In this article were considered methods and ways of information security implementation in wireless telecommunication networks, and was explored a method of increasing information security in telecommunications networks based on stochastic application of orthogonal signals.
e ective signaling sequences for multi-user CDMA communication that show performance for binary sequences optimized for brute force. However, security problems of such sequences are not considered.
As part of the progress of IoT (Internet-of-Things), articles [Mat17, Sag17] propose a design of a PHY/MAC layer using Software De ned Radios (SDRs) that is backward compatible with existing OFDM based LTE protocols and supports CDMA based transmissions for low power IoT devices as well.. In the future, it is possible to use the method of increasing the low power IoT security in telecommunications networks based on the stochastic application of orthogonal signals. Nevertheless, in these works the problems of their safety are not fully covered. In the article [Ray18] The IoT make possible the physical things or home appliances or hand held devices or objects (e.g., smart phones, TVs, cars) can be interconnected by means of suitable communication protocols and information technology infrastructure to share the data to each other and access a range of applications and services like data storage, analytics. Hence, it is necessary to provide methods of ensuring wireless communication security, including increasing the structural concealment of information carrier signals to ensure the con dentiality of personal information. 1.1
Analysis of information security methods in wireless telecommunications networks CDMA technology is widely used for ensuring con dentiality in the exchange of information between users.
The increase in energy secrecy is achieved due to the expansion of the spectrum of the NLS, which increases the time of signal analysis in the detector. Structural concealment is provided by choosing a signal close in appearance to the background.
The analysis showed that of all the above methods the most relevant is the second, due to the least elaboration of this direction. This is the reason for writing this work.
To ensure the structural concealment of signals, it is necessary that they be orthogonal, have good correlation properties.
To evaluate the characteristics of orthogonal signals, from the point of view of their possible application in real communication channels, correlation functions (autocorrelation, intercorrelation) are commonly used.
At the same time, the following requirements are imposed on orthogonal signals: the maximum CCF emission level should be as small as possible and the maximum level of the side lobes of the ACF should be as small as possible.
Determine the condition under which the requirement of minimum spectrum value for the broadband signal of the ensemble (condition y1) will be ensured and its maximum for the narrowband ensemble signal (condition y2). It follows from the analysis that the rst side peak of the ACF R1( ) of the ensemble signals can be for di erent signals at the same absolute value, both positive and negative. In this connection, the range in the spectral characteristic of a discrete signal is determined by the relation:
T 2
m t k t P i=1 2 ki
Wk2 Wo2
T 2
m t k t P i=1 2 ki [1
R1 ( t )] [1 + R1 ( t )] (1)
It is obvious that the left-hand side of the expression (1) determines the condition y2, , and the right-hand side of the expression (1) determines the condition y1. As noted above, when synthesizing ensembles of discrete orthogonal signals, the case in which the shift of the frequency spectra of the ensemble signals is minimal is of interest, that is, in other words, when the left and right sides of inequality (1) tend to one another in magnitude.
ACF and CCF of the Walsh sequences have large side peaks and, therefore, do not meet the requirements for orthogonal signals. Figure 1 shows the ACF of eight Walsh functions for a system of volume N=8.
From analysis of gure 1 it follows that Walsh functions as the largest side peaks: wal (7,0), wal (6,0), wal (4,0), wal (3,0). This disadvantage leads to high-level inter-channel interference, and it is therefore inappropriate to use Walsh functions as address sequences in communication systems with channels divided by code.
However, based on Walsh systems, it is possible to construct derivative (composite) signal systems that will have good correlation properties. Barker codes can be used as such systems.
Table 1 shows the levels of the side peaks of ACF of Walsh systems and derived systems, for systems with a volume N=8, 16, 32, 64.
Analysis of Table 1 showed that Walsh systems are signi cantly inferior to derived systems in terms of the quality of the correlation properties.
Thus, the main disadvantages of CDMA systems using Walsh sequences are: poor correlation properties, familiarity of the species of these sequencesm, limited number of them. Since Walsh sequences and signal system derivatives do not allow to provide the required structural concealment even with their stochastic application, it is necessary to propose using orthogonal signals in systems with channels divided by code, the number of which will allow them to be used randomly, which will increase the security of information in the wireless telecommunication networks (WTN). Therefore, initially it is necessary to receive such signals, further investigate their characteristics and determine the number of unique signals. All of the above will make it possible to implement a mathematical model. A rational model for the synthesis of orthogonal signal systems (OSS) is the use of eigenvectors (EV) of Hermitian matrices (HM). In thimodel, the diagonal coe cients of the matrices are randomly assigned, which will determine the orthogonality properties of the signals.
