On Reciprocity in 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 Multiple Output (MU-MIMO) systems in the up- and downlink. Specifically, we assume that the transmit and receive chains are reciprocal. We take the mutual coupling between the antenna elements at the base station and at the mobiles into account. Mutual coupling influences how to calculate transmit power and noise covariance. 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 due to the coupling, the information-theoretic up- and downlink channels do not fulfill the ordinary reciprocity relation, 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 in the uplink, is reciprocal. This is a fundamental effect that is not considered otherwise. We show via Monte Carlo simulations that both, using the ordinary reciprocity relation, and not taking the coupling into account, significantly decreases the ergodic rates in single-user and the ergodic sum rates in multi-user systems.