RU2428795C1 - Method to transfer information based on chaotically generated ensembles of discrete multi-level orthogonal signals - Google Patents

Abstract

FIELD: information technologies. ^ SUBSTANCE: to transfer messages changed from one information symbol to another, orthogonal code combinations are used, such as ensembles of discrete orthogonal signals generated by calculation of own numbers and own vectors of a diagonal positively determined symmetrical matrix, diagonal coefficients of which are chaotically generated numerical sequences. ^ EFFECT: increased structural security of information transfer system with code division of channels by using ensembles of orthogonal signals, which are chaotically generated on the basis of own vectors of the diagonal positively determined symmetrical matrix with N dimension. ^ 3 dwg

Description

FIELD OF THE INVENTION

The invention relates to the field of information transmission and can be used for message transmission in broadband radio systems with code division multiplexing.

State of the art

A known method of multi-station access with code division multiplexing in data transmission systems (see Gromakov Yu.A. Standards and mobile radio communication systems. - M .: AOZT Eco-Trends KO, 1996), the essence of which is to expand the frequency spectrum based on the use of 64 kinds of sequences formed by the law of Walsh functions. The base station can transmit information on 64 channels simultaneously. In each channel, one of 64 Walsh sequences is used to transmit information. As the bit of the information message changes, the phase of the used Walsh sequence changes by 180 degrees. Since the applied sequences are mutually orthogonal, there is no mutual interference between the transmission channels of the base station.

Information signals are transmitted against the background of a special synchronizing signal, the structure of which is formed according to the law of random sequences of maximum length. The synchronizing signal serves to introduce the transmitter of the base station and the receiver of the subscriber station in the cyclic phase, and its manipulation at the stage of entering into communication provides the transmission of service information.

The disadvantage of this method is that the Walsh signals have a regular structure, which is known in advance and therefore a code-division-wide broadband radio communication system based on this method will have low structural secrecy.

The Popenko-Turko function generator is known (see USSR patent No. 1753464 A1, class G06F 1/02 of 08/07/1992), which allows generating discrete orthogonal basis functions containing a matrix of calculators, a group of division blocks, a group of blocks of elements "AND", a matrix operating blocks, delay elements, synchronization block, shift register, memory blocks and ring shift register.

The disadvantage of this generator is the inability to generate chaotic ensembles of orthogonal signals (eigenvectors) of various structures.

The closest in technical essence to the proposed method is the method used in the data transmission system with code division multiplexing (see patent of the Russian Federation No. 2234191, CL Н04В 7/216, H04L 9/26 from 07/24/2001), which includes simultaneous operation transmission of complex broadband signals based on non-linear de Bruin sequences with a change in the shape of the sequence during the transmission of a message from one information symbol to another.

De Bruin sequences as well as Walsh dictionaries have the property of orthogonality at a point, and a wide variety of de Bruin dictionaries and the presence of nonlinear operations in the algorithm for generating this class of sequences allows them to be used in systems with multiple access for code compression of a transmission channel.

A distinctive feature of this method is the use of de Bruyne orthogonal code dictionaries in the channels of messages exchanged from one information symbol to another, each code word of which can be constructed by modulo summing two signals taken from the bits of the shift register with nonlinear feedbacks one at a time , two and so on up to m inclusive, where m is the number of bits of the shift register, the feedback function, which is given by the relation:

,

,

- разрешенный набор двоичных чисел, определяющий порядок подключения прямых и инверсных выходов элементов памяти регистра сдвига;Where

- an allowed set of binary numbers that determines the connection order of direct and inverse outputs of the shift register memory elements;

d is the number of allowed binary sets needed to generate the maximum period of the sequence L equal to 2m;

Despite the fact that the number of orthogonal signals generated on the basis of de Bruin code dictionaries is greater than the number of Walsh orthogonal signals of dimension N, however, their number is finite for any dimension N, which allows us to conclude that they have low structural secrecy.

The aim of the invention is. the development of a method and device to increase the structural secrecy of the information transmission system with code division multiplexing.

Disclosure of invention

The objective of the invention is to increase the level of structural secrecy of broadband radio communication systems with code division multiplexing.

Technical result

The technical result that can be achieved using the present invention is that for the transmission of messages, changing from one information symbol to another, it is proposed to use stochastically generated orthogonal signal systems described by eigenvectors of diagonal positive definite symmetric matrices of dimension N. When this uses the property of orthogonality of the eigenvectors, which consists in the fact that the eigenvectors corresponding to the times ary eigenvalues normal operator are orthogonal (see G.Korn, T.Korn Handbook of mathematics (for scientists and engineers) -... M .: "Science" Publishing House, 1974. - S.436).

It is known that every nonzero vector x is called an eigenvector of the matrix λ if there is a number λ such that the equality holds:

This number λ is called the eigenvalue of the matrix A corresponding to the eigenvector x.

If a specific basis is chosen in space, then equation (1) for the eigenvectors and eigenvalues of the linear transformation can be written in matrix form:

Any nonzero column X for which equality (2) holds is called an eigenvector of matrix A corresponding to the eigenvalue λ.

линейного преобразования

в выбранном базисе.The eigenvector of matrix A is a column of the form (3), composed of the coordinates of the eigenvector

linear transformation

in the selected basis.

The eigenvectors of a real diagonal symmetric matrix corresponding to different eigenvalues are orthogonal, i.e. their scalar product is equal to zero (see Kliot-Dashinsky M.I. Algebra of matrices and vectors. 3rd ed., ster., / - St. Petersburg: Publishing House "Lan", 2001. - 160 pp. - (Textbooks for universities . Special literature)).

и каждому собственному значению соответствует собственный вектор X, который попарно ортогонален с любым из векторв ансамбля.From the foregoing, it follows that for any real diagonal symmetric matrix A, relation (4) has a set of eigenvalues

and each eigenvalue corresponds to an eigenvector X, which is pairwise orthogonal to any of the ensemble vectors.

The extension of the information sequence occurs in such a way that if the information bit is equal to one, then the orthogonal signal of the inverse structure is used, and if the information bit is equal to zero, then the orthogonal signal of the direct structure is used (see Stolings B. Wireless communication lines and networks .: Per . from the English. - M.: Williams Publishing House, 2003. - P.213).

The nonlinearity of the generated signal structures is achieved due to the fact that at each information transmission step, an expanding sequence in the form of one of the signals of the orthogonal system of signals described by the eigenvectors of diagonal positive definite symmetric matrices is formed by stochastic specification of a set of diagonal coefficients, a positive definite symmetric matrix A (of the form 4), a generator of random positive numbers.

-й строки матрицы, выход вычислителя i-го столбца матрицы соединен с информационным входом соответствующего вычислителя

-го столбца матрицы, третьи информационные входы вычислителей первого столбца матрицы соединены с входом логического нуля блока формирования хаотических ансамблей ортогональных сигналов, регистр сдвига, первый и второй блоки памяти, матрицу операционных блоков, кольцевой регистр сдвига, причем выход вычислителя

-й строки

-го столбца матрицы соединен с первыми входами делителя блоков деления, вход делимого j-го блока деления

соединен с вторым входом вычислителя j-й строки (N-i+1)-го столбца матрицы, выход j-го блока деления соединен с первым входом j-го блока элементов «И», вторые входы блоков элементов «И» соединены с выходом i-го разряда регистра сдвига, выходы блока синхронизации соединены соответственно с тактовыми входами операционных блоков матрицы, с тактовым входом элемента задержки, с входом разрешения сдвига регистра сдвига, с входами разрешения записи первого блока памяти, с входами разрешения записи второго блока памяти, с тактовыми входами первого и второго блоков памяти, с входами разрешения считывания первого и второго блоков памяти и входом разрешения сдвига кольцевого регистра сдвига, вторые выходы вычислителей последней строки матрицы соединены с 1-го по N-й информационный вход второго блока памяти, первый информационный вход операционного блока i-й строки первого столбца матрицы соединен с i-м выходом второго блока памяти, первые выходы операционных блоков i-й строки S-x(S=i, N-1) столбцов матрицы соединены с (N-i+1)-м информационным входом второго блока памяти, первый информационный вход операционного блока k-й (k=1, N-2) строки М-го (М=2, N-1) столбца матрицы соединен с первым выходом операционного блока (k+1)-й строки (M-1)-го столбца матрицы, первый информационный вход операционного блока (Р-2)-й строки М-го столбца матрицы подключен к выходу элемента задержки, информационный вход которого подключен к второму выходу операционного блока

