RU2160498C2 - Adaptive noise suppresser - Google Patents

Abstract

FIELD: systems for message transmission over communication channels suffering additive correlated noise. SUBSTANCE: noise suppresser uses correlation function read-out shaping unit for implementing correlation principle of discriminating lumped noise along with connection of first and second adaptive filters to noise separation channel; first and second inputs of correlation function read-out shaping unit function as device inputs and their first and second outputs are connected to first and second adaptive filters, respectively; third output is connected to first input of adaptive filter control factor computing unit. EFFECT: improved reliability of noise suppression, capability of operating under a priori uncertain conditions concerning noise properties. 4 dwg

Description

 The invention relates to radio communications and can be used in transmission systems of both discrete and continuous messages over communication channels subject to additive correlated interference.

 A device is known [1, p. 276, Fig. 12.1], depicted in FIG. 1 of this description, containing the adaptive filter and the adder connected in series, the adaptive filter output is connected to the first input of the adder, the adaptive filter input being the device input reference, the second adder input being the device signal input, the adder output being the device output and connected to the adaptive filter control input .

 However, the known device has a significant disadvantage associated with the fact that the device requires for its operation the presence of an additional signal at the reference input of the device. This signal should not be correlated with the input signal that carries information, and not strongly correlated with the noise contained with the input signal at input 1 of the device. It should be noted that in practice, in order to find a suitable reference signal, it is necessary to solve a number of complex problems, and if in reality such a signal existed, then an adaptive system would not be needed, it would be possible to do only with a subtractor. Under conditions of a priori uncertainty regarding the properties of additive interference, this device could be used in conjunction with the ideas of diversity reception, when the signal and reference inputs of the device are signals of two diversity branches.

 The closest in technical essence to the claimed device is a device [1, p. 354, Fig. 13.15] for the case of two diversity branches (K = 2), shown in FIG. 2 of this description, containing the first and second adaptive filters and the adder, the outputs of the adaptive filters are connected to the first and second inputs of the adder, the inputs of the adaptive filters are the signal inputs of two diversity branches, and the output of the adder is connected to the control inputs of the adaptive filters.

 The disadvantage of this device is that this device also turns out to be practically inoperative, like its counterpart in the case when signals and interference in the diversity branches are uncorrelated. The main condition for the operability of the device is the presence of strongly correlated interference components at its inputs.

 The essence of the invention is to improve the quality of adaptive interference suppression, the ability to work in conditions of a priori uncertainty regarding their properties.

 This essence is achieved by the fact that the adaptive noise suppression device containing the first and second adaptive filters and the adder, the outputs of the adaptive filters are connected to the first and second inputs of the adder, a unit for calculating the correlation function samples, a unit for calculating the adaptive filter control coefficients, an averaging unit, large-scale block, first and second adders, and the inputs of the device are the first and second inputs of the block for calculating samples of the correlation function, the first output of which is connected to the input w of the adaptive filter and to the first input of the first adder, the second output of the correlation function sample calculation unit is connected to the input of the first adaptive filter and to the first input of the second adder, the third output of the correlation function sample calculation unit is connected to the third input of the scale unit and to the first input of the coefficient calculation unit adaptive filter control, the second input of which is connected to the output of the adder, and the output is connected to the control inputs of the first and second adaptive filters, the output of the adder and connected to the first input of the scale block, and through the averaging block with the second input of the scale block, the output of which is connected to the second inputs of the first and second adders, the outputs of which are the outputs of the entire device.

 In FIG. 1 shows a functional diagram of an adaptive filter (analogue); in FIG. 2 shows a functional diagram of a matrix adaptive filter (prototype); in FIG. 3 is a functional block diagram of the calculation of samples of the correlation function; in FIG. 4 presents a functional diagram of the proposed device.

 The adaptive interference suppression device (Fig. 4) comprises a first adaptive filter 1, an adder 2, a second adaptive filter 3, a correlation function calculation unit 4, an adaptive filter control coefficient calculation unit 5, an averaging unit 6, a scale unit 7, a first adder 8, second adder 9.

