Wait to Learn: Lobes and Dead Zones in Physical Backpropagation over an Aging Single-Antenna Channel

Sometimes the best way to correct an aged gradient is to wait. In physical backpropagation, a receiver returns its loss gradient through the reciprocal channel. With a single moving antenna, the mean gradient returned at the antenna is the true one counter-rotated by the phase of the temporal correlation. In simulation, uncorrected training fails in negative correlation lobes and revives in positive ones. At correlation zeros the return is independent of the forward channel, so no linear correction has a mean to recover; near them, more calibration barely helps, but holding the return until the next correlation extremum does.