RU2476986C1 - Method of measuring time of arrival of signal and apparatus for realising said method - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method of measuring the time of arrival of a four-position quadrature phase-shift keyed signal with a π/4 shift is characterised by that the signal is received, analogue-to-digital conversion of two signals is carried out using fast Fourier transform (FFT), spectrum values of one of the signals are multiplied with complex-conjugate spectrum values of the other signal, a discrete cross-correlation function (DCCF) of the signal is calculated using inverse FFT, a plurality of in-phase and quadrature readings are obtained and filtered with a cut-off frequency which corresponds to half the rate of the initial bit message, modulo 2π subtraction of the corresponding value of the delayed current signal phase from each obtained current phase is carried out, and the time of arrival of the signal is determined as an argument of the maximum of the DCCF of the signal by further correlation processing. The apparatus has units for implementing the method.

EFFECT: eliminating measurement errors caused by non-multiplicity of the duration of the signal symbol and sampling frequency of analogue-to-digital conversion of the received signal.

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Description

The invention relates to radio engineering and can be used to measure the arrival time of signals with four-position (quadrature) phase shift keying with a shift of π / 4 at the receiving position.

The measurement of the arrival time (VP) of signals at the receiving position with known coordinates is of great importance in systems of long-distance space communications with spacecraft (SC) of the Mars Polarlander, Mars Pathfinder type [1] or with the Voyager and Galileo type spacecraft [2], including to determine the motion parameters of such spacecraft.

A number of methods are known for measuring VP signals, including from spaced receiving positions [3-6], based on finding the arguments for the maximum of a two-dimensional cross-correlation function, which potentially give statistically optimal, most plausible estimates. However, the potential accuracy of the methods [3-6] is not feasible in practice due to the lack of continuously adjustable standards of time and frequency [7, 8].

A number of digital methods are known for measuring VP signals from spaced receiving positions [8], based on finding the argument of the maximum of the cross-correlation function or the argument of the minimum of the differential discrete cross-correlation functions (DKKF), allowing to realize the potential accuracy of the methods [3-6] by eliminating discreteness errors by parabolic interpolation of the neighborhoods of the maximum or minimum of the corresponding functions. However, digital methods for measuring VP signals [8–9] are not applicable in the presence of uncertainty in the frequency of reception, which occurs in systems of long-distance space communications with spacecraft. Another disadvantage of the digital measurement methods presented in [8] is the low computational efficiency on large data sample sizes, since they are based on the direct calculation of cross-correlation functions (with this method of finding cross-correlation functions, the number of multiplication operations is proportional to the square of the length (n ) data sampling, such proportionality is usually denoted as O (n ² )).

When measuring the airborne signal for determining the distance to the spacecraft, the uncertainty in the reception frequency inevitably arises, which can be caused both by the difference in the reference frequencies on the spacecraft and on the ground, as well as due to the Doppler effect caused by the mutual movement of the ground receiving position and the spacecraft. Therefore, in such cases, when measuring the IP signal, it is necessary to find the maximum of the two-dimensional cross-correlation function with the simultaneous resolution of the frequency uncertainty and, thus, measuring the reception frequency or the difference in the reception frequency (RFI).

In patents [10-12], a number of digital methods are presented for jointly measuring the difference in arrival time (RWP) and RFI of signals from spaced receiving positions, based on finding the arguments of the maximum of two-dimensional DKKF (DKKF), which allow measurements in the presence of movement of the signal source or receiving position . The main goal set by the author of patents [10-12] is devoted to reducing the flow of information transmitted between spaced receiving positions and compensating for the systematic error arising from the correlation of the compressed and reference signals. However, in the methods of joint measurement of RVP and RFI [10-12], the issues of eliminating discreteness errors are not resolved (the correlation between RVP and RFI [13] does not allow an obvious way to extend the approaches described in [8] to joint measurements) and questions of increasing the computational efficiency, since the cross-correlation functions in methods [10-12] are generated by the direct method through the convolution of two data sequences, as in [8], but due to n-fold repetition (to ensure the search for the maximum argument in the frequency domain), The number of multiplication operations increases and is proportional to the cube of the length (n) of the data sample, i.e. O (n ³ ).

Closest to the proposed method for measuring the VP signals, according to the totality of the actions used on the signal, is the method [14], based on finding the arguments of the maximum DKKF (computationally significantly more effective than analogues), adopted as a prototype.

According to this method:

1. Receive a signal at two spaced receiving positions.

2. Convert the signal received from one receiving position to the first digital data stream, which digitally represents the signal as a series of values of the time function.

3. Convert the signal received from another receiving position into a second digital data stream, which digitally represents the signal as a series of values of the time function.

4. Using the fast Fourier transform (FFT), the aforementioned first digital data stream is converted into the values of the first spectrum, which represents the signal as a series of values of the frequency function S ₁ (k), where k is an integer index variable that varies within the data length.

