Geometric Inductive Biases for Semi-Supervised Equalization: The Constellation-Aware Transformer

Decoding signals over unknown channels with minimal pilot overhead is a critical challenge in next-generation communications. Existing deep learning approaches typically rely on generic encoders that struggle to model long-range temporal dependencies or efficiently capture the channel's physical properties from scarce data. We argue that standard architectures suffer from fundamental *agnostic estimation gaps*, as they must implicitly learn the constellation geometry that is already known. We introduce the *Constellation-Aware Transformer* (CAT), a novel architecture that explicitly injects geometric inductive biases into the equalization process. CAT is composed of a stack of custom *TransFIRmer* blocks, which utilize an “early interaction” paradigm to co-process received signals and ideal constellation symbols. Each block features a split Feed-Forward Network that applies a Finite Impulse Response (FIR)-inspired filter for robust deconvolution and a parallel MLP for geometric refinement. We theoretically prove that this design creates a structural isomorphism to the optimal MIMO Wiener Receiver and eliminates the ambiguity floor inherent to blind estimators. In the challenging semi-supervised setting, CAT achieves state-of-the-art performance, significantly reducing pilot overhead compared to VAE and standard Transformer baselines.