-й строки

-го столбца матрицы, второй информационный вход операционного блока М-й строки i-го столбца матрицы подключен к второму выходу операционного блока (М-1)-й строки i-го столбца матрицы, входы значения компонент исходной матрицы блока формирования хаотических ансамблей ортогональных сигналов соединены с информационными входами первого блока памяти, выходы которого соединены с третьими информационными входами вычислителей соответствующих строк матрицы, k-й выход второго блока памяти соединен с k-м дополнительным информационным входом первого блока памяти, выходы разрядов кольцевого регистра сдвига соединены с соответствующими входами разрешения считывания второго блока памяти, выходы которого являются выходами блока формирования ансамблей хаотических ортогональных сигналов, генератор случайных положительных чисел (ГСПЧ), вход которого соединен с выходом блока синхронизации, а информационные с 1-го по N-й выходы ГСПЧ являются информационными с 1-го по N-й входами второго запоминающего устройства, элемент «И», а также запоминающие устройства каждого из каналов, на первый вход которых подается информационная последовательность, а на второй управляющий сигнал с элемента «И». Причем в каждом канале передающей аппаратуры исключен блок перестройки структуры сигнала, генератор де Брейна, блок служебной информации и соответствующие связи этих устройств; приемную аппаратуру абонентской станции, содержащую блок высокочастотной селекции, вход которого соединен с приемной антенной, а выход одновременно подключен к первому входу блока обнаружения сигнала синхронизации и первому входу блока корреляционной обработки, выход которого через блок выделения информации подключен к блоку получения информации, причем первый выход блока обнаружения сигнала синхронизации через блок поиска и первый вход генератора копии сигнала синхронизации подключен ко второму входу блока обнаружения сигнала синхронизации, выход которого подключен ко входу блока выделения служебной информации, первый выход блока выделения служебной информации одновременно подключен к первым входам блока перестройки структуры сигнала и генератору копии сигнала де Брейна, второй выход блока выделения служебной информации параллельно подключен ко вторым входам генератора копии сигнала де Брейна и блока перестройки структуры сигнала, а третий выход к третьему входу блока перестройки структуры сигнала, четвертый вход которого одновременно соединен с выходом генератора тактовых импульсов, со вторым входом генератора копии сигнала синхронизации и вторым входом блока выделения информации, при этом первый, второй и третий выходы блока перестройки структуры сигнала подключены соответственно к третьему, четвертому и пятому входам генератора копии сигнала де Брейна, а четвертые d(m-1) выходы к шестым входам генератора копии сигнала де Брейна, выход которого подключен ко второму входу блока корреляционной обработки, дополнительно введены блок формирования хаотических ансамблей ортогональных сигналов, содержащий матрицу вычислителей, блоки деления, блоки элементов «И» и блок синхронизации, причем с 1-го по N-й выходы блока генерации копий сигналов управления итерационным процессом, происходящим в блоке формирования копий хаотических ансамблей ортогональных сигналов, соединены со вторыми входами с 1-го по N-й вычислитель первой строки матрицы, второй вход вычислителя i-й строки матрицы соединен с вторым информационным входом вычислителя (i+1)-й строки матрицы, выход вычислителя г-го столбца матрицы соединен с вторым информационным входом вычислителя (i+1)-го столбца матрицы, третьи информационные входы вычислителей первого столбца матрицы соединены с входом логического нуля блока формирования копий ансамблей хаотических ортогональных сигналов, регистр сдвига, первый и второй блоки памяти, матрицу операционных блоков, элемент задержки и кольцевой регистр сдвига, причем выход вычислителя (i+1)-й строки (i+1)-го столбца матрицы соединен с первыми входами делителя блоков деления, вход делимого j-го блока деления (j=1, N-1) соединен с вторым входом вычислителя j-й строки (N-i+1)-го столбца матрицы, выход j-го блока деления соединен с первым входом j-го блока элементов «И», вторые входы блоков элементов «И» соединены с выходом i-го разряда регистра сдвига, выходы блока синхронизации соединены соответственно с тактовыми входами операционных блоков матрицы, с тактовым входом элемента задержки, с входом разрешения сдвига регистра сдвига, с входами разрешения записи первого блока памяти, с входами разрешения записи второго блока памяти, с тактовыми входами первого и второго блоков памяти, с входами разрешения считывания первого и второго блоков памяти и входом разрешения сдвига кольцевого регистра сдвига, выходы j-x блоков элементов «И» с первой по (N-1) соединены с первым информационным входом вычислителя (j+1)-й строки j-го столбца матрицы, вторые выходы вычислителей последней строки матрицы соединены с информационными входами второго блока памяти, первый информационный вход операционного блока i-й строки первого столбца матрицы соединен с i-м выходом второго блока памяти, первые выходы операционных блоков i-й строки S-x(S=i, N-1) столбцов матрицы соединены с (N-i+1)-м информационным входом группы второго блока памяти, первый информационный вход операционного блока k-й (k=1, N-2) строки М-го (М=2, N-1) столбца матрицы соединен с первым выходом операционного блока (k+1)-й строки (М-1)-го столбца матрицы, первый информационный вход операционного блока (N-2)-й строки М-го столбца матрицы подключен к выходу элемента задержки, информационный вход которого подключен к второму выходу операционного блока (N-1)-й строки (M-1)-го столбца матрицы, второй информационный вход операционного блока М-й строки i-го столбца матрицы подключен к второму выходу операционного блока (М-1)-й строки i-го столбца матрицы, входы значения компонент исходной матрицы блока формирования копий хаотических ансамблей ортогональных сигналов соединены с информационными с 1-го по N-й входами первого блока памяти, выходы которого соединены с первыми информационными входами с 1-го по N-й вычислитель соответствующей строки матрицы, выходы с 1-го по N-й разрядов кольцевого регистра сдвига соединены с 1-го по N-й входами разрешения считывания второго блока памяти, генератор случайных положительных чисел (ГСПЧ), управляющий вход которого соединен с выходом блока синхронизации, а информационные с 1-го по N-й выходы являются информационными с 1-го по N-й входами запоминающего устройства, элемент «И», а также запоминающее устройство каждого из каналов, на первый вход которого подается управляющий сигнал, а на второй - копии ансамблей ортогональных сигналов. Причем в каждом канале приемной аппаратуры исключен блок перестройки структуры сигнала, блок выделения служебной информации, генератор копии сигнала де Брейна и соответствующие связи этих устройств.To achieve the named technical result in the transmitting equipment of the base station of the closest technical solution (see patent of the Russian Federation No. 2234191, class Н04В 7/216, H04L 9/26 from 07.24.2001), consisting of N equal to 2 ^m-1 channels , each of which contains a digital information unit connected to the first input of the modulator of each channel, and the second m inputs are connected to the output of the de Bruin generator, and the outputs of each channel are connected to the combiner of the group signal generation unit, the output of which is connected to the first input of an oscillator, the second input of which is connected to the output of the pseudo-random synchronization signal generator, and the output is the output of the group signal generating unit, which is connected to the transmitting antenna through the phase modulation unit and the power amplifier, the first input of the pseudo-random synchronization signal generator of the group signal generating unit being simultaneously connected to the first the output of the service information block, with the first input of the de Bruyne generator and the first input of the signal structure adjustment unit, and the second input is the gene a pseudo-random synchronization signal generator is simultaneously connected to the output of the clock generator and the fourth input of the signal structure adjustment unit, while the second output of the service information unit is simultaneously connected to the second input of the de Bruyne generator and the second input of the signal structure adjustment unit, and the third output of the service information unit is connected in parallel to the input of the digital information block and the third input of the signal structure adjustment unit, the first output of which is connected to the third input of the generator ora de Brain, the second to the fourth input of the de Brain generator, the third to the fifth input of the de Brain generator, and the fourth d (m-1) inputs are connected to the sixth corresponding inputs of the de Brain generator, an additional block for the formation of chaotic ensembles of orthogonal signals, containing a matrix of calculators , division blocks, blocks of the And element, and a synchronization block, and from the 1st to the Nth outputs of the signal generation block for controlling the iterative process occurring in the block for generating chaotic ensembles of orthogonal signals, dineny to second inputs from the 1st to N-th calculator of the first row of the matrix, the second input of the calculator i-th (i = 1, N-1, where N - order of a square symmetric matrix of coefficients) of the matrix line connected to second data input of the respective calculator

