RSMA-low-complexity-maxmin-K-user

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RSMA-low-complexity-maxmin-K-user

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Simulation code for the paper: F. Luo and Y. Mao, "An Efficient Max-Min Fair Resource Optimization Algorithm for Rate-Splitting Multiple Access," in IEEE Transactions on Wireless Communications, doi: 10.1109/TWC.2025.3586919.

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# An Efficient Max-Min Fair Resource Optimization Algorithm for Rate-Splitting Multiple Access
This is a code package related to the following [paper](https://ieeexplore.ieee.org/document/11080259/):

F. Luo and Y. Mao, "An Efficient Max-Min Fair Resource Optimization Algorithm for Rate-Splitting Multiple Access," in IEEE Transactions on Wireless Communications, doi: 10.1109/TWC.2025.3586919.

# Content of Code Package

Here is a detailed description of the package:

- The code of SCA is implemented in MATLAB environment with CVX toolbox assisted.
- Fig. 4 of the above paper will be reproduced by running MATLAB script './Figure4/perfect/main.m' and './Figure4/imperfect/main.m'.
- The procedure for Fig. 6:
    - Run './Figure6/channel_generate.m' and you will get a 'channel.mat' file.
    - Copy the 'channel.mat' file to every subfolders corresponding to each method.
    - Run every '\*_main.m' MATLAB script and you will get corresponding '\*.mat' files.
    - Copy the '\*.mat' files to corresponding subfolders that is in 'data_processing' folder.
    - Run 'data_processing.m' MATLAB script.
- The procedure for Fig. 10:
    - Run './Figure10/channel_generate.m' and you will get a 'channel.mat' file.
    - Check whether the generated 'channel.mat' files are copied to every subfolders corresponding to each method.
    - Run every '\*_main.m' MATLAB script and you will get corresponding '\*.mat' files.
    - Copy the '\*.mat' files to corresponding subfolders that is in 'data_processing' folder.
    - Run 'data_processing.m' MATLAB script.

# Abstract of the Article

The max-min fairness (MMF) problem in rate-splitting multiple access (RSMA) is known to be challenging due to its non-convex and non-smooth nature, as well as the coupled beamforming and common rate variables. Conventional algorithms to address this problem often incur high computational complexity or degraded MMF rate performance. To address these challenges, in this work, we propose a novel optimization algorithm named extragradient-fractional programming (EG-FP) to address the MMF problem of downlink RSMA. The proposed algorithm first leverages FP to transform the original problem into a block-wise convex problem.
For the subproblem of precoding block, we show that its Lagrangian dual is equivalent to a variational inequality problem, which is then solved using an extragradient-based algorithm. Additionally, we discover the optimal beamforming structure of the problem and based on which, we introduce a low-dimensional EG-FP algorithm with computational complexity independent of the number of transmit antennas. This feature is especially beneficial in scenarios with a large number of transmit antennas. The proposed algorithms are then extended to handle imperfect channel state information at the transmitter (CSIT). Numerical results demonstrate that the  MMF rate achieved by our proposed algorithms closely matches that of the conventional successive convex approximation (SCA) algorithm and significantly outperforms other baseline schemes. Remarkably, the average CPU time of the proposed algorithms is less than 10\% of the runtime required by the SCA algorithm, showing the efficiency and scalability of the proposed algorithms.

# License and Referencing

This code package is licensed under the GPLv2 license. If you in any way use this code for research that results in publications, please cite our original article listed above.

# Acknowledgements

This work has been supported in part by the National Natural Science Foundation of China under Grant 62201347.

RSMA-low-complexity-maxmin-K-user

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