# Synchronization of Acoustic Signals for Steganographic Transmission
## 4 Technique Development and Implementation
### Direct Spread Spectrum  
The synchronizing signal generation circuit is shown in Figure 9. The input signal here is a Stego Object. The _SMR(k)_ masking curve was determined as described in the Monotonic Phase Correction method. In an OFDM block, a signal is formed which is the sum of 6 harmonic components. The OFDM signal is contained in the band from 416.7 Hz to 500 Hz and from 3083.3 Hz to 3166.7 Hz. The OFDM signal frame duration is 24 ms. All harmonics of the OFDM signal act as pilot spectral lines. In the implementation, the value of the phase angle was assumed to be equal to 0. The second component of the synchronization signal, next to the OFDM signal, is the DSS signal (Direct Spread Spectrum). The block scheme of the DSS signal generation system is shown in Figure 10.  
Figure 8: Cumulative normalized Fréchet distance between the expected cumulative phase and the measured phase. Figure 7: Cumulative normalized Mahalanobis distance between the expected cumulative phase and the measured phase. The first stage of DSS signal synthesis is the generation of a pseudo-random sequence with appropriate properties [56]. Gold sequences and primary polynomials were used:  
\[ \begin{array}{c}x^{13}+x^{9}+x^{7}+x^{5}+x^{3}+1=[8873]_{DEC}\\ x^{13}+x^{9}+x^{5}+1=[8737]_{DEC}\end{array} , \tag{4}\]  
with initial condition  
\[[0000000000001]\]  
The size of the Gold string used to generate the DSS signal has been limited to 6096 symbols. The duration of a single symbol has been set to \(T_{c}=1\) ms. The duration of the entire sequence is therefore \(T=6.096\) s.  
In the next stage, the generated pseudo-random sequence is fed to the input of the filter block. First of all, it is an interpolation filter with the characteristic of the root raised cosine (RRC, Root Raised Cosine) and then the low-pass filter such as FIR (Finite Impulse Response). These filters are designed to properly shape the pseudorandom sequence pulses and narrow the signal band. Figure 11 shows a fragment of the signal at the output of the low-pass filter. Additionally, the corresponding fragment of the pseudorandom sequence is marked (top picture, red dotted line). The final step in generating the DSS signal is to transfer the signal from the low-pass filter output to a higher range of audio frequencies. This is due to the fact that frequencies below 300 Hz can be strongly suppressed during signal transmission in telecommunications links. The frequency of the carrier wave used is \(f_{c}=2000\) Hz. Figure 10: The block diagram of the DSS signal generation system. Figure 9: Block diagram of the synchronizing signal synthesis system for the DSS method. Spread spectrum systems are characterized by two important parameters processing gain \(G\) and the interference margin \(M\)[57]. The processing gain is a parameter that determines the degree of dispersion of the information signal spectrum:  
\[ \begin{array}{c}G=\frac{T_{b}}{T_{c}}\\ G[dB]=10\log_{10}\left(\frac{T_{b}}{T_{c}}\right)\end{array} , \tag{5}\]  
where:  
\(T_{b}\)--duration of the data bit--synchronization bit,  
\(T_{c}\)--the duration of the spreading sequence chip. Determining that the duration of the sync bit is equal to the duration of the spreading sequence \(T_{b}=T=6.096\) s, the processing gain of the considered system is \(G=37.85\) dB. The obtained value of the processing profit meets the condition related to perceptual transparency. The interference margin \(M\) is a measure of the receiver's immunity to interference. It determines the maximum ratio of the noise power to the signal power at the receiver input, at which we obtain the minimum bit energy level to the noise power \(E_{b}/N_{0}\) ensuring an acceptable error probability [56]. \[M=G-\left(\frac{E_{b}}{N_{0}}\right)[dB], \tag{6}\]  
After generating the DSS and OFDM signals, these signals are fed to the input of the amplitude correction circuit and then summed with the steganographic signal. Both the OFDM signal and the DSS signal are corrected based on the \(SMR(k)\) masking curve.