We analyze the noise characteristics of an optical transmission system
repeated by two-mode phase-sensitive optical parametric amplifiers. In
such a system, the non-degenerated signal and idler waves co-propagate
through the link, interacting with each other in the optical parametric
amplifiers. For the first time, we derive a closed-form expression for
the accumulated noise using the quantum-mechanical Langevin-equation
approach. The derived noise formula allows calculating the noise figure
of the optical-amplifier chain under the influence of the internal loss
of the amplifiers and the transmission loss of the link, thereby
theoretically demonstrating its low-noise characteristics.