This article investigates the noise performance of a two-element phased array and interferometer containing a recently introduced self-interference canceler, which in the context of this work acts as a mutual-coupling canceler. To this end, a general framework is proposed to permit noise analysis of this network and a large variety of other networks. The framework-based numerical analysis for a two-element-phased array shows that the addition of the canceler significantly increases the beam-equivalent noise temperature. For a two-element interferometer used in cosmology, this increase in noise temperature is still acceptable as the sky noise temperature in the 20-to-200 MHz band is high. When used in an interferometer, the canceler provides the ability to null mutual coherence at the interferometer output. The ability to provide matching to reduce the sensitivity of the null in mutual coherence to the phase of the 90deg hybrids in the canceler is discussed.