-th row of the matrix, the output of the calculator of the i-th column of the matrix is connected to the information input of the corresponding calculator

-th column of the matrix, the third information inputs of the calculators of the first column of the matrix are connected to the logical zero input of the block for the formation of chaotic ensembles of orthogonal signals, the shift register, the first and second memory blocks, the matrix of operating blocks, the ring shift register, and the output of the calculator

row

-th column of the matrix is connected to the first inputs of the divider of the division blocks, the input of the dividend of the j-th division block

connected to the second input of the calculator of the j-th row of the (N-i + 1) -th column of the matrix, the output of the j-th division block is connected to the first input of the j-th block of elements "AND", the second inputs of the blocks of elements "AND" are connected to the output i-th category of the shift register, the outputs of the synchronization block are connected respectively to the clock inputs of the operating blocks of the matrix, with the clock input of the delay element, with the input of the shift register shift enable, with the write enable inputs of the first memory block, with the write enable inputs of the second memory block, with the first and of the second memory blocks, with the read enable inputs of the first and second memory blocks and the shift enable input of the ring shift register, the second outputs of the last row of calculators are connected from the 1st to the Nth information input of the second memory block, the first information input of the i the rows of the first column of the matrix are connected to the i-th output of the second memory block, the first outputs of the operating blocks of the i-th row Sx (S = i, N-1) of the columns of the matrix are connected to the (N-i + 1) -th information input of the second memory block first information input the operation block of the kth (k = 1, N-2) row of the Mth (M = 2, N-1) column of the matrix is connected to the first output of the operation block of the (k + 1) th row of the (M-1) th column matrix, the first information input of the operation unit (P-2) of the row of the Mth column of the matrix is connected to the output of the delay element, the information input of which is connected to the second output of the operation unit

row

-th column of the matrix, the second information input of the operation block of the Mth row of the i-th column of the matrix is connected to the second output of the operation block (M-1) of the row of the i-th column of the matrix, inputs of the values of the components of the original matrix of the block for the formation of chaotic ensembles of orthogonal signals connected to the information inputs of the first memory block, the outputs of which are connected to the third information inputs of the computers of the corresponding rows of the matrix, the k-th output of the second memory block is connected to the k-th additional information input of the first about the memory block, the outputs of the discharges of the annular shift register are connected to the corresponding read permission inputs of the second memory block, the outputs of which are the outputs of the unit for generating ensembles of chaotic orthogonal signals, a random positive number generator (GPRS), the input of which is connected to the output of the synchronization block, and the information from 1 the Nth outputs of the GSPCH are informational from the 1st to Nth inputs of the second storage device, the element "And", as well as the storage devices of each channel, to the first input d which is fed information sequence and the second control signal from "AND" element. Moreover, in each channel of the transmitting equipment, the signal structure adjustment block, the de Bruyne generator, the service information block, and the corresponding communications of these devices are excluded; receiving equipment of a subscriber station containing a high-frequency selection unit, the input of which is connected to the receiving antenna, and the output is simultaneously connected to the first input of the synchronization signal detection unit and the first input of the correlation processing unit, the output of which is connected to the information acquisition unit through the information extraction unit, the first output the synchronization signal detection unit through the search unit and the first input of the synchronization signal copy generator is connected to the second input of the signal detection unit s synchronization, the output of which is connected to the input of the service information allocation unit, the first output of the service information allocation unit is simultaneously connected to the first inputs of the signal structure adjustment unit and the de Brain signal copy generator, the second output of the service information separation unit is connected in parallel to the second inputs of the de Brain signal generator and a signal structure adjustment unit, and a third output to a third input of a signal structure adjustment unit, a fourth input of which is simultaneously connected to an output g a clock pulse generator, with a second input of the synchronization signal copy generator and a second input of the information extraction unit, while the first, second, and third outputs of the signal structure adjustment unit are connected to the third, fourth, and fifth inputs of the de Brain signal copy generator, and the fourth d (m -1) the outputs to the sixth inputs of the de Bruyne signal copy generator, the output of which is connected to the second input of the correlation processing unit, a block for the formation of chaotic ensembles of orthogonal signal is additionally introduced s containing a matrix of calculators, dividing blocks, blocks of "And" elements and a synchronization block, and from the 1st to the Nth outputs of the copy generation block of the iterative process control signals occurring in the copy generation block of chaotic ensembles of orthogonal signals, connected to the second inputs from the 1st to the Nth calculator of the first row of the matrix, the second input of the calculator of the i-th row of the matrix is connected to the second information input of the calculator of the (i + 1) -th row of the matrix, the output of the calculator of the ith column of the matrix is connected to the second information input m of the calculator of the (i + 1) -th column of the matrix, the third information inputs of the computers of the first column of the matrix are connected to the logical zero input of the copy unit of the ensembles of chaotic orthogonal signals, the shift register, the first and second memory blocks, the matrix of operational blocks, the delay element and the ring register shift, and the output of the calculator of the (i + 1) -th row of the (i + 1) -th column of the matrix is connected to the first inputs of the divider of the division blocks, the input of the dividend of the j-th division block (j = 1, N-1) is connected to the second input calculator of the j-th row (N-i + 1) -th column and the matrices, the output of the jth division block is connected to the first input of the jth block of “And” elements, the second inputs of the blocks of “And” elements are connected to the output of the i-th digit of the shift register, the outputs of the synchronization block are connected respectively to the clock inputs of the operating blocks of the matrix , with the clock input of the delay element, with the shift enable input of the shift register, with the write enable inputs of the first memory block, with the write enable inputs of the second memory block, with the clock inputs of the first and second memory blocks, with the read permission inputs о and the second memory blocks and the shift resolution input of the circular shift register, the outputs jx of the blocks of elements “I” from the first to (N-1) are connected to the first information input of the calculator of the (j + 1) -th row of the j-th column of the matrix, the second outputs calculators of the last row of the matrix are connected to the information inputs of the second memory block, the first information input of the operational block of the i-th row of the first column of the matrix is connected to the i-th output of the second memory block, the first outputs of the operational blocks of the i-th row Sx (S = i, N- 1) the columns of the matrix are connected to the (N-i + 1) -m infor by the input of the group of the second memory block, the first information input of the operational block of the kth (k = 1, N-2) row of the Mth (M = 2, N-1) column of the matrix is connected to the first output of the operational block (k + 1) -th row of the (M-1) -th column of the matrix, the first information input of the operating unit (N-2) of the -th row of the M-th column of the matrix is connected to the output of the delay element, the information input of which is connected to the second output of the operation block (N-1 ) th row of the (M-1) th matrix column, the second information input of the operation block of the Mth row of the i-th matrix column is connected to the next output of the operation block (M-1) of the i-th column row of the matrix, the inputs of the values of the components of the original matrix of the block of the formation of copies of chaotic ensembles of orthogonal signals are connected to the information from the 1st to the N-th inputs of the first memory block, the outputs of which are connected to the first information inputs from the 1st to the Nth transmitter of the corresponding row of the matrix, the outputs from the 1st to the Nth bits of the circular shift register are connected from the 1st to the Nth inputs of the read permission of the second memory block, the generator of random positive numbers ( SHG ), the control input of which is connected to the output of the synchronization unit, and the information from the 1st to the Nth outputs are information from the 1st to the Nth inputs of the storage device, the element "And", as well as the storage device of each channel, the first input of which a control signal is supplied, and the second - copies of ensembles of orthogonal signals. Moreover, in each channel of the receiving equipment, a block for restructuring the signal structure, a block for extracting overhead information, a de Brain signal copy generator, and the corresponding communications of these devices are excluded.

Brief Description of the Drawings

Figure 1 shows the structural diagram of the transceiver equipment of the information transmission device based on randomly formed ensembles of discrete multilevel orthogonal signals.

