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Two-Timescale Design for Active STAR-RIS Aided Massive MIMO Systems

Anastasios Papazafeiropoulos, Hanxiao Ge, Pandelis Kourtessis, Tharmalingam Ratnarajah, Symeon Chatzinotas, Symeon Papavassiliou

TL;DR

This work introduces ASTARS, a two-timescale architecture that fuses active RIS with STAR-RIS to overcome double fading and achieve full-space coverage in mMIMO downlinks. It develops a channel-estimation-and-transmission framework based on statistical CSI, deriving a closed-form SE expression and optimizing the AM, phase, and AACs via projected gradient ascent for reduced overhead. The ES/MS surface protocols and a unified channel model enable jointly efficient active-beamforming at the BS and surface design, with complexity scaling and practical convergence advantages demonstrated. Numerical results show substantial gains over passive STAR-RIS for moderate surface sizes, while highlighting the power- and element-count-dependent tradeoffs that determine when ASTARS is advantageous in realistic deployments.

Abstract

Simultaneously transmitting and reflecting \textcolor{black}{reconfigurable intelligent surface} (STAR-RIS) is a promising implementation of RIS-assisted systems that enables full-space coverage. However, STAR-RIS as well as conventional RIS suffer from the double-fading effect. Thus, in this paper, we propose the marriage of active RIS and STAR-RIS, denoted as ASTARS for massive multiple-input multiple-output (mMIMO) systems, and we focus on the energy splitting (ES) and mode switching (MS) protocols. Compared to prior literature, we consider the impact of correlated fading, and we rely our analysis on the two timescale protocol, being dependent on statistical channel state information (CSI). On this ground, we propose a channel estimation method for ASTARS with reduced overhead that accounts for its architecture. Next, we derive a \textcolor{black}{closed-form expression} for the achievable sum-rate for both types of users in the transmission and reflection regions in a unified approach with significant practical advantages such as reduced complexity and overhead, which result in a lower number of required iterations for convergence compared to an alternating optimization (AO) approach. Notably, we maximize simultaneously the amplitudes, the phase shifts, and the active amplifying coefficients of the ASTARS by applying the projected gradient ascent method (PGAM). Remarkably, the proposed optimization can be executed at every several coherence intervals that reduces the processing burden considerably. Simulations corroborate the analytical results, provide insight into the effects of fundamental variables on the sum achievable SE, and present the superiority of 16 ASTARS compared to passive STAR-RIS for a practical number of surface elements.

Two-Timescale Design for Active STAR-RIS Aided Massive MIMO Systems

TL;DR

This work introduces ASTARS, a two-timescale architecture that fuses active RIS with STAR-RIS to overcome double fading and achieve full-space coverage in mMIMO downlinks. It develops a channel-estimation-and-transmission framework based on statistical CSI, deriving a closed-form SE expression and optimizing the AM, phase, and AACs via projected gradient ascent for reduced overhead. The ES/MS surface protocols and a unified channel model enable jointly efficient active-beamforming at the BS and surface design, with complexity scaling and practical convergence advantages demonstrated. Numerical results show substantial gains over passive STAR-RIS for moderate surface sizes, while highlighting the power- and element-count-dependent tradeoffs that determine when ASTARS is advantageous in realistic deployments.

Abstract

Simultaneously transmitting and reflecting \textcolor{black}{reconfigurable intelligent surface} (STAR-RIS) is a promising implementation of RIS-assisted systems that enables full-space coverage. However, STAR-RIS as well as conventional RIS suffer from the double-fading effect. Thus, in this paper, we propose the marriage of active RIS and STAR-RIS, denoted as ASTARS for massive multiple-input multiple-output (mMIMO) systems, and we focus on the energy splitting (ES) and mode switching (MS) protocols. Compared to prior literature, we consider the impact of correlated fading, and we rely our analysis on the two timescale protocol, being dependent on statistical channel state information (CSI). On this ground, we propose a channel estimation method for ASTARS with reduced overhead that accounts for its architecture. Next, we derive a \textcolor{black}{closed-form expression} for the achievable sum-rate for both types of users in the transmission and reflection regions in a unified approach with significant practical advantages such as reduced complexity and overhead, which result in a lower number of required iterations for convergence compared to an alternating optimization (AO) approach. Notably, we maximize simultaneously the amplitudes, the phase shifts, and the active amplifying coefficients of the ASTARS by applying the projected gradient ascent method (PGAM). Remarkably, the proposed optimization can be executed at every several coherence intervals that reduces the processing burden considerably. Simulations corroborate the analytical results, provide insight into the effects of fundamental variables on the sum achievable SE, and present the superiority of 16 ASTARS compared to passive STAR-RIS for a practical number of surface elements.
Paper Structure (23 sections, 10 theorems, 82 equations, 5 figures, 1 algorithm)

This paper contains 23 sections, 10 theorems, 82 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. ASTARS
  4. ES protocol
  5. MS protocol
  6. Channel Model
  7. ASTARS Channel Estimation and Downlink Transmission
  8. Channel Estimation Under Statistical CSI
  9. Downlink Transmission
  10. Achievable Spectral Efficiency
  11. Benefits of ASTARS
  12. mMIMO without any surface
  13. ASTARS-assisted mMIMO with independent fading
  14. Problem Formulation
  15. ASTARS Optimization for ES protocol
  16. ...and 8 more sections

Key Result

Lemma 1

The estimated end-to-end channel by MMSE is written as where ${\mathbf{Q}}_{k}\!=\! \left({\mathbf{R}}_{k} +\frac{{\tilde{ \beta}_{g}}\sigma_{v}^{2}}{{\tau p}}\sum_{j=1}^{K}\tr({\mathbf{R}}_{\mathrm{RIS}}{\mathbf{A}}^2{\mathbf{C}}_{w_{j}}){\mathbf{R}}_{\mathrm{BS}} + \frac{\sigma^2}{ \tau p }{\bm{\mathrm{I}}}_{M}\right)^{\!-1}$ with ${\mathbf{C}}_{w_{j} with

Figures (5)

  • Figure 1: A mMIMO ASTARS-aided system with numerous UEs at each side of the surface.
  • Figure 2: Convergence of Algorithm \ref{['Algoa1']}: (a) Sensitivity of initial points, (b) Comparison with AO for different $N$, (c) Comparison with AO for different $M$.
  • Figure 3: Achievable sum SE versus the SNR.
  • Figure 4: Achievable sum SE versus the number of elements $N$ for: (a) conventional $N$, (b) large $N$ (Analytical results).
  • Figure 5: Achievable sum SE versus the versus the number of BS antennas $M$.

Theorems & Definitions (18)

  • Remark 1
  • Lemma 1
  • proof
  • Corollary 1
  • Corollary 2
  • proof
  • Remark 2
  • proof
  • Theorem 1
  • proof
  • ...and 8 more