## 2 Fbmc-OQAM System Model  
In this section, we present a brief mathematical description of the FBMC-OQAM system model used. The information transmission system implemented using filter bank technology is based on algorithms of multirate synthesis and analysis filter banks with perfect reconstruction, as presented in [17]. From a set of narrowband signals, just as in an OFDM demodulator, a wideband signal is divided into subcarrier signals using a Fourier transform. The synthesis algorithm, in turn, generates a wideband signal from a set of narrowband channel signals, while the perfect reconstruction (PR) conditions imposed on the prototype filter design imply that the conversion of a set of narrowband signals to a wideband one occurs without distortion. Ideal signal recovery will be achieved if the aliasing signal component after channel filtering is equal to zero (i.e., the part of the signal that remains unfiltered outside the passband):  
\[\sum_{\tau=-\infty}^{\infty}g\Big{[}l+\tau\tfrac{M}{2}\Big{]}g\Big{[}l+\tau \tfrac{M}{2}+nM\Big{]}=\delta(n)\quad \begin{array}{c}n=0,1,2,\ldots\\ l=0,1,2,\ldots,M-1\end{array} , \tag{1}\]  
where \(g(k)\) is the real and symmetric impulse response (IR) of the prototype filter, and \(M\) is the number of channels of the filter bank. Obviously, the strict observance of these conditions for physically realizable filters is impossible; therefore, the scientific community has performed work on the synthesis of quasi-optimal prototype filter designs that are close to the conditions of perfect reconstruction. These prototypes differ mainly in the properties of the frequency (determining the level of distortion) and time localization. As part of a comparative analysis carried out by the PHYDYAS research project, the filter presented in the work by Bellanger [18] and later called the PHYDYAS prototype filter was adopted for use. This filter provides good localization in the frequency domain and low distortion at a relatively short IR length (numerically equal to the number of channels times 4), which can be seen in the discrete ambiguity function of this prototype filter \(A_{g}\) presented in Figure 1, defined as:  
\[ \begin{array}{c}A_{g}(\tau,\mu)=\int\limits_{-\infty}^{\infty}g\big{(}t+ \tfrac{\tau}{2}\big{)}g^{*}\big{(}t+\tfrac{\tau}{2}\big{)}e^{-j2\pi\mu t}dt\\ \Downarrow\\ A_{g}[n,m]=\sum\limits_{i}g\big{[}i+\tfrac{\eta}{2}\big{]}g^{*}\big{[}i-\tfrac {\eta}{2}\big{]}e^{-\frac{j2\pi i\mu}{M}}\end{array}  \tag{2}\]FBMC-OQAM uses a computationally efficient algorithm analysis and synthesis filter banks based on the modified discrete Fourier transform (MDFT) filter bank presented in [19]. This algorithm allows the use of subchannels twice as wide in frequency, but the perfect reconstruction conditions are met only in the real part of the signal, and in the imaginary part, there is a pseudo-noise composition equal to the sum of the surrounding symbols, with weights determined by the ambiguity function of the prototype filter [20]. The application of this algorithm for information transmission was presented in [4], where it was shown that the shift of the real and imaginary parts of the QAM symbol modulated using the MDFT synthesis bank (in-phase and quadrature components of the symbol are transmitted using two pulse-amplitude-modulated (PAM) symbols with a twofold shorter duration and shift relative to each other), as was shown in [21], allows for a lower level of self-interference.