на выходе первого канала, з) промодулированный информационный сигнал

на выходе второго канала, и) промодулированный информационный сигнал

на выходе третьего канала.Figure 2 shows the timing diagrams of the principle of operation of the information transmission device based on randomly formed ensembles of discrete multilevel orthogonal signals, where: a) clock signals, b) a signal received in the first communication channel S _{inf. 1} (t), c) a signal entering the second communication channel S _inf.2 (t), d) the signal entering the third communication channel S _inf.3 (t), e) the orthogonal chaotic signal entering the first communication channel S ₁ (t), e) orthogonal chaotic signal from the second communications channel S ₂ (t), g) ortho tional chaotic signal, S ₃ (t) supplied to the third communication channel, g) the modulated information signal

at the output of the first channel, h) a modulated information signal

at the output of the second channel, i) a modulated information signal

at the output of the third channel.

Figure 3 presents a comparative analysis of the number of ensembles of orthogonal signals generated by an information transmission device based on randomly formed ensembles of discrete multi-level orthogonal signals and a prototype.

The implementation of the invention

The proposed method is carried out in the following sequence: first, using the auxiliary synchronizing complex signal, the transmitting equipment of the base station and the receiving equipment of each of 2 ^m-1 subscriber stations are introduced into the cyclic phase. Then, by manipulating the auxiliary synchronization signal, service information is transmitted to each channel (a single starting block for all subscriber stations). After performing this procedure, the simultaneous transmission of digital information to all subscribers begins, with each bit of information of a fixed channel a complex signal is assigned, the structure of which depends on the values of the coefficients of the diagonal positive definite symmetric matrix, which are generated by the generator of random positive numbers, and the information sequence is expanded in if the information bit is equal to one due to the use of orthogonal with drove the inverse structure, if the information bit is equal to zero due to the use of an orthogonal signal of direct structure (see Stolings B. Wireless communication lines and networks.: Transl. from English. - M.: Williams Publishing House, 2003. - C .213).

After the transmission of the next information bit on the transmitting and receiving sides, the coefficients of the diagonal positive definite symmetric matrix are simultaneously changed, coming from identical GSPCs in the receiving and transmitting sides, on the basis of which the orthogonal signal systems generated by stochastic methods are described, which are described by the eigenvectors of the diagonal positive definite symmetric matrices . In this case, the signal used at the receiving side for correlation processing will have a structure coinciding with the signal emitted by the transmitter, and, therefore, can be used to process the information stream addressed to the recipient of digital information.

The device contains in the transmitting equipment (Fig. 1) N = 2 ^m-1 channels 12, each of which consists of a storage device 11, the second input of which is connected to the first output of the block of element "And" 47, the second output of which is connected to the control input of the block synchronization 6, and the input of the block of the element "And" 47 is connected to the control output of the senior bit of the annular shift register 10, the input of which is connected to the synchronization block 6, the output of which is connected to the input of the shift register 7, the outputs of which, in turn, are connected with the second inputs element blocks that “I” 3, and the outputs of the memory unit 8 are the first inputs of the calculators 1, and the second input of the Nth (N is the dimension of the coefficient matrix) calculator receives a signal from the Nth output of the signal generation block for controlling the iterative process 50, and the third inputs calculators 1 of the first column of the matrix are connected to the logical zero input of the block for the formation of chaotic ensembles of orthogonal signals, from the outputs of calculators 1, the signals are fed to the first and second inputs of the division blocks 2 and through the first inputs of the blocks of the element "And" 3 are fed to the second the moves of the first and second columns of the matrix of calculators 1, the second outputs of the calculators 1.3.1, 1.3.2, 1.3.3 are connected to the information from the 1st to the Nth input of the memory block 9, information from the 1st to (N-1) whose outputs are associated with the first inputs of the operating units 4 of the first column, and the output of the operating unit 4 of the first column and the first row is connected to the Nth input of the memory unit 9, and the outputs of the operating units 4 of the first column of the i-th (i = 2, N -1) the rows are connected to the first inputs of the operating blocks of the 4th jth (j = 2, N-1) column of the i-th (i = 1, N-1) row, while the operational blocks are Each of the columns is interconnected, the second inputs of the operating units 4 are connected to the output of the synchronization unit 6, and the second output of the operating unit 4 (N-1) of the first column is connected to the second input of the delay element 5, the first input of which is connected to the output of the unit synchronization 6, and the output is connected to the first operating unit of the 4th (N-1) -th row of the (N-1) -th column, while the information outputs of the operating blocks of the 4th j-th (j = Nl) column of the i-th (i = 1, N-1) the lines are connected to the information from the 2nd to the Nth inputs of the memory block 9, while the clock pulses from the block synchronization 6 simultaneously arrive at the input of the annular shift register 10, the control inputs of the memory blocks 8 and 9, the control input of the random random number generator 22 and the storage device 23, the information inputs of which from the 1st to the Nth are connected to the information from the 1st to The N-th outputs of the generator of random positive numbers 22, and the information from the 1st to the N-th outputs are connected to the information inputs of the memory block 8, the first control output of the ring shift register 10 is connected to the input of the block of the element "And" 47, and the second from 1 Nth exit s are connected from the 1st to the Nth control input of the memory unit 9, and the output of the storage device 11 is connected to the first input of the digital information unit 13, the second input of which is connected to the second output of the synchronization signal generator 21, the output of the digital information unit 13 is connected to the first the input of the modulator 14 of each of the transmission channels 12, and the second input of the modulator 14 is connected to the information outputs of the memory unit 9, the output of each N-th modulator 14 is the output of each N-th channel 12, which through the input combiner 15 of the grouping unit The first signal 16 is connected to the first input of the modulator 17 of the group signal generating unit 16, the second input of which is connected to the first output of the synchronization signal generator 21, and the output is the output of the group signal generating unit 16, which is connected to the transmitting unit through the phase modulation unit 18 and the power amplifier 19 an antenna 20, wherein the input of the clock generator 21 is connected to the output of the clock 52, which is connected in parallel to the clock input of the clock 6; receiving equipment (Fig. 1) comprising a high-frequency selection unit 40, the input of which is connected to the receiving antenna 39, and the output is connected to the first input of the synchronization signal detection unit 41 and the second inputs of the correlation processing unit 36 of each of the 2 ^m-1 channels 35, and the output of the correlation processing unit 36 is connected to the first input of the information extraction unit 37, the second input of which is connected to the output of the clock pulse generator 53, and the output of the synchronization signal detection unit 41 through the search unit 42 is connected to the generator input copies of synchronization signals 43, the first output of which is connected to the second input of the synchronization signal detection unit 41, the second is connected to the control input of the synchronization unit 29, the output of which is connected to the control input of the shift register 30, the outputs of which are the second inputs of the corresponding blocks of “And” elements 26 and the third output of the generator of copies of synchronization signals 43 is connected to the first control input of the block of the element "AND" 44, the output of which is connected to the control input of the storage device 34, information from the 1st to the Nth input the odes of which are connected to the information from the 1st to the Nth outputs of the memory block 32, and the output of the synchronization block 29 is connected to the control input of the memory block 31, the information from the 1st to the Nth outputs of which are the first inputs of the calculators 24, and the second input of each Nth (N is the dimension of the coefficient matrix) calculator 24 receives a signal from the Nth output of the iterative process control signal generation unit 51, which is completely identical to the signal generated by the iterative process control signal generation unit 50 on the third side, and the third inputs of the calculators 24 of the first column of the matrix are connected to the logical zero input of the copying unit of chaotic ensembles of orthogonal signals, and from the outputs of the calculators 24 the signals are sent to the first and second inputs of the division blocks 25 and through the first inputs of the blocks of the element “And” 26 to the second inputs of the first and second columns of the matrix of calculators 24, the second outputs of the calculators 24.3.1, 24.3.2, 24.3.3 are connected to the information from the 1st to the Nth input of the memory block 32, the information from the 1st to (N- 1) whose outputs are connected with the first inputs of the operating units 27 of the first column, and the output of the operating unit 27 of the first column and the first row is connected to the Nth input of the memory block 32, and the outputs of the operating units 27 of the first column of the jth (i = 2, N-1) row connected to the first inputs of the operational blocks 27 of the jth (j = 2, N-1) column of the i-th (i = 1, N-1) row, while the operational blocks of each of the columns are interconnected, the second inputs of the operational blocks 27 associated with the output of the synchronization unit 29, and the second output of the operational unit 27 of the (N-1) -th row of the first column is connected to the second m the input of the delay element 28, the first input of which is connected to the output of the synchronization unit 29, and the output is connected to the first operation unit of the 27th (N-1) -th row of the (N-1) -th column, while the information outputs of the operation units 27 j- of the ith (j = N-1) column of the ith (i = 1, N-1) row are connected to the information from the 2nd through the Nth inputs of the memory block 32, while the clock pulses from the synchronization block 29 simultaneously arrive at the input of the ring shift register 33, to the control input of the memory unit 31 and 32, the control input of the random random number generator 45 and the memory Property 46, the information inputs of which from the 1st to the Nth are connected to the information from the 1st to the Nth outputs of the random positive number generator 45, and the information outputs from the 1st to the Nth are connected to the information from the 1st on the N-th inputs of the memory block 31, while the control output of the annular shift register 33 is connected to the second input of the block of the element "And" 44, the output of which is connected to the control input of the storage device 34, the N-th output of which is connected to the second input of the N-th block correlation processing 36 of each of the channels 35, the second control output The ring register 33 from the 1st to the Nth are connected from the 1st to the Nth control input of the memory unit 32, and the output of each of the correlation processing units 36 is connected to the first input of the information extraction unit 37, the second input of which is connected to the output a clock generator 53, which is parallel connected to the clock input of the synchronization unit 29 and the clock input of the generator of copies of the synchronization signals 43, while the output of the information extraction unit 37 is connected to the input of the information reception unit 38.