5. Using the FFT, the mentioned second digital data stream is converted into the values of the second spectrum, which represents the signal as a series of values of the frequency function S ₂ (k).

6. Mutually multiply the spectrum values of one of the signals with the complex conjugate values of the spectrum of another signal to generate a cross spectrum.

7. The spectrum of one of the signals S _i (k), where i = 1, 2 is the number of one of the two spectra, is converted in frequency by the values of m, selected according to the requirements for resolution of the RFI, from an integer series of values from unity to (N-1) where N is the length of the processed digital data stream, with the creation of a sequence of frequency-converted spectra S _{i, m} (k) obtained from the original spectral components of the signal according to the following rule

,

,

where i is the number of one of the two received signals.

8. The values of the spectra S _{i, m} (k) of the frequency-converted signals are mutually multiplied with the complex conjugate values of the spectrum of the second of the two source signals to generate multiple cross-spectra.

9. Calculate the DKKF signal using the inverse FFT multiple cross-spectra.

10. Determine the difference in the time of arrival and frequency of reception of signals as the arguments of the maximum DCCF signal.

In fact, the method described above [14] implements a computationally efficient, in comparison with analogs [10-12], finding the arguments of the maximum DKKF using fast Fourier transforms when calculating the DKKF based on the Wiener-Khinchin theorem [15], which determines the relationship between the spectrum and signal correlation function.

In the description of the prototype [14], an estimate of the amount of computational costs for finding a two-dimensional cross-correlation function in the prototype method and in analogues is presented, showing that ordering data of length n = 1024 with k = n in the prototype method for finding the DKKF requires about O (k · n · log ₂ n + k · n) or 10 million operations (page 10 of the description of the prototype method), and in analogs it is required from O (3 · k · n · log ₂ n + k · n) to O ( n ³ ) or from 30 million to a billion operations (page 5 of the description of the prototype method).

Despite a significant reduction in computing costs compared with analogues, one of the disadvantages of the prototype method is the lack of computing efficiency. Another disadvantage of the prototype method is, like its counterparts [10-12], a long time for finding the maximum argument, that is, a long measurement time.

The prototype device [14] contains the first means of receiving signals connected to the device for determining the arguments of the maximum DKKF through sequentially connected the first analog-to-digital Converter (ADC), the first FFT processor, a cross-spectrum computer and a second FFT processor. The output of the DCDCF maximum argument determination device is the output of the measurement device. Between the second signal receiving means and the second input of the cross-spectrum calculator, a second ADC and a third FFT processor are connected in series. Between the output of the first FFT processor and the third input of the cross-spectrum calculator, an arithmetic device is turned on.

The disadvantage of the prototype device is the lack of speed. Another disadvantage of the prototype device is the long time it takes to find the maximum argument, that is, a long measurement time.

The technical result of the invention is to increase computational efficiency by eliminating the uncertainty of the reception frequency, which eliminates the need for a two-dimensional search for the arguments of the maximum DKKF for a signal with four-position (quadrature) phase shift keying with a shift of π / 4, and thus dispense with the search for the maximum argument of the one-dimensional DKKF.

The technical result is achieved by the fact that in the method of measuring the time of arrival of a signal with four-position (quadrature) phase shift keying with a shift of π / 4, including receiving the signal, analog-to-digital conversion of the received signal into the first digital data stream representing the signal as a series of values of the time function converted to digital form, using the fast Fourier transform (FFT) for two signals, representing both signals as a series of discrete values of the frequency function S _i (k), where k is an integer index a variable that varies within the length of the data, and i = 1, 2 is an index variable that means the serial number of the digital data stream converted using the FFT into the values of the frequency function, the mutual multiplication of the spectrum values of one of the signals with the complex conjugate values of the spectrum of another signal, generating cross-spectrum, calculating a discrete cross-correlation function (DCF) of a signal using the inverse FFT, determining the arrival time (VP) of a signal as an argument of the maximum DCF of a signal according to the invention quadrature decomposition of the first digital data stream relative to the nominal center frequency of the modulated signal is carried out, corresponding to the specified stream, a plurality of in-phase and quadrature samples, the obtained in-phase and quadrature samples are independently low-pass filtered with a cut-off frequency corresponding to half the speed of the original bit message, a plurality of current signal phases are obtained, as arguments of complex numbers, the real part of which use the appropriate filter common-mode samples, and, as imaginary, the corresponding filtered quadrature signal samples, delay the set of received current signal phases by half the duration of the modulating symbol, subtract modulo 2π from each received current phase the corresponding value of the delayed current signal phase, and the resulting differential digital data stream is converted using the FFT in the values of the first frequency function S ₁ (k), the original bit message is sequentially-parallel divided into an in-phase bit signal Nal and quadrature bit signal, the received bit signals are converted into bipolar two-level signals with a single level, the quadrature two-level signal is sequentially multiplied by π / 4 and taken with the opposite sign and increased by two in-phase two-level signal, each value of the multiplication result is displayed by the corresponding number samples of the digitized received signal relative to the time scale of the receiving position and thus form a second digital data stream, which convert using FFT in the values of the second frequency function S ₂ (k).

