## 2 The Features of FM-OFDM Communications Scheme
Using the QPSK modulation of OFDM subcarriers, the expression (2) looks as follows:  
\[s_{FM}(t)=U_{0}\cdot\cos\left(\int\limits_{0}^{t}\left[\omega_{0}+2\pi\cdot \Delta fN\cdot m_{FM}\cdot\overline{s(t)}\right]dt\right), \tag{2}\]1  
where \(\dot{G_{n}}\) is the complex information QPSK symbol on the \(n\)th OFDM subcarrier. The structural scheme of transmitting and receiving process is demonstrated in \[s_{FM}(t)=U_{0}\cdot\cos\left(\int\limits_{0}^{t}\left[\omega_{0}+2\pi\cdot \Delta fN\cdot m_{FM}\cdot\overline{s(t)}\right]dt\right), \tag{2}\]2 In this structure, the system of high-frequency synchronization is missing and the receiving path is implemented using a non-coherent scheme. For the frame synchronization of OFDM-QPSK symbols, the pseudo-random binary sequences are used in combination with a matched filter on the receiver. Analyzing the noise-sustainability of the FM-OFDM-QPSK method, it is necessary to estimate the error probability under AWGN channel with spectral power density \(N_{0}\). Average power in the bandwidth of modulating multi-frequency signal is \(P_{us}=\frac{\Delta\omega^{2}}{2}\). When the power of harmonic noise of frequency \(\omega\) is low, the law of phase changing can be expressed as: \(\varphi(t)=\omega_{0}t+\frac{U_{0}}{U_{0}}\sin(\omega_{0}t-\omega t)\), where \(U_{\theta}\) is distortion amplitude. In this case, the law of frequency deviation is described by expression \(\omega(t)=\omega_{0}+\frac{U_{\theta}}{U_{0}}(\omega_{0}-\omega)\cos(\omega_{0 }t-\omega t)\), taking into attention that \(\omega(t)=\frac{d\varphi(t)}{dt}\). In this case low amplitude additive harmonic distortion results in the parasitic angle modulation. The frequency modulation function, depending on the distortion frequency \(\omega\) and the distortion amplitude \(dU_{\theta}\) on the output of demodulator, is equal to \(\delta\omega(t)=\frac{dU_{\theta}}{U_{0}}(\omega_{0}-\omega)\cos(\omega_{0}t- \omega t)\). The average power of this function equals to the power \(dP_{\omega\theta}\) accounted on the frequency range of \(d\omega\): \(dP_{\omega\theta}=\overline{\delta\omega^{2}(t)}=\overline{\frac{dU_{\theta} ^{2}}{2U_{0}^{2}}}(\omega_{0}-\omega)^{2}\), where \(\overline{\frac{dU_{\theta}^{2}}{2}}=\frac{4N_{0}d\omega}{\pi U_{0}^{2}}\). The energy spectrum of the distortion is uniform in the bandwidth from \(\omega_{L}=\omega_{0}-2\pi N\Delta f\cdot m_{FM}\) to \(\omega_{H}=\omega_{0}+2\pi N\Delta f\cdot m_{FM}\) and equal to the null out of this range, so \(P_{\omega\theta}=\int_{\omega_{L}}^{\omega_{H}}\frac{4N_{0}(\omega_{0}-\omega )^{2}d\omega}{\pi U_{0}^{2}}\). The noise power in the modulating signal bandwidth \(P_{\omega\theta}=\int_{0}^{2\pi N\Delta f\cdot m_{FM}}\frac{8N_{0}\omega_{0}^{ 2}d\omega_{1}}{\pi U_{0}^{2}}=\frac{8N_{0}(2\pi N\Delta f\cdot m_{FM})^{3}}{3 \pi U_{0}^{2}}\) can be achieved by substituting variable \(\omega_{1}\) with \(\omega_{1}=\omega_{0}-\omega\). That allows for finding the SNR in the modulating signal bandwidth \(\frac{P_{\omega\theta}}{P_{\omega\theta}}=\frac{\Delta\omega^{2}}{2}\times \frac{3\pi U_{0}^{2}}{8N_{0}(2\pi N\Delta f\cdot m_{FM})^{3}}\). Taking into attention that SNR on the input of FM demodulator is defined by the expression: \(SNR=\frac{U_{0}^{2}}{2}\cdot(2\pi N\Delta f\cdot m_{FM}N_{0})^{-1}\); and expression for BER for OFDM-QPSK modulated signals can be expressed as: \(P_{e}=Q\Big{[}\sqrt{2E_{b}/N_{0}}\Big{]}\), where \(Q(x)=\frac{1}{\sqrt{2\pi}}\cdot\int_{x}^{\infty}e^{-\frac{x^{2}}{2}}du\)., then, after simplification, we can get an expression:  
\[s_{FM}(t)=U_{0}\cdot\cos\left(\int\limits_{0}^{t}\left[\omega_{0}+2\pi\cdot \Delta fN\cdot m_{FM}\cdot\overline{s(t)}\right]dt\right), \tag{2}\]3  
Further, it is necessary to consider operational feature of digital frequency demodulator according to the expression (3) under influence of multipath components at the input of the detector.