On reciprocity of physically consistent TDD systems with coupled antennas

We consider the reciprocity of the information theoretic channel of Time Division Duplex (TDD) Multi User-Multiple Input Single Output (MU-MISO) systems in the up- and downlink. Specifically, we assume that the transmit and receive chains are reciprocal. We take the mutual coupling between antenna elements at the base station into account. The analysis is based on the Multiport Communication Theory, which ensures that the information theoretic model is consistent with physics. It also includes a detailed noise model. We show that the coupling makes the information theoretic channel non-reciprocal, even if the input-output relation of the transmit voltage sources and the receive load voltages, i.e. the channel which is estimated with the help of pilot signals, is reciprocal. We show via Monte Carlo simulations that both, not taking the non-reciprocity into account and not taking the coupling into account, significantly decreases the single user ergodic rate.