Another technical result of the invention is the elimination of measurement error caused by the non-multiplicity of the duration of the signal symbol and the sampling frequency of the analog-to-digital conversion of the received signal.

The technical result is achieved by the fact that in the method of measuring the arrival time of the signal according to the invention for a signal for which the signal symbol duration is not a multiple of the sampling frequency of the analog-to-digital conversion of the received signal, the filtered in-phase and quadrature samples are additionally decimated and interpolated to provide a frequency multiplicity of the samples of the first digital data stream duration of the modulating signal symbol.

Another technical result of the invention is the elimination of the discreteness error due to the fact that the neighborhood of the main maximum of the discrete cross-correlation signal function has the shape of a parabola [13, p. 8-9], and due to the development of an optimal, in the mean-square sense, analytical method of estimation parameters of the parabola and determining the argument of its maximum.

определяют по следующему правилуThe technical result is achieved by the fact that in the method of measuring the time of arrival of the signal according to the invention, to the left and to the right of the maximum argument DKKF signal is selected by L points of the specified function, the DKKF values for the selected points and maximum points are combined in the order of time in a column vector c, from units form a column vector v ₀ of the same dimension as the vector corresponding to the selected points DKKF arguments expressed as index variable l = 0, ± 1, ..., ± L, where the indices l with a negative sign correspond to times d maximum point DKKF, zero index l corresponds to the maximum point DKKF and indices l with positive sign correspond to times when the maximum point DKKF arguments selected DKKF points are ordered in the same way as vector components, and combined into the column vector v _1, the squares of the components vectors v _{1 are} likewise combined into a column vector v ₂ , and the refined value of VP

determined by the following rule

- скалярное произведение векторов v₁ и с, коэффициент Р определяется выражениемwhere N = 2L + l is the dimension of the generated vectors, the superscript T denotes the transpose of the vector, T _s is the sampling period of the signal,

is the scalar product of vectors v ₁ and c, the coefficient P is determined by the expression

,

,

the coefficient Q is determined by another expression

,

,

and (NPv ₂ -P ² v ₀ ) ^T c is the scalar product of the difference vector (NPv ₂ -P ² v ₀ ) with the vector с.

The method is implemented by a signal arrival measuring device with a four-position (quadrature) phase shift keying with a shift of π / 4, containing a signal receiving means, the input of which is the input of a measuring device connected to an analog-to-digital converter (ADC), the first FFT processor, a cross computer are connected in series -spectrum, a second FFT processor and a device for determining the maximum arguments of a discrete cross-correlation function (DKKF) of the signal, the output of which is the output of the measurement device, while m, a third FFT processor is connected to the second input of the cross-spectrum calculator, according to the invention, between the ADC output and the input of the first FFT processor, a quadrature signal decomposition device, a first low-pass filter (LPF), read-only memory (ROM), and a subtraction modulo 2π , between the second output of the quadrature signal decomposition device and the second input of the ROM, a second low-pass filter is turned on, the subtracting input of the subtraction device is connected to the output of the ROM through a delay element for the duration of the symbols la signal and the third input of the FFT processor is connected to output driver bit message through successively connected in series-parallel converter, an arithmetic unit (AU) and a sampling frequency of the expander, wherein the second input UE connected to the second output serial-parallel converter.

Another technical result of the invention is the elimination of discreteness errors in the device due to the fact that the neighborhood of the main maximum of the DCQF signal has the shape of a parabola, and due to the analytical method for estimating the parameters of the parabola and determining the argument of its maximum.

The technical result is achieved in that in the device for measuring the signal arrival with four-position (quadrature) phase shift keying by π / 4 according to the invention, a second arithmetic device is additionally connected to the output of the device for determining the maximum argument of the discrete cross-correlation function of the signal.

Figure 1 presents an example of the complete phase of the signal in the presence of frequency detuning.

Figure 2 presents an example of a phase difference of signals with a shift by the duration of the symbol T.

Figure 3 shows the structural diagram of a device in which the proposed method is implemented.

According to the proposed method:

1. Receive a signal.

2. The received signal is converted into a first digital data stream representing the signal as a series of values of a time function converted to digital form.

3. Quadrature decomposition of the first digital data stream relative to the nominal center frequency of the modulated signal is carried out, in accordance with the specified stream, a plurality of in-phase and quadrature samples.

4. The obtained in-phase and quadrature samples are independently low-pass filtered with a cutoff frequency corresponding to half the speed of the original bit message.

5. A lot of current phases of the signal are obtained as arguments of complex numbers, the corresponding filtered common-mode samples are used as the real part, and the filtered filtered quadrature samples of the signal are used as the imaginary part.

