abstract

Integrated sensing and communication (ISAC) is widely recognized as a fundamental enabler for future wireless communications. In this paper, we present a joint communication and radar beamforming framework for maximizing a sum spectral efficiency (SE) while guaranteeing desired radar performance with imperfect channel state information (CSI) in multi-user and multi-target ISAC systems. To this end, we adopt either a radar transmit beam mean square error (MSE) or receive signal-to-clutter-plus-noise ratio (SCNR) as a radar performance constraint of a sum SE maximization problem. To resolve inherent challenges such as non-convexity and imperfect CSI, we reformulate the problems and identify first-order optimality conditions for the joint radar and communication beamformer. Turning the condition to a nonlinear eigenvalue problem with eigenvector dependency (NEPv), we develop an alternating method which finds the joint beamformer through power iteration and a Lagrangian multiplier through binary search. The proposed framework encompasses both the radar metrics and is robust to channel estimation error with low complexity. Simulations validate the proposed methods. In particular, we observe that the MSE and SCNR constraints exhibit complementary performance depending on the operating environment, which manifests the importance of the proposed comprehensive and robust optimization framework.

Joint and Robust Beamforming Framework for Integrated Sensing and Communication Systems

TL;DR

A joint communication and radar beamforming framework for maximizing a sum spectral efficiency (SE) while guaranteeing desired radar performance with imperfect channel state information (CSI) in multi-user and multi-target ISAC systems is presented.

Abstract

Integrated sensing and communication (ISAC) is widely recognized as a fundamental enabler for future wireless communications. In this paper, we present a joint communication and radar beamforming framework for maximizing a sum spectral efficiency (SE) while guaranteeing desired radar performance with imperfect channel state information (CSI) in multi-user and multi-target ISAC systems. To this end, we adopt either a radar transmit beam mean square error (MSE) or receive signal-to-clutter-plus-noise ratio (SCNR) as a radar performance constraint of a sum SE maximization problem. To resolve inherent challenges such as non-convexity and imperfect CSI, we reformulate the problems and identify first-order optimality conditions for the joint radar and communication beamformer. Turning the condition to a nonlinear eigenvalue problem with eigenvector dependency (NEPv), we develop an alternating method which finds the joint beamformer through power iteration and a Lagrangian multiplier through binary search. The proposed framework encompasses both the radar metrics and is robust to channel estimation error with low complexity. Simulations validate the proposed methods. In particular, we observe that the MSE and SCNR constraints exhibit complementary performance depending on the operating environment, which manifests the importance of the proposed comprehensive and robust optimization framework.
Paper Structure (26 sections, 6 theorems, 55 equations, 9 figures, 2 tables, 2 algorithms)

This paper contains 26 sections, 6 theorems, 55 equations, 9 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model
  5. Signal Model
  6. Channel Model
  7. Radar Model
  8. Performance Metrics
  9. Communication Performance Metric
  10. Radar Performance Metric
  11. Proposed Optimization Framework
  12. Problem Formulation
  13. Problem Reformulation with MSE Constraint
  14. Proposed Algorithm with MSE Constraint
  15. Interpretation
  16. ...and 11 more sections

Key Result

Lemma 1

The KKT stationarity condition of the problem in eq:prob_reformulation_omit_power is satisfied if the following condition holds: where Here, $\mu$ in eq:Psi and eq:Omega is the Lagrangian multiplier and where $\lambda_{\sf num}(\bar{\bf{f}})$ and $\lambda_{\sf den}(\bar{\bf{f}})$ are any functions that satisfy eq:lambda.

Figures (9)

  • Figure 1: (a) The ergodic sum SE and (b) the average NMSE with respect to the SNR for $N = 8$, $K = 4$, $M = 8$, and $T_{\rm nmse} = -7.5$ dB. Since SDR-based algorithms achieve a lower NMSE $\approx (-10.5 \sim -10)$ dB, the GPI-ISAC result with $T_{\rm nmse} = -10.5$ dB is also included for comparison.
  • Figure 2: A normalized transmit beam pattern with the achieved NMSE $\approx -10.5$ dB for the GPI-ISAC and SDR-based algorithms at ${\rm SNR} = 25$ dB. Corresponding sum SEs of GPI-ISAC-MSE and SDR-Rank1 are $13.4$ and $11.1$${\rm bps/Hz}$, respectively.
  • Figure 3: (a) The ergodic sum SE and (b) the average NMSE with respect to the target NMSE $T_{\rm nmse}$ for $N = 8$, $K = 4$, $M = 8$, and ${\rm SNR} = 40$ dB.
  • Figure 4: (a) The ergodic sum SE and (b) the average SCNR with respect to the SNR for $N = 8$, $K = 4$, $M = 8$, and $25$ dB SNR.
  • Figure 5: Normalized receive beam patterns of GPI-based algorithms and WMMSE-MM with the achieved sum SEs of $\sim\! 11.5\ {\rm bps/Hz}$ and $\sim\! 10\ {\rm bps/Hz}$ for GPI-ISAC-SCNR and WMMSE-MM, respectively.
  • ...and 4 more figures

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • proof
  • Proposition 1
  • Remark 4
  • Remark 5
  • Lemma 2
  • proof
  • ...and 6 more