Method for transmitting information using a MIMO system

Abstract

The invention relates to information transmission systems, and more particularly to methods for implementing a MIMO system. The present method for transmitting information uses a MIMO system in an N=2n, n=2, 3, 4 hypercomplex space, wherein trains of binary data pulses that consist of zeros and ones, arriving at the input of a transmitting device, are converted into bipolar pulses which are converted into an N-dimensional information vector consisting of N information pulses and forming a hypercomplex number represented by a vector. The technical result is an increase in interference resistance and information transmission speed in wireless and wired communication.

Description

[0001] METHOD OF TRANSMITTING INFORMATION USING MIMO SCHEME

[0002] DESCRIPTION

[0003] The invention relates to information transmission systems and, in particular, to methods for implementing the MIMO scheme [H04B7 / 0413].

[0004] The prior art discloses a METHOD AND SYSTEM FOR WIRELESS COMMUNICATION MIMO,

[0005] USING JOINT HADAMAR TRANSFORM AND ALAMUTI SCHEME

[0006] (KR20160010799(A), published 28.01.2016) comprising: modulating data into digital symbols, performing a Hadamard transform on the modulated symbols to generate a new constellation; and encoding the generated constellation using the Alamouti method as input data. Wherein, in the modulation step, the QPSK scheme is modulated by a combination of the Hadamard transform and the Alamouti scheme. Wherein, in the transform step, two points of the modulated symbol are combined into one symbol by using a combination of the Hadamard transform and the Alamouti scheme. Wherein, in the transform step, a new constellation is created by summing or subtracting two points by using a combination of the Hadamard transform and the Alamouti method.In this case, the MIMO wireless communication system comprises: a modulator for modulating data into digital symbols on the transmission side of the MIMO wireless communication system; a converter for Hadamard transforming the modulated symbol to create a new constellation; and an encoder for encoding the generated constellation as input data using the method.

[0007] Alamouti. In this case, the modulator is a MIMO wireless communication system with QPSK modulation using a combination of the Hadamard transform and the Alamouti transform, and the converter combines two points of the modulated symbol into one symbol by combining the Hadamard transform and the Alamouti scheme. In this case, the converter generates a new constellation by summing or subtracting two points.

[0008] The disadvantage of the analogue is the low speed of information transfer. Also known is the METHOD OF DATA TRANSMISSION IN THE COMMUNICATION SYSTEM "MIMO" (RU2553679C2, published 20.06.2015) using space-time coding, which uses a mapping table that maps a set of symbols to antennas and to transmission resources, which can be time intervals or sections of the OFDM frequency band. The mapping table contains nested primary segments of Alamouti codes, namely Alamouti coding at the symbol level, inside secondary segments, which can contain Alamouti coding of primary segments.

[0009] The disadvantage of the analogue is the low speed of information transfer.

[0010] The closest in technical essence is the METHOD OF DATA TRANSFER

[0011] USING SPACE-TIME BLOCK CODES (US2008063110

[0012] A1, publ., 13.03.2008) which is characterized by the fact that For data transmission a set of at least 2 is provided m nxn matrices that represent an extension of the group without fixed points. Each of the 2 m matrices are assigned a unique binary number in the range from 0 to 2 m -1, thereby ensuring that data is identified and displayed according to a particular distribution.

[0013] For optimal transmission, the mapped matrices are recommended to be sent using n antennas, where each antenna corresponds to one row of each matrix, which provides multidimensional space-time coding with maximum bandwidth and data transmission reliability.

[0014] The main technical problem of the prototype is the limited throughput, since the use of the space-time block code method

[0015] (STBC) in the multiple-input multiple-output (MIMO) scheme, the system requires the transmission of additional information to encode data blocks, which leads to an increase in the transmission duration. This limits the throughput of the system and can lead to deterioration in performance under conditions with limited data transmission time. As a result, the information transfer rate is low.

[0016] Another technical problem of the prototype is low noise immunity, since the space-time block codes (STBC) method can be sensitive to interference and distortion, especially in channels with negative correlation between MIMO antennas. This can lead to deterioration of the quality of received data and increase the probability of errors during decoding, as a consequence of low noise immunity.

[0017] The objective of the invention is to eliminate the shortcomings of analogues and the prototype.

