We consider an underlay coexistence scenario where secondary users (SUs) must keep their interference to the primary users (PUs) under control. However, the channel gains from the PUs to the SUs are uncertain due to a lack of cooperation between the PUs and the SUs. Under this circumstance, it is preferable to allow the interference threshold of each PU to be violated occasionally as long as such violation stays below a probability. In this article, we employ Chance-Constrained Programming (CCP) to exploit this idea of occasional interference threshold violation. We assume the uncertain channel gains are only known by their mean and covariance. These quantities are slow-changing and easy to estimate. Our main contribution is to introduce a novel and powerful mathematical tool called Exact Conic Reformulation (ECR), which reformulates the intractable chance constraints into tractable convex constraints. Further, ECR guarantees an equivalent reformulation from linear chance constraints into deterministic conic constraints without the limitations associated with Bernstein Approximation, on which our research community has been fixated on for years. Through extensive simulations, we show that our proposed solution offers a significant improvement over existing approaches in terms of performance and ability to handle channel correlations (where Bernstein Approximation is no longer applicable).

中文翻译：

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底层不确定性与信道不确定性共存时使频谱效率最大化

我们考虑了一个底层共存方案，其中次要用户（SU）必须保持其对主要用户（PU）的干扰处于受控状态。然而，由于PU与SU之间缺乏合作，所以不确定从PU到SU的信道增益。在这种情况下，优选的是，允许偶尔违反每个PU的干扰阈值，只要这种违反保持在概率以下即可。在本文中，我们采用机会约束编程（CCP）来开发这种偶尔违反干扰阈值的想法。我们假设不确定的信道增益仅通过其均值和协方差知道。这些数量变化缓慢且易于估算。我们的主要贡献是推出了一种新颖而强大的数学工具，称为精确圆锥重构（ECR），它将难处理的机会约束重新形容为易处理的凸约束。此外，ECR保证了从线性机会约束到确定性圆锥约束的等价重构，而没有与伯恩斯坦近似法相关的局限性，多年来我们的研究团体一直将其限制于此。通过广泛的仿真，我们证明了我们提出的解决方案在性能和处理通道相关性（其中不再适用伯恩斯坦近似法）方面，对现有方法进行了重大改进。多年来，我们的研究社区一直专注于此。通过广泛的仿真，我们证明了我们提出的解决方案在性能和处理通道相关性（其中不再适用伯恩斯坦近似法）方面，对现有方法进行了重大改进。多年来，我们的研究社区一直专注于此。通过广泛的仿真，我们证明了我们提出的解决方案在性能和处理通道相关性（其中不再适用伯恩斯坦近似法）方面，对现有方法进行了重大改进。