This paper investigates the impact of real noise, particularly from snowfall conditions, on speech transmission over the \(\alpha \) - \(\eta \) - \(\kappa \) - \(\mu \) wireless fading channel. The \(\alpha \) - \(\eta \) - \(\kappa \) - \(\mu \) wireless fading channel is widely recognised as a suitable model for next-generation wireless networks, particularly at the mmWave range and has not been investigated in real-world microphone noise conditions. To replicate real-world interference, snowfall noise as microphone noise is introduced at the transmitter to simulate the effects of environmental disturbances on speech signals. At the receiver end, a Weighted Sigmoid-Based Frequency-Selective Noise filter is employed to enhance speech quality by mitigating noise and preserving intelligibility. The effectiveness of the proposed approach is assessed at both the speech processing and the bit levels. At the speech processing level, widely accepted quantitative evaluation metrics, such as Perceptual Evaluation of Speech Quality (PESQ), Short-Time Objective Intelligibility (STOI), and Segmental Signal-to-Noise Ratio (Seg. SNR), are considered. Whereas the Average Symbol Error Rate (ASER) is considered to measure overall transmission performance over the wireless channel at the bit level. The results indicate that even in challenging low channel-SNR environments, the filtering technique provides substantial improvements in speech clarity and intelligibility. For example, at 0 dB received average channel SNR, where the ASER is only 0.35, after applying the filter, PESQ increased from 0.8829 to 1.2035, STOI increased from 0.4825 to 0.4938, and Seg. SNR increased from −6.2371 to −3.9257. Additionally T-test has also been performed to strengthen our claim. These enhancements demonstrate the potential of the proposed system to improve speech transmission reliability in adverse conditions, making it a promising solution for wireless communication systems affected by challenging, noisy environments.