RU2446558C1 - Method of differential pulse-code modulation-demodulation of signals - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method of differential pulse-code modulation - demodulation of signals consisting in quantisation of error signals, their coding and recovery of quantised error signals after transfer in a channel, at the same time for each interval of time [t_i, t_i+1], t_i+1>t_i, i=0, 1, 2, … forecasting of spline-approximation coefficients of an information signal is done, they are confirmed by recovered quantised error signals, a recovered information signal is generated by confirmed estimates of coefficients in the form of a continuous spline process.

EFFECT: improved noise immunity of signals transfer and reception.

Description

The object of the invention is a method of differential pulse code modulation - demodulation (DIKMD) signals. The proposed method relates to radio engineering and communication, since the class of modulation-demodulation problems of this type forms the basis for the organization of the transmission and reception of signals in many digital radio and wired information systems.

A known method of DIKMD signals [1]. Its disadvantage is the focus on working with noiseless information processes. If the observed signal is the sum of the information signal and the noise (usually broadband) noise, then to use this method it is necessary to provide special measures for preliminary filtering. The method itself does not provide a reduction in the variance of the interference when restoring the signal at the receiving side.

, предсказании с шагом h их оценок, формировании сигналов ошибки путем вычитания из отсчетов информационного сигнала их предсказанных оценок, квантовании сигналов ошибки, их кодировании, восстановлении квантованных сигналов ошибки после передачи в канале, предсказании оценок отсчетов информационного сигнала на приемной стороне, уточнении этих оценок по принятым квантованным сигналам ошибки, формировании восстанавливаемого непрерывного информационного сигнала по уточненным оценкам отсчетов.There is also a known method of DICMD [2], which consists in the formation of a sequence of samples of an information signal based on its sampling with a frequency

, predicting their estimates with step h, generating error signals by subtracting their predicted estimates from the information signal samples, quantizing error signals, coding them, reconstructing quantized error signals after transmission in the channel, predicting estimates of the information signal samples on the receiving side, refining these estimates by received quantized error signals, the formation of a restored continuous information signal according to updated estimates of the samples.

It is also focused on processing noisy information signals when the latter are observed directly, and not against the background of interference. For the observed process, representing the composition of the information signal and noise, this method does not allow to reduce the influence of interference on the information process restored on the receiving side. Indeed, when generating the error signal, the predicted samples of the information signal are subtracted from the observed signal (composition of the information process and noise). As a result, the error signal, in addition to the information one, also contains an interfering component with a dispersion determined by the dispersion of the input noise.

As a result, the input interference is transmitted almost unchanged to the receiving side.

The purpose of the invention: improving noise immunity by combining processes of differential pulse-code modulation-demodulation and filtering based on a common procedure for predicting signal estimates for these two classes of problems.

The essence of the invention is based on the use in the task DIKMD piecewise polynomial (spline) representation of the estimates of the information signal. Such a description adequately reflects the process of pulse-code modulation-demodulation, which implies the conversion of a continuous signal into a discrete and discrete into a continuous one.

The invention consists in the following. For each time interval [t _i , t _{i + 1} ], t _{i + 1} > t _i i = 0, 1, 2, ..., the coefficients of spline approximation of the information signal are predicted. With their help, at each time interval [t _i , t _{i + 1} ], i = 0, 1, 2, ... an estimate of this signal is generated in the form of a process that varies according to the polynomial law. The resulting score is subtracted from the input signal. Subtraction results are averaged over [t _i , t _{i + 1} ], i = 0, 1, 2, .... The results of this averaging, which serve as error signals, are used to refine the predicted estimates of the coefficients of the spline approximation. Error signals are quantized, encoded, and transmitted to the channel. After transmission in the channel at the receiving side, the quantized error signals are restored. For each time interval [t _i , t _{i + 1} ], i = 0, 1, 2, ..., prediction of the coefficients of the spline approximation coefficients of the restored information signal and their refinement based on the restored quantized error signals are carried out. According to refined estimates of the coefficients, a reconstructed information signal is generated in the form of a continuous piecewise polynomial process.

A comparative analysis of the proposed method and the described method DIKMD shows the following significant differences of the proposed method.

Modulation stage.

1. The prediction of the information signal is carried out in two stages:

- according to a priori information about the information signal for each time interval [t _i , t _{i + 1} ], i = 0, 1, 2, ..., the coefficients of its spline representation are extrapolated;

- according to these coefficients on each time interval [t _i , t _{i + 1} ], i = 0, 1, 2, ... prediction of the spline approximation of the information signal is carried out.

