## 4 Realization of the Processing Algorithm  
Analog processing of input process (8) with transfer to the zero frequency of the spectrum of the sequence of FTN signals is carried out when implementing the preliminary reception algorithm. The radio modem is built on the SDR NI USRP 2920 platform and the signal spectrum is transferred from the carrier frequency to the zero frequency in the analog (hardware) part of the platform. Phase Locked Loop (PLL) and timing are used to achieve coherent reception. PLL and timing are implemented in the platform in the controller and processor in PCHost. The software part of algorithm (9) and its block diagram are shown Figures 2 and 3. The software part determines the computational complexity of the receiving device. The input of the software part of algorithm (9) receives digital samples from the function. These samples are distributed among the correlator blocks. The upper correlator (the left side of algorithm (9)) performs processing on the observation interval \([0;LT]\), equal to the duration of the FTN signal. The remaining correlators are used for preliminary assessment of subsequent symbols falling within the observation interval (the right side of inequality (9)). The introduction of decision feedback when receiving previous symbols occurs in the block \"Decision feedback with estimation of subsequent symbols in observation interval by maximum likelihood ratio\" and the block \"Correlation coefficient of previously received symbols\" \(R_{ri}^{(p)}\) in accordance with \(\delta(i,q)\) in (9). The correlator block process is performed with digital \"sliding\" integration by using memory integrators and continuously performing the integration process. This is due to the fact that the duration of the FTN signal exceeds the duration \(T\), so several consecutive signals will be included in integration processes during integration. Note that a digital matched filter can be used instead of a digital \"sliding\" integrator. The processing of subsequent signals is performed on the observation interval \([0;LT]\) in accordance with the maximum likelihood estimate in the digital block \"Correlation coefficient of subsequent symbols\" \(K_{rq}^{(p)}\). Evaluations of the received symbols \(d_{r}^{*(p)}\) are formed at the output of the decision unit (DU). The threshold value of the DU is equal to \(\delta(i,q)\). These values are formed by taking into account the correlation coefficients of the subsequent symbols \(K_{r,q}^{(p)}=\int_{0}^{LT}a(t)\sum_{p=1}^{\left\lfloor LR_{n}-1\right\rfloor} d_{rq}^{(p)}a(t-p\xi T)dt\) and the correlation coefficients of the evaluations of the received symbols \(R_{r,i}^{(p)}=\int_{0}^{LT}a(t)\sum_{p=-\left\lceil LR_{n}-1\right\rceil}^{(-1 )}d_{ri}^{*(p)}a(t-p\xi T)dt\) with the amplitude pulse shape \(a(t)\). Blocks \"\(d_{rq}^{(p)}\)\" are needed to calculate the values of the correlation integral \(\int_{0}^{LT}A_{xc}(t)\sum_{(p=1)}^{\left\lfloor LR_{n}-1\right\rfloor}d_{rq}^ {(p)}a(t-p\xi T)dt\). Note that the value of \(\delta(i,q)\) depends on the coefficient \(\mu\), which is determined by the attenuation level of the channel. The computational complexity of proposed algorithm (9) is determined by the number of operations for the calculation of the maximum. The upper limit for the number of additions is equal to \(2(M^{\left\lceil LR_{n}-1\right\rceil})\) and no multiplications, but there are many effective realizations. Note that the complexity of proposed algorithm (9) does not depend on the length of the message packet. The complexity gain for the comparison with the processing algorithm based on the MLSE is more than two orders in terms of the memory consumption for the case of the length of the received message packet equal to \(N=100\). The computational complexity of algorithm (9) is given in Table 2. It is determined by the number of additions and multiplications and depends on the number \(Q\) of subsequent symbols which fall within the observation interval. Also, it is determined by the number of samples per bit \(N_{s}\).