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Design of Uplink ISAC Systems with Cooperative Sensing: Power Control and Receive Beamforming

Ling He, Vaibhav Kumar, Roberto Bomfin, Yingyang Chen, Miaowen Wen, Marwa Chafii

Abstract

Integrated sensing and communication (ISAC) has emerged as a key paradigm for next-generation wireless systems, which allows wireless resources to be used for data transmission and target sensing simultaneously. In this paper, multi-user collaborative target detection in the uplink ISAC system is investigated. To incorporate the target sensing functionality, the system relies on the reuse of uplink signals from the communication users. Specifically, we analyze an uplink multi-user single-input multiple-output (MU-SIMO) communication system with bistatic sensing. Using the channel statistics, we formulate the problem of joint optimal pilot and data power allocation to maximize the uplink ergodic sum rate while meeting communication and sensing quality-of-service (QoS) requirements. To address this non-convex problem, we propose an alternating optimization (AO)-based iterative framework, where the joint power allocation problem is decomposed into two sub-problems. Specifically, the pilot power allocation is optimized using a penalty dual decomposition (PDD)-based gradient ascent algorithm, while the data power allocation is solved via successive convex approximation (SCA). Once the long-term power allocation is determined, the base station (BS) estimates the instantaneous channels using a minimum mean-squared error (MMSE) estimator. Subsequently, based on the estimated instantaneous channel state information (CSI), the receive beamforming for communication users is optimized via another SCA-based method to maximize the sum rate. Meanwhile, the optimal receive beamforming for the target is obtained in closed-form through eigenvalue decomposition (EVD).

Design of Uplink ISAC Systems with Cooperative Sensing: Power Control and Receive Beamforming

Abstract

Integrated sensing and communication (ISAC) has emerged as a key paradigm for next-generation wireless systems, which allows wireless resources to be used for data transmission and target sensing simultaneously. In this paper, multi-user collaborative target detection in the uplink ISAC system is investigated. To incorporate the target sensing functionality, the system relies on the reuse of uplink signals from the communication users. Specifically, we analyze an uplink multi-user single-input multiple-output (MU-SIMO) communication system with bistatic sensing. Using the channel statistics, we formulate the problem of joint optimal pilot and data power allocation to maximize the uplink ergodic sum rate while meeting communication and sensing quality-of-service (QoS) requirements. To address this non-convex problem, we propose an alternating optimization (AO)-based iterative framework, where the joint power allocation problem is decomposed into two sub-problems. Specifically, the pilot power allocation is optimized using a penalty dual decomposition (PDD)-based gradient ascent algorithm, while the data power allocation is solved via successive convex approximation (SCA). Once the long-term power allocation is determined, the base station (BS) estimates the instantaneous channels using a minimum mean-squared error (MMSE) estimator. Subsequently, based on the estimated instantaneous channel state information (CSI), the receive beamforming for communication users is optimized via another SCA-based method to maximize the sum rate. Meanwhile, the optimal receive beamforming for the target is obtained in closed-form through eigenvalue decomposition (EVD).
Paper Structure (22 sections, 2 theorems, 53 equations, 9 figures, 2 algorithms)

This paper contains 22 sections, 2 theorems, 53 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions and Organization
  4. System Model and Problem Formulation
  5. Channel Estimation
  6. Communication
  7. Sensing
  8. Problem Formulation
  9. Proposed Solution
  10. Receive Beamforming Design Before Transmitting Pilots
  11. Optimizing Power Allocation
  12. Optimal pilot power allocation $\mathbf{p}_{\mathrm{p}}$
  13. Optimal data-transmission power allocation $\mathbf{p}_{\mathrm{d}}$
  14. Optimizing Receive Beamforming After Transmitting Pilots
  15. Complexity Analysis
  16. ...and 7 more sections

Key Result

Theorem 1

A closed-form expression for ${{\bar{\gamma }}_{k}}$ is given by where ${{\mathbf{R}}_{k}}={{\mathbf{R}}_{\text{h},k}}+{{\mathbf{R}}_{\mathrm{g},k}}$ and ${{\mathbf{R}}_{\text{est},k}}={{\mathbf{R}}_{\hat{\mathrm{h}},k}}+{{\mathbf{R}}_{\hat{\mathrm{g}},k}}={{P}_{\text{p},k}}{{T}_{\text{p}}}{{\mathbf{R}}_{k}}{\left( {{P}_{\text{p},k}}{{T}_{\text{p}}}{{\mathbf{R}}_

Figures (9)

  • Figure 1: Multi-user uplink communication assisted target detection in ISAC systems.
  • Figure 2: Frame structure of the pilot and data transmitted by user-$k$.
  • Figure 3: Convergence results for the power allocation (Algorithm \ref{['algorithm-AO-P']}) on the left and the receive beamforming (Algorithm \ref{['algorithm-SCA-U']}) on the right.
  • Figure 4: Impact of the power budget per user on the average sum rate.
  • Figure 5: Impact of the number of users on the average sum rate for $N_{\text{b}} = 8$.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2