Automatic Modulation Recognition (AMR) is critical in identifying various modulation types in wireless communication systems. Recent advancements in deep learning have facilitated the integration of algorithms into AMR techniques. However, this integration typically follows a centralized approach that necessitates collecting and processing all training data on high-powered computing devices, which may prove impractical for bandwidth-limited wireless networks. In response to this challenge, this study introduces two methods for distributed learning-based AMR on the collaboration of multiple receivers to perform AMR tasks. The TeMuRAMRD 2023 dataset is employed to support this investigation, uniquely suited for multi-receiver AMR tasks. Within this distributed sensing environment, multiple receivers collaborate in identifying modulation types from the same RF signal, each possessing a partial perspective of the overall environment. Experimental results demonstrate that the centralized-based AMR, with six receivers, attains an impressive accuracy rate of 91%, while individual receivers exhibit a notably lower accuracy, at around 41%. Nonetheless, the two proposed decentralized learning-based AMR methods exhibit noteworthy enhancements. Based on consensus voting among six receivers, the initial method achieves a marginally lower accuracy. It achieves this while substantially reducing the bandwidth demands to a 1/256th of the centralized model. With the second distributed method, each receiver shares its feature map, subsequently aggregated by a central node. This approach also accompanies a substantial bandwidth reduction of 1/8 compared to the centralized approach. These findings highlight the capacity of distributed AMR to significantly enhance accuracy while effectively addressing the constraints of bandwidth-limited wireless networks.