 The adaptive interference suppression device comprises first 1 and second 3 adaptive filters and an adder 2, a correlation function calculation unit 4, adaptive filter control coefficient calculation unit 5, averaging unit 6, a scale unit 7, a first adder 8, a second adder 9, and the outputs of the first 1 and the second 3 adaptive filters are connected to the first and second inputs of the adder 2, the inputs of the device are the first and second inputs of the unit 4 for calculating the samples of the correlation function, the first output of which is connected to the input of the second a an active filter 3 and to the first input of the first adder 8, the second output of the correlation function sample calculation unit 4 is connected to the input of the first adaptive filter 1 and to the first input of the second adder 9, the third output of the correlation function sample calculation unit 4 is connected to the third input of the scale unit 7 and with the first input of the adaptive filter control coefficient calculation unit 5, the second input of which is connected to the output of the adder 2, and the output is connected to the control inputs of the first 1 and second 3 adaptive filters, the output of the sum Ator 2 is connected to the first input of scaling unit 7, and through the averaging unit 6 to a second input of scaling unit 7, whose output is connected to the second inputs of the first 8 and second 9 adders whose outputs are the outputs of the entire device.

 The device operates as follows.

 Under the conditions of a priori uncertainty regarding the properties of lumped interference, we consider one of the possible methods for preliminary processing of the received mixture of the useful signal S (t), lumped interference ξ (t), and fluctuation noise n (t), based on the use of adaptive filtering together with diversity reception.

 In this case, we will assume that the processing is carried out in the low-frequency region after frequency conversion in the band determined by the spectrum width of the useful signal. Such analysis conditions suggest the use of the filtering method under consideration in radio channels of various wavelength ranges in which the concept of “concentrated interference” is used in that the interference spectrum width ξ (t) is less than or comparable with the spectrum width of the useful signal S (t) regardless of the type of transmitted messages and types of modulation used.

 It is known [1] that in the circuit shown in FIG. 1, adaptive filter (AF) - block 1, which changes its impulse response under the influence of the output signal, for example, according to the least squares algorithm, filters out all the components correlated with the signal at the input of the AF from the signal at the second input of adder 2 according to the minimum root-mean-square error criterion. Moreover, after the end of the adaptation process in the tracking mode for a slow change in the correlation properties of the signal at the AF input, the AF is identical to the Kolmogorov-Wiener filter [1].

где

- взаимный энергетический спектр сигналов z₂(t) и z₁(t),

- энергетический спектр сигнала на вх.2 (эталонном входе).Let the useful signal, interference and noise be stationary random processes, and the signals of two diversity branches z ₂ (t) and z ₁ (t) are supplied to input 1 and input 2 of the device of FIG. 1:
z ₁ (t) = S ₁ (t) + ξ ₁ (t) + n ₁ (t);
z ₂ (t) = S ₂ (t) + ξ ₂ (t) + n ₂ (t). (1)
In the future, we assume that S ₁ (t) is independent of ξ _i (t), i, j = 1,2, and from the white noise n ₁ (t) and n ₂ (t). The AF transmission coefficient module in stationary mode is written as

Where

- the mutual energy spectrum of the signals z ₂ (t) and z ₁ (t),

- energy spectrum of the signal at input 2 (reference input).

однако формула (2) учитывает особенности рассматриваемой схемы. В нашем случае взаимный энергетический спектр зависит только от коррелированных составляющих процессов на первом и втором входах, поэтому

Будем предполагать, что G_S(ω) и G_ξ(ω) - энергетические спектры сигнала и помехи на передаче (в месте возникновения), a K_i(j ω ) и L_i(j ω ), i,j = 1,2, - коэффициенты передачи соответствующих путей распространения сигнала и помехи к месту приема. Тогда

Исходя из определения взаимного энергетического спектра как преобразования Фурье взаимной корреляционной функции, можно показать, что

