A calibration apparatus for calibrating a transceiver includes a loop back circuit, an estimation circuit, and a calibration circuit. The loop back circuit is coupled between a mixer output port of a transmitter (Tx) of the transceiver and a mixer input port of a receiver (Rx) of the transceiver, and applies a sequence of different loop gains. The estimation circuit receives a loop back receiving signal that is output from the Rx under the sequence of different loop gains, and generates at least one estimated value of impairment of the transceiver by performing channel estimation according to at least the loop back receiving signal. The calibration circuit performs calibration upon the transceiver according to the at least one estimated value.