[0018] The technical result of the invention is to increase noise immunity and information transfer speed in wireless and wired communication systems.

[0019] The specified technical result is achieved due to the fact that the method of transmitting information using the MIMO scheme in N=2 n, n = 2, 3, 4 hypercomplex space, characterized in that the sequences of binary data pulses consisting of zeros and ones arriving at the input of the transmitting device are converted into bipolar pulses, which are converted into an N-dimensional information vector consisting of N information pulses and forming a hypercomplex number in vector representation, wherein the modulation on the transmitting side is carried out by multiplying the information vector by a hypercomplex carrier, which is a hypercomplex number in polar form with different N-1 reference frequencies in matrix representation and which plays the role of the channel matrix MIMO channel, wherein the multi-frequency channel matrix MIMO is decomposed into a sum of single-frequency matrices, which are modulated separately and their results are added, forming multi-frequency elements of the N-dimensional vector,wherein the phase-modulated elements of the output multi-frequency modulated vector are transmitted sequentially in time either with code division or with frequency division, wherein the signal vectors are coherently demodulated by multiplying the received vector by the transposed basis matrices of single-frequency matrices representing an orthogonal basis, and the reception of the signal vector arriving at the input of the receiver is carried out using the integration of the results of the multiplication with subsequent addition for each single-frequency matrix of the orthogonal basis and making a decision in the decision device about the value of the vector elements.

[0020] In particular, a hypercomplex carrier is a hypercomplex number in polar form and in matrix representation as a square matrix NxN with N-1 reference frequencies, the combinations of which form 2 N-2 combination frequencies, and the same number of single-frequency matrices.

[0021] Brief description of the drawings.

[0022] Fig. 1 shows the vectors of information pulses in the form of a quaternion for a positive value of the first element of the information vector.

[0023] Fig. 2 shows the vectors of information pulses in the form of a quaternion for a negative value of the first element of the information vector.

[0024] Fig. 3 shows a three-frequency phase-modulated vector with information vector X0=[11-11] No. 2.

[0025] Fig. 4 shows a three-frequency phase-modulated vector with information vector X0=[1-1-11] No. 6.

[0026] Fig. 5 shows single-frequency phase-modulated vectors for the information vector X0=[11-11] No. 2.

[0027] Fig. 6 shows single-frequency phase-modulated vectors for the information vector X0=[1-1-11] No. 6.

[0028] Fig. 7 shows the orbit of rotation of the scalar part of the three-frequency quaternion for the initial vector X0=[11-11].

[0029] Fig. 8 shows the orbit of rotation of the scalar part of a three-frequency quaternion for the initial vector X0=[1-1-11].

[0030] Fig. 9 shows the orbit of rotation of the scalar part of the three-frequency quaternion for the initial vector X0=[-11-11].

[0031] Fig. 10 shows the orbit of rotation of the scalar part of the three-frequency quaternion for the initial vector X0=[-1-1-11].

[0032] Fig. 11 shows the result of demodulation using the basis matrix E, with a frequency

[0033] Fig. 12 shows the result of demodulation using the basis matrix I, with a frequency

[0034] Fig. 13 shows the result of demodulation using the basis matrix J, with a frequency

[0035] Fig. 14 shows the result of demodulation on the basis matrix with frequency Fig. 15 shows the sum of the values ​​for the basis matrices with frequency

[0036] Fig. 16 shows the result of demodulation using the basis matrix with frequency

[0037] Fig. 17 shows the result of demodulation on the basis matrix with frequency

[0038] Fig. 18 shows the result of demodulation using the basis matrix ) with frequency

[0039] Fig. 19 shows the result of demodulation on the basis matrix with frequency

[0040] Fig. 20 shows the sum of the values ​​over the basis matrices with frequency

[0041] Fig. 21 shows the result of demodulation on the basis matrix with frequency

[0042] Fig. 22 shows the result of demodulation on the basis matrix with frequency

[0043] Fig. 23 shows the result of demodulation on the basis matrix with frequency

[0044] Fig. 24 shows the result of demodulation using the basis matrix. with frequency

[0045] Fig. 25 shows the sum of the values ​​for the basis matrices with frequency

[0046] Fig. 26 shows the result of demodulation using the basis matrix with frequency

[0047] Fig. 27 shows the result of demodulation on the basis matrix with frequency

[0048] Fig. 28 shows the result of demodulation on the basis matrix with frequency

[0049] Fig. 29 shows the result of demodulation on the basis matrix with frequency

[0050] Fig. 30 shows the sum of the values ​​for the basis matrices with frequency. Fig. 31 shows the sum of the values ​​for all frequencies.

