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You've challenged me to rethink things through carefully. Let me begin with what I believe are the facts involved and go from there.
1) even though we can use complex numbers to represent them, what we're ultimately dealing with are modulated sine waves.
2) the impedance of the antenna does vary by frequency, but for a single frequency it remains the same no matter the direction the signal comes from.
3) therefore, the ratio of power delivered into the transmission line remains the same no matter the arrival angle.
4) signals that take different paths to the receive antenna are no longer in time, or phase, sync. A phase delay has been added. Additionally, indirect paths have increased variability in phase and polarity.
My view of what is happening is the multiplicity of signals out of phase with each other march down the coax until they hit a detector. It is the mixing of these signals in the detector that causes the problem. As an example, when the skywave and ground wave signals of an AM station are both present at a receiver, the effect of the delay between the two is a slow selective fade. A notch filter runs across the passband, and when it hits the carrier, distortion like over modulation results. I'll have to brush up on the modulation scheme used in ATSC to comment on why a spectrum that has non-uniform amplitude is a bad thing.
Reciprocity holds here only in the sense that if I turn around and transmit a single signal, it will arrive back at the transmitter in a hodge-podge from scattering and multiple-path. You can't steer a frequency by changing its properties. You have to add delay across the antenna.
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