The device operates as follows. Information signals are received in the storage device 11 of each of the transmission channels 12 and stored in it until the control signal is received from the block of the "I" element 47, indicating the completion of the stage of stochastic formation of the orthogonal system of signals described by the eigenvectors of diagonal positive definite symmetric matrices of dimension N in the block for generating chaotic ensembles of orthogonal signals 48. Then, the information bit of each of the channels 12 through the digital information block AI 13 is fed to modulator 14, where it is modulated by an expanding sequence from the memory block 9 of the block for generating chaotic ensembles of orthogonal signals 48. The signals taken from the output of the modulator 14 of each channel are simultaneously fed to the adder 15 of the group signal generating block 16, where after combining and superimposing in the modulator 17 a synchronization signal from the output of the synchronization signal generator 21, a group signal is formed, the spectrum of which, after being transferred to the carrier region The frequencies in the phase modulation unit 18 and the power amplifier 19 are radiated through the antenna 20. At the receiving side, the incoming signal is received by the antenna 39 and pre-processed in the high-frequency selection block 40. From the output of this block, the signal is simultaneously supplied to the synchronization signal detection unit 41 and the correlation processing units 36 of each channel 35. In this case, the synchronization signal detection unit 41 together with the unit search 42 enter into synchronism the generator of the copy of the synchronization signals 43. Then, from the generator of copies of the synchronization signals 43, a control signal is supplied to the synchronization unit 29 of the block the formation of copies of ensembles of chaotic orthogonal signals 49, indicating the beginning of the formation of copies of chaotic ensembles of orthogonal signals by the block of the formation of copies of chaotic ensembles of orthogonal signals 49. The supply of the control signal to the block of the element “I” 44 from the ring shift register 33 of the block of the formation of copies of chaotic ensembles of orthogonal signals 49 says the completion of the stage of formation of orthogonal code sequences and recording them in the storage device 34. Then, under the influence receiving the control signal from the block of the “I” element 44, copies of chaotic ensembles of orthogonal signals are supplied from the memory 34 to the correlation processing blocks 36 of each of the communication channels 35 and, passing through the first input of the information extraction unit 37, the second input of which contains a copy of the synchronization signal with a generator of copies of synchronization signals 43 are sent to the input of the information receiving unit 38.

At the same time, on the transmitting side, the block for the formation of chaotic ensembles of orthogonal signals 48 functions as follows: if there is no information signal at the input of the And element 47 from the ring shift register 10, the synchronization block 6 of the block for the formation of chaotic ensembles of orthogonal signals 48 is activated, from the output of which a control signal to the control input of the random random number generator 22 and the storage device 23, resulting in the generation and recording of random coefficients ienti matrix A in the memory block 8, after this begins the calculation of the 1st eigenvalue and its corresponding eigenvector, which is carried out during the time spent "1" in the 1st digit of the shift register 7, therefore, the period of receipt of clock pulses on the clock input of the register shift 7 is equal to the convergence time of the iterative process and the calculation of the remaining part of the components of the eigenvector.

During the first period of operation "1" from the output of the first bit of the shift register 7 is supplied to the second inputs of the blocks of elements "And" 3.1.1 and 3.1.2. At the second input of the block of the element “AND” 3.2.1, “0” comes from the output of the second bit of the first shift register 7, as a result, “0” is formed at the output of block 3.2.1.

With the arrival of a sequence of clock pulses from the synchronization unit 6, the coefficients in the first memory unit 8 are sequentially fed to the first inputs of the calculators 1 and stored in them. The calculators also perform the accumulation function each time a new term is supplied to their input.

с блока генерации сигналов управления итерационным процессом 50.At the second inputs of the calculators 1, in addition to the last, arbitrary signals

from the iterative process control signal generation unit 50.

At the second inputs of the computers 1 of the last column there is a signal "1".

.Therefore, to implement the iterative procedure for finding the eigenvalue λ _{1 of the} matrix A, the vector is chosen as the initial approximation

.

At the output of the last calculator 1 of the last row of the matrix, a signal is formed:

which is the first approximation of the eigenvalue λ ₁ .

At the output of the last calculator of the 11th line (i = 1 ... n-1), a signal is generated

where i = 1,2 ... n-1.

This signal is the ith component of the first non-normalized approximation of the first eigenvector of the coefficient matrix A:

.

.

. Так как в результате нормирования последняя компонента равна 1, то ее деление не производится и «1» поступает на вторые входы последнего столбца матрицы вычислителей 1. Нормирование остальных компонент осуществляется при помощи блоков 2.1.1 и 2.1.2 путем деления компонент на величину последней компоненты

. Сигнал с выхода блока 2.1.1 деления через первый вход блока 3.1.1 поступает на вторые входы вычислителей 1.2.1 и 1.3.1, т.е. вычислителей 1 первого столбца матрицы. Сигнал с выхода блока деления 2.1.2 через первый вход блока 3.1.2 поступает на второй вход вычислителя 1.3.2, т.е. вычислителя 1 второго столбца матрицы.The first approximation of the first vector is normalized by dividing all its components by the value of the last component

. Since, as a result of normalization, the last component is equal to 1, its division is not performed and “1” goes to the second inputs of the last column of the matrix of calculators 1. The remaining components are normalized using blocks 2.1.1 and 2.1.2 by dividing the components by the value of the last component

. The signal from the output of division block 2.1.1 through the first input of block 3.1.1 is fed to the second inputs of calculators 1.2.1 and 1.3.1, i.e. calculators 1 of the first column of the matrix. The signal from the output of the division block 2.1.2 through the first input of the block 3.1.2 goes to the second input of the calculator 1.3.2, i.e. calculator 1 of the second column of the matrix.

Thus, in accordance with the ratio:

where i = 1,2 ..., N-1, after the end of the first iteration, at the second outputs of the calculators 1.3.1, 1.3.2, 1.3.3 there are signals corresponding to the components of the first normalized approximation of the first eigenvector:

.

.

Then the iterative process is repeated and after the second iteration is over, the second outputs of the calculators 1.3.1, 1.3.2, 1.3.3 present signals corresponding to the components of the second normalized approximation of the first eigenvector:

The iterations will be repeated until the iterative process is completely convergent. As a result, at the 'second outputs of calculators 1.3.1, 1.3.2, 1.3.3 there are signals corresponding to the components of the normalized first eigenvector:

,

,

.and at the output of the calculator 1.3.3 there is a signal corresponding to the eigenvalue

.

Thus, for matrix A, the system of equations solved by the iteration method, in accordance with relations (5) and (7), is as follows:

After convergence of the iterative process is realized at the second outputs of calculators 1.3.1, 1.3.2, 1.3.3, the values of the components of the first eigenvector will be obtained, and at the output of the calculator 1.3.3, the first eigenvalue will be obtained.

