Throughput Maximization for Double RIS-Assisted MISO Systems

Objective With the continuous advancement of research on Reconfigurable Intelligent Surfaces (RIS), various application scenarios have emerged. Among these, Active Reconfigurable Intelligent Surfaces (ARIS) attracts significant attention from the academic community. While some studies focus on dual Passive RIS-assisted communication systems, others investigate dual RIS-assisted systems incorporating ARIS. Existing literature consistently demonstrates that dual RIS configurations outperform single RIS setups in terms of achievable Signal-to-Noise Ratio (SNR), power gain, and energy transfer efficiency, with dual RIS systems achieving approximately ten times higher energy transfer efficiency. However, most existing studies on RIS focus on optimizing the performance of reflection coefficients in one or more distributed RIS-aided systems, primarily serving users within their respective coverage areas, without sufficiently addressing the benefits of single-reflection links. While dual RIS systems can effectively mitigate the limitations of antenna numbers and improve transmission reliability and efficiency, single-reflection links can still significantly enhance channel capacity, especially under low transmission power conditions. This paper proposes a novel approach wherein dual-reflection links and two single-reflection links jointly serve users. The goal is to maximize the downlink capacity of dual RIS-assisted Multiple-Input Single-Output (MISO) systems by strategically configuring the interaction between the two RISs. Methods In this paper, four combinatorial models of RIS are investigated: the Transmitter-PRIS PRIS-Receiver (TPPR), Transmitter-ARIS PRIS-Receiver (TAPR), Transmitter-PRIS ARIS-Receiver (TPAR), and Transmitter-ARIS ARIS-Receiver (TAAR). The optimization objective of all models is to maximize the communication rate by optimizing the antenna beamforming vector of the base station and the phase shift matrix of the RIS. Due to the coupling of the three variables in the objective function, the model is non-convex, making it difficult to obtain an optimal solution. To address the coupling problem, the Alternating Optimization (AO) algorithm is employed, where one phase shift vector is fixed while the other is optimized alternately. To tackle the non-convex problem, SCA is applied to iteratively approximate the optimal solution by solving a series of convex subproblems. Results and Discussions Building on the research methods outlined above and employing the SCA and AO algorithms, experimental results are obtained. The system capacity of each combination model increases with rising amplification power ( Fig. 2). However, once the amplification factor reaches a certain threshold, the capacity curves of all models begin to flatten due to the constraints imposed by the maximum amplification power. Further demonstration of the system capacity performance of different combination models as transmit power increases is shown in (Fig. 3). Across all dual-RIS combination models, system capacity improves with higher transmit power and outperforms the Single-Active model in all scenarios. In (Fig. 3(a)), under low transmit power conditions, regions of the curves corresponding to higher amplification power overlap due to the constraint of the amplification factor. As transmit power increases, system capacity stabilizes, which can be attributed to the proximity of ARIS to the base station, allowing it to receive stronger signals. Under high transmit power, system capacity continues to improve due to the influence of PRIS. Unlike ARIS, PRIS reflects the optimized signal path without being constrained by amplification power. Consequently, as transmit power increases, the signal strength received by PRIS is enhanced. In (Fig. 3(b)), system capacity increases with transmit power, showing trends similar to those in (Fig. 3(a)). In the TPAR combined model, the amplification factor constraint dominates, causing the system capacity curves to exhibit similar behavior across different amplification power levels. Under low transmit power, the signal strength at ARIS does not exceed the maximum amplification power budget. As transmit power increases, the amplification power constraint increasingly affects system capacity, leading to a gradual slowdown in the curve's upward trend until it flattens. At high transmit power levels, the system capacity curve of the TPAR model levels off due to the low signal strength received by ARIS when it is positioned farther from the base station. This positioning necessitates higher transmit power to overcome the amplified power constraint. Thus, it is recommended that ARIS be deployed as close to the user as possible. In (Fig. 3(c)), the TAAR combined model leverages the characteristics of both ARIS and PRIS in a dual ARISassisted scenario. Under low transmit power conditions, significant capacity gains are achieved. However, at high transmit power, the system capacity is constrained by the maximum amplification power of ARIS and eventually levels off. The system capacity trends in (Fig. 3(a)) and (Fig. 3(b)) consistently increase with higher transmit power. This is because both combination models integrate the advantages of PRIS and ARIS, ensuring high performance under both high and low transmit power conditions. In (Fig. 3(d)), where ARIS is positioned on the user side, comparison with (Fig. 3(c)) reveals that, under high transmit power, the system capacity of both combination models is nearly identical, regardless of the amplification power level. This suggests that in strong transmit power scenarios, the additional gains from ARIS are limited. Conclusions This paper provides an in-depth analysis of the optimization of dual RIS-assisted MISO communication systems, confirming their superiority over single RIS configurations. However, several potential research directions remain unexplored. Most current studies assume ideal channel models, whereas real-world applications often involve complex channel conditions that significantly affect system performance. Future research could investigate the performance of dual RIS systems under these practical conditions, paving the way for more robust and applicable solutions.