Cramér-Rao Bound Optimization for Active RIS-Empowered ISAC Systems

This repository contains the MATLAB simulation code for the paper:

Q. Zhu, M. Li, R. Liu, and Q. Liu, "Cramér-Rao bound optimization for active RIS-empowered ISAC systems," IEEE Trans. Wireless Commun., vol. 23, no. 9, pp. 11723--11736, Sep. 2024. [IEEE Xplore]

Overview

We propose a joint transmit beamforming and active reconfigurable intelligent surface (RIS) phase-shift design framework for integrated sensing and communication (ISAC) systems. The Cramér-Rao bound (CRB) for target angle estimation is minimized subject to communication quality-of-service (QoS) constraints and active RIS power budgets. The code implements:

• Active RIS-empowered ISAC system model with joint BS beamforming and RIS phase-shift design
• CRB minimization via alternating optimization: SDP-based beamformer design and SCA-based RIS optimization
• Comparison between active and passive RIS under equivalent total power budgets
• Performance evaluation across multiple system parameters (transmit power, SINR threshold, number of antennas/elements/users, RIS position)
• Beampattern visualization showing spatial power distribution

Requirements

• MATLAB R2022b or later
• CVX (version 2.2 or later) with a compatible SDP solver — http://cvxr.com/cvx/
  • If MOSEK is unavailable, CVX will fall back to SDPT3 or SeDuMi automatically
• Manopt (Manifold optimization toolbox) — https://www.manopt.org/
  • Used for RIS phase-shift initialization via Riemannian conjugate gradient

Repository Structure

Active-RIS-ISAC-CRB/
├── README.md                  # This file
├── LICENSE                    # MIT license
│
├── main_Pb.m                 # Fig. 4:  CRB vs. transmit power
├── main_Gamma.m              # Fig. 5:  CRB vs. SINR requirement
├── main_M.m                  # Fig. 6:  CRB vs. number of RIS elements
├── main_N.m                  # Fig. 7:  CRB vs. number of BS antennas
├── main_K.m                  # Fig. 8:  CRB vs. number of users
├── main_dis.m                # Fig. 9:  CRB vs. RIS position
├── main_beam.m               # Fig. 10: Beampattern visualization
│
└── function/                  # Supporting functions
    ├── design_main.m          # Joint AO-based beamforming and RIS design
    ├── get_W.m                # SDP-based transmit beamformer optimization (CVX)
    ├── get_phi.m              # SCA-based RIS phase-shift optimization (CVX)
    ├── channel.m              # Channel generation (BS-RIS, RIS-target, RIS-user, BS-user)
    ├── Phi_initial.m          # RIS phase-shift initialization (Manopt)
    └── eigsort.m              # Eigenvalue sorting utility

Quick Start

Step 1: Install dependencies

% Install CVX: download from http://cvxr.com/cvx/ and run
cvx_setup

% Install Manopt: download from https://www.manopt.org/ and add to path
addpath(genpath('/path/to/manopt'));

Step 2: Run figure-generation scripts

Each main script is self-contained and can be run independently:

run('main_Pb.m')     % Generates Fig. 4
run('main_Gamma.m')  % Generates Fig. 5

Script-to-Figure Mapping

Script	Paper Figure	Description
main_Pb.m	Fig. 4	CRB vs. transmit power at BS
main_Gamma.m	Fig. 5	CRB and SER vs. SINR requirement
main_M.m	Fig. 6	CRB vs. number of RIS elements
main_N.m	Fig. 7	CRB vs. number of BS antennas
main_K.m	Fig. 8	CRB vs. number of communication users
main_dis.m	Fig. 9	CRB vs. horizontal position of RIS
main_beam.m	Fig. 10	Spatial beampattern (single realization)

Note: Each script uses 1000 Monte Carlo iterations by default. For a quick test, reduce ITER to 2–3. Full runs may take several hours depending on your hardware.

System Parameters

The default parameters correspond to an active RIS-assisted ISAC system:

Parameter	Value	Description
BS antennas (N)	16	Uniform linear array
RIS elements (M)	8	Active RIS with amplification
Users (K)	4	Downlink communication users
Noise power	−80 dBm	Receiver noise floor
BS power (P_b)	23 dBm	Transmit power budget (varies by script)
RIS power (P_r)	10 dBm	Active RIS amplification budget
Max amplitude (a_max)	8	Maximum RIS reflection amplitude
SINR threshold (Γ)	16 dB	Per-user QoS requirement
Samples (L)	1024	Number of radar snapshots

Citation

If you use this code in your research, please cite:

@article{zhu2024crb,
  author  = {Zhu, Qi and Li, Ming and Liu, Rang and Liu, Qian},
  title   = {Cram\'{e}r-Rao Bound Optimization for Active {RIS}-Empowered {ISAC} Systems},
  journal = {IEEE Trans. Wireless Commun.},
  year    = {2024},
  doi     = {10.1109/TWC.2024.3384501}
}

Contact

• Qi Zhu — Dalian University of Technology — qzhu@mail.dlut.edu.cn
• Rang Liu — Dalian University of Technology — liurang520@gmail.com

More resources: https://www.minglabdut.com/resource.html

License

This code is provided under the MIT License for academic and research purposes. Please contact the authors for commercial use.