SATR-DL: Dual STAR-RIS Downlink Optimization

• SATR-DL is a dual STAR-RIS design that uses simultaneous transmission and reflection to provide full-plane downlink coverage in joint uplink/downlink networks.
• It employs an alternating optimization approach integrating active beamforming with passive STAR-RIS design, using methods like ADMM and PCCP for interference mitigation.
• Numerical results demonstrate that SATR-DL can improve downlink sum-rate by up to 50–60% over baseline systems while maintaining robust performance under hardware quantization.

SATR-DL refers to the Simultaneously Transmitting And Reflecting DownLink design within dual STAR-RIS (Reconfigurable Intelligent Surface) architectures, as introduced in the context of joint uplink/downlink (JUD) wireless networks. It specifically denotes the downlink optimization and system design for full-plane coverage using dual, spatially separated STAR-RIS panels, supporting both uplink and downlink user groups while maximizing spectral efficiency and interference mitigation (Shen et al., 2023).

1. System Architecture and Problem Setting

The SATR-DL system operates with a full-plane JUD base station (BS) equipped with $N_T$ transmit and $N_R$ receive antennas. The user population consists of four groups:

• $\mathcal{K}_{\mathrm{PD}}$, $\mathcal{K}_{\mathrm{PU}}$: Primary Downlink and Primary Uplink users, located in the "P-region" including the BS.
• $\mathcal{K}_{\mathrm{SD}}$, $\mathcal{K}_{\mathrm{SU}}$: Secondary Downlink and Secondary Uplink users, in the "S-region" away from the BS.

A dual STAR-RIS configuration is employed to achieve 360° service:

• STAR-P (Primary STAR-RIS): Reflection side toward the BS for serving the P-region.
• STAR-S (Secondary STAR-RIS): Transmission side away from the BS to reach the S-region.

Each STAR-RIS element controls both amplitude (transmission/reflection splitting) and phase, governed by the constraint

$$\beta_{\mathrm{PT},m}^2 + \beta_{\mathrm{PR},m}^2 = 1, \quad \beta_{\mathrm{ST},m}^2 + \beta_{\mathrm{SR},m}^2 = 1,$$

with diagonally parameterized phase matrices $$\boldsymbol{\Theta}_x = \operatorname{diag}(\beta_{x,1} e^{j\vartheta_{x,1}},\ldots,\beta_{x,M_x} e^{j\vartheta_{x,M_x}})$$ where $0 \le \beta_{x,m} \le 1$, $|e^{j\vartheta_{x,m}}|=1$.

The architecture simultaneously mitigates inter-user interference, uplink-induced self-interference at the BS, and cross-region interference for both downlink and uplink users.

2. Mathematical Formulation of the SATR-DL Optimization

The design objective of SATR-DL is to maximize the total downlink throughput $N_R$0, while maintaining minimum uplink rates $N_R$1 and $N_R$2, subject to BS transmit power $N_R$3 and STAR-RIS element constraints.

The formal problem is:

$N_R$4

The received signal at a primary DL user $N_R$5 is a superposition of the direct BS$N_R$6PD link, STAR-P-aided reflection, STAR-P-to-SD transmission-induced interference, and uplink interference from both regions, with all channels parameterized per the system's geometry.

3. Solution Methodology: Alternating Optimization and DBAP

The nonconvex optimization for SATR-DL is solved using an Alternating Optimization (AO) approach, decomposed into active and passive design subproblems:

a) Active Beamforming at BS:

The problem is transformed via:

• Lagrange-Dual Transform (introducing $N_R$7 scalars to linearize log-SINR terms).
• Dinkelbach’s Transformation (simplifying fractional objectives).