[0051] Fig. 32 is a functional block diagram showing the structure of an illustrative wireless transmitter.

[0052] Fig. 33 is a functional block diagram illustrating the structure of an illustrative wireless receiver.

[0053] The figures indicate: 1 - information source, 2 - hypercomplex number encoder, 3 - hypercomplex number modulator, 4 - transmitting antenna, 5 - receiving antenna,

[0054] 6 - hypercomplex number demodulator, 7 - hypercomplex number decoder, 8 - information receiver.

[0055] Implementation of the invention.

[0056] Let us consider a method of transmitting information using the MIM0 scheme in a hypercomplex space using a quaternion.

[0057] A quaternion represents a hypercomplex number that has three imaginary units i, j, k.

[0058] In algebraic form, we write the quaternion as

[0059] (1) where s, x, y, z are real numbers.

[0060] Let us present operations with imaginary units in the form of a table.

[0061] Table 1. Operation of multiplication of imaginary units of a quaternion.

[0062] As is known, in radio engineering and information transmission problems real signals are used, therefore, in order to get rid of imaginary units, we will represent the quaternion in algebraic form (1) in matrix form:

[0063] (2)

[0064] Determinant of the matrix |Q| . The matrix Q is orthogonal because

[0065] We write imaginary units in the matrix representation for matrix (2) as

[0066] The matrices of imaginary units together with the identity matrix with units on the main diagonal E diag[l 1 1 1], are called the basis matrices of the quaternion. The matrix of the quaternion (2) is written using the basis matrices (3) and the identity matrix

[0067] E, how

[0068] (4)

[0069] For the basis matrices (3), a multiplication table similar to Table 1 is valid:

[0070] Table 2. Operation of multiplication of imaginary units of a quaternion in matrix representation.

[0071] For quaternion (1) we write the exponential function as

[0072] (5)

[0073] Note that when x = y = z, expression (5) takes the form: ) Where

[0074] Just as for a complex number in an exponential mapping, the coefficients of the imaginary units of a quaternion in polar notation have the physical meaning of the angle of rotation. Therefore, we write the angles in (5) as functions of time: - angular frequencies on the axes We will assume that is the radius of rotation in 4D space.

[0075] After multiplying the expressions in parentheses in formula (5) and grouping by real and imaginary parts, we obtain an exponential function in the form of a three-frequency quaternion, which we denote as

[0076] After reducing similar terms, the components in expression (6) of the exponential function of the three-frequency quaternion will take the form:

[0077] We write the exponential function of the three-frequency quaternion (5) in matrix form using the obtained expressions (7), as

[0078] With the matrix representation (8) of expression (6), we obtain a three-frequency fundamental matrix

[0079] (9) We represent the basis matrices (9) in the form (4):

[0080] (10) j ( y y )

[0081] We write the decomposition of the fundamental matrix (9) in terms of basis matrices as Expression (5) for a unit radius can also be represented in matrix form, using single-frequency matrices:

[0082] (12)

[0083] By multiplying single-frequency basis matrices (12), we obtain matrix (9).

[0084] Thus, the fundamental matrix of a 3-frequency quaternion (9) can be represented as the sum of the basic 3-frequency matrices (11) or as the product of single-frequency matrices (12).

[0085] Let us consider the basic properties of the fundamental matrix of a three-frequency quaternion in the form of a sum (11) and a product (12). The fundamental matrix (9) is orthogonal, since

[0086] The determinant of matrix (9) is calculated using (7) as

[0087] Substituting expression (7) into the determinant formula, we obtain

[0088] The determinant of the product of basis single-frequency matrices (12) is equal to the determinant

[0089] 3-frequency matrix (9):

[0090] According to the well-known property of the product of determinants, the determinant of the product of single-frequency fundamental matrices for different frequencies is equal to the product of the determinants of these matrices:

[0091] From here,

[0092] As can be seen from (10), we have obtained 8 combinations of products of cosines and sines of different frequencies. To transform expressions (7), we use the well-known trigonometry formulas for products of three combinations with sines and cosines. According to these formulas, products of three sines and cosines in different combinations are transformed into the sum of sines and cosines from the sum of frequencies in different combinations.

