Antenna calibration is mandatory to exploit channel reciprocity in time-division-duplex multiple-input-multiple-output systems. In this letter, we present in detail an over-the-air total-least-square (TLS)-based reciprocity calibration scheme. It takes place, not only at the base station side, but also with the assistance of the user, such that the overall reciprocity is achieved. The calibration parameter estimation is formulated by a two-step optimization problem. The first-step is to solve a TLS problem and the second-step can be treated as a low-rank matrix approximation. Explicit solutions are derived, respectively, and extensive simulation results compared with existing schemes are given.