Which Chains to Calibrate for Physical Backpropagation: Per-User Factors Versus Base-Station Chains
Abstract
In physical backpropagation, users return loss derivatives over the time-division duplex uplink, giving the base station the downlink gradient without channel reconstruction. Reciprocity calibration conventionally prioritizes base-station chains, as column-normalized zero-forcing reduces a per-user factor to a stream rotation. This priority can reverse. With ideal base-station chains and no noise, per-user amplitude errors make the returned field a weighted sum-rate gradient. With zero-forcing full service at both optima, the loss is independent of array size. Otherwise the selection penalty, serving the wrong users, carries 86 to 94 percent of the amplitude-induced loss in five of six configurations. Per-user phase errors mainly slow the iteration. Base-station chain errors scale the returned field per antenna, and at 3 dB and 25 degrees they cost one user 1.3 dB of signal-to-noise ratio (SNR) that no array size removes. With 80 users, such errors on both sides, and mismatched pilots, oracle per-user and base-station calibration leave 6.2 and 12.3 percent loss at 256 antennas on clustered channels. This ordering holds at 30 dB SNR and reverses for 1 dB, 10 degree user errors. A capped one-echo estimator comes within 2.4 percentage points of oracle per-user calibration but underperforms no calibration at 10 dB SNR.
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BibTeX
@misc{li2026which,
title = {{Which Chains to Calibrate for Physical Backpropagation: Per-User Factors Versus Base-Station Chains}},
author = {Xianzhong Li and Yuzhi Yang and Tianhao Guo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02390},
eprint = {2611.02390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02390},
}
RIS
TY - UNPB
TI - Which Chains to Calibrate for Physical Backpropagation: Per-User Factors Versus Base-Station Chains
AU - Xianzhong Li
AU - Yuzhi Yang
AU - Tianhao Guo
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02390
UR - https://arxiv.org/abs/2611.02390
AB - In physical backpropagation, users return loss derivatives over the time-division duplex uplink, giving the base station the downlink gradient without channel reconstruction. Reciprocity calibration conventionally prioritizes base-station chains, as column-normalized zero-forcing reduces a per-user factor to a stream rotation. This priority can reverse. With ideal base-station chains and no noise, per-user amplitude errors make the returned field a weighted sum-rate gradient. With zero-forcing full service at both optima, the loss is independent of array size. Otherwise the selection penalty, serving the wrong users, carries 86 to 94 percent of the amplitude-induced loss in five of six configurations. Per-user phase errors mainly slow the iteration. Base-station chain errors scale the returned field per antenna, and at 3 dB and 25 degrees they cost one user 1.3 dB of signal-to-noise ratio (SNR) that no array size removes. With 80 users, such errors on both sides, and mismatched pilots, oracle per-user and base-station calibration leave 6.2 and 12.3 percent loss at 256 antennas on clustered channels. This ordering holds at 30 dB SNR and reverses for 1 dB, 10 degree user errors. A capped one-echo estimator comes within 2.4 percentage points of oracle per-user calibration but underperforms no calibration at 10 dB SNR.
ER -