6. Delay the set of received current signal phases for the duration of the modulating signal symbol.

7. Subtract modulo 2π from each received current phase the corresponding value of the delayed current phase of the signal.

8. Using the fast Fourier transform (FFT), the resulting differential digital data stream is converted, as the first digital data stream, to the discrete values of the first frequency function S ₁ (k), where k is an integer index variable that varies within the data length.

9. The original bit message is sequentially-parallel divided into a common-mode bit signal and a quadrature bit signal.

10. The received bit signals are converted into bipolar two-level signals with a single level.

11. A quadrature two-level signal is sequentially multiplied by π / 4 and taken with the opposite sign and increased by two in-phase two-level signal.

12. Each symbol of the received difference signal is mapped to the corresponding number of samples of the digitalized received signal relative to the time scale of the receiving position and, thus, a second digital data stream is generated.

13. Using the FFT, the said second digital data stream is converted into the values of the second spectrum, which represents the signal as a series of values of the frequency function S ₂ (k).

14. Mutually multiply the spectrum values of one of the signals with the complex conjugate values of the spectrum of another signal to generate a cross spectrum.

15. Calculate the discrete cross-correlation function (DKKF) signal using the inverse FFT cross-spectrum.

16. Determine the time of arrival of the signal as an argument to the maximum DKKF signal.

We show that in the proposed method of measuring the time of arrival of a signal with four-position (quadrature) phase shift keying with a shift of π / 4, the need for a two-dimensional search can be eliminated when finding the argument of the maximum DKKF.

A signal with four-position (quadrature) phase shift keying with a shift by π / 4 (often denoted as π / 4-QPSK) is described as follows [24]:

where θ _k is the value of the modulating phase symbol at the kth time interval, ϕ _c (t) = ω _c t + ϕ ₀ is the phase of the carrier, p (t) is a rectangular pulse with a unit amplitude of duration T, determined on the interval [-T / 2, T / 2], A is the amplitude of the signal, and ω _c is the carrier frequency.

The set of modulating phase positions θ _k for a signal with π / 4-QPSK is defined as θ _k ∈ {0, ± π / 4, ± π / 2, ± 3π / 4, ± π} [24]. Moreover, each k-th signal symbol can be represented as

s (t) = u _k cosϕ _c (t) -v _k sinϕ _c (t) = Acos (ϕ _c (t) + θ _k ), kT≤t≤ (k + 1) T

where the differentially encoded characters u _k and v _{k are} defined [24] in the form

the initial conditions of the differential encoder (3) of the signal with π / 4-QPSK u ₀ = 1 and v ₀ = 1, and the quadrature symbols I _k ∈ {± 1} and Q _k ∈ {± 1} are formed by series-parallel separation of the original bit messages [24-25] to a common-mode bit signal and a quadrature bit signal, followed by converting the received bit signals to bipolar two-level signals with a single level. The phase relations between two consecutive symbols are determined by the expressions [24]:

θ _k = θ _k-1 + Δθ _k

.

.

The full phase of the signal with π / 4-QPSK, taking into account (1), has the form

In the quadrature decomposition of signal (1), the carrier frequency of which is a priori unknown in the full phase of the signal, there will almost always be a frequency mismatch between the frequency of the signal carrier ω _c and the nominal frequency ω ₀ , relative to which the quadrature decomposition is performed, i.e., a component will be present in the full phase of the signal, linearly time-dependent, which corresponds to the second term of expression (4), which does not allow directly using the expression for the full phase for the formation of DKKF.

Figure 1 presents an example of the full phase of a signal with π / 4-QPSK in the presence of frequency detuning, showing the influence of a component that is linearly dependent on time.

From the example shown in Fig. 1, it can be seen that in the presence of a frequency detuning, the complete phase of the signal is not identical to the modulating function of the signal, and it cannot be directly used for one-dimensional correlation processing when determining the signal arrival time.

The phase difference with a shift by the duration of the symbol T eliminates the frequency detuning as a component that linearly depends on time

As can be seen from expression (5), the phase difference Ψ (t), with the exception of the constant bias ω ₀ T, determined by the magnitude of the frequency detuning, is uniquely associated with the differential-decoded modulating function of the signal (see figure 2).

Since the constant bias does not affect the argument of the cross-correlation function [19], the one-dimensional correlation processing of the difference modulating function of the signal (generated in the same way as the phase difference Ψ (t), that is, as the difference between the modulating function and the modulating function delayed by the symbol ) with the function of the phase difference of the signal позволит (t) will determine the time of arrival of the signal as an argument of the maximum cross-correlation function of these signals.

The correspondence of phase differences Δθ _k and quadrature symbols I _k and Q _k for a signal with π / 4-QPSK [24] is presented in the table below.

