Nearest Is Not Safest: Fluid-Antenna Port Selection for Over-the-Air Backpropagation in Urban Multipath
Xianzhong Li, Yuzhi Yang, Tianhao Guo
Abstract
Over-the-air backpropagation returns a loss gradient through the reciprocal channel, which requires the return port to see the channel of the forward port. If the terminal moves in between, a fluid antenna system can return through the port nearest to the forward position. In ray-traced Chicago streets, with a pedestrian displacement of about half a wavelength and a street-level base station, this rule reverses 20 percent of the gradients at a port spacing of 0.7 wavelengths and 49 percent at 0.9 wavelengths, while one of the four nearest ports stays aligned in all but 2 and 9 percent. We derive a certificate for the sign of the mean correlation from the second moment of a planar angular spectrum. It reduces to a linear program with three variables and infinitely many constraints, is tight, and holds over a region of second moments. In a static Gaussian model, observations collected along a line cannot tell an angular spectrum from its mirror image, so the sign of the cross moment must come from other information. At unsurveyed positions of the same city, a knowledge map that transports surveyed paths through virtual sources and fits them to the causal channel history lowers the reversal rate at 0.9 wavelengths from 49 to 27 percent. Its gain over the nearest port survived every tested error, while its gain over a geometry rule stayed significant at the tested single-error levels of 5 degrees of phase drift per step and 2 mm of position error but not at the next tested levels. Without any survey, across five cities and ten base stations, the nearest port reverses 37 percent of the returns at 0.9 wavelengths and a rule based on the direction and elevation of the base station 20.5 percent. The multilayer perceptrons we tested did not beat these physical rules by the margin fixed in advance in the primary settings.