[0093] Let us denote the resulting combinations of angular frequencies as

[0094] (13)

[0095] The corresponding matrix for transforming reference frequencies into combination frequencies has the form:

[0096] (14)

[0097] The corresponding combination frequencies are obtained in the form of a vector by multiplying the vector of reference frequencies by matrix

[0098] The matrix of transformation of combination frequencies into reference frequencies is calculated from (14) as

[0099] Let's look at an example:

[0100] After calculating the products of sines and cosines in (10) using the indicated trigonometry formulas, reducing similar terms and grouping by frequencies, we obtain the following expressions For exponential functions (10) For combination frequencies (13): Substituting expressions (15) for combination frequencies into the product matrix (12) and grouping the terms by frequencies, we obtain a representation of the fundamental matrix as a sum of single-frequency matrices: (16) where The corresponding normalized basis matrices for combination frequencies are denoted as .

[0101] In the process of correlation reception, when integrating the products of the basis matrices by the corresponding transposed matrices (17) over the duration T=1, we obtain that where m=l, 2, 3, 4.

[0102] Thus, we have obtained expressions for the exponential function (5) of a three-frequency quaternion in the form of a sum of functions (6), which are represented by 8 combinations of products of cosines and sines of reference frequencies (7). Also, using trigonometry formulas for products of three combinations with sines and cosines, we have obtained the exponential function (5) in the form of sums of cosines and sines

[0103] (15) different frequency combinations (13).

[0104] Multi-frequency matrix manipulation.

[0105] We will represent possible combinations of binary symbols as vectors of initial states written in a matrix:

[0106] (18)

[0107] The amplitude of the information vectors is equal to

[0108] The power of information vectors is equal to

[0109] The three-frequency fundamental matrix (9) will be used as the channel matrix of the MIMO channel in the mathematical model of the information transmission system. When using the carrier frequency, the reference frequencies will be shifted by the value of the carrier, forming spectra on positive and negative reference frequencies. Since the inverse transformation occurs when receiving signals on the carrier frequency, we will consider the channel matrix on the reference and combination frequencies.

[0110] We will write the manipulation in the form of multiplication of the initial state vector by a three-frequency fundamental matrix of reference frequencies, which we will define by analogy with the methods of modulation of signals considered on the real axis or plane, as a “quaternion carrier”, in the general case - a “hypercomplex carrier”:

[0111] (19)

[0112] As a result of multiplication, we obtain the modulated output vector

[0113] Since the multi-frequency matrix is ​​equal to the sum of single-frequency matrices (16), then the manipulation of single-frequency matrices will, accordingly, have the form:

[0114] (20)

[0115] Let us write (20) in the form of separate output vectors: (21)

[0116] Possible combinations of information vectors (18) are represented as states in

[0117] 3D space, as shown in Figures 1 and 2. In Figure 1, the nodal points show the positive values ​​of the most significant bit of the information vector, in Figure 2, the nodal points show the negative values ​​of the most significant bit of the information vector.

[0118] The elements of the vector (19) can be transmitted using different types of division: code, frequency or time.

[0119] Figures 3 and 4 show the output vector (19) plotted in time for the reference frequencies for two possible combinations initial state vectors. A negative frequency for a sine wave simply means a change in the sign of the amplitude.

[0120] Since the fundamental matrix (9) is orthogonal and does not change the norm of the information vector, the powers of the elements of the output vector are equal to 1.

[0121] Figures 5 and 6 show graphs of the elements of the output vectors (21) for four single-frequency matrices with two combinations of information vectors.

[0122] With 4 non-zero values ​​of the elements, the amplitude will be the power taking into account the coefficient for the harmonic we get 1 / 4.

[0123] The amplitude of the elements of the output vectors of single-frequency matrices can be for 2 elements and 0 for the other 2 elements. The power of an element taking into account the coefficient 1 / 2 for the harmonic will be , i.e. the power of 1 element will be 2 times less.