At the end of the time necessary to realize the convergence of the iterative process, the components of the first eigenvector are written by means of clock pulses supplied from the synchronization unit 6 to the second memory unit 9. At the next time, the clock input of the shift register 7 receives a clock pulse, under the influence of which "1" from the first bit of the shift register 7 is shifted to the second bit.

Thus, “1” from the output of the second digit of the shift register 7 goes to the second input of the second factor of the multiplication block 3.2.1. At the second inputs of the second factors of the multiplication blocks 3.1.1 and 3.1.2, “0” is received from the output of the first bit of the shift register 7, as a result, “0” is generated at the outputs of the blocks 3.1.1 and 3.1.2.

,

второго собственного вектора необходимо методом итерации решить систему уравненийTo determine the second eigenvalue and component

,

the second eigenvector, iteratively solve the system of equations

и

. Полученную систему уравнений необходимо решить методом итерации, но для этого нужно предварительно сформировать коэффициенты

. Для этого используются коэффициенты

, записанные в блоке памяти 8.For matrix A, the second system of equations solved by the iteration method is determined from the condition of orthogonality of the vectors

and

. The resulting system of equations must be solved by the iteration method, but for this it is necessary to form the coefficients first

. For this, the coefficients are used

recorded in memory unit 8.

, а на входы вторых вычислителей 1.1.2 и 1.2.2 сигнала «1» начнется реализация итерационного процесса. После достижения сходимости итерационного процесса на выходе делителя 2.2.1, а соответственно на выходе вычислителя 1.2.1 будет получено значение

, на выходе вычислителя 1.2.2 будет присутствовать сигнал

, а также значение

.After applying to the inputs of the second calculators 1.1.1 and 1.2.1 an arbitrary signal

, and the inputs of the second calculators 1.1.2 and 1.2.2 of the signal "1" will begin to implement the iterative process. After convergence of the iterative process is achieved, at the output of the divider 2.2.1, and, accordingly, at the output of the calculator 1.2.1, the value

, at the output of the calculator 1.2.2 there will be a signal

as well as the meaning

.

и

второго собственного вектора окажутся записанными в элементах памяти блока памяти 9.At the end of the time necessary to realize the convergence of the iterative process due to the arrival of clock pulses, the components

and

the second eigenvector will be recorded in the memory elements of the memory block 9.

определяется за счет решения уравнения с одним неизвестным с использованием известного устройства для операций над матрицами, способного решать уравнения или системы из n уравнений с n неизвестными по методу Гаусса-Жордана. В его состав входят операционные блоки 4.1.1,4.1.2,4.1.3,4.1.4, элемент задержки 5. В нем выполняется обработка матрицы размерности N×M (N=1,2), которая представляет собой матрицу коэффициентов при неизвестных системы линейных уравнений, к которой справа дописана матрица размерности N×1 свободных членов.Component

determined by solving an equation with one unknown using a known device for operations on matrices, capable of solving equations or systems of n equations with n unknowns using the Gauss-Jordan method. It includes operational blocks 4.1.1,4.1.2,4.1.3,4.1.4, delay element 5. It processes the matrix of dimension N × M (N = 1,2), which is a matrix of coefficients for unknown a system of linear equations, to which a matrix of dimension N × 1 free terms is added to the right.

Thus, for example, to solve a system of two linear equations, matrix B of the form will arrive at the inputs of the device:

where B ₁₁ V ₁₂ V ₂₁ V ₂₂ are the coefficients of the unknowns, and B ₁₃ V ₂₃ are free terms.

Elements of the matrix B are supplied to the first inputs of the operating units 4 line by line with a shift by one clock cycle under the influence of clock pulses from the outputs of the synchronization unit 6 supplied to the second inputs of the operating units 4, i.e. the first line goes to the first input of the operation block 4.1.1, starting from the first clock cycle, the second line goes to the first input of the operation block 4.2.1, starting from the second clock, etc. At the outputs of the operating blocks 4.i.j (i = 1 ... n, j = n), a family of solutions of a system of linear equations is obtained.

Thus, solutions of a system of two equations are obtained at the outputs of operating blocks 4.1.2 and 4.2.2. Solving the equation with one unknown - at the output of the operating unit 4.1.1.

будет задействован только операционный блок 4.1.1. Коэффициент при неизвестном и свободный член будут вычислены блоком памяти 9.Therefore, when calculating the value

only operation block 4.1.1 will be involved. The unknown coefficient and the free term will be calculated by the memory unit 9.

с выхода операционного блока 4.1.1 поступает на информационный вход блока памяти 9 и с поступлением синхроимпульса оказывается записанным в элементе блока памяти 9.Value

from the output of the operation unit 4.1.1 is fed to the information input of the memory unit 9 and with the arrival of the clock pulse is recorded in the element of the memory unit 9.

Thus, the components of the second eigenvector of matrix A will be recorded in the memory unit 9.

At the end of the time required to calculate the components of the second eigenvector, a clock pulse is supplied to the clock input of the shift register 7, as a result of which the second bit of the shift register 7 is reset. Since the second input of the second factor of block 3.2.1 receives “0” from the output of the second bit of register 7, then “0” is generated at the output of block 3.2.1.

поступает на информационный вход блока памяти 9.The components of the third eigenvector are calculated as follows. The second inputs of the calculators 1.1.1, 1.2.1, 1.3.1 signal “1”. From the output of block 1.3.1 value

arrives at the information input of the memory block 9.

и

.After that, the components are calculated

and

.

вычислено и записано в элементе памяти, то полученная система линейных уравнений легко решается методом Гаусса-Жордана.Since the value

calculated and written in the memory element, the resulting system of linear equations is easily solved by the Gauss-Jordan method.

и

поступающие на входы блока памяти 9.In accordance with the algorithm of operation of operating blocks 4, the outputs of blocks 4.1.2 and 4.2.2 will generate values, respectively

and

arriving at the inputs of the memory block 9.

Thus, the components of the third eigenvector of the matrix A will be recorded in the elements of the memory unit 9. This completes the process of calculating the components of the eigenvectors of the matrix A. The values of the components of the eigenvectors are stored in the memory unit 9.

The clock pulses from the synchronization unit 6 simultaneously arrive at the clock input of the annular shift register 10, the control input of the random random number generator 22, where the coefficients of the matrix A are randomly generated and fed to the information inputs of the storage device 23, which is under the influence of a control signal supplied to its second input, writes the generated coefficients to the memory unit 8.

Before starting work, a code of the form “10 ... 0” is written in the ring shift register 10, with “1” in the first bit of the ring shift register 10. Since a periodic sequence of pulses arrives at the clock input of the ring shift register 10, then “1” moving from the discharge in the category of the annular shift register 10, controls the formation of discrete basis functions at the outputs of the memory unit 9. In this case, the reading is performed in columns.

Along with applying a sync pulse to the annular shift register 10, an information signal “1” is supplied to the element “AND” 47, as a result of which a control signal is generated at the output of the element 47.

In a similar way, a block for generating copies of chaotic ensembles of orthogonal signals 49 functions on the receiving side, which is triggered by a generator of a copy of synchronization signals 43.

An example of a specific implementation of the method of transmitting information in systems with code division multiplexing

As an example, we consider the case when 3 communication channels are used to transmit a sequence of information bits, in which the information bit is modulated by a chaotic spreading sequence (N = 3 is chosen to simplify the calculations). Suppose that the information sequence “1 0 1” is fed to the inputs of the storage devices 11 of each of the transmission channels 12 and a random sequence of matrix coefficients A of 3 × 3 dimension generated by a random number generator 22 is pre-entered into the memory unit 8:

.

.

A code of the form “100” is recorded in the shift register 7, wherein “1” is recorded in the first bit of the shift register 7.

The sequence of information bits shown in Fig.2 b, c, d, bit by bit arrive at the first inputs of the storage devices 11 of the respective transmission channels 12. Next, the bits are written to the storage devices 11 of each of the transmission channels 12 and wait for the control signal from the block of the element “AND” 47 for their further transmission to the digital information block 13 and modulation by the expanding sequence in the modulator 14. The absence of a signal from the block of the “I” element 47 indicates the beginning of the formation of orthogonal systems in a stochastic manner signals described by the eigenvectors of diagonal positive definite symmetric matrices, as a result of which the synchronization unit 6 begins to function, from the output of which a control signal is supplied to the control input of the random random number generator 22 and memory 23, as a result of which random matrix coefficients are generated and recorded And in the memory block 8, after that, the calculation of the 1st eigenvalue and the corresponding eigenvector (first expanding The sequence) that is carried out during the residence time of "1" in the 1st discharge of the shift register 7, however period Incoming clock pulses to the clock input of the shift register 7 is the convergence time of the iterative calculation process and the remaining part of the eigenvector components.