где (°)^* и

- символы комплексной сопряженности и усреднения.Strictly speaking, the modulus of the transmission coefficient of the Kolmogorov-Wiener filter, which gives an estimate of ξ _i (t), is defined as

however, formula (2) takes into account the features of the considered scheme. In our case, the mutual energy spectrum depends only on the correlated components of the processes at the first and second inputs, therefore

We assume that G _S (ω) and G _ξ (ω) are the energy spectra of the signal and the interference in the transmission (at the origin), a K _i (j ω) and L _i (j ω), i, j = 1, 2, - transmission coefficients of the corresponding signal propagation paths and interference to the receiving location. Then

Based on the definition of the mutual energy spectrum as the Fourier transform of the mutual correlation function, we can show that

where (°) ^* and

- symbols of complex conjugation and averaging.

где N₂ - энергетический спектр n₂(t).Substituting (3), (4) and (5) in (2) we obtain:

where N ₂ is the energy spectrum of n ₂ (t).

Из (8) следует, что возможные искажения полезного сигнала являются линейными, т.к. не появляется новых спектральных составляющих.For the energy spectrum of noise and signal at the output of the circuit of figure 1 when acting on the input. 1 and in. 2 signals z ₂ (t) and z ₁ (t) can be obtained

From (8) it follows that the possible distortions of the useful signal are linear, because no new spectral components appear.

а также отношением:

где P_с и P_ш - мощности сигнала и шума соответственно.The effectiveness of the suppression of concentrated interference is estimated by the energy gain:

as well as the ratio:

where P _with and P _W - signal power and noise, respectively.

В выражении (11) R_K и R_L определяют корреляцию замираний сигнала и сосредоточенной помехи в ветвях разнесения.For the convenience of analysis, we introduce the parameters

In expression (11), R _K and R _L determine the correlation of signal fading and concentrated interference in the diversity branches.

i,j = 1,2, и учитывая, что

для (7) и (8) можно получить

где B(ω) = 1+a²(ω)+h $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ (ω),

M(ω) = R_KF(ω)+R_L. (15)
При этом

a η может быть рассчитано после интегрирования полученных энергетических спектров в заданном диапазоне частот.Considering that after the completion of the adaptation process in stationary mode

i, j = 1,2, and considering that

for (7) and (8) we can obtain

where B (ω) = 1 + a ² (ω) + h $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ (ω),

M (ω) = R _K F (ω) + R _L. (fifteen)
Wherein

a η can be calculated after integrating the obtained energy spectra in a given frequency range.

For a fixed value of ω, the largest value of ρ takes at K ₂ (j ω) = 0 and N ₂ = 0. This corresponds to the case of ideal “training” of the adaptive filter, when interference is applied to its reference input, correlated with the interference in the main diversity branch. Moreover, ρ = 1 / (1-R $\genfrac{}{}{0ex}{}{\text{2}}{\text{L}}$ ) and when R _L ---> 1, it is possible to completely suppress interference in the main diversity branch for any form of its spectrum, even coinciding with the spectrum of the useful signal. The latter is characteristic of radio communication systems with moving objects with the cellular principle of system construction [3].

An analysis of the expression for ρ (ω) for a fixed value of ω, when a ² , b ² , h ₁ ² , h ₂ ² are constant parameters, shows that with an arbitrary choice of the values of these parameters, the maximum value of ρ is achieved at R _K = 0 and R _L = 1. This corresponds to the uncorrelated fading of the signal in the diversity branches and the complete correlation of the interference. At R _K = 0, there are no distortions of the output signal, as follows from (12), and the largest value of the energy gain η is provided.