[0124] In sum over the elements, the vector power will be 1 for the elements of the vectors in figure 5 and in figure 6. The power of one vector of a single-frequency matrix will be 1. For 4 vectors over single-frequency matrices, the power will be equal to 4.

[0125] Thus, the power of the output vector will be equal to the power of the input vector over the multi-frequency and the sum over the single-frequency matrices.

[0126] Figures 7 and 8 show the graphs of the orbits of rotation of the scalar part of the quaternion for various initial vectors normalized to 1 with a positive scalar part representing the most significant digit of the binary vector. Figures 9 and 10 show the graphs of the orbits of rotation of the scalar part of the quaternion for the same initial vectors normalized to 1 with a negative scalar part representing the most significant digit of the binary vector.

[0127] In total, we obtain 8 orbits for the positive value of the scalar part and 8 orbits for the negative scalar part. We group these orbits by identical trajectories and write them down as numbers of information vectors (18):

[0128] 1, 6 and 11,16 2,3 and 14,15 4, 7 and 10, 13 5, 8 and 9,12.

[0129] As can be seen, we have a total of 4 different trajectory configurations for four different information vectors. When exposed to interference in the form of a 4D white noise vector with central symmetry, the interference will not be correlated even if the trajectory is the same, since the initial states are located in different places on the trajectory.

[0130] It is known that for a single-frequency quaternion there are also 4 trajectories of rotation of the scalar part. However, these trajectories are located on planes in 3D. For a three-frequency quaternion, since the rotation for 4 combination frequencies will be at different speeds, the trajectory will be more complex and in 3D the trajectories cover a much larger 3D space and, as a result, the signals have a significantly greater diversity. As is known, the greater the diversity of the signal, the less it is susceptible to interference and the higher the speed of information transfer can be obtained. In the extreme case, when the signal is similar to white noise and occupies the entire volume, we obtain the bandwidth of the MIM0 channel. Note also that the power, and, consequently, the length of the rotation vector, remains constant.

[0131] When passing through the communication channel, interference is added to the modulated oscillations from combination frequencies. As interference, we consider 4D white noise with circular symmetry. As a result, we obtain a signal vector with interference:

[0132] Since white noise is considered as interference, the optimal receiver for each element is a correlator.

[0133] Demodulation of the received vector will be performed by normalized transposed basis matrices (17) for each single-frequency matrix separately, in which the combination frequencies will be replaced by reference frequencies in accordance with (13). Multiplication of the received sequence of vector elements s(t) by the elements of the basis matrices and their integration with subsequent summation of the results is performed in real time without pulse delay. At the end of the accumulation of signal energy, a reading is made, which is stored. Since each element of the sequence s(t) contains all the elements of the information vector, then when multiplying it by the elements of the columns of the basis matrices, we obtain estimates of all four information elements. Subsequently, all readings of each element for all the basis matrices of each single-frequency matrix are added up and fed to the decision device.

[0134] Figures 11-30 show the results of multiplying the received vector by the basis matrices of single-frequency matrices after integration over the pulse duration.

[0135] Figure 31 shows the sum of the results for the 4-frequency matrices.

[0136] When receiving the elements of the output vector (19) by multiplying by the basic orthogonal matrices, the vector norm does not change. However, in this case, the elements of the interference vector are rearranged in accordance with the structure of the matrices E, I, J, K.

[0137] Therefore, when adding the elements of the vectors, they are added by energy, and the elements of the interference vector are added by power. Therefore, for each matrix, we obtain a gain in the signal / noise ratio, compared to receiving real signals with BPSK, by a factor of 4. Since the reception of the same values ​​is carried out at different frequencies, the total gain in the signal / noise ratio with uncorrelated interference and with sufficient frequency spacing to eliminate their influence on each other will be equal to 16, if we do not consider the increase in the frequency band. Usually, when working in high-frequency wave ranges, an increase in the band does not entail any large costs.