Let's consider the given model on an example of HM of the fourth order with all zero arguments of factors in the second diagonals and zero coe cients in the main diagonal. Such a matrix has the form: Q =
0 A21 ei '
In the matrix (2), the coe cients of the second-second diagonals are symmetric, that is, A12 = A21; B23 = B32; C34 = C43 and are complex numbers represented in exponential form. The symbol denotes the phases of the coe cients. Stochastic lling of the diagonal elements of HM allows to obtain a model of stochastic orthogonal signals, its EV have the following form:
X = a11ei '1;1 a21ei '2;1
: an1 ei 'n;1 a12ei '1;2 : : : a1mei '1;m a22ei '2;2 : : : a2mei '2;m
: : : an2 ei 'n;2 : : : anmei 'n;m (3)
The EV of the above matrix is one signal from this ensemble, which can be described as a set of unit cells as follows: x_ y (t) = a1ej 1 ; a2ej 2 ; a3ej 3 ; : : : am=2 1 ej m=2 1 ; am=2ej m=2 ; am=2+1ej m=2+1 ; : : : ; amej m (4) 2 2.1
Investigation of the e ect of the phases of the HM coe cients on their coordinates The problem: to synthesize the ensemble of signals, described by the EV of a symmetric bidiagonal matrix of the fourth order. To synthesize the ensemble of signals, we choose an HM of the fourth order (N = 4) for which all the elements except the second diagonal are zero.
The phase coordinates of the synthesized signal ensemble take only two values: ' = 1800; 00. The amplitudes of this ensemble of signals take four values: U= 0.6533, 0.2706.
Analyzing Figure 2, it can be argued that for a fourth-order matrix with zero phase values of all coe cients, the program makes it possible to obtain an ensemble consisting of four non-repeating signals. Therefore, we can assume that using the entire range of degrees and Hermitian matrices of di erent orders, it is possible to obtain the required number of orthogonal signals for their stochastic application.
The purpose of this experiment is to determine the dependencies between the phase changes of each of the HM coe cients and their combinations and the resulting phases of the EV coordinates. The tasks of the experiment are: 1. calculation of EV and phases of their coordinates for the coe cients A, B, C, AB, AC, BC at '=15,30,45; 2. compilation of tables indicating the number of changing phases of the EV coordinates for each of the coe cients and their combinations.
Below is only an analysis of calculations without listing the results of calculations of A, B and C. For this, let us analyze the calculated phases of the coordinates of the EV. Based on the results of the analysis, a table is drawn up, shown in Figure 3, cells with varying phase coordinates of the EV.
The orthogonal phase-shifted signals are denoted as S1-S4, and the digits 1-4 indicate their coordinates. Thus, analyzing Figure 3, we can conclude that 1. A change in the phase of the coe cient A leads to a change in the phases of the three signal coordinates. 2. A change in the phase of the coe cient B leads to a change in the phases of the two signal coordinates. 3. Changing the phase of the coe cient C, as in the case of the coe cient A, leads to a phase change in the three coordinates of the signal.
Let us investigate the e ect of changing the phases of combinations of the fourth-order HM coe cients on the coordinates of EV. The results of calculations are shown in Fig. 4. Therefore, after analyzing the results of the experiments, it is necessary to draw conclusions: a change in the phases of the coe cients A and C leads to a change in the phases of the three coordinates EV, and in the case of the coe cient B, two; changing the phases of the combination of the coe cients AB and BC causes phase changes in the three coordinates EV, and AC - two; simultaneous change of phases of two coe cients leads to overlapping of their zones of in uence on each other and the invariance of the phases of the coordinates of EV; the change in the phases of the HM coe cients entails a change in the amplitude of the EV.
The phases of the co-ordinate coordinates obtained when the amplitude of the coe cients A, B, and C are changed are shown in Fig. 6.
Figure 5 shows the initial phase matrix, for further changes in signs and amplitudes.
