The Indian Air Force inducted the Airborne Early Warning and Control System (AEWACS) in 2009, and the system is called Phalcon. The other options listed in the question, namely Phoenix, Eagle, and Kite, are not the correct names for the AEWACS system in the Indian Air Force.
It is important to note that the Phalcon system is not exclusive to the Indian Air Force. Phalcon is the name given to the AEWACS system developed jointly by Israel Aerospace Industries (IAI), Elta Systems, and Indian defense companies. The system combines an advanced radar system mounted on an aircraft to provide early warning and control capabilities. It allows the Indian Air Force to detect and track airborne threats and provides command and control functions in a variety of operational scenarios.
It is worth mentioning that the Phalcon AEWACS system has significantly enhanced the surveillance and defense capabilities of the Indian Air Force, as it enables them to have better situational awareness and improved command and control capabilities during both offensive and defensive operations.