[0138] The technical result of the invention is an increase in noise immunity and the speed of information transmission in wireless and wired communication systems, which is achieved due to the fact that the sequences of binary data pulses consisting of zeros and ones and y's arriving at the input of the transmitting device are converted into bipolar pulses, which are converted into an N-dimensional information vector consisting of N information pulses and forming a hypercomplex number in a vector representation, while ensuring a greater energy distance (in comparison with physical space, space-time code), as well as the effective use of the N-dimensional hypercomplex space of the hypercomplex number in time and frequency, an increase in the noise immunity of the transmitted information, as a result, an increase in the speed of information transmission is achieved.

[0139] In this case, modulation on the transmitting side is carried out by multiplying the information vector by a hypercomplex carrier, which is a hypercomplex number in polar form with different N-1 reference frequencies in matrix representation and plays the role of the channel matrix MIMO channel, while the multi-frequency channel matrix MIMO is decomposed into a sum of single-frequency matrices, which are modulated separately and their results are added, forming multi-frequency elements of an N-dimensional vector, while the phase-modulated elements of the output multi-frequency modulated vector are transmitted sequentially in time or with code division, or with frequency division, thereby achieving a reduction in the number of transmitting and receiving antennas due to the use of one antenna for transmission and one antenna for reception,whereby the use of N-dimensional hypercomplex space and rotation of information elements during modulation of the quaternion carrier allows maximizing the energy distance between information elements, which leads to improved noise immunity, higher speed of transmitted information, efficient use of frequency resources and increased secrecy of information transmission, as a result of which an increase in noise immunity and speed of information transmission is achieved.

[0140] In this case, since the channel matrix of the MIMO channel is orthogonal, the norm of the information vector before data transmission through the communication channel will be equal to the norm of the information vector after transmission, if the channel does not change it, as a result of which an increase in noise immunity and information transmission speed is achieved.

[0141] In this case, the gain in signal-to-noise ratio when using a single-frequency quaternion channel matrix, compared to receiving real signals with

[0142] BPSK, 4x and 16x for 4-frequency channel matrix of combination frequencies.

[0143] In this case, the output vector power will be equal to the input vector power for multi-frequency and in total for single-frequency matrices, thus, the information transmission system maintains the signal power at each frequency or in each individual channel, as a consequence: 1. Resources are used effectively: there is no excess energy loss or sharp changes in power (peak factor) at different frequencies. This allows for optimal use of the transmitter amplifier power and the available bandwidth of the communication channel;

[0144] 2. Interference suppression: Since each information pulse is transmitted at each time position and at each frequency of the modulated signal and the signal power is maintained at all frequencies and all time positions, the system can be more resistant to external interference. Interference at one frequency will not affect the signal power at other frequencies and time positions.

[0145] This is especially important in the case of multipath fading or the presence of other sources of interference, as well as in the case of frequency-selective and time-selective fading;

[0146] 3. Maintaining high-quality information transmission: Since the signal power does not change, the quality of the transmitted data is maintained. This is especially important for the transmission of analog or digital signals, where changing the power can lead to data distortion;

[0147] 4. Convenient processing: When the input vector power is equal to the output vector power, signal processing becomes more predictable and convenient. There is no need to correct or compensate for differences in signal power at different frequencies.

[0148] As a result, increased noise immunity and information transfer speed are achieved.

[0149] In this case, the overall gain in signal-to-noise ratio with uncorrelated interference will be equal to 16, not counting the increase in frequency band.

[0150] In this case, the interference on the orthogonal basis is not correlated, as a consequence:

[0151] 1. Improved signal separability: interference can be more effectively separated from desired signals;

[0152] 2. Improved reception quality: Interference does not add up or amplify with each other. This means that signals can be received with less distortion and loss of quality. Uncorrelated interference does not interfere with the main transmission frequencies;

[0153] 3. Increased Security: Uncorrelated interference makes it more difficult or more difficult for unauthorized people to access or hack into a communications system. Uncorrelated interference can make it difficult or impossible to extract sensitive information from a transmitted signal;

[0154] 4. More efficient use of RF spectrum: Uncorrelated interference can be better isolated and suppressed by using RF spectrum. This allows for efficient use of available frequency bands, minimizing the mutual influence of signals and interference.

[0155] As a result, increased noise immunity and information transfer speed are achieved.

