The performance of free-space optical (FSO) communication systems can be significantly degraded by environmental effects such as atmospheric conditions, humidity, and fog. In this paper, the performance of pulse position modulation (PPM), non-return-to-zero (NRZ), and return-to-zero (RZ) modulation schemes is evaluated and compared in terms of signal-to-noise ratio (SNR) and bit error rate (BER) under various atmospheric conditions, including fog. The FSO system is simulated in MATLAB using a 1550 nm optical source and the Kim atmospheric attenuation model with different visibility ranges, along with analytical formulations of FSO channel propagation. The impact of low, moderate, and high atmospheric attenuation, as well as different transmitter power levels, on the BER and SNR performance of the three modulation schemes is investigated. The results demonstrate that PPM outperforms NRZ and RZ modulation schemes by achieving lower BER and higher SNR under all atmospheric attenuation conditions. In particular, PPM shows superior performance under low, moderate, and severe attenuation scenarios at transmitter powers of 1 mW and 5 mW, indicating its robustness for FSO communication links in adverse atmospheric environments. The novelty of this research is the presentation of a real-time power allocation scheme with low latency and near-analytical accuracy, which helps increase the received data rate and improve system performance under various attenuation conditions.