# Covert Channel Based on Quasi-Orthogonal Coding
## 3 Proposed Model  
### Basic Assumptions  
In the presented model, a single covert symbol is superimposed on several cover signal symbols. Such a solution stems from the need to reduce the distortion/interference of the cover signal (in order to preserve the energy per bit, variance of the covert signal is reduced), and thus the detection by outsiders of the fact that a covert channel exists. In the analyzed model, as in previous solutions [2; 3; 7; 10], we assume that the cover is QAM amplitude-phase modulation in the form of IQ samples. In order to facilitate the process of demodulation of covert information from Figure 1, it is proposed to cross-orthogonalize the cover and covert signals by sorting. It is assumed that the coherence time of the radio channel, and therefore the channel estimation error, remains constant at least for a single data block for which the sorting operation is performed. Knowing that a typical channel coherence time is between approximately 10 ms to 200 ms [22; 23; 24], this assumption will usually remain. Sorting occurs in both the transmitter and receiver as shown in Figure 2, whereby:  
* At the transmitter, samples of the covert signal \(x_{2}(t)\) are sorted based on a given sequence of the cover (QAM modulation) signal \(x_{1}(t)\). In this way, the sorted signal \(x_{2_{p}}\) has a pseudo-random (noise) form. * At the receiver, the \(\hat{x}_{2}(t)\) signal re-sorting is performed after the SIC operation. Sorting in the receiver aims to: 1. [label=()] 2. restore the original sample order of the covert signal after the SIC operation \(\hat{x}_{2_{p}}\) to the original order (in an ideal case \(\hat{x}_{2_{i}}=x_{2}\)) 3. restoring the original order of \(\hat{x}_{2_{p}}\) is followed by a simultaneous change in the sample order of the residual signal associated with \(x_{1}\) Thus, the residual signal becomes orthogonal (quasi-orthogonal) to the covert signal. 3. The covert signal \(\hat{x}_{2_{i}}\) is fed to the input of the covert channel demodulator Sorting involves dividing covert information into blocks. The block length depends on the covert information modulation used, the value of the cover modulation and the number of IQ samples per signal. Every covert symbol consists of several IQ points imposed on the several cover symbols. In Section 4 are presented simulation results for blocks equalling 16 or 64 cover symbols with (imposed) 1 to 4 covert symbols, respectively. From the proposed principle of sorting, in order to correctly reproduce the covert signal, it is necessary to correctly (without error) reproduce the unclassified (cover) signal (the equation \(\hat{x}_{1}=x_{1}\) must be true) because based on the cover signal, the reverse operation of sorting in the transmitter is reproduced (in the covert samples reorder system). Any error in the reception of the cover data in the block results in an error in the covert signal. That means, for example, that if the block has a length of 16 cover symbols with one imposed covert symbol, we lose one covert symbol in case of any cover error. And similarly, for a larger number of covert symbols per block, we lose all covert symbols. Therefore, the block length and the number of covert symbols in the block should be taken carefully. As shown in Figure 2, the proposed solution, compared with traditional SIC (Figure 1), is based on two additional sorting operations: one in the transmitter and one in the receiver. It can be assumed that the complexity of every sorting operation has complexity O(\(n^{2}\)). The selection of the optimal modulation of covert information was preceded by simulation tests included in the following chapters. The easiest way to explain orthogonalization (the creation of quasi-orthogonal signals) is to assume that the covert signal is 8 FSK modulation. By orthogonalization we mean the mutual transformation of signals in such a way that their spectra are disjointed, i.e., they do not overlap. The 8 FSK signal spectrum has eight peaks corresponding to each symbol.