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Downlink coherent multiuser transmission is an essential technique for cell-free massive multiple-input multiple output (MIMO) systems, and the availability of channel state information (CSI) at the transmitter is a basic requirement. To avoid CSI feedback in a time-division duplex system, the uplink channel parameters should be calibrated to obtain the downlink CSI due to the radio frequency circuit mismatch of the transceiver. In this paper, a design of a reference signal for over-the-air reciprocity calibration is proposed. The frequency domain generated reference signals can make full use of the flexible frame structure of the fifth generation (5G) new radio, which can be completely transparent to commercial off-the-shelf (COTS) remote radio units (RRUs) and commercial user equipments. To further obtain the calibration of multiple RRUs, an interleaved RRU grouping with a genetic algorithm is proposed, and an averaged Argos calibration algorithm is also presented. We develop a cell-free massive MIMO prototype system with COTS RRUs, demonstrate the statistical characteristics of the calibration error and the effectiveness of the calibration algorithm, and evaluate the impact of the calibration delay on the different cooperative transmission schemes.