# On Reciprocity in Physically Consistent TDD Systems with Coupled Antennas

## TL;DR

This paper investigates how mutual coupling in TDD MU-MIMO systems affects channel reciprocity, revealing that physical coupling causes deviations from ideal reciprocity and impacts system performance.

## Contribution

It introduces a physics-consistent analysis of reciprocity in coupled antenna systems, highlighting fundamental effects often overlooked in traditional models.

## Key findings

- Mutual coupling breaks the standard reciprocity relation in TDD MU-MIMO channels.
- Ignoring coupling leads to significant rate performance degradation.
- Accounting for coupling improves the accuracy of channel estimation and system design.

## Abstract

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.