The subproblem yields a convex quadratic program in the BS beamformers $N_R$8.

b) Passive STAR-RIS Design:

The STAR-RIS element optimization is further separated:

• Amplitude design $N_R$9 (fixed phase), using SCA (successive convex approximation) to relax nonconvex quadratic equality, solved via ADMM.
• Phase design $\mathcal{K}_{\mathrm{PD}}$0 (fixed amplitude), employing a penalty convex–concave procedure (PCCP) to enforce unit modulus, or, optionally, a coupled-phase update respecting electromagnetic constraints.

The "DBAP" (Downlink Beamforming and Amplitude/Phase passive design) scheme iterates between active and passive subproblems until convergence.

4. Performance Evaluation and Numerical Results

Extensive Monte Carlo simulations (100 runs, Rician fading for RIS-augmented links, Rayleigh for direct, $\mathcal{K}_{\mathrm{PD}}$1 dBm noise floor) validate SATR-DL performance under varying system sizes and restrictions.

Key metrics and findings:

• Convergence: The AO-based DBAP algorithm converges in fewer than 20 iterations.
• Quantization robustness: 2–3 bits amplitude/phase quantization incurs less than 5% loss; phase quantization is more critical.
• Deployment insights: ~100 m inter-RIS separation maximizes DL sum-rate, balancing coverage and path gains.
• Panel partitioning: Dividing a large dual panel (e.g., 48 elements) into eight subpanels optimizes sum-rate due to diversity gains.
• Scalability: DL sum-rate increases with $\mathcal{K}_{\mathrm{PD}}$2, $\mathcal{K}_{\mathrm{PD}}$3, and $\mathcal{K}_{\mathrm{PD}}$4 (panel size).

Architecture	DL Sum-Rate Gain over Baseline
D-STAR (Dual STAR-RIS, DBAP)	+30–40% (vs Single STAR-RIS)
D-STAR vs Double-RIS (HDx/JUD)	+20–30%
D-STAR vs Single-RIS (HDx)	+50–60%

SATR-DL, as realized in D-STAR with DBAP, outperforms mode-switching, amplitude-only, phase-only, and genetic heuristic benchmarks under comparable hardware and propagation conditions (Shen et al., 2023).

5. Architectural and Practical Insights

The dual STAR-RIS architecture of SATR-DL provides:

• 360° DL coverage by deploying two optimized panels with complementary reflecting/transmitting roles.
• Simultaneous management of intra-region, cross-region, and self-interference, especially critical for dense joint UL/DL deployments.

Design guidelines:

• STAR-P/STAR-S should be deployed roughly 100 m from the BS and from user clusters to maximize throughput and coverage.
• Panel sizing in the range $\mathcal{K}_{\mathrm{PD}}$5 to $\mathcal{K}_{\mathrm{PD}}$6 per surface, subdivided into approximately 8 subpanels, yields the best spectral efficiency–diversity trade-off.
• Hardware quantization can be safely set to 3–4 bits for phase and 2 bits for amplitude without significant performance degradation.

6. Limitations, Open Issues, and Future Directions

SATR-DL has demonstrated state-of-the-art sum-rate performance for downlink-dominated scenarios in JUD networks with STAR-RIS, but several considerations remain:

• All results are based on simulation using standard channel models; practical real-world demonstration is pending.
• UL constraints (QoS) can restrict the achievable DL rate and system feasibility with dense UL traffic.
• The optimality is local due to the AO decomposition and nonconvex nature of the underlying optimization.
• While the design is scalable, increased granularity in panel partitioning or more complex electromagnetic constraints may necessitate novel algorithmic approaches.

A plausible implication is that further integration with low-latency control and distributed optimization could enable real-time adaptation and wider practical deployment in heterogeneous cellular and IoT scenarios.

7. Significance and Impact within Reconfigurable Intelligent Surface Networks

SATR-DL, as embedded in the D-STAR architecture, constitutes a significant step for practical, high-efficiency, and robust full-plane downlink provisioning in next-generation wireless networks. The design achieves near-optimal joint handling of active and passive resources, full-duplex-like operation, and offers clear, data-driven deployment strategies for maximizing network spectral efficiency (Shen et al., 2023).