[0156] In this case, the signal vectors are coherently demodulated by multiplying the received vector by the transposed basis matrices of single-frequency matrices, which represent an orthogonal basis, and the signal vector arriving at the receiver input is received using the integration of the multiplication results with subsequent addition for each single-frequency matrix of the orthogonal basis and making a decision in the decision device about the value of the vector elements. In this case, it is sufficient to calculate the carrier oscillation phase using conventional synchronization methods and there is no need to know the phase from each transmitting antenna to each receiving antenna in order to determine the parameters of the space-time code. Usually, feedback, a pilot signal and a complex computing device are used to obtain such data. Thus, the technology of separate reception of information elements by the basis matrices of the quaternion is implemented, as a consequence:

[0157] 1. Improved spectral efficiency: increasing the signal-to-noise ratio and the ability to transmit information at a higher speed;

[0158] 2. Increased noise immunity of reception;

[0159] 3. Increased data transmission secrecy, since each information symbol is contained in each symbol of the transmitted vector and in one way or another changes its modulation parameters. Therefore, without knowing the channel matrix and its frequencies, it is impossible to isolate the information symbols.

[0160] In this case, it is possible to evaluate each element of the information vector under the influence of various interferences, since the interferences are decomposed into components on an orthogonal basis, and with a narrow-band spectrum they do not affect the information elements transmitted at other frequencies. As a result, an increase in noise immunity and the speed of information transmission is achieved.

[0161] In this case, the hypercomplex carrier is a hypercomplex number in polar form and in matrix representation as a square matrix NxN with N-1 reference frequencies, the combinations of which form 2 N-2 combination frequencies, and the same number of single-frequency matrices.

[0162] When using multi-frequency hypercomplex carriers in general, or, in the particular case, three-frequency quaternion carriers, the modulated signals have a greater variety, i.e. they occupy a larger volume of hypercomplex space, as shown in Figures 7-10. As a consequence, they are less susceptible to interference that differs from white noise and is concentrated in time (pulse interference) or in frequency (narrowband interference). Since when exposed to interference of the type

[0163] "white noise" bandwidth is determined by the difference between the diversity of the signal and the entropy of the interference, then using hypercomplex multifrequency space it is possible to achieve a higher diversity of the signal than with conventional methods of modulating real signals on the plane, even with an increase in the number of levels of signal amplitudes or frequencies. As a result, the bandwidth of such channels is significantly increased.

[0164] According to Fig. 32 and 33, Information source 1 converts binary pulses 0, 1 arriving at the input into bipolar pulses 1, -1 and, in the general case, forms an N-dimensional information vector from them by appropriately delaying the pulses. In this case, the last pulse arrives without delay.

[0165] The hypercomplex number encoder 2 generates, in general, a hypercomplex multifrequency carrier in the form of an NxN matrix, in particular, a quaternion carrier in the form of a 4x4 matrix with three frequencies. The hypercomplex carrier is an exponential mapping of a hypercomplex number in matrix representation, which, in turn, is decomposed into a sum of single-frequency matrices.

[0166] The hypercomplex number modulator 3 performs the modulation of the hypercomplex carrier by multiplying the single-frequency matrices by the information vector with the subsequent addition of the results to obtain a modulated multi-frequency oscillation, in the particular case, a four-frequency oscillation. The modulated signals at the carrier frequency and amplified by the power amplifier are fed to the transmitting antenna 4. The antenna 4 radiates them in a given direction.

[0167] Receiving antenna 5 amplifies the received signal, which is then fed to a low-noise amplifier and transferred to the frequencies of the hypercomplex carrier.

[0168] The demodulator of hypercomplex numbers 6 carries out correlation reception in real time of the received modulated elements of the vector by multiplying it by the elements in the columns of the transposed basis matrices of single-frequency matrices of combination frequencies, followed by integration and addition of the results.

[0169] The hypercomplex number decoder 7 sums up the results of the correlation reception for all multifrequency matrices, in a particular case, for all 4-frequency matrices of a three-frequency quaternion, and feeds them to the decision device. The decision can be made for each information element of the vector separately or with the calculation of the Frobenius norm.

[0170] The information receiver 8 converts bipolar pulses 1, -1 into 0, 1 and supplies them to the consumer in the required representation.

[0171] Example of implementation.

