Deep joint source--channel coding (Deep JSCC) can suffer from domain shift between training and deployment data. We study single-source domain adaptation for image classification over wireless channels. A Gaussian example shows that improving channel quality does not necessarily improve target-domain accuracy under a fixed source-trained classifier. We further proposed an information objective to reduce domain information while preserving class information. Motivated by the analysis, we develop a domain-adaptive Deep JSCC method that combines class-wise adversarial alignment with pseudo-label supervised contrastive learning. The former uses all target samples to reduce class-conditional domain differences, while the latter selects high-confidence target samples to obtain class-discriminative received representations. We relate these losses to the information objective, and analyze the effects of pseudo-label errors and confidence-based selection. Experiments on SVHN--MNIST and PACS over AWGN and Rayleigh channels demonstrate improved target-domain classification without additional inference-time networks. The proposed method achieves 98.15\% accuracy on SVHN $\rightarrow$ MNIST at 10~dB CSNR.

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