There are two major barriers in deploying wireless communication systems in nuclear power plants (NPPs): (a) the electromagnetic compatibility (EMC) between the wireless devices and the existing plant instrumentation and control systems, and (b) the high levels of electromagnetic noise and interference from high-powered devices and ionizing radiation sources. In a typical NPP there exist strict regulations that limit transmission power levels to avoid interfering with the sensitive safety systems inside the containment such as ion chambers. This will result in performance degradation of wireless communication systems. This paper proposes a wireless communication scheme based on low-power chirp spread spectrum (CSS) signals, which meet with the EMC requirements of NPPs and also are capable of providing interference rejection. The advantage of such a scheme is that satisfactory performance can be obtained using low levels of transmission power. The structure of the optimal receiver for low-power binary CSS signals and a closed-form expression for asymptotic bit error rate of this receiver are derived. The electromagnetic environment within an NPP is modeled as a Gaussian-Gaussian mixture process, which is based on the measurement data published in a U.S. Nuclear Regulatory Commission Regulation (NUREG). The parameters in the model can be adjusted to suit a particular NPP site.