Table 1 I _k Q _k Δθ _k Δ _k +1 +1 π / 4 one +1 -one -π / 4 -one -one +1 3π / 4 3 -one -one -3π / 4 -3

Based on table 1, it is easy to show that the variable Δ _k is associated with the symbols I _k and Q _{k by the} following relation

Δ _k = Q _k (2-I _k )

,

,

and the difference phase Δθ _k corresponding to the phase difference Ψ (t) in continuous time is obtained from Δ _k after multiplying by π / 4. After each symbol of the received difference signal Δθ _k is mapped to the corresponding number of samples of the received signal digitized into digital form, it can be used as a reference copy for correlation with the signal Ψ (t) and for estimating the time of arrival of the signal by the argument of the maximum DKKF signal.

According to the second variant of the proposed method, eliminating the measurement error caused by the non-multiplicity of the duration of the signal symbol and the sampling frequency of the analog-to-digital conversion of the received signal:

1. Receive a signal.

2. The received signal is converted into a first digital data stream representing the signal as a series of values of a time function converted to digital form.

3. Quadrature decomposition of the first digital data stream relative to the nominal center frequency of the modulated signal is carried out, in accordance with the specified stream, a plurality of in-phase and quadrature samples.

4. The obtained in-phase and quadrature samples are independently low-pass filtered with a cutoff frequency corresponding to half the speed of the original bit message.

5. The filtered in-phase and quadrature samples are additionally decimated and interpolated to provide a frequency multiplicity of the samples of the first digital data stream of the signal symbol duration.

6. A plurality of current signal phases are obtained as arguments of complex numbers, the corresponding in-phase samples are used as the real part, and the corresponding quadrature samples of the signal are used as the imaginary part.

7. The set of received current signal phases is delayed by the duration of the modulating signal symbol.

8. Subtract modulo 2π from each received current phase the corresponding value of the delayed current phase of the signal.

9. Using the fast Fourier transform (FFT), the resulting differential digital data stream is converted, as the first digital data stream, into discrete values of the first frequency function S ₁ (k), where k is an integer index variable that varies within the data length.

10. The original bit message is sequentially-parallel divided into a common-mode bit signal and a quadrature bit signal.

11. The received bit signals are converted into bipolar two-level signals with a single level.

12. A quadrature two-level signal is sequentially multiplied by π / 4 and taken with the opposite sign and increased by two in-phase two-level signal.

13. Each symbol of the received difference signal is mapped to the corresponding number of samples of the digitized received signal relative to the time scale of the receiving position and, thus, a second digital data stream is generated.

14. Using the FFT, the said second digital data stream is converted into the values of the second spectrum, which represents the signal as a series of values of the frequency function S ₂ (k).

15. Mutually multiply the spectrum values of one of the signals with the complex conjugate values of the spectrum of another signal to generate a cross spectrum.

16. The discrete cross-correlation function (DKKF) of the signal is calculated using the inverse FFT cross-spectrum.

17. Determine the time of arrival of the signal as an argument of the maximum DKKF signal.

Irrelevance of the signal symbol duration and the sampling frequency of the analog-to-digital conversion of the received signal can be eliminated, for example, by polyphase filtering [18], which allows, due to interpolation and decimation, to provide an integer number of signal samples for the symbol duration over a finite time interval.

According to another variant of the proposed method, eliminating the discreteness error:

1. Receive a signal.

2. The received signal is converted into a first digital data stream representing the signal as a series of values of a time function converted to digital form.

3. Quadrature decomposition of the first digital data stream relative to the nominal center frequency of the modulated signal is carried out, in accordance with the specified stream, a plurality of in-phase and quadrature samples.

4. The obtained in-phase and quadrature samples are independently low-pass filtered with a cutoff frequency corresponding to half the speed of the original bit message.

5. A lot of current phases of the signal are obtained as arguments of complex numbers, the corresponding filtered common-mode samples are used as the real part, and the filtered filtered quadrature samples of the signal are used as the imaginary part.

6. Delay the set of received current signal phases for the duration of the modulating signal symbol.

7. Subtract modulo 2π from each received current phase the corresponding value of the delayed current phase of the signal.

8. Using the fast Fourier transform (FFT), the resulting differential digital data stream is converted, as the first digital data stream, to the discrete values of the first frequency function S ₁ (k), where k is an integer index variable that varies within the data length.

9. The original bit message is sequentially-parallel divided into a common-mode bit signal and a quadrature bit signal.

10. The received bit signals are converted into bipolar two-level signals with a single level.

11. A quadrature two-level signal is sequentially multiplied by π / 4 and taken with the opposite sign and increased by two in-phase two-level signal.

12. Each symbol of the received difference signal is mapped to the corresponding number of samples of the digitalized received signal relative to the time scale of the receiving position and, thus, a second digital data stream is generated.

13. Using the FFT, the said second digital data stream is converted into the values of the second spectrum, which represents the signal as a series of values of the frequency function S ₂ (k).

14. Mutually multiply the spectrum values of one of the signals with the complex conjugate spectrum values of another signal to produce a cross spectrum.

