## 1 Introduction
A binary random signal was also used in the issue of blind identification of linear systems using symbolic dynamics [36; 37]. Most of these existing blind algorithms are focused on linear system models due of their simplicity. However, many practical systems are nonlinear, and these nonlinearities cannot be ignored without serious performance degradation. This applies to many practical fields, including signal processing, prediction, communication channels, biomedicine, control of industrial processes, detection, equalization and many others [38; 39; 40; 41]. Blind nonlinear system identification has received great attention in the literature (see, e.g., [42; 43; 44; 45]). In the nonlinear domain, discrete Volterra representations were used to describe the input-output relation, thus that characterization, analysis and synthesis are easily amenable [42]. [PERSON] et al. [43] proposed to identify the Volterra kernels by using the third cumulant with a constraint of the second-order cumulant. It has been demonstrated that this constrained optimization approach can achieve excellent results for nonlinear system identification. An inconvenience of this method is its sensitivity to additive Gaussian noise since it is based on second-order cumulant, as pointed out in [44]. To overcome this issue, [PERSON] et al. [44] used a fourth-order-based method link as alternative solution of the second-order cumulant to smooth out the additive Gaussian noise and improve the convergence by proposing a hybrid optimization method of simplex and genetic algorithms. In the same frame, [PERSON] et al. [38] contributed to Volterra system identification by developing an efficient adaptive transversal algorithm, with the advantages of low complexity and modular structure. There are also many existing works in the context of nonlinear Volterra system identification (see, e.g., [46; 47; 48]). In [47], the authors used the third-order moment (TOM) domain for blind identification of nonlinear Volterra systems with studies on the computational complexity and demonstrated via simulation that the proposed approach can be applied in a practical scenario to identify blindly the primary path of active-noise-control. A class of truncated sparse Volterra systems was identified blindly by using the second-order moment (SOM) or TOM sequences of the system outputs in [48]. The authors of [42] investigated the third-order Volterra nonlinear systems with a novel approach based only second-order statistics and proved that was able to remove white noise with any distribution offering significant reduction in the computational burden. A complex random sequence input coupled with output HOC was employed in [40] to identify blindly the linear quadratic Volterra systems by examining different cases and the simulations were also used to illustrate the performance of the proposed approaches. The authors in [45] proposed an extension of the main concept behind the error whitening criterion (EWC) in the linear case to the unbiased identification by analytically examining the true parameters of order-2 Volterra series models of nonlinear dynamical systems. It was emphasized by the authors that this extension does not apply to higher-order Volterra systems. A hydroturbine shaft system modeled as a quadratic Volterra system has been identified blindly using third-order cumulants and a reversely recursive method by [PERSON] and [PERSON] in [46]. The proposed method was tested using engineering applications and three numerical experiments, and their applicability was demonstrated by the blind identification of the hydroturbine shaft system. Furthermore, identification of the quadratic nonlinear systems has been reported in the past (see, e.g., [49; 50; 51; 52]). In [49], the properties of higher-order moment sequences and the calculation of the higher-order spectral moments of an i.i.d for various frequencies were used to develop algorithms to identify time-invariant quadratic nonlinear systems.