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There is currently a great deal of interest in the use of phased array receivers for radio astronomy. The Square Kilometer Array (SKA) project plans to utilize phased arrays in at least three different forms: as sparse and dense aperture arrays on the ground, and as phased array feeds on dishes. At frequencies above a few hundred MHz it will be vital to obtain very low noise temperature performance from these arrays in order for them to be practical as radio astronomy receivers. Receiver noise coupled between antenna elements has been thought to be a significant contributor to overall system noise in such phased arrays. This paper uses fundamental principles of noisy networks to estimate the noise waves emanating from the input of each LNA towards the antenna element. The theory has been implemented using MATLAB, and successfully used to predict the noise levels emanating from the input ports of two packaged amplifiers. The theory has been applied to an example two-antenna array model. Results from the noise wave analysis suggest that in reality the coupled noise contribution to system noise temperature should be quite small for practical low noise amplifiers of the type to be used in the SKA.