The Effect of Pseudorandom Sequence Systematicity on Signal-to-Noise Ratio in Hadamard Transform Ion Mobility Spectrometry

The formation of an artefact signal can greatly influence the sensitivity of the drift tube ion mobility spectrometer (IMS) in multiplex mode (Hadamard transform mode). This signal is a systematic error of multiplexed signal modulation via pseudorandom sequence (PRS), and it can appear as false peaks, or it can be similar to interference or noise. The artefact signal usually cannot be differentiated from the latter by standard mathematical processing algorithms. In Hadamard transform ion mobility spectrometry, the presence of an artefact signal when utilizing standard data processing algorithms results in the following situation. Even though each individual recovered spectrum demonstrates a noticeable improvement in signal-to-noise ratio due to forward Hadamard transform, this improvement is reduced or even disappears completely for averaged recovered multiplexed spectra when compared to the conventional IMS averaging mode. A noticeable improvement in signal-to-noise ratio can be achieved by modifying PRSs by incorporating fixed numbers of additional zeros after every element (modulation bin) of the conventional PRSs. The improvement can be explained because the addition suppresses systematic noise-like artefact signals. In this paper, we analyze the observed signal-to-noise ratio in averaged spectra for simulated via theoretical model and experimental data for various multiplexing modes of Hadamard transform. We also analyzed the influence of modulating PRSs’ “randomness” on signal-to-noise ratio in the resulting spectra in the case of non-modified sequences. We chose the standard deviation of PRS’s autocorrelation function, or the autocorrelation coefficient, to serve as the “randomness” criterion. For modulation with PRSs modified with additional zeros, we observed a considerable correlation between theoretical and experimental values of relative improvement of the signal-to-noise ratio. This indirectly proves the existence of constraints in Hadamard multiplexing mode when a statistically significant amount of individual spectra is averaged. This also leads to the necessity of improved strategies of data multiplexing and decoding for further sensitivity improvement. The choice of optimal PRS is part of the strategy’s search. One of the choice’s criterion is the minimization of the artefact signal. The data presented in this paper suggests that the autocorrelation coefficient as the criterion of choice for PRS is justified but not sufficient: it leaves the problem of PRS selection when searching for a strategy for sensitivity improvement in Hadamard transform ion mobility spectrometry.