[Paper Review] Robust Joint Design for Intelligent Reflecting Surfaces Assisted Cell-Free Networks

Xie Xie, Chen He+3 more|arXiv (Cornell University)|Jan 24, 2022

Advanced Wireless Communication Technologies4 citations

TL;DR

This paper proposes a robust joint beamforming design for intelligent reflecting surface (IRS)-assisted cell-free massive MIMO networks under imperfect channel state information (CSI). By employing stochastic programming to maximize the average sum-rate, the algorithm decouples active beamforming at access points and passive beamforming at IRSs, achieving high performance despite CSI uncertainty. The key contribution is proving that CSI uncertainty affects active beamforming but not passive IRS beamforming design, enabling a low-complexity, robust framework with guaranteed convergence.

ABSTRACT

Intelligent reflecting surfaces (IRSs) have emerged as a promising economical solution to implement cell-free networks. However, the performance gains achieved by IRSs critically depend on smartly tuned passive beamforming based on the assumption that the accurate channel state information (CSI) knowledge is available, which is practically impossible. Thus, in this paper, we investigate the impact of the CSI uncertainty on IRS-assisted cell-free networks. We adopt a stochastic programming method to cope with the CSI uncertainty by maximizing the expectation of the sum-rate, which guarantees robust performance over the average. Accordingly, an average sum-rate maximization problem is formulated, which is non-convex and arduous to obtain its optimal solution due to the coupled variables and the expectation operation with respect to CSI uncertainties. As a compromising approach, we develop an efficient robust joint design algorithm with low-complexity. Particularly, the original problem is equivalently transformed into a tractable form, and then, the locally optimal solution can be obtained by employing the block coordinate descent method. We further prove that the CSI uncertainty impacts the design of the active transmitting beamforming of APs, but surprisingly does not directly impact the design of the passive reflecting beamforming of IRSs. It is worth noting that the investigated scenario is flexible and general, and thus the proposed algorithm can act as a general framework to solve various sum-rate maximization problems. Simulation results demonstrate that IRSs can achieve considerable data rate improvement for conventional cell-free networks, and confirm the resilience of the proposed algorithm against the CSI uncertainty.

Motivation & Objective

• Address the performance degradation in IRS-assisted cell-free networks due to imperfect and uncertain channel state information (CSI).
• Develop a robust transmission design that ensures stable performance under CSI uncertainty without relying on worst-case (min-max) optimization.
• Formulate a stochastic programming problem to maximize the expected sum-rate across all CSI realizations.
• Decouple the joint optimization of active beamforming at access points and passive beamforming at IRSs to enable efficient computation.
• Establish theoretical insight that CSI uncertainty impacts active beamforming but not passive IRS beamforming design.

Proposed method

• Formulate a non-convex average sum-rate maximization problem under stochastic CSI uncertainty using a statistical error model.
• Transform the original problem into an equivalent, tractable form via expectation simplification and matrix trace identities.
• Apply the block coordinate descent (BCD) method to iteratively optimize active beamforming vectors and IRS phase shifts.
• Use a stochastic programming approach to maximize the expected sum-rate, ensuring robustness over the average CSI distribution.
• Prove that the optimal passive beamforming of the IRS is independent of CSI uncertainty, simplifying the design.
• Ensure convergence of the proposed algorithm by bounding the objective function and leveraging eigenvalue and norm constraints.

Experimental results

Research questions

• RQ1 How does CSI uncertainty affect the design of active and passive beamforming in IRS-assisted cell-free networks?
• RQ2 Can a stochastic programming approach outperform worst-case robust designs in terms of average sum-rate and complexity?
• RQ3 Is the optimal IRS passive beamforming design independent of CSI uncertainty, and if so, why?
• RQ4 Can the joint active and passive beamforming problem be decoupled effectively to reduce computational complexity?
• RQ5 What is the performance gain of IRS-assisted cell-free networks compared to conventional cell-free systems under practical CSI estimation errors?

Key findings

• The proposed robust joint design achieves significant sum-rate gains over conventional cell-free networks, even under CSI uncertainty.
• The algorithm converges to a locally optimal solution due to monotonic improvement and bounded objective function, as proven via convergence analysis.
• CSI uncertainty impacts the design of active beamforming at access points but does not directly affect the optimal passive beamforming at the IRS.
• The stochastic programming approach ensures robust performance across all CSI realizations by maximizing the expected sum-rate.
• Simulation results confirm the resilience of the proposed algorithm to CSI estimation errors, with substantial data rate improvements compared to non-IRS and non-robust designs.
• The framework is general and can be adapted to solve various sum-rate maximization problems in IRS-assisted wireless networks.