15. Calculate the discrete cross-correlation function (DKKF) signal using the inverse FFT cross-spectrum.

16. Determine the time of arrival of the signal as an argument to the maximum DKKF signal.

17. To the left and right of the argument of the maximum DKKF signal select L points of the specified function.

18. The values of DKKF for the selected points and maximum points are combined in the order of temporal sequence in the column vector c.

19. The column vector v _{0 of} the same dimension as the vector c is formed from units.

20. The arguments corresponding to the selected DKKF points are expressed through the index variable l = 0, ± 1, ..., ± L, where the indices l with a negative sign correspond to the times to the maximum point of the DKKF, the zero index l corresponds to the maximum point of the DKKF, and the indices l with the positive sign correspond to the times after the maximum point DKKF.

21. The arguments of the selected DKKF points are ordered as well as the components of the vector c, and combined into a column vector v ₁ .

22. The squares of the components of the vector v _{1 are} likewise combined into a column vector v ₂ .

23. Determine, according to the following rule, the specified value of VP

,

,

- скалярное произведение векторов v₁ и с, коэффициент Р определяется выражениемwhere N = 2L + 1 is the dimension of the generated vectors, the superscript T denotes the transpose of the vector, T _s is the signal sampling period,

is the scalar product of vectors v ₁ and c, the coefficient P is determined by the expression

,

,

the coefficient Q is determined by another expression

,

,

and (NPv ₂ -P ² v ₀ ) ^T c is the scalar product of the difference vector (NPv ₂ -P ² v ₀ ) with the vector с.

When digitally transforming a continuous signal, discreteness errors inevitably appear [17-18], their influence can be significantly reduced by interpolating the DCQF in the vicinity of the extremum, which does not entail significant computational costs arising from the interpolation of the signal as a whole.

A variant of the proposed method, which eliminates the discreteness error when estimating the parameters of a discrete cross-correlation function, is based on the fact that in the vicinity of the maximum the specified function has the shape of a parabola [13, p. 8-9], evaluating the parameters of which as a result of solving a system of linear equations, we can clarify the value of the arrival time, as an argument of the maximum DKKF, since DKKF is selective from the cross-correlation function in continuous time.

The equation describing the vertex of the cross-correlation function C _XY (γ) as a parabola has the form

For given samples with _n cross-correlation functions C _XY (τ)

where ξ _n is the error in specifying the CF samples, T _s is the sampling period.

For parabola (6), the estimate of the extremum point (in this case, the maximum, based on the meaning of the problem and the assumption of uniqueness of the extremum in the considered neighborhood) is determined by the relation

The estimates for the coefficients a, b in (8) can be obtained from a linear system of the form

where ξ is the vector of errors in specifying the samples of the cross-correlation function (7). In addition, an odd number of source data (7) is assumed in (9) and symmetric indexing n = -K, - (K-1), ..., -1, 0, 1, 2, ..., K is accepted, and although these assumptions are not essential for a general least squares (LSM) estimate, they do not detract from the generality, and their meaning will be explained later.

According to [22] OLS, the estimate of the coefficient vector for (9) and the delay estimate corresponding to (8) are of the form

where V ^† is a pseudo-inverse matrix, which, if there is W = (V ^T V) ^-1, has the form V ^† = WV ^T [22-23].

, определяемую в (8) за требуемое решение, заметим, что для ее получения в указанном виде должна быть использована операция обращения матрицы, что не всегда вычислительно эффективно, особенно при реализации слежения за задержкой в реальном времени. Матрица V^† не зависит от исходных измерений (7), и может быть рассчитана априорно, но она зависит от объема данных N. При таком подходе необходимо хранить набор матриц для различных N, либо требовать работы с всегда фиксированным объемом, что тоже может оказаться не оптимальным. Кроме того, при вычислении оценки

согласно первому выражению в (10) осуществляются затраты на оценку

не используемую далее. С целью повышения вычислительной эффективности получим для величины

тождественные соотношения видаAccepting grade

defined in (8) for the required solution, we note that to obtain it in the indicated form, the matrix inversion operation should be used, which is not always computationally effective, especially when real-time delay tracking is implemented. The matrix V ^† does not depend on the initial measurements (7), and can be calculated a priori, but it depends on the volume of data N. With this approach, it is necessary to store a set of matrices for different N, or to require work with an always fixed volume, which may also not be optimal. In addition, when calculating the score

according to the first expression in (10), the costs of assessment

not used further. In order to increase computational efficiency, we obtain for

identical relations of the form

where α _N , β _N are weighted N-vectors defined by explicit arithmetic dependences on N.

как совокупность ее столбцов, определения которых очевидно из (9), заметим, что в силу симметрии, имеют место следующие свойстваConsidering the matrix in (9)

as a set of its columns, the definitions of which are obvious from (9), we note that, due to symmetry, the following properties hold

Then the matrix W used in estimate (10) and requiring inversion takes the form

where D = det (V ^T V) = S (NQ-S ² ) is a determinant, the value of which for later can not be calculated.

