Novel Probabilistic Reformulation Technique for Unconstrained Discrete RIS Optimization
Novel Probabilistic Reformulation Technique for Unconstrained Discrete RIS Optimization
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DOI：
10.1109/pimrc56721.2023.10293983
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发表时间：
2023-09
期刊：
影响因子：
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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
在RIS辅助无线系统中，确定离散可重构智能表面（RIS）的最佳相位是一个具有挑战性的问题。本文提出了一种新的概率重构技术，将离散优化问题转化为连续域问题。其思想是将优化变量视为具有独立但非同分布（i.n.i.d）条目的分类随机向量，并用其期望替换目标函数。在无约束情况下，我们严格地建立了原问题的唯一最优解与变换后问题的退化概率密度函数（PDF）之间的等价性。此外，我们导出了与二次型和二元随机向量相关的关键解析矩和梯度，这些分析矩和梯度在ris辅助无线系统的优化中很有用。为了具体证明该技术的优势，我们重新制定了一个标准离散ris辅助信噪比（SINR）最大化问题，并使用梯度下降（GD）技术解决了重新制定的问题。我们的解决方案包括一种分析方法，该方法依赖于期望的封闭形式近似，结合力矩结果，以及基于对数导数梯度估计器的随机抽样方法。数值结果表明，我们基于期望的算法优于最先进的传统算法，从而证明了我们方法的有效性。
Determining optimal phases for a discrete reconfigurable intelligent surface (RIS) in RIS-aided wireless systems is known to be a challenging problem. This paper develops a novel probabilistic reformulation technique to transform such discrete optimization problems into continuous domain problems. The idea is to treat optimization variables as a categorical random vector with independent but non-identically distributed (i.n.i.d.) entries and replace the objective function with its expectation. In the unconstrained case, we rigorously establish the equivalence between the original problem’s unique optimal solution and the corresponding degenerate probability density function (PDF) of the transformed problem. Furthermore, we derive key analytical moments and gradients associated with the quadratic form and binary random vectors that are useful in the optimization of RIS-aided wireless systems. In order to concretely demonstrate the benefits of the proposed technique, we reformulate a canonical discrete RIS-aided signal-to-interference-plus-noise ratio (SINR) maximization problem and solve the reformulated problem with the gradient descent (GD) technique. Our solution includes an analytical approach that relies on closed-form approximations for the expectation, incorporating moment results, and a stochastic sampling method based on a log-derivative gradient estimator. Numerical results show that our expectation-based algorithms outperform state-of-the-art conventional algorithms, thereby demonstrating the effectiveness of our approach.