A Probabilistic Reformulation Technique for Discrete RIS Optimization in Wireless Systems
A Probabilistic Reformulation Technique for Discrete RIS Optimization in Wireless Systems
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DOI：
10.1109/twc.2023.3326091
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发表时间：
2023-03
影响因子：
10.4
通讯作者：
Anish Pradhan;Harpreet S. Dhillon
中科院分区：
文献类型：
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作者：
Anish Pradhan;Harpreet S. Dhillon
可重构智能表面（RIS）的使用可以通过修改无线链路来创建虚拟视距链路、绕过阻塞、抑制干扰和增强定位，从而改善无线通信。然而，使RIS能够修改无线信道需要仔细优化RIS相移。尽管在硬件限制下，离散RIS更实用，但连续RIS相移优化比离散RIS优化吸引了更多的关注，后者存在量化误差和可扩展性等问题。为了克服这些问题，我们开发了一种综合概率技术，通过将离散优化变量解释为分类随机向量并计算有关这些参数的期望，将离散优化问题转化为连续域概率参数的优化问题。严格地证明了在无约束情况下，重新表述的最优点与原问题重合。对于有约束的情况，我们证明了变换后的问题是原问题的松弛。我们将提出的技术应用于两个典型的离散RIS应用：SINR最大化和开销感知率和能源效率（EE）最大化。正如我们在RIS应用程序中所演示的那样，重新表述可以对原始问题进行随机和分析解释。前一种解释产生随机抽样技术，而后一种解释产生分析梯度下降（GD）方法，该方法对期望采用封闭形式的近似。我们明确地推导了所提出算法的最坏情况计算复杂性。数值结果表明，该方法适用于各种离散RIS优化问题，并优于其他一般方法，如最近点投影（CPP）和半定松弛（SDR）方法。
The use of reconfigurable intelligent surfaces (RIS) can improve wireless communication by modifying the wireless link to create virtual line-of-sight links, bypass blockages, suppress interference, and enhance localization. However, enabling the RIS to modify the wireless channel requires careful optimization of the RIS phase-shifts. Although discrete RIS is more practical given hardware limitations, continuous RIS phase-shift optimization has attracted significantly more attention than discrete RIS optimization, which suffers from issues like quantization error and scalability. To overcome these issues, we develop a comprehensive probabilistic technique to transform discrete optimization problems into optimization problems of continuous domain probability parameters by interpreting the discrete optimization variable as a categorical random vector and computing expectations with respect to those parameters. We rigorously establish that for the unconstrained case, the optimal points of the reformulation and the original problem coincide. For the constrained case, we prove that the transformed problem is a relaxation of the original problem. We apply the proposed technique to two canonical discrete RIS applications: SINR maximization and overhead-aware rate and energy efficiency (EE) maximization. The reformulation enables both stochastic and analytical interpretations of the original problems, as we demonstrate in our RIS applications. The former interpretation yields a stochastic sampling technique, whereas the latter yields an analytical gradient descent (GD) approach that employs closed-form approximations for the expectation. We have explicitly derived the worst-case computational complexities of the proposed algorithms. The numerical results demonstrate that the proposed technique is applicable to a variety of discrete RIS optimization problems and outperforms other general approaches, such as closest point projection (CPP) and semidefinite relaxation (SDR) methods.