[0172] The claimed method was implemented for a quaternion using a 4x4 channel matrix. An M-sequence generator on JK-triggers with feedback was used as a data source. To form a 4-dimensional data vector from incoming pulses, the first pulse was delayed by D-triggers for 3 cycles, the 2nd - for 2, the third for 1, and the 4th was received without delay in real time.

[0173] The three-frequency channel matrix of reference frequencies was represented as a sum of four single-frequency matrices of combination frequencies. To form single-frequency channel matrices, a high-frequency generator was used, which produced at the output two harmonic oscillations of combination frequencies shifted by n / 2, which formed the sum of a cosine and a sine with different signs in accordance with the structure of the channel matrix. Modulation was performed by multiplying the data vector by the elements of the columns of four single-frequency channel matrices using four multipliers for each matrix. A signal from a carrier generator of a given frequency was fed to one input of the multipliers, and the corresponding element of the pulse vector was fed to the other. The results obtained at the outputs of the multipliers for matrices of different combination frequencies were summed in adders, resulting in a four-dimensional vector of a multi-frequency signal.The described procedure corresponds to the multiplication of a 4-dimensional information vector by a three-frequency matrix of reference frequencies of a quaternion carrier.

[0174] The multiplication of the information vector by each column was carried out in one cycle of the information pulse duration and the resulting pulse in the form of a sum of 4 combination frequencies was transferred to the carrier frequency and transmitted sequentially in time through the power amplifier to the antenna. In this case, each element was transmitted using the entire power of the power amplifier.

[0175] When passing through the communication channel, noise was added to the signal. To obtain noise immunity characteristics, noise from a noise generator was additionally fed to the receiver input.

[0176] The received signal was transferred to the initial combination frequencies and received using correlators. Elements of 4 single-frequency basis matrices were used as reference frequencies, into which single-frequency matrices of combination frequencies were decomposed and represented an orthogonal basis.

[0177] All 16 multipliers with integrators for each single-frequency matrix were combined into a bus with 4 in each wire. Demodulation was performed in real time. When the first element arrived, it was fed to the first wire of the bus and multiplied by the elements of the first columns of the basic single-frequency matrices. At the end of accumulation, the results were counted and summed up over all elements of the column for all

[0178] 4 single-frequency matrices. The result of the sum of 16 readings was fed to the decision device, which made a decision on the value of the information pulse.

[0179] The error probability was determined by comparing the transmitted pulse with the received one.

[0180] Similar operations were performed upon receipt of the 2nd received pulse, which was fed to the 2nd bus wire, etc.

[0181] The signal-to-noise ratio was measured using a selective millivoltmeter. The result was a 16-fold increase in signal-to-noise ratio compared to BPSK and an 8-fold increase compared to the Alamouti scheme with MIM0 2x2.

Claims

FORMULA 1. Method of transmitting information using the MIMO scheme in N=2 n, n = 2, 3, 4 hypercomplex space, characterized in that the sequences of binary data pulses consisting of zeros and ones arriving at the input of the transmitting device are converted into bipolar pulses, which are converted into an N-dimensional information vector consisting of N information pulses and forming a hypercomplex number in vector representation, wherein modulation on the transmitting side is carried out by multiplying the information vector by a hypercomplex carrier, which is a hypercomplex number in polar form with different N-1 reference frequencies in matrix representation and which plays the role of the channel matrix MIMO channel, wherein the multi-frequency channel matrix MIMO is decomposed into a sum of single-frequency matrices, which are modulated separately and their results are added, forming multi-frequency elements of an N-dimensional vector,wherein the phase-modulated elements of the output multi-frequency modulated vector are transmitted sequentially in time either with code division or with frequency division, wherein the signal vectors are coherently demodulated by multiplying the received vector by the transposed basis matrices of single-frequency matrices representing an orthogonal basis, and the reception of the signal vector arriving at the input of the receiver is carried out using the integration of the results of the multiplication with subsequent addition for each single-frequency matrix of the orthogonal basis and making a decision in the decision device about the value of the vector elements.

2. A method for transmitting information using a MIMO scheme in a hypercomplex space according to claim 1, characterized in that the hypercomplex carrier is a hypercomplex number in polar form and in a matrix representation in the form of a square matrix NxN with N-1 reference frequencies, the combinations of which form 2 N-2combination frequencies, and the same number of single-frequency matrices.

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