где T - длительность тактового интервала, а энергетический спектр помехи в месте возникновения:

На входах 1 и 2 схемы фиг. 1 действует аддитивная смесь полезного сигнала, помехи и "белого" шума в соответствии с (1), причем статистическая связь сигналов S₁(t) и S₂(t) определяется коэффициентом корреляции R_K путей распространения сигнала к входам 1 и 2. Корреляция путей распространения помехи к входам 1 и 2 определяется коэффициентом R_L. Полоса анализируемых частот, [ω₁,ω₂] , где

Из проведенных расчетов следует, что искажения сигнала на выходе практически отсутствуют при малых R_K. Энергетический спектр шума на выходе существенно отличается от спектра "белого" шума и при малом отношении P_{с вх.}/P_n1 на входе 1 практически повторяет форму спектра помехи на входе 1.Consider an example. Let the energy spectrum of the useful signal at the modulator output have the form

where T is the duration of the clock interval, and the energy spectrum of the interference at the place of occurrence:

At the inputs 1 and 2 of the circuit of FIG. 1, an additive mixture of the useful signal, interference and white noise is applied in accordance with (1), and the statistical relationship of the signals S ₁ (t) and S ₂ (t) is determined by the correlation coefficient R _{K of the} signal propagation paths to inputs 1 and 2. Correlation interference propagation paths to inputs 1 and 2 is determined by the coefficient R _L. The band of the analyzed frequencies, [ω ₁ , ω ₂ ], where

From the calculations it follows that the distortion of the output signal is practically absent at small R _K. The energy spectrum of the noise at the output differs significantly from the spectrum of “white” noise and with a small ratio of P _{with in.} / P _n1 at input 1 practically repeats the shape of the interference spectrum at input 1.

на входе 1 мало), то ее подавление весьма эффективно и дает приемлемое значение энергетического выигрыша. Увеличение P_{с вх.}/P_n1 c 1,19 до 23,7 приводит к изменению выигрыша от η = 1,89 до η = 8,49. Следует заметить, что для практики разнесенного приема в декаметровом канале ситуация с большим отношением P_{с вх.}/P_n1 весьма характерна.In the case of "white" noise at the input can be almost ignored (the ratio of P _{with Rin.} / P _n1 is large), the energy spectrum of the noise at the output is determined mainly by the signal and, if concentrated hindrance has a large capacity (ratio

input 1 is small), then its suppression is very effective and gives an acceptable value of energy gain. Increase P _{with int.} / P _n1 from 1.19 to 23.7 leads to a change in the gain from η = 1.89 to η = 8.49. It should be noted that for the practice of diversity reception in a decameter channel, the situation is with a large ratio of P _{with input.} / P _{n1 is} very characteristic.

Calculations show that for small (P _c / P _w ) _in. the gain can be very significant, for example, with (P _c / P _w ) _in. = 0.258 (R _K = 1, R _L = 0) η = 29.3. However, the deviation of the reception conditions from "ideal" when R _K = 1, R _L = 0, significantly reduces the gain. With R _K = 0.8 and R _L = 0.2 for (P _s / P _w ) _in. = 0.258 win is 2.76.

The analysis allows us to conclude that the use of adaptive filtering with a low level of "white" noise at the main and reference input is very effective for a diversity reception situation, when R _K = 0 and R _L = 1. Deviation from these conditions significantly reduces the efficiency of suppression of concentrated noise , which requires the development of other adaptive signal processing schemes.

 It should be noted that the “correlation” principle of lumped interference separation used in an adaptive filter is quite universal and allows filtering out any additive interference regardless of the shape and width of its spectrum, the location of the spectrum on the frequency axis, etc. The main condition for the operability of the circuit is the presence of interference components at the reference input that are correlated with the interference at the main input.

 The practical use of AF in the processing of received signals at a low frequency involves its implementation in the form of a transverse filter with a linear phase characteristic [4] with the number of taps of the delay line 2N-1, where N is the number of parameters of the signal model and interference as random processes that allow reproducing signal spectra and interference with a given accuracy [5]. Such a choice leads in practice to a value of N equal to 3 ... 5.

 Computer simulation of this adaptive filtering scheme using the least squares algorithm for changing the AF transmission coefficient, carried out for various spectra of the useful signal and interference (including those that completely coincide), confirmed the above conclusions.

The presence of some a priori information about the properties of the filtered process ξ ₁ (t) and the possibility of diversity reception can improve the quality of the estimates generated by the adaptive filter in the circuit of FIG. 1.

