In the era of wireless technologies, orthogonal frequency division multiplexing (OFDM) techniques and their modifications gained huge popularity. Despite all their benefits they still have several Achilles' heels. One of them is the negative influence of a narrowband or continuous wave (CW) electromagnetic disturbance (EMD). In this paper, a specific CW EMD removal algorithm for OFDM communication systems was investigated for its stability when both a CW EMD and additive white Gaussian noise (AWGN) were affecting the OFDM communication system. By using the spectral leakage phenomenon, the algorithm estimates a mismatch between the subcarriers and CW EMD frequencies and subsequently calculates all the needed CW parameters, i.e. amplitude and phase. The goal of the investigation was to find out which modulation scheme gives the best algorithm's performance. Therefore after a number of simulations on the algorithm with different power variations of CW EMD and AWGN, the results turned out to be better when lower order modulation schemes were in use. These results were explained in the frequency domain as the AWGN's fraction with regard to the CW EMD error was minimum within the subcarriers close to the CW EMD's frequency bin and much higher for other subcarriers. In the end, prepositions on how to maximise the CW removal algorithm's performance under simultaneous CW EMD and AWGN were outlined.