## 1 Introduction  
Device-free sensing implements human gesture recognition (HGR) using optical sensors [1], radio frequency (RF) [2; 3] or ultra-wide bandwidth (UWB) [4] signals to achieve a higher gesture recognition accuracy. However, HGR using commercial off the shelf (COTS) Wi-Fi devices attracts significant research interest as it preserves privacy, is easy to deploy, low cost and readily available in an indoor environment. Wi-Fi based HGR systems capture signal reflections due to human movements between the transmitter and receiver pair as raw CSI traces. It has a wide range of application in the field of surveillance [5], physical analytics [6], healthcare [7] and have become a potential study in the smart home environment [8; 9]. It is evident that the following factors, namely the number of users [10] and access point (AP) [11], orientation and distance between the users, as well as the transmitter and receiver pair [12; 13], environmental factors [14], interferences, and multipath fading effect in the sensing environment influence the recognition accuracy [15]. Extensive researches were reported for feature extraction and selection, as it has a high impact on recognition accuracy of learning algorithms. Most of the existing recognition systems use Principal Component Analysis (PCA), a popular feature extraction technique to extract the principal components from the signal. For example, a CSI-based human activity recognition and monitoring system (CARM) [16] uses PCA for feature extraction and achieves a classification accuracy of 96% for eight different activities. The gesture recognition task initially acquires raw CSI traces of human reflections in subcarrier level with the implementation of the 802.11n standard in COTS Wi-Fi devices. The raw CSI traces consist of high-frequency noise and represents non-Gaussian signal distribution. Therefore, existing sensing methods pre-process the raw signal to reduce noise and apply transformations for unwrapping raw CSI measurement that reveals the phase change of the signal. The noise reduction phase mainly removes the phase offset, with outliers using the regression and filtering technique to de-noise the high-frequency signal. Fast fourier transform (FFT), inverse fast fourier transform (IFFT) and discrete wavelet transform (DWT) are the widely used signal transformation techniques for performing a linear transformation on the de-noised signal [17]. This pre-processed signal is of use in many applications that detect and locate human targets using CSI traces [18]. However, it pays little attention to addressing the linear phase error that prevails in CSI measurement, due to hardware limitations [19]. Ignoring useful information, such as the non-linear characteristic of the signal, will consequently affect the recognition accuracy in the later stage. Gesture recognition generally uses two approaches, namely deep learning (DL) and machine learning (ML). Recently, the research direction has migrated from traditional ML approaches to a DL approach, as DL methods report higher recognition accuracy. However, DL approaches demands a high volume of data for auto feature selection and better recognition accuracy and have a poor interpretation of data. Conversely, ML approaches can achieve satisfactory recognition accuracy even with a relatively lesser sample size but relies on the quality of hand-crafted features. The limitations of the existing studies motivate the proposed work to study the non-Gaussian signal distribution with non-linearity, which carries useful signal information. The present work Higher Order Statistics based Recognition (HOS-Re) adopts a machine learning approach and proposes a HOS based third order cumulant feature extraction to maximize the recognition accuracy. The complexity of the classification model of the ML classifier increases with the number of feature inputs.