As a result, it is not the instantaneous value of the evaluation of the information signal that is predicted, as in the known method, but its continuous assessment on [t _i , t _{i + 1} ], in the form of a process that varies according to the polynomial law.

2. An error signal is generated by subtracting at each interval [t _i , t _{i + 1} ] from the input signal the estimate of the information signal predicted for this interval and averaging the obtained difference on [t _i , t _{i + 1} ].

As a result, unlike the known method, the error signal is determined not for the instantaneous values of the observed signal and the predicted estimate of the information signal, but based on the averaging operation, i.e. the error signal is integral.

Stage of demodulation.

1. According to a priori data on the information signal, the estimates of the coefficients of its spline approximation are predicted.

2. The predicted values of the coefficient estimates are refined based on the received quantized error signal.

3. Based on the adjusted coefficients of the spline approximation, a restored continuous information signal is generated in the form of a piecewise polynomial process.

Since the restoration of the information signal is based on the use of a time-averaged error signal, the influence of the noise contained in the observed process is significantly attenuated.

Theoretical basis of the method of differential pulse code modulation - signal demodulation.

In solving the problems of DIKMD, as a rule, they proceed from the assumption that the information signal is observed directly without noise. However, in practice, there are often situations when the input signal is a composition (usually additive) of the information signal and interference (usually broadband). In this case, first you need to solve the filtering problem, and only then modulation.

At the same time, both the differential pulse code modulation (digital prediction coding) procedure and the filtering procedure involve the implementation of the prediction or extrapolation of the information signal estimation [1, 2, 3].

This makes it possible to combine filtering and DICMD based on a common prediction procedure. As a result, the differential pulse-code modulator acquires the properties of a filter and allows to reduce the influence of noise contained in the input signal on the signal restored at the receiving side.

Based on the specifics of DIKMD, which consists in sampling with a given frequency of a continuous signal, it is necessary to use a class of models with a continuously discrete structure. The most effective in this class is the apparatus of spline functions.

Usually, the information signal λ ₁ (t) is considered as a component of the vector process λ (t) ∈R ^m [3] satisfying the differential equation

; λ^T(t)=[λ₁(t),λ₂(t),…,λ_n(t)]; N_λ∈R^r×r - диагональная матрица. Примерами, иллюстрирующими (1), могут служить [3]:where A∈R ^{m × m} ; n _λ ∈R ^r ; g∈R ^{m × r} ; n _λ (t) is the vector forming Gaussian noise; M [n _λ (t)] = 0;

; λ ^T (t) = [λ ₁ (t), λ ₂ (t), ..., λ _n (t)]; N _λ ∈R ^{r × r} is the diagonal matrix. Examples illustrating (1) can serve [3]:

- voice message model λ ₁ (t), which is a component of the Markov process

where α ₁ , α ₂ - constants that determine the frequency bandwidth λ ₁ (t);

- telemetry message model λ ₁ (t) defined by equations

- narrowband communication model λ ₁ (t) corresponding to the system

where χ = const> 0, etc.

Consider the observed signal, which is associated with the information ratio

where n (t) is a Gaussian broadband interference for which M [n (t)] = 0; M [n (t) n (t-τ)] = N ₀ δ (τ).

To determine the sequence of operations corresponding to the DICMD of the information signal λ ₁ (t) observed against the background of noise in accordance with (5), we use the principles of filtering.

The filtering procedure of process (1) (and therefore its components λ ₁ (t)) has the form [3]

where K is the matrix of weight coefficients, defined as the result of solving the matrix algebraic equation

H∈R ^m ; h = [1.0 ... 0]

We introduce two grids on the time axis

, i=-2, -1, 0, 1, ….where t _{i + 1} -t _i = h;

, i = -2, -1, 0, 1, ....

Consider the time interval [t _i , t _i + h], i = 0, 1, 2, ... For it, we represent the estimate λ ^* (t) in the form of a vector parabolic spline function [4]

where S _i - parabolic vector-spline defect 1;

b _i ∈ (i = -1, 0, 1, ...) is the vector of spline coefficients.

The choice of parabolic spline functions is due to a compromise between the accuracy of the representation of the approximated processes and the complexity of their implementation.