,

являются второй и третьей строками матрицы V^†, соответственно получимIt follows from definitions (10) and (11) that the desired weight functions

,

are the second and third rows of the matrix V ^† , respectively, we obtain

Then, taking into account (14), from definition (11) we can find the updated desired estimate of the arrival time in the form

Thus, with the appropriate choice of points in the vicinity of the DQF maximum, which is, in discrete time, a sample function for the cross-correlation function C _XY (τ), with the corresponding formation of a vector c from the selected DQF samples, with the formation of the selected samples and their squares from the arguments vectors v ₁ and v ₂ , as well as with the formation of the vector v ₀ from units, you can find an updated estimate of the time of arrival using rule (15).

The sequence of actions obtained on the basis of the transformations derived here above the signal implements the patented method.

A device for implementing a method of measuring the time of arrival of a signal with a four-position (quadrature) phase shift keying with a shift of π / 4 (Fig. 3) contains a signal receiving means 1 connected to an analog-to-digital converter 2 (ADC), the first FFT processor 3 is connected in series, a cross-spectral calculator 4, a second FFT processor 5 and a device for determining the maximum argument DKKF signal 6. The input of the signal receiving means 1 is the input of the measuring device. The output of device 6 is the output of the measurement device. A third FFT processor 7 is connected to the second input of the cross-spectrum calculator 4. Between the ADC 2 output and the input of the first FFT processor 3, the quadrature decomposition of signal 8, the first low-pass filter 9, read-only memory (ROM) 10, and the subtractor modulo 2π 11 Between the second output of the quadrature decomposition device of signal 8 and the second input of the ROM 10, a second low-pass filter is connected 12. The subtracting input of the subtractor 11 is connected to the output of the ROM 10 through a delay element for the duration of the signal symbol 13. FFT processor 7 is connected to the output of the bitmap message driver 14 through serially-connected serial-parallel converter 15, arithmetic device 16 (AU) and the sampling frequency expander 17. The second input of AU 16 is connected to the second output of the serial-parallel converter 15.

In another embodiment, the device for measuring the time of arrival of the signal to the output of the device for determining the argument of the maximum DCFK signal 6 is additionally connected to an arithmetic device 18.

The proposed device for implementing the method of measuring the time of arrival of a signal with four-position (quadrature) phase shift keying with a shift of π / 4 works as follows.

Means for receiving signals 1 receives a signal. From the output of the first signal receiving means 1, the received signal is fed to the input of the ADC 2 and the signal is converted into a first digital data stream, which digitally represents the signal as a series of values of the time function. The quadrature decomposition of signal 8 performs quadrature decomposition of the first digital data stream relative to the nominal center frequency of the modulated signal into a plurality of in-phase and quadrature samples corresponding to the specified stream. The obtained in-phase and quadrature samples independently low-pass filter the low-pass filters 9 and 12 with a cutoff frequency corresponding to the speed of manipulation of the modulating signal. In ROM 10, a plurality of current signal phases are obtained as arguments of complex numbers, the corresponding filtered common-mode samples are used as the real part, and the corresponding filtered quadrature signal samples are used as the imaginary part. The delay element 13 delays the set of received current signal phases by the duration of the modulating signal symbol. In the subtractor 11, the corresponding value of the delayed current phase of the signal is subtracted modulo 2π from each received current phase. In the first processor, the FFT 3 converts the resulting differential digital data stream as the first digital data stream into discrete values of the first frequency function S ₁ (k), where k is an integer index variable that varies within the data length. Shaper 14 generates the original bit message. The serial-parallel Converter 15 separates the original bit message into a common-mode bit signal I _k and a quadrature bit signal Q _k and delivers these signals to AU 16, where they are converted into a differential phase Δθ _k as follows

.

.

Each difference phase is mapped to the corresponding number of samples of the digitized received signal relative to the time scale of the receiving position by increasing the sampling frequency using the sampling frequency expander 17, and thus form a second digital data stream. In the third processor, the FFT 7 converts said second digital data stream into the values of the second spectrum, which represents the signal as a series of values of the frequency function S ₂ (k). In the cross-spectral calculator 4, the spectrum values of one of the signals are mutually multiplied with the complex conjugate values of the spectrum of the other signal coming from the first 3 and third 7 FFT processors to generate the cross spectrum. The output signal from the calculator 4 is fed to the input of the second FFT processor 5, in which the DCFF signal is calculated using the inverse FFT cross-spectrum. Received DKKF signal from the output of the second processor FFT 5 is fed to the input of device 2, where they determine the time of arrival of the signal as an argument of the maximum DKKF signal.

In another embodiment of the device for measuring the time of arrival of the signal, the output signal of the device for determining the argument of maximum 6 is additionally supplied to the arithmetic device 18, which operates in accordance with rule (15) and determines the updated value of the time of arrival of the signal.