During the first period of operation "1" from the output of the first bit of the shift register 7 is supplied to the second inputs of the blocks of elements "And" 3.1.1 and 3.1.2. At the second input of the block of the element “AND” 3.2.1, “0” comes from the output of the second bit of the first shift register 7, as a result, “0” is formed at the output of block 3.2.1.

With the arrival of a sequence of clock pulses, the coefficients in the first memory block 8 are sequentially fed to the first inputs of the calculators 1 and stored in them. Moreover, the calculator also performs the accumulation function each time a new term is applied to its input.

На вторых входах вычислителей 1 последнего столбца присутствует сигнал «1».At the second inputs of the calculators 1, in addition to the last, arbitrary signals

At the second inputs of the computers 1 of the last column there is a signal "1".

.Therefore, to implement the iterative procedure for finding the eigenvalue λ _{1 of the} matrix A, the vector is chosen as the initial approximation

.

At the second output of the last calculator 1 of the last row of the matrix, a signal is formed in accordance with relation (5), which is the first approximation of the eigenvalue λ ₁ .

.At the output of the last calculator 1 of the 1st row (i = 1 ... n-1), a signal is generated that is formed on the basis of relation (6). This signal is the ith component of the first non-normalized approximation of the first eigenvector of the coefficient matrix A

.

. Так как в результате нормирования последняя компонента равна «1», то ее деление не производится и «1» поступает на вторые входы последнего столбца матрицы вычислителей 1. Нормирование остальных компонент осуществляется при помощи блоков 2.1.1 и 2.1.2 путем деления компонент на величину последней компоненты

. Сигнал с выхода блока 2.1.1 деления через блок 3.1.1 поступает на вторые входы вычислителей 1.2.1 и 1.3.1, т.е. вычислителей 1 первого столбца матрицы. Сигнал с выхода блока 2.1.2 деления через блок 3.1.2 поступает на второй вычислителя 1.3.2, т.е. вычислителя 1 второго столбца матрицы.The first approximation of the first vector is normalized by dividing all its components by the value of the last component

. Since, as a result of normalization, the last component is “1”, its division is not performed and “1” is fed to the second inputs of the last column of the matrix of calculators 1. The remaining components are normalized using blocks 2.1.1 and 2.1.2 by dividing the components by the value last component

. The signal from the output of division block 2.1.1 through block 3.1.1 is fed to the second inputs of calculators 1.2.1 and 1.3.1, i.e. calculators 1 of the first column of the matrix. The signal from the output of block division 2.1.2 through block 3.1.2 goes to the second calculator 1.3.2, i.e. calculator 1 of the second column of the matrix.

.Thus, in accordance with relation (7), after the end of the first iteration, the outputs of calculators 1.3.1, 1.3.2, 1.3.3 present signals corresponding to the components of the first normalized approximation of the first eigenvector

.

.Then the iterative process is repeated and after the second iteration is over, the second outputs of the calculators 1.3.1,1.3.2,1.3.3 present signals corresponding to the components of the second normalized approximation of the first eigenvector

.

, а на втором выходе вычислителя 1.3.3 присутствует сигнал, соответствующий собственному значению λ₁.The iterations will be repeated until the iterative process is completely convergent. As a result, at the second outputs of the calculators 1.3.1, 1.3.2, 1.3.3 there are signals corresponding to the components of the normalized first eigenvector

, and at the second output of the calculator 1.3.3 there is a signal corresponding to the eigenvalue λ ₁ .

Thus, for matrix A, the system of equations solved by the iteration method is presented in relation (8).

,

,

а на втором выходе вычислителя 1.3.3 будет получено первое собственное значение λ₁=0,8077.After the convergence of the iterative process is realized at the second outputs of calculators 1.3.1, 1.3.2, 1.3.3, the values of the components of the first eigenvector will be obtained

,

,

and at the second output of the calculator 1.3.3, the first eigenvalue λ ₁ = 0.8077 will be obtained.

At the end of the time necessary for convergence of the iterative process to be realized, by means of a clock pulse, the components of the first eigenvector, which is presented in Fig. 2, are recorded in the second memory block 9. At the next time moment, a clock pulse arrives at the clock input of the shift register 7, under the impact of which "1" from the first bit of the shift register 7 is shifted to the second bit.

Thus, “1” from the output of the second bit of the shift register 7 is input to the second factor of the multiplication block 3.2.1. At the inputs of the second multipliers of the blocks 3.1.1 and 3.1.2 of the multiplication, “0” is received from the output of the first bit of the shift register 7, as a result, “0” is generated at the outputs of the blocks 3.1.1 and 3.1.2.

,

второго собственного вектора необходимо методом итерации решить систему уравнений в соотношении (9).To determine the second eigenvalue and component

,

of the second eigenvector, it is necessary to solve the system of equations in relation (9) using the iteration method.

и

. Так какFor matrix A, the second system of equations solved by the iteration method is determined from the condition of orthogonality of the vectors

and

. As

,

,

Then

Substituting this expression into the view system

, получимand putting

we get

с использованием соотношения (9). Для этого используются коэффициенты

, записанные в блоке 8 памяти.System (13) must be solved by the iteration method, but for this it is necessary to formulate the coefficients first

using relation (9). For this, the coefficients are used

recorded in block 8 of the memory.

, а на входы вторых вычислителей 1.1.2 и 1.2.2 сигнала «1» начнется реализация итерационного процесса. После достижения сходимости итерационного процесса на выходе делителя 2.2.1, а соответственно на выходе вычислителя 1.2.1 будет получено значение

, на выходе вычислителя 1.2.2 будет присутствовать сигнал

, а также второе собственное значение

.After applying to the inputs of the second calculators 1.1.1 and 1.2.1 an arbitrary signal

, and the inputs of the second calculators 1.1.2 and 1.2.2 of the signal "1" will begin to implement the iterative process. After convergence of the iterative process is achieved, at the output of the divider 2.2.1, and, accordingly, at the output of the calculator 1.2.1, the value

, at the output of the calculator 1.2.2 there will be a signal

as well as the second eigenvalue

.

и

второго собственного вектора окажутся записанными в элементах памяти блока памяти 9.At the end of the time necessary to realize the convergence of the iterative process due to the arrival of clock pulses, the components

and

the second eigenvector will be recorded in the memory elements of the memory block 9.

определяется из соотношения (12), т.е. уравнения с одним неизвестным с использованием известного устройства для операций над матрицами, способного решать уравнения с одним неизвестным или системы из n уравнений с n неизвестными по методу Гаусса-Жордана. В его состав входят операционные блоки 4.1.1, 4.1.2, 4.1.3, 4.1.4, элемент 5 задержки, блок 6 синхронизации. В нем выполняется обработка матрицы размерности N×M (N=1,2), которая представляет собой матрицу коэффициентов при неизвестных системы линейных уравнений, к которой справа дописана матрица размерности N×1 свободных членов.Component

is determined from relation (12), i.e. single-unknown equations using a well-known device for operations on matrices capable of solving equations with one unknown or a system of n equations with n unknowns using the Gauss-Jordan method. It includes operational blocks 4.1.1, 4.1.2, 4.1.3, 4.1.4, delay element 5, synchronization block 6. It performs processing of a matrix of dimension N × M (N = 1,2), which is a matrix of coefficients for unknown systems of linear equations, to which a matrix of dimension N × 1 free terms is added to the right.

Thus, for example, to solve a system of two linear equations, the inputs of the device will receive the matrix B, relation (10).

The elements of the matrix are supplied to the inputs of the operating units 4 line by line with a shift of one clock cycle under the influence of clock pulses from the outputs of the synchronization unit 6, i.e. the first line goes to the first input of the operation block 4.1.1, starting from the first clock cycle, the second line goes to the first input of the operation block 4.2.1, starting from the second clock, etc. At the outputs of the operating blocks 4.i.j (i = 1 ... n, j = n), a family of solutions of a system of linear equations is obtained.

