A direct derivation of a single-antenna reciprocity relation for the time domain

By Glenn S. Smith. IEEE Transactions on Antennas and Propagation, 2004

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Deep Learning for UL/DL Channel Calibration in Generic Massive MIMO Systems (2019, background): “In practice, however, although in TDD mode the UL and DL wireless propagation channels are physically reciprocal [8], the analog front-end circuitry for transmission and reception at the BS and the mobile users is in general not [9]–[12].”
A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System (2016, background): “TDD systems seem promising because they operate on the same carrier frequency and the physical forward and backward channels are considered reciprocal [138].”
Channel Identification: Secret Sharing Using Reciprocity in Ultrawideband Channels (2007, background): “This behavior, known as the reciprocity theorem, arises from the reciprocity of the radiating and receiving patterns of antennas and applies when the medium between the antennas is linear and isotropic [1], [2].”