We represent (6) in terms of (9). As a result, for t∈ [t _i , t _i + h] we get:

- predicted (extrapolated) estimates of the coefficients of spline approximation of the information signal

,Where

,

I is the identity matrix (m × m);

- the predicted (extrapolated) estimate of the information signal in the form of a process that varies according to the polynomial (in this case, parabolic) law

where b ₁ is the first element of the vector b;

- average error signal

- refined value of the vector

.Where

.

Note that the initial conditions in (10) are determined from the initial conditions in (6).

The set of operations (10) - (13), supplemented by quantization of the error signal δ _i → δ _qi ; and its encoding, constitute the essence of differential pulse-code modulation, which lies at the heart of the proposed method DIKMD.

The demodulation process is based on (10) - (13) and consists in the following:

predicting estimates of the coefficients of spline approximation of the information signal at the receiving side

уточняют- based on the δ _qi value obtained after decoding, the estimate

specify

,

,

на [t_i, t_i+h] восстанавливают непрерывный информационный сигнал- by the values of the coefficients

,

,

on [t _i , t _i + h] restore the continuous information signal

Note that, due to the spline representation, the reconstructed information signal, together with its first derivatives, is continuous over the entire time interval of its existence.

Computing Experiment Results

Let us consider an example of a DICMD as applied to a narrow-band message λ ₁ (t) defined by model (4). In the MathCAD environment, a computational experiment was conducted on differential pulse-code modulation-demodulation based on operations (10) - (16) for the observed signal specified by (5).

It was assumed that α = 1200, χ = 2 · 10 ⁴ , N _λ = 10 ^-7 , N ₀ = 10 ⁹ , t∈ [0, T],

T = 0.1, h = (4, 8, 10, 16, 20, 25, 32) · 10 ^-6 . All parameters are given in dimensionless units.

The values of λ ₁ (t) and λ ₂ (t) were determined from the numerical solution of equation (4) in accordance with the Euler scheme and the step Δt = 5 · 10 ^-7 .

, восстановленного на приемной стороне (М=31, h=20·10^-6). Они оказываются достаточно близкими. Для оценки степени этой близости, то есть качества предлагаемого способа ДИКМД, был проведен расчет зависимости относительной дисперсии оценки восстановленного на приемной стороне процесса

The formation of n _λ (t) in (4) and n (t) in (5) was carried out using sensors of normally distributed random numbers. The number of quantization levels during the transition δ _i (t) → δ _qi (t) was assumed to be M = 15, 31. Quantization errors were set using a sensor of uniformly distributed random numbers. The Figure 1 presents a fragment of the information signal λ ₁ (t). The Figure 2 presents fragments of information λ ₁ (t) and the observed y (t) signals. Obviously, it is impossible to apply the DIKMD methods considered in [1, 2] directly to y (t). The Figure 3 shows fragments of the information signal λ ₁ (t) and signal

restored on the receiving side (M = 31, h = 20 · 10 ^-6 ). They are quite close. To assess the degree of this proximity, that is, the quality of the proposed DIKMD method, the dependence of the relative variance of the estimate restored on the receiving side of the process was calculated

, U=T/Δt,

, λ_1j=λ₁(jΔt),

- априорная дисперсия λ₁(t)Where

, U = T / Δt,

, λ _1j = λ ₁ (jΔt),

- a priori dispersion λ ₁ (t)

from step h (Figure 4) at M = 15 (curve 1) and M = 31 (curve 2). Curve 3 on the same graph characterizes the dependence of the relative variance of the estimate of the information signal, which can be formed on the transmitting side, in accordance with the relation

ошибок квантования.It is the lower bound to which the dependences (17) tend to as M. grows. From the graphs it follows that for each M the optimal value h _{opt of the} spline approximation step can be chosen, which ensures the minimum value of the error in reconstructing the information signal. The concave nature of curves 1, 2 is due, on the one hand, to a decrease in the accuracy of the spline approximation with increasing h, and on the other hand, to an increase in the decrease in the step h, the effect on the estimation accuracy

quantization errors.

Determine - how the noise immunity of the proposed method DIKMD increases compared with the prototype method [2]. Once again, we note that when using the prototype method, the noise component contained in the observed signal (6) is not suppressed. In the conditions of the example, its dispersion is (see Figure 2)

The variance of the estimated signal recovery for h = h _opt = 1.6 · 10 ⁵ , M = 31 turned out to be equal (see Figure 4, curve 2)

(см. Фиг.1).Where

(see Figure 1).