Thus, solutions of a system of two equations are obtained at the outputs of operating blocks 4.1.2 and 4.2.2. Solving the equation with one unknown - at the output of the operating unit 4.1.1.

будет задействован только операционный блок 4.1.1. Коэффициент при неизвестном и свободный член будут вычислены блоком 9 памяти.Therefore, when calculating the value

only operation block 4.1.1 will be involved. The unknown coefficient and the free term will be calculated by the memory unit 9.

с выхода операционного блока 4.1.1 поступает на информационный вход блока 9 памяти и с поступлением синхроимпульса оказывается записанным в блоке памяти 9.Value

from the output of the operation unit 4.1.1 is fed to the information input of the memory unit 9 and with the arrival of the clock pulse is recorded in the memory unit 9.

;

;

, который представлен на фиг.2, е.Thus, in the block of memory 9 will be written the components of the second eigenvector of matrix A:

;

;

, which is presented in figure 2, e.

At the end of the time required to calculate the components of the second eigenvector, a clock pulse is supplied to the clock input of the shift register 7, as a result of which the second bit of the shift register 7 is reset. Since the input of the second factor of block 3.2.1 receives “0” from the output of the second bit of register 7, then “0” is generated at the output of block 3.2.1.

поступает на информационный вход блока 9 памяти. С поступлением синхроимпульса на вход блока 9 памяти значение

записывается в элемент памяти.The components of the third eigenvector are calculated as follows. The second inputs of the calculators 1.1.1, 1.2.1, 1.3.1 signal “1”. From the output of block 1.3.1 value

arrives at the information input of block 9 of the memory. With the arrival of the clock on the input of block 9 of the memory value

written to the memory element.

и

с использованием соотношений ортогональности:After that, the components are calculated

and

using orthogonality relations:

вычислено и записано в элементе памяти, то систему уравнений (14) можно представить в виде:Since the value

calculated and written in the memory element, the system of equations (14) can be represented as:

This system of linear equations is easily solved by the Gauss-Jordan method. Since the coefficients' for unknowns and free terms are written in block 9 of the memory, then equation (15) is solved as follows.

When a clock pulse arrives, the value 0.7720 is read and fed to the input of the operating unit 4.1.1.

Upon receipt of the clock, the value "1" is read and fed to the input of the operating unit 4.2.1.

Similarly, all remaining values are read.

;

, поступающие на входы блока 9 памяти.In accordance with the algorithm of operation of operating blocks 4, the outputs of blocks 4.1.2 and 4.2.2 will generate values, respectively

;

coming to the inputs of block 9 of the memory.

;

;

, которые представлены на фиг.2, е. На этом процесс вычисления компонент собственных векторов матрицы А заканчивается. Значения компонент собственных векторов хранятся в блоке 9 памяти.Thus, the components of the third eigenvector of matrix A will be recorded in the elements of memory block 9:

;

;

, which are presented in figure 2, e. On this process of calculating the components of the eigenvectors of the matrix A ends. The values of the components of the eigenvectors are stored in block 9 of the memory.

After the extension sequences are generated, clock pulses are sent from the synchronization unit 6 to the input of the shift register 10 and, as a result, to the second control input of the block of the “I” element 47. After that, the information bits are modulated by the extension sequence in the modulator 14 of each of the transmission channels 12. Moreover, the expansion of the information sequence occurs if the information bit is equal to one due to the use of the orthogonal signal of the inverse structure, if the information the ith bit is equal to zero due to the use of an orthogonal signal of direct structure (see Stolings B. Wireless communication lines and networks: Transl. from English. - M.: Williams Publishing House, 2003. - P.213).

Then, in the group signal generation unit, all the modulated signals are combined and, through the phase modulation unit 18 and the power amplifier 19, are transmitted through the transmission antenna 20.

Simultaneously with the modulation process, the formation of new coefficients of the diagonal symmetric matrix A in the random random number generator 22 and their recording in the memory unit 8 through the storage device 23.

On the receiving side, the reverse procedure occurs.

The use of random numbers as coefficients of a diagonal positive definite symmetric matrix of matrices makes it possible to increase the number of possible code sequences used to transmit a sequence of informational messages.

To confirm that the proposed information transmission system has increased structural secrecy in comparison with the prototype, we calculate the number of all possible ensembles of orthogonal signals generated by these systems. Therefore, we will consider matrix A of the following structure:

.

.

where α _1,1 , α _2,2 , α _3,3 ... α _{N, N} - coefficient of the main diagonal;

(α _1,2 , and _2,1 ), (α _1,3 , α _3,1 ) ... (α _{N-1, N} , α _{N, N-1} ) are symmetrical elements of the upper and lower diagonal.

To calculate the number of signal ensembles in the proposed device, the formula for disordered combinations with repeating elements was used (see Volkovets A.I. Probability Theory and Mathematical Statistics: Workshop for students of all special BSUIR full-time courses / A.I. Volkovets, A. B. Gurinovich. - Mn .: BSUIR, 2003. P.5):

where n is the range of possible values of the diagonal coefficients of the matrix A;

k is the number of elements of a diagonal symmetric matrix of dimension N located below or above the main diagonal.

The formula for calculating k:

where N is the dimension of matrix A.

To calculate the number of de Bruin code dictionaries used in the prototype, the formula was used as extension sequences (see patent of the Russian Federation No. 2234191, CL Н04В 7/216, H04L 9/26 07/24/2001):

where b _i is the number of elements in the i-th substitution cycle V ₁₀ containing two or more elements;

m is the number of memory elements of the shift register;

d is the total number of substitution cycles V ₁₀ with two or more elements.

The calculation results, which are presented in Fig. 3, show that with an increase in the n elements used to calculate chaotic ensembles of orthogonal multilevel signals, the number M of possible signal structures increases compared to the number of Q signals generated from de Bruin code dictionaries.

In accordance with the proposed method, for the transmission of each bit, a new chaotic ensemble of orthogonal multilevel signals should be used, therefore, if we ensure the change of chaotic ensembles of orthogonal multilevel signals with a period equal to T ₀ , where T ₀ = 1 / R is the time interval for using the chaotic ensemble of orthogonal multilevel signals equal to the duration of the information bit, and R is the information bit rate, then the repetition period of the chaotic ensemble of orthogonal multilevel signals will be determined by the ratio:

According to relation (19), when the data transfer rate R is 1 Mbit / s, the dimension N of matrix A is 256 and the range of possible values of n is 10, then the repetition period of one chaotic ensemble of orthogonal multilevel signals will be 3.54 × 10 ²² years.

This suggests that when transmitting identical sequences of bits, the generated spreading sequences will not be repeated for a long time.

In accordance with relations (16) and (17), the calculation of the number of signal ensembles, which can be generated on the basis of a diagonal symmetric matrix A of dimension N = 4 × 4, is carried out as follows:

.

.

where α _1,1 , α _2,2 , α _3,3 , α _4,4 are the coefficients of the main diagonal of the matrix A;

α _1,2 , α _1,3 , α _1,4 , α _2,3 , α _2,4 , α _3,4 are the coefficients of the matrix A, located above the main diagonal;

α _2,1 , α _3,1 , α _3,2 , α _4,1 , α _4,2 , α _4,3 - the coefficients of the matrix A, located under the main diagonal;

Assume that the range of n possible values of the diagonal coefficients of matrix A is 5 (n = 5).

1. The number of elements of the diagonal symmetric matrix A, located below or above the main diagonal, is calculated in accordance with the relation (17):

.

.

2. The number of ensembles of discrete multilevel orthogonal signals is calculated in accordance with relation (16):

3. In accordance with relation (19), we calculate the repetition period of one chaotic ensemble of orthogonal multilevel signals for a diagonal symmetric matrix A at a transmission rate equal to R = 1000 kBit / s:

.

.

For clarity in figure 2, the same signal was repeated 3 times, while, as can be seen in figure 2 g, h, and, none of the extension sequences were repeated.

Claims (1)

The method of transmitting information in systems with code division multiplexing consists in the use of orthogonal code combinations for transmitting messages exchanged from one information symbol to another, characterized in that ensembles of discrete orthogonal signals are used as orthogonal code combinations formed by calculating their own of numbers and eigenvectors of a diagonal positive definite symmetric matrix whose diagonal coefficients are randomly formed numerical sequence.

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