Initial matrix of phases
Based on the results of alternating changes in the amplitude of the coe cient, the following conclusions can be drawn: as the amplitude decreases, the rst, second and third rows in the matrix of the phase coordinates of the change places; as the amplitude of the phase of the coordinates increases, EV have the same values as for the initial amplitude, respectively, of the coe cients A, B, and C; a decrease in the amplitude of the coe cient A leads to a decrease in the amplitude of one coordinate of the signals: for S1 and S2 (1.3); (2.3), for S3 and S4 (3.1); (4.1) and an increase in the amplitudes of the remaining coordinates of the signals; a decrease in the amplitude of the coe cient B leads to a decrease in the amplitudes of the two signal coordinates: for S1: (1,1), (1,4); S2: (2.2), (2.3); S3: (3.1), (3.4); S4: (4,2), (4,3) and an increase in the amplitudes of the remaining coordinates of the signals; an increase in the amplitude of the coe cient C leads to a decrease in the amplitudes of the two coordinate signals: for S1: (1.3), (1.4); S2: (2.2), (2.3); S3: (3.1), (3.4); S4: (4,1), (4,2) and an increase in the amplitudes of the remaining coordinates of the signals; It is known from the source [Zhu13] that the absolute values of the coordinates of the eigenvectors of the bidiagonal symmetric matrix are determined by the absolute values of the coe cients of the diagonals of the matrix. Let's check this theoretical situation.
Thus, the purpose of this experiment is to determine the dependencies between the coe cients of HM, the values of EV and the phases of EV when the signs of the HM coe cients change. In Figure 7, three columns of the phase matrix are lled, therefore, a change in the sign of the coe cient A changes the phase of three coordinates for each EV.
Experimental calculations are feasible for the matrix. In this case, we will successively change the sign of each of the coe cients, as well as their combinations by a negative one. An analysis of Figure 7 for B showed that the coe cient B is less in uential than the coe cient A, since it changes the phases of the two coordinates EV. Thus, a change in the sign of the coe cient C leads to a change in the phase of one coordinate of the EV, so this coe cient can be considered to be insigni cant. Next, we change the signs of the combinations of the coe cients of HM. The results of these changes are shown in Fig. 8.
Thus, changing the signs of the combination of the coe cients AB leads to a change in one coordinate of the EV (second). So, after analyzing the results of the experiment when changing the signs of the HM coe cients, it is necessary to draw the following conclusions: the results of the experiment fully correspond to the theory; the coe cient A changes the phases of three coordinates EV, B-two, C-one; changing the signs of a combination of coe cients leads to overlapping their zones of in uence on each other. To calculate the number of possible orthogonal signal structures for matrices of the fourth, eighth, sixteenth, thirty-second and sixty-fourth order, it is necessary to derive a formula in which the following parameters will be taken into account:
So, the formula for calculating the number of possible orthogonal signal structures (C) taking into account the above parameters will take the form:
C = 2N 1 ' (5) The results of calculations of the number of possible orthogonal signal structures are shown in Fig. 9.
Thus, based on the results of calculations, it is possible to plot the dependence of the number of possible orthogonal signal structures on the order of the matrix, that is, Cn.
The initial data N := 4; 8; 16; 32; 64' := 360 := 1 and 10
The number of sequences obtained with the resolving power of the phase detector is 1 and 10 degrees, respectively
For the mathematical modeling of orthogonal signals, a model and a program were developed which look for eigenvectors and their coordinates for given matrices, calculate the values of the ACF, CCF, and plot the graphs of these functions. The results of the work are analyzed and a conclusion is drawn that it will allow obtaining the necessary number of orthogonal signals for realization of their stochastic application. Therefore, it is advisable to apply the results obtained with the use of the program to improve the structural concealment of the WTN. 4
In this article, conclusions were drawn about the methods and possibilities for implementing information security in wireless telecommunications networks. The most relevant is to improve the structural concealment of signalsbearers of information to ensure the con dentiality of information. ZA method for increasing the security of information in telecommunications networks based on stochastic application of orthogonal signals was also investigated. A formula is proposed that allows obtaining the necessary number of orthogonal signals for their stochastic application, and a graph of the dependence of the number of possible orthogonal signal structures on the order of the matrix is presented. [Ge04]
Ge, Q., Yin, L., Lu, J., Mei, S. Channel estimation algorithm in OFDM systems combined with the Walsh transform and LDPC codes (2004) QinghuaDaxueXuebao/Journal of Tsinghua University, 44 (6), pp. 837-839.