Surrounding perceptions are quintessential for safe driving for connected and autonomous vehicles (CAVs), where the Bird's Eye View has been employed to accurately capture spatial relationships among vehicles. However, severe inherent limitations of BEV, like blind spots, have been identified. Collaborative perception has emerged as an effective solution to overcoming these limitations through data fusion from multiple views of surrounding vehicles. While most existing collaborative perception strategies adopt a fully connected graph predicated on fairness in transmissions, they often neglect the varying importance of individual vehicles due to channel variations and perception redundancy. To address these challenges, we propose a novel Priority-Aware Collaborative Perception (PACP) framework to employ a BEV-match mechanism to determine the priority levels based on the correlation between nearby CAVs and the ego vehicle for perception. By leveraging submodular optimization, we find near-optimal transmission rates, link connectivity, and compression metrics. Moreover, we deploy a deep learning-based adaptive autoencoder to modulate the image reconstruction quality under dynamic channel conditions. Finally, we conduct extensive studies and demonstrate that our scheme significantly outperforms the state-of-the-art schemes by 8.27\% and 13.60\%, respectively, in terms of utility and precision of the Intersection over Union.
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