Active-phased-array system noise temperature

In calculating the antenna system noise temperature the question always arises as to how to account for the antenna mismatch. In this paper it is shown that the antenna mismatch introduces another term into the antenna system temperature equation. This term increases the system temperature. It is due to the reflection of the noise coming out of the receiver in the direction of the antenna that is reflected back into the receiver towards its signal output port. For a single port reflector antenna system this term is equal to the temperature T_r of the noise coming out of the receiver towards the antenna times the antenna power reflection coefficient |Gamma²|. This is usually included in the radiometer field but not by those in the radar and communication fields. For an active phased array the question that arises is: What reflection coefficient to use? It is shown that for an active phased array the reflection coefficient to use for this incoherent noise is the same one used for a coherent signal transmitted in the direction of the main beam. This result is new for those in the radiometer, radar and communication fields.