The relative gain in noise immunity was

The gain is due to the presence of an averaging operation error (12) in the signal generation procedure, which provides a significant reduction in the influence on the quality of signal recovery of broadband interference, against which an information signal is observed.

The structural diagram of a device that implements the method DIKMD, presented in Figure 5.

In Figure 5, the following notation is used: 1 — first adder; 2 - a predicted signal estimation generator; 3 - block subtraction; 4 - averaging unit; 5 - block sampling-storage; 6 - analog-to-digital Converter (ADC); 7 - communication channel; 8 - digital-to-analog converter; 9 - the second block determining the amendment; 10 - the third adder; 11 - generator restored signal estimates; 12 - second conversion unit; 13 - the fourth adder; 14 - second block delay; 15 - the fourth block delay; 16 is a first conversion unit; 17 - the third conversion unit; 18 - the first block delay; 19 - the third block delay; 20 - second adder; 21 is a first amendment determination unit; 22 is a fourth conversion unit.

The input signal is fed to the input 3 ₂ of the subtraction block 3. At the input 3 _{1 of} the same block, a predicted estimate of the information signal is supplied as a polynomial process at each time interval [t _i , t _i + h]. This estimate is generated in the generator 2 of the predicted signal estimate based on the i-th (output of the first delay unit 18) (i-1) -th (output of the second delay unit 14) and (i + 1) -th predicted (output of the first adder 1) spline approximation coefficients. The indicated coefficients are fed respectively to the inputs 2 of ₃ , 2 _2, and 2 _{1 of} block 2. The extrapolation (prediction) of the (i + 1) -th coefficient is carried out by summing in the adder 1 the i-th coefficient of the spline approximation converted in the first transform block 16 and the (i-1) th coefficient of the transform converted in the second block 12. These blocks implement the operations of multiplying the vector by matrices corresponding to procedure (10).

In block 3, for each interval [t _i , t _i + h], a differential signal is generated that is input to input 4 ₁ of the averaging unit 4. The results of averaging the difference signal are fed to input 5 _{1 of} block 5 of the sample-storage and by the control pulse at input 5 ₂ formed at the end of each interval are recorded and stored. Thus, an error signal is generated at the output of block 5. The output signal of block 5 is input to the first block of determination of amendment 21, in which the error signal is converted into a correction vector by multiplying it by vector F ₃ in (13). In the second adder 20, the predicted (i + 1) -th value of the coefficient supplied to the input 20 _{1 of} block 20 is refined by adding to it the correction vector fed to the input 20 ₂ . The adjusted value of the (i + 1) th coefficient is fed to the input of the delay unit 18, the output of which, in addition to the input 2 _{3 of the} adder 2, is also connected to the input of the delay unit 14 and the input of the conversion unit 16. The delay units delay by the value of the prediction step h.

Error signals from the output of block 5 are fed to the input of the ADC 6, where they are quantized and converted into code sequences. These code sequences are transmitted to channel 7, the output of which is connected to the input of the DAC 8. At the output of the DAC 8, the quantized values of the error signals received by the second block for determining amendments 9 are restored from the code sequences. The principle of its operation is similar to the principle of functioning of the first block for determining amendments 21. On at its output, on the received quantized error signal, a correction vector is generated that is fed to input 10 _{1 of the} third adder 10. At the same time, its input 10 ₂ from the output of the fourth adder 13 the predicted value of the (i + 1) -th coefficient of the spline approximation of the receiving side is supplied. As a result, at the output of adder 10, an estimate of the (i + 1) th spline approximation coefficient is reconstructed from the received error signal, which is used along with the ith and (i-1) th coefficients to generate a reconstructed signal estimate in the generator 11. In addition to Moreover, the estimate of the (i + 1) th coefficient is fed to the input of the fourth delay block 15. The output of this block is in turn connected to the input of the third delay block 19.

The delay blocks 15 and 19 are similar to blocks 14, 18. The output signals from the outputs of blocks 15, 19 are supplied to the inputs of the third 17 and fourth 22 conversion blocks, the outputs of which are connected to the inputs 13 ₂ and 13 ₁ ), respectively. The structure of the blocks 17, 22 is identical to the structure of the blocks 16, 12, respectively. The output of the generator 11 is the output of the device. It forms the evaluation of the information signal restored after transmission and demodulation in the form of a piecewise polynomial spline-type process.