INFORMATION SOURCES

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Claims (5)

1. A method of measuring the time of arrival of a signal with four-position (quadrature) phase shift keying with a shift of π / 4, including receiving a signal, analog-to-digital conversion of the received signal into a first digital data stream, representing the signal as a series of values of the time function converted to digital form, the use of a fast Fourier transform (FFT) for the two signals representing the two signals as a series of discrete frequency values of the functions S _i (k), where k - integer index variable which varies within the length data, ai = 1, 2 - an index variable, which means the serial number of the digital data stream converted using the FFT into the values of the frequency function, the mutual multiplication of the spectrum values of one of the signals with the complex conjugate values of the spectrum of another signal, which generates a cross spectrum, calculates a discrete cross correlation function (DKKF) of the signal using the inverse FFT, determining the time of arrival (VP) of the signal as an argument of the maximum DKKF signal, characterized in that they perform quadrature decomposition of the first of the digital data stream relative to the nominal center frequency of the modulated signal into a plurality of in-phase and quadrature samples corresponding to the specified stream, the obtained in-phase and quadrature samples are independently low-pass filtered with a cut-off frequency corresponding to half the speed of the original bit message, and many current phases of the signal are received as arguments of complex numbers, in as the real part of which the corresponding filtered in-phase samples are used, and as imaginary d - the corresponding filtered quadrature signal samples, delay the set of received current signal phases by half the modulating symbol duration, subtract modulo 2π from each received current phase the corresponding value of the delayed current signal phase, and the resulting differential digital data stream is converted using the FFT into the values of the first function frequency S ₁ (k), the original bit message is sequentially-parallel divided into a common-mode bit signal and a quadrature bit signal obtained bit signals are converted into bipolar two-level signals with a single level, a quadrature two-level signal is sequentially multiplied by π / 4 and taken with the opposite sign and increased by two in-phase two-level signal, each value of the multiplication result is displayed by the corresponding number of samples of the received signal converted into digital form relative to time scales of the receiving position and thus form the second digital data stream, which is converted using FFT into WTO values th frequency function S ₂ (k). 2. The method of measuring the time of arrival of a signal according to claim 1, characterized in that for a signal for which the duration of the signal symbol is not a multiple of the sampling frequency of the analog-to-digital conversion of the received signal, the filtered in-phase and quadrature samples are additionally decimated and interpolated to provide a frequency multiplicity of the first digital samples data stream signal symbol duration. 3. The method of measuring the time of arrival of a signal according to claim 1 or 2, characterized in that to the left and to the right of the maximum argument DKKF signal select L points of the specified function, the DKKF values for the selected points and maximum points are combined in the order of time following in a column vector c , from units form a column vector 1 of the same dimension as the vector c , the arguments corresponding to the selected DKKF points are expressed through the index variable l = 0, ± 1, ..., ± L, where the indices l with a negative sign correspond to the times to the DKKF maximum point, zero and index l corresponds to the maximum point of DCCF, and the indices l with a positive sign correspond to the times after the maximum point of DCCF, the arguments of the selected points of DCCF are ordered in the same way as the components of vector c , and are combined into a column vector x , the squares of the components of vector x are similarly combined into a vector- column q , and the adjusted value of the VP

determined by the following rule

where N = 2L + 1 is the dimension of the generated vectors, the superscript T denotes the transpose of the vector, T _s is the sampling period of the signal, x ^T c is the scalar product of the vectors x and c , the coefficient P is determined by the expression

the coefficient Q is determined by another expression

a (NP q -P ² 1) ^T c is the scalar product of the difference vector (NP q -P ² 1) with vector c . 4. A device for implementing a method of measuring the time of arrival of a signal with four-position (quadrature) phase shift keying with a shift of π / 4, containing an arithmetic device (AU), as well as a means for receiving signals, the input of which is the input of the measuring device connected to an analog-to-digital converter (ADC), the first FFT processor, the cross-spectrum calculator, the second FFT processor and the device for determining the maximum discrete cross-correlation function (DCF) of the signal, the output of which This is the output of the measurement device, and a third FFT processor is connected to the second input of the cross-spectrum calculator, characterized in that a quadrature decomposition device, a first low-pass filter (LPF), and a read-only memory device are connected in series between the ADC output and the input of the first FFT processor. (ROM) and a subtraction device modulo 2π, between the second output of the quadrature signal decomposition device and the second input of the ROM, a second low-pass filter is included, the subtracting input of the subtraction device is connected to the output th ROM through the delay element for the duration of the signal symbol, and the input of the third FFT processor is connected to the output of the bitmap driver through a series-parallel converter, an arithmetic device (AU) and a sampling frequency expander, while the second input of the AU is connected to the second output in series parallel converter. 5. A device for implementing the method of measuring the time of arrival of a signal according to claim 4, characterized in that a second arithmetic device is additionally connected to the output of the device for determining the argument of the maximum of the discrete cross-correlation function of the signal.

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