# Covert Channel Based on Quasi-Orthogonal Coding
## 1 Introduction  
Wireless transmission, in its physical layer, is susceptible to all kinds of manipulation, which can be used to create covert channels [1]. It is currently assumed that any method of communication used to illegally transmit information, which violates the system security policy, is a covert channel. Steganography of the physical layer of a radio signal essentially boils down to subtle changes of the parameters of the modulated cover signal. Such parameters can be the carrier frequency and, in the case of an orthogonal frequency-division multiplexing (OFDM) signal, the training sequence of the cover signal [2]. The vast majority of physical layer steganography methods consist of manipulating the position of the constellation points of the in-phase (I) and quadrature (Q) components of the cover signal. Small changes in position correspond to transmitted classified (covert) information, and an uninformed receiver (with no knowledge or ability to ascertain additional transmission) treats them as (channel or hardware) noise. Examples of such solutions are presented in the literature:  
1. In [3], quadrature amplitude modulation (QAM) covert information constellation points are distributed around the QAM cover constellation points, forming the so-called dirty constellation. Thus, an additional constellation is formed based on the cover constellation. 2. The authors [4] propose a similar solution, with the dirty constellation being formed using phase drift [5]. The solution can be applied to phase-shift keying (PSK) and QAM modulation. * Hiding the data by moving the constellation points by a given angle (right or left) is shown in [1]. In this case, binary PSK (BPSK) modulation was used for practical implementation. * In [6], the use of 8 frequency-shift keying (8 FSK) modulation to embed information in QAM constellation points is presented. In this case, artificial neural networks were used to extract hidden data. * The authors [7] noted that PSK modulations do not use the channel fully in terms of Shannon capacity. Therefore, the so-called residual capacity can be used to hide information. In order to hide this emission from potential observers, pseudo-noise asymmetric shift keying (PN-ASK) modulation is proposed. * An extension to the pseudo randomness element of the [7] method is presented in [8]. The solution, called SteaLTE or Stegano LTE, is a steganographic technique for transmitting hidden data over Long-Term Evolution (LTE) radio networks. The developed method is resistant to steganalysis. * The approach described in [9] is based on the [3] method with elements of additional randomness, which involves an additional shift in the phase of the constellation points of the covert signal. In addition, the authors [9] propose using polar codes to reduce bit error rate (BER). * The transmission of stealth information in the form of noise on a QAM basis is presented in [10]. In this case, the cover's signal is not used to carry information. The aforementioned literature on the covert channel ignores the issue of channel estimation error [11] and, directly related to this, non-perfect (non-ideal) successive interference cancellation (SIC) [12; 13; 14; 15]. The assumption of being able to easily separate the cover signal from the very low-power covert signal is fundamentally difficult to implement. Hence, in this paper, the authors propose an original and novel approach, which is to transmit the covert signal in such a way that it is quasi-orthogonal to the cover signal at the receiver. This is accomplished by sorting, that is, by appropriately ranking the IQ samples of the covert signal against the cover signal over time. In the receiver this results in mutual orthogonalization, thus, easier frequency separation of the signals. The method used can be used for both amplitude-phase and frequency modulations. In the paper, however, FSK modulation is indicated as the optimal solution in terms of transmission capabilities (calculated by transmission speed) as well as protection against steganalysis.