## 2 The Features of FM-OFDM Communications Scheme  
A great number of modern researches in the field of underwater digital communication are dedicated to methods utilizing the orthogonal frequency division multiplexing [11]. This direction was adopted from radio communication systems, the majority of which are based on OFDM nowadays. In radio communications OFDM is implemented as a standard, providing high data throughput and high resistance to multipath signal propagation. On the other hand, a wide variety of OFDM underwater acoustic communication solutions found in the literature show that an active scientific search is being made to find ways of saving natural advantages of OFDM in harsh conditions of the underwater environment [12]. The demand for high-precision underwater navigation and reliable high-speed communication is growing fast with active implementation of robotics in different aspects of World Ocean research and exploration. Undoubtedly, this demand is linked with the organization of communication in conditions of high mobility of underwater and surface vehicles participating in the mission. Exactly in mobile systems of underwater acoustic communication is where the OFDM method shows vulnerability. To fight this problem, different methods of signal pre-correction in combination with the noise-sustainable coding are used to reach reasonable ratio of data-rate-to-noise-sustainability. One of the most effective modes of reception in non-stationary channels is the non-coherent reception of carrier signal. The usage of frequency modulation for OFDM signals makes it possible to implement non-coherent detection techniques, provides sustainability for Doppler shifts, and tremendously reduces Peak-to-Average ratio (PAPR) of the OFDM signal [13]. To form an FM-OFDM signal, the model of multifrequency stochastic signal with the normal distribution to image part of OFDM symbol is accepted. The OFDM signal representation after rationing has a following form:  
\[\overline{s(t)}=\frac{1}{4}\sqrt{\frac{2}{N}}\sum_{n=1}^{N}C_{n}\cdot\sin(2 \pi\cdot\Delta f\cdot n\cdot t), \tag{1}\]  
where \(\Delta f\) is the spacing between OFDM sub-carriers, \(C_{n}\) is the information symbol (of the \(n\)th frequency domain), and \(N\) is the number of subcarriers [14]. FM-OFDM signal for carrier frequency \(f_{0}=\frac{\omega_{0}}{2\pi t}\) and for the index of frequency modulation \(m_{FM}\) can be represented by the following expression:  
\[s_{FM}(t)=U_{0}\cdot\cos\left(\int\limits_{0}^{t}\left[\omega_{0}+2\pi\cdot \Delta fN\cdot m_{FM}\cdot\overline{s(t)}\right]dt\right), \tag{2}\]  
where \(U_{0}\) is the signal amplitude. Forming FM signal in the transmitter and its demodulation in the receiving path are conducted by using the quadrature processing in digital signal processor (DSP). Expression (2) is presented as a sum of two quadrature components \(s_{FM}(t)=\cos(\omega_{0}t)\cos\left(\Delta\omega\int_{0}^{t}\overline{s(t)} dt\right)-\sin(\omega_{0}t)\sin\left(\Delta\omega\int_{0}^{t}\overline{s(t)} dt\right)\), where \(U_{0}\) can be set to 1 V, and the frequency deviation is determined by OFDM signal bandwidthand frequency modulation index \(\Delta\omega=2\pi\cdot\Delta fN\cdot m_{FM}\). Here, quadrature low frequency signals \(I\) and \(Q\): \(y_{I}=\cos\left(\Delta\omega\int_{0}^{t}\overline{s(t)}dt\right)\), \(y_{Q}=\sin\left(\Delta\omega\int_{0}^{t}\overline{s(t)}dt\right)\).