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Robust unsupervised feature learning is a critical yet tough task for synthetic aperture radar (SAR) automatic target recognition (ATR) with limited labeled data. The developing contrastive self-supervised learning (CSL) method, which learns informative representations by solving an instance discrimination task, provides a novel method for learning discriminative features from unlabeled SAR images. However, the instance-level contrastive loss can magnify the differences between samples belonging to the same class in the latent feature space. Therefore, CSL can dispel these targets from the same class and affect the downstream classification tasks. In order to address this problem, this paper proposes a novel framework called locality preserving property constrained contrastive learning (LPPCL), which not only learns informative representations of data but also preserves the local similarity property in the latent feature space. In LPPCL, the traditional InfoNCE loss of the CSL models is reformulated in a cross-entropy form where the local similarity of the original data is embedded as pseudo labels. Furthermore, the traditional two-branch CSL architecture is extended to a multi-branch structure, improving the robustness of models trained with limited batch sizes and samples. Finally, the self-attentive pooling module is used to replace the global average pooling layer that is commonly used in most of the standard encoders, which provides an adaptive method for retaining information that benefits downstream tasks during the pooling procedure and significantly improves the performance of the model. Validation and ablation experiments using MSTAR datasets found that the proposed framework outperformed the classic CSL method and achieved state-of-the-art (SOTA) results. Full article