In this paper we present DS-Pnet, a novel framework for FM signal-based positioning that addresses the challenges of high computational complexity and limited deployment in resource-constrained environments. Two downsampling methods-IQ signal downsampling and time-frequency representation downsampling-are proposed to reduce data dimensionality while preserving critical positioning features. By integrating with the lightweight MobileViT-XS neural network, the framework achieves high positioning accuracy with significantly reduced computational demands. Experiments on real-world FM signal datasets demonstrate that DS-Pnet achieves superior performance in both indoor and outdoor scenarios, with space and time complexity reductions of approximately 87% and 99.5%, respectively, compared to an existing method, FM-Pnet. Despite the high compression, DS-Pnet maintains robust positioning accuracy, offering an optimal balance between efficiency and precision.