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Despite the substantial success of deep learning for modulation classification, models trained on a specific transmitter configuration and channel model often fail to generalize well to other scenarios with different transmitter configurations, wireless fading channels, or receiver impairments such as clock offset. This paper proposes Contrastive Learning with Self- Reconstruction called CLSR-AMC to learn good representations of signals resilient to channel changes. While contrastive loss focuses on the differences between individual modulations, the reconstruction loss captures representative features of the signal. Additionally, we develop three data augmentation operators to emulate the impact of channel and hardware impairments without exhaustive modeling of different channel profiles. We perform extensive experimentation with commonly used datasets. We show that CLSR-AMC outperforms its counterpart based on contrastive learning for the same amount of labeled data by significant average accuracy gains of 24.29%, 17.01%, and 15.97% in Additive White Gaussian Noise (AWGN), Rayleigh+AWGN, and Rician+AWGN channels, respectively.