From High-Level Requirements to KPIs: Conformal Signal Temporal Logic Learning for Wireless Communications

TL;DR

C-STLL leverages signal temporal logic (STL), a formal language for specifying temporal properties of time series, to learn interpretable formulas that distinguish KPI traces satisfying high-level requirements from those that do not.

Abstract

Softwarized radio access networks (RANs), such as those based on the Open RAN (O-RAN) architecture, generate rich streams of key performance indicators (KPIs) that can be leveraged to extract actionable intelligence for network optimization. However, bridging the gap between low-level KPI measurements and high-level requirements, such as quality of experience (QoE), requires methods that are both relevant, capturing temporal patterns predictive of user-level outcomes, and interpretable, providing human-readable insights that operators can validate and act upon. This paper introduces conformal signal temporal logic learning (C-STLL), a framework that addresses both requirements. C-STLL leverages signal temporal logic (STL), a formal language for specifying temporal properties of time series, to learn interpretable formulas that distinguish KPI traces satisfying high-level requirements from those that do not. To ensure reliability, C-STLL wraps around existing STL learning algorithms with a conformal calibration procedure based on the Learn Then Test (LTT) framework. This procedure produces a set of STL formulas with formal guarantees: with high probability, the set contains at least one formula achieving a user-specified accuracy level. The calibration jointly optimizes for reliability, formula complexity, and diversity through principled acceptance and stopping rules validated via multiple hypothesis testing. Experiments using the ns-3 network simulator on a mobile gaming scenario demonstrate that C-STLL effectively controls risk below target levels while returning compact, diverse sets of interpretable temporal specifications that relate KPI behavior to QoE outcomes.

Figures (5)

• Figure 1: From high-level requirements to KPI requirements: The radio access network (RAN) collects traces of KPIs such as throughput and latency over time. High-level QoE evaluations are provided by end users. The goal of this work is to infer interpretable properties of KPI traces that are predictive of whether high-level requirements are satisfied or not. These properties are expressed by the formal language signal temporal logic (STL), which provides tools to describe temporal constraints as time series.
• Figure 2: Illustration of the proposed conformal STL learning (C-STLL) scheme. As illustrated in Fig. \ref{['gaming']}, KPI traces are labeled as $Y=1$ or $Y=-1$ based on whether or not they correspond to settings in which positive or negative higher-level requirements are satisfied. Via any STLL algorithm li2024tlinet, the dataset $\mathcal{D}$ of labeled KPI traces can be leveraged to produce an STL formula $\phi$, providing interpretable conditions on the KPI time series that are consistent with positive labels. However, this approach provides no guarantees on the reliability and accuracy of the formula $\phi$. The proposed C-STLL wraps around any STLL procedure to produce a set of STL formulas with reliability and quality assurance. Through a sequential application of the STL algorithm, each newly learned formula is either accepted for inclusion in the set or rejected, and the process is continued or stopped, based on calibrated threshold-based procedures. In this example, formula $\phi_2$ is rejected due to its high complexity, while $\phi_3$ is rejected for being too similar to $\phi_1$, which is already in the set.
• Figure 3: An illustration of a parameterized template for the construction of an STL formula $\phi$. In this example, the STL formula $\phi$ is constructed by the following steps: 1) a number of predicates $\mu$, as in \ref{['mu']}, are selected; 2) the predicates are combined via Boolean operators, either $\land$ or $\lor$; 3) temporal operators $\Diamond_{[t_1,t_2]}$ or $\Box_{[t_1,t_2]}$ are applied to the resulting partial STL formulas; and 4) another Boolean operator is used to combine the partial STL properties constructed at the previous steps. Each layer is specified by parameters that are optimized by addressing the STLL problem.
• Figure 4: Average test performance as a function of the target risk $\epsilon$ (the probability that the set $\mathcal{C}_{\hbox{\boldmath{$\lambda$}}}(\mathcal{D})$ includes no STL formulas with validation accuracy above $\varphi=0.8$) with data labeled using the ground-truth STL formula \ref{['true']}: (a) Average risk. (b) Average set size. (c) Average complexity \ref{['lambda1']}. (d) Average diversity \ref{['distance']}.
• Figure 5: Average test performance as a function of the target risk $\epsilon$ (the probability that the set $\mathcal{C}_{\hbox{\boldmath{$\lambda$}}}(\mathcal{D})$ includes no STL formulas with validation accuracy above $\varphi=0.8$) with data labeled using LLM: (a) Average risk. (b) Average set size. (c) Average complexity \ref{['lambda1']}. (d) Average diversity \ref{['distance']}.

Theorems & Definitions (2)

• Theorem 1: Reliability of C-STLL via LTT
• proof