Channels rotate backpropagation gradients causing errors in training
Coherent but Discordant: Rotate, Don't Invert, to Backpropagate Through an Aging Channel
Information Theory
Summary
When sending signals through wireless channels that change over time, the usual way of sending feedback signals back to improve transmission can get confused. The problem is not just noise but a rotation that twists the feedback information, causing the system to learn the wrong things. The paper shows that fixing this rotation—by turning feedback information the right way rather than flipping or stretching it—greatly improves learning accuracy even for complex antenna arrays. The authors explain this phenomenon and how to correct it with simple mathematical steps.
What this means in practice
- •For wireless system engineers: Improve training accuracy of over-the-air learning systems in mobile scenarios by correcting phase rotation in feedback signals.
- •For antenna array designers: Enhance channel estimation and adaptation techniques by applying a unitary rotation correction instead of direct inversion on gradients in multi-antenna setups.
Tested on simulated data.
Authors
Xianzhong Li, Yuzhi Yang, Tianhao Guo
Abstract
A channel can be almost perfectly coherent and still teach a transmitter the wrong direction. In physical ("over-the-air") backpropagation, the receiver sends its loss gradient back through the reciprocal channel; when the terminal moves in between, mobility does not merely add noise to the returned gradient, it rotates it. Under a scalar conditional mean model the rotation is set by the phase of the temporal correlation, so coherence, which measures only its magnitude, is the wrong ruler: in simulation, channels with absolute value of rho greater than 0.9 drive uncorrected training to 51.7% accuracy, while phase correction restores 92.5%. Arrays add a twist. Near zeros of the trace correlation, scalar correction fails even with rho known exactly, yet most of the information is still there: noise has moved it onto neighbouring antennas. Re-indexing the ports by the displacement, with zero digital feedback, recovers the lost performance in simulation, and so does rotating the returned seed with the unitary polar factor of the conditional mean operator, never inverting it; aligning each antenna's phase with its own past makes things worse. An exact array identity explains all three. The lesson fits in one line: correct the rotation, not the stretch.