Phase-Error-Robust Practical Channel Estimation Using Special Orthogonal Group Equivariant AI/ML

In wireless channel estimation (CE), AI/ML-based models have mainly focused on removing additive noise, but multiplicative noise such as oscillator phase noise or timing offsets significantly degrades the performance of data-driven systems. There was a dilemma where handling the two types of noise separately causes errors to propagate stage by stage, while handling them jointly causes model complexity to surge.

To address this, Qi Xiong of Samsung R&D China-Beijing proposed SOGeCE (Special Orthogonal Group equivariant Channel Estimation). The core idea is to leverage the fact that all phase rotations mathematically belong to the Special Orthogonal Group (SOG), projecting the AI model's weights and biases into a subspace that is invariant to SOG group actions.

The key architectural features are as follows:

• Uses a heterogeneous vector space composed of the direct sum of scalars, vectors, and tensors for input/output representation
• Applies a gated nonlinear activation function that preserves SOG equivariance instead of ReLU
• Reduces computational cost with a sparse projector algorithm that combines small matrix SVDs and permutations instead of large SVDs when computing the projection matrix

In experiments with a 5G PUSCH link-level simulator, SOGeCE with a 2-hidden-layer configuration showed superior performance compared to existing AI-based CE under phase error conditions, while maintaining low model complexity.