,; блок 3 - формирование на [t_i, t_i+h] разности наблюдаемого и экстраполируемого процесса; блок 4 - усреднение по времени на [t_i, t_i+h] разностного сигнала в соответствии с (12); блок 5 - выборка и хранение результатов усреднения; блок 6 - квантование сигнала ошибки и его кодирование; блок 7 - передача кода на приемную сторону; блок 8 - формирование квантованного сигнала ошибки; блок 9 - определение сигнала поправки путем домножения квантованного сигнала ошибки на вектор F₃, (значение F₃ определено в (13)); блок 10 - суммирование двух векторов в соответствии с (15); блок 11 - генерация восстанавливаемого информационного сигнала в соответствии с (16) по восстановленным коэффициентам

,

,

; блок 12 - домножение вектора b_i-1 на матрицу F₁ (структура F₁ определена в (10)); блок 13 - суммирование двух векторов в соответствии с (14); блок 14 - задержка значений b_i на время h; блок 15 - задержка значений

на время h; блок 16 - домножение вектора b_i на матрицу F₂ (структура F₂ определена в (10)); блок 17 - домножение вектора

на матрицу F₂; блок 18 - задержка значений b_i+1 на время h; блок 19 - задержка значений

на время h; блок 20 - суммирование векторов в соответствии с (13); блок 21 - домножение сигнала ошибки δ_i на вектор F₃; блок 22 - домножение вектора

на F₁.Functions of blocks: block 1 - summation of two vectors in accordance with (10); block 2 - generation at each time interval [t _i f _i + h) of a predicted (extrapolated) estimate of the information signal in the form of a polynomial dependence (11) based on the values of the coefficients b _1i-1 , b _1i ,

,; block 3 - the formation on [t _i , t _i + h] of the difference between the observed and extrapolated process; block 4 - time averaging over [t _i , t _i + h] of the difference signal in accordance with (12); block 5 - selection and storage of averaging results; block 6 - quantization of the error signal and its coding; block 7 - code transmission to the receiving side; block 8 - the formation of a quantized error signal; block 9 - determination of the correction signal by multiplying the quantized error signal by the vector F ₃ , (the value of F _{3 is} defined in (13)); block 10 - summation of two vectors in accordance with (15); block 11 - generation of the restored information signal in accordance with (16) according to the restored coefficients

,

,

; block 12 - multiplication of the vector b _i-1 by the matrix F ₁ (the structure of F _{1 is} defined in (10)); block 13 - summation of two vectors in accordance with (14); block 14 - delay values b _i at time h; block 15 - delay values

at time h; block 16 - multiplication of the vector b _i by the matrix F ₂ (the structure of F _{2 is} defined in (10)); block 17 - vector multiplication

to the matrix F ₂ ; block 18 - delay values b _{i + 1} at time h; block 19 - delay values

at time h; block 20 - summation of vectors in accordance with (13); block 21 - multiplication of the error signal δ _i by the vector F ₃ ; block 22 - vector multiplication

on F ₁ .

Information sources

1. Prokis J. Digital Communications. - M .: Radio and communications, 2000.

2. Interference immunity and efficiency of information transmission systems. / Ed. A.G. Zyuko. - M .: Radio and communications, 1985.

3. Yarlykov M.S. application of the Markov theory of nonlinear filtering in radio engineering. - M .: Owls. radio, 1980.

4. Khutortsev VV, Fedorenko O.S. Using the spline function method in the synthesis of digital filtering algorithms with grouping of observations. / - Radio engineering, 2010, No. 2, C.4-8.

Claims (1)

The method of differential pulse-code modulation - demodulation of signals, which consists in quantizing error signals, their coding and restoration of quantized error signals after transmission in the channel, characterized in that for each time interval [t _i , t _{i + 1} ], t _{i + 1} > t _i , i = 0, 1, 2, ... predicting the coefficients of the spline approximation of the information signal, using them on each time interval [t _i , t _{i + 1} ], i = 0, 1, 2, ... generate an estimate of this signal in the form of a process that varies according to the polynomial law, subtract such an estimate from one signal, and subtracting the results are averaged to [t _i, t _{i + 1],} the averaging results serve error signals are used to update the predicted estimates spline approximation coefficients at the receiving side for each interval [t _i, t _{i + 1} ], i = 0, 1, 2, ... carry out the prediction of estimates of the coefficients of the spline approximation of the reconstructed information signal, refine them according to the reconstructed quantized error signals, and generate the reconstructed information signal in the form of continuous estimates of the refined estimates of the coefficients th piecewise-polynomial process.

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