## 1 Introduction  
With the rapid advancement of autonomous driving technology, urban autonomous mobility services are regarded as the preferred scenario for large-scale commercial application of this technology [1, 2]. However, the complex and dynamic urban traffic environment, particularly at intersections, poses unprecedented challenges to autonomous driving systems [3]. Urban intersections are often dense and somewhat chaotic and are filled with the various dynamic interactions that significantly increase the difficulty for autonomous systems in perception, decision-making, and control [4, 5]; this imposes stringent requirements on their safe driving capabilities. Furthermore, in addition to ensuring safe driving, autonomous systems must navigate these uncontrolled intersections efficiently to maintain service reliability and efficiency. Thus, establishing a comprehensive and objective evaluation of autonomous driving performance in complex intersection environments has become crucial for advancing the commercial deployment of autonomous systems. Traditional autonomous driving testing methods, such as closed-field and real-world road tests [6, 7, 8], allow direct performance assessment in physical environments. However, they are limited in scene diversity and complexity and have high testing costs, making it challenging to efficiently generate diverse and challenging intersection scenarios under controlled conditions [9, 10, 11]. To overcome these limitations, scenario-based simulation testing has increasingly become a key approach for evaluating autonomous driving systems in intersection scenarios [12, 13, 14]. Simulation testing can flexibly generate highly complex intersection scenes at low cost and with high safety, simulating various traffic flows, vehicle behaviors, and interaction patterns. This provides more efficient and diverse evaluation support for assessing the performance of autonomous driving systems in complex intersections [15]. To ensure simulation testing is truly effective, two key issues must be addressed. First, the generated scenarios must have sufficient complexity to effectively test the performance of autonomous driving systems in real-world driving conditions. Second, the scenario complexity should align with the actual performance level of the autonomous system. If the scenario complexity far exceeds the system's current capabilities, it may result in system failures, preventing meaningful evaluation outcomes. Therefore, establishing reasonable complexity metrics closely related to system performance is essential. This not only ensures that the test scenarios accurately reflect the system's capabilities but also avoids ineffective testing due to excessive complexity. However, in terms of complexity quantification, current mainstream evaluation methods are typically based on the spatiotemporal proximity between the primary vehicle and surrounding vehicles, using advanced models such as information entropy and gravitational models [16; 17; 18] to describe nonlinear interactions. Although these methods measure scenario complexity from the perspective of local interactions, their results often rely on the specific performance of the primary vehicle, which lack a global perspective and objectivity. Additionally, the consistency between the quantitative results of these models and the actual performance of autonomous driving systems in testing scenarios has not yet been validated. Therefore, there is an urgent need to develop an objective assessment framework capable of characterizing intersection complexity from a global perspective while correlating with autonomous system performance. To address the issues outlined above, this study proposes an objective complexity evaluation framework that does not rely on the dynamic performance of the primary vehicle.