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A Selective Secure Precoding Framework for MU-MIMO Rate-Splitting Multiple Access Networks Under Limited CSIT

Sangmin Lee, Seokjun Park, Jeonghun Park, Jinseok Choi

TL;DR

This work addresses secure downlink MU-MIMO transmission where legitimate users have heterogeneous security requirements and multiple eavesdroppers may be present. It develops a selective secure RSMA framework that smooths the non-convex, non-smooth objective with LogSumExp and solves a generalized eigenvalue problem via a power-iteration method, first under perfect CSIT and then extended to limited CSIT using conditional-average rates and lower bounds. The proposed SSSE-GPI-RSMA and its robust variant RSSSE-GPI-RSMA endow RSMA with explicit security constraints, achieving higher sum secrecy spectral efficiency than baselines across varied scenarios while maintaining fast convergence. The approach is practical for realistic networks with imperfect channel knowledge and diverse security requirements, offering a scalable, adaptable solution for secure RSMA in future wireless systems.

Abstract

In this paper, we propose a robust and adaptable secure precoding framework designed to encapsulate a intricate scenario where legitimate users have different information security: secure private or normal public information. Leveraging rate-splitting multiple access (RSMA), we formulate the sum secrecy spectral efficiency (SE) maximization problem in downlink multi-user multiple-input multiple-output (MIMO) systems with multi-eavesdropper. To resolve the challenges including the heterogeneity of security, non-convexity, and non-smoothness of the problem, we initially approximate the problem using a LogSumExp technique. Subsequently, we derive the first-order optimality condition in the form of a generalized eigenvalue problem. We utilize a power iteration-based method to solve the condition, thereby achieving a superior local optimal solution. The proposed algorithm is further extended to a more realistic scenario involving limited channel state information at the transmitter (CSIT). To effectively utilize the limited channel information, we employ a conditional average rate approach. Handling the conditional average by deriving useful bounds, we establish a lower bound for the objective function under the conditional average. Then we apply the similar optimization method as for the perfect CSIT case. In simulations, we validate the proposed algorithm in terms of the sum secrecy SE.

A Selective Secure Precoding Framework for MU-MIMO Rate-Splitting Multiple Access Networks Under Limited CSIT

TL;DR

This work addresses secure downlink MU-MIMO transmission where legitimate users have heterogeneous security requirements and multiple eavesdroppers may be present. It develops a selective secure RSMA framework that smooths the non-convex, non-smooth objective with LogSumExp and solves a generalized eigenvalue problem via a power-iteration method, first under perfect CSIT and then extended to limited CSIT using conditional-average rates and lower bounds. The proposed SSSE-GPI-RSMA and its robust variant RSSSE-GPI-RSMA endow RSMA with explicit security constraints, achieving higher sum secrecy spectral efficiency than baselines across varied scenarios while maintaining fast convergence. The approach is practical for realistic networks with imperfect channel knowledge and diverse security requirements, offering a scalable, adaptable solution for secure RSMA in future wireless systems.

Abstract

In this paper, we propose a robust and adaptable secure precoding framework designed to encapsulate a intricate scenario where legitimate users have different information security: secure private or normal public information. Leveraging rate-splitting multiple access (RSMA), we formulate the sum secrecy spectral efficiency (SE) maximization problem in downlink multi-user multiple-input multiple-output (MIMO) systems with multi-eavesdropper. To resolve the challenges including the heterogeneity of security, non-convexity, and non-smoothness of the problem, we initially approximate the problem using a LogSumExp technique. Subsequently, we derive the first-order optimality condition in the form of a generalized eigenvalue problem. We utilize a power iteration-based method to solve the condition, thereby achieving a superior local optimal solution. The proposed algorithm is further extended to a more realistic scenario involving limited channel state information at the transmitter (CSIT). To effectively utilize the limited channel information, we employ a conditional average rate approach. Handling the conditional average by deriving useful bounds, we establish a lower bound for the objective function under the conditional average. Then we apply the similar optimization method as for the perfect CSIT case. In simulations, we validate the proposed algorithm in terms of the sum secrecy SE.
Paper Structure (21 sections, 3 theorems, 50 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 3 theorems, 50 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Prior Work
  3. Contributions
  4. System Model
  5. Signal Model
  6. Problem Formulation
  7. Selective Secure Rate-Splitting Precoding with Perfect CSIT
  8. Extension to Limited CSIT: Robust and Selective Secure Rate-Splitting Precoding
  9. Conditional Average Rate
  10. Limited CSIT Handling Appraoch
  11. Problem Reformulation
  12. Complexity Analysis
  13. Numerical Results
  14. Performance Evaluation
  15. Secrecy SE versus SNR
  16. ...and 6 more sections

Key Result

Lemma 1

With perfect CSIT, the first-order optimality condition of problem eq:op_Rayleigh without the power constraint is satisfied if the following condition holds: where with $w_{{\sf{c}},k}(\bar{\bf{f}}) = \left(\frac{\bar{\bf{f}}^{\sf{H}} {\bf{A}}_{{\sf{c}},k}\bar{\bf{f}}}{\bar{\bf{f}}^{\sf{H}} {\bf{B}}_{{\sf{c}},k}\bar{\bf{f}}}\right)^{-\frac{1}{\alpha\ln{2}}}$, $w_{{\sf{e}}}^{(s)}(\bar{\bf{f}}) =

Figures (8)

  • Figure 1: An example scenario of a multiuser MIMO downlink system employing RSMA with multiple eavesdroppers.
  • Figure 2: The sum secrecy SE versus SNR for $N = 4$ AP antennas, $K = 4$ total users, $S = 2$ secret users, $M = 2$ normal users, and $E = 2$ eavesdroppers.
  • Figure 3: The sum secrecy SE versus SNR for $N = 4$ AP antennas, $K=4$ users, $E = 0$ eavesdroppers under partial CSIT.
  • Figure 4: The sum secrecy SE versus the number of secret users $S$ for $N = 8$ AP antennas, $K = 8$ total users, $E = 0$ eavesdroppers, and SNR = 10 dB under partial CSIT.
  • Figure 5: The sum secrecy SE versus the number of eavesdroppers for $N = 4$ AP antennas, $S = 4$ secret users, $M = 0$ normal users and SNR = 20 dB under partial CSIT.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof