Visible Light Communications (VLC) is the type of communication, which processes high-speed data transmission using the visible Light Emitting Diodes (LED). The VLC acts as an important supplementary that is used to define the hotspots for heterogeneous networks and plays an important role for 5G networks in wireless communications. However, performance of visible light systems is affected by various noises and Allan variance is used to analyze such noises in 5G networks. The Massive Multiple-Input and Multiple-Output (M-MIMO) technique is used for noise modeling which utilizes the mitigation circuit to find whether the noise is white noise, shot noise, random walk noises or typical noises. The existing Kalman Filter approach failed to attain the required bandwidth and higher spectral efficiency. Therefore, to achieve high data rates, the spectral efficient technologies such as Single Carrier Frequency Division Multiplexing (SCFDM) is performed in the research. The Allan Variance is utilized for analyzing the time-series that extracts the noise features of the data and the major noise is verified and considered by the M-MIMO technique. The present research uses the Extended Kalman Filter (EKF) which determines the observation models and the state transition that does not need linear functions to define the states. The proposed SCFDM was constructed based on the VLC for 5G networks that analyzes in terms of Bit Error Rate (BER) and Signal to Noise Ratio (SNR). The proposed SCFDM obtains a high SNR of 14% for the channels with white LED option when compared to the existing methods.