 Consider the circuit shown in FIG. 2.

по критерию минимума среднеквадратической ошибки [1]. При разнесенном приеме в предположении R_K=0, R_L=1 оценка отсчетов корреляционной функции ξ (t) может быть получена согласно схеме фиг. 3. Оценка отсчетов функции корреляции (выход блока 4 вычисления отсчетов корреляционной функции) при этом может быть определена, например, в виде

где z (t_j) - значение сигнала на j-ом отводе линии задержки ЛЗ, а К определяется полосой частот ожидаемой сосредоточенной помехи ξ (t).If the autocorrelation function of the stationary random process ξ (t) is known, and z ₁ (t) and z ₂ (t) contain processes correlated with ξ (t), then the least squares algorithm that controls the change in the transmission coefficients AF1 (block 1) and AF2 (block 3), leads to the formation of the output evaluation scheme

by the criterion of the minimum standard error [1]. With an exploded reception, assuming R _K = 0, R _L = 1, an estimate of the samples of the correlation function ξ (t) can be obtained according to the scheme of FIG. 3. An estimate of the samples of the correlation function (the output of the block 4 for calculating the samples of the correlation function) can be determined, for example, in the form

where z (t _j ) is the signal value at the jth tap of the delay line of the LZ, and K is determined by the frequency band of the expected concentrated interference ξ (t).

Strictly speaking, formula (17) gives an estimate of the readings of the cross-correlation function z ₁ (t) and z ₂ (t). For R _K = 0, R _L = 1, these estimates coincide with the estimates of the readings of the autocorrelation function ξ (t).

- вектор коэффициентов передачи АФ1 и АФ2 в установившемся режиме. Вектор W(ω) может быть найден из матричного выражения
W(ω) = G $\genfrac{}{}{0ex}{}{\text{-1}}{\text{zz}}$ (ω)G_ξz(ω) (19)
соответствующего уравнению Винера-Хопфа. В выражении (19) G_zz(ω) - матрица энергетических спектров входных сигналов, G_ξz(ω) - вектор взаимных
энергетических спектров выделяемой оценки и входных сигналов. Выражения для G_zz(ω) и G_ξz(ω) имеют вид

Подставляя (20) в (19), с учетом обозначений (11) для W₁( ω ) и W₂ ( ω ) в установившемся режиме можно получить

где A(ω) = 1+a²(ω)+h $\genfrac{}{}{0ex}{}{\text{2}}{\text{1}}$ (ω),

,

.We denote

- vector transmission coefficients AF1 and AF2 in steady state. The vector W (ω) can be found from the matrix expression
W (ω) = G $\genfrac{}{}{0ex}{}{\text{-1}}{\text{zz}}$ (ω) G _ξz (ω) (19)
corresponding to the Wiener-Hopf equation. In expression (19), G _zz (ω) is the matrix of energy spectra of the input signals, G _ξz (ω) is the vector of mutual
energy spectra of the allocated estimation and input signals. The expressions for G _zz (ω) and G _ξz (ω) have the form

Substituting (20) into (19), taking into account the notation (11) for W ₁ (ω) and W ₂ (ω) in the steady state, we can obtain

where A (ω) = 1 + a ² (ω) + h $\genfrac{}{}{0ex}{}{\text{2}}{\text{1}}$ (ω),

,

.

на выходе сумматора 2 имеет вид

где

(23)

Для выше рассмотренного примера результаты вычисления нормированного энергетического спектра оценки для относительно тяжелых условий работы матричного фильтра, представленного на фиг. 2,

;

дают довольно хорошее совпадение энергетических спектров сосредоточенной помехи и ее оценки. Подчеркнем, что данные результаты относятся к устройству фиг. 1, получены в предположении известности корреляционной функции процесса ξ (t).Now, according to the circuit of FIG. 2 steady state energy spectrum of interference assessment

at the output of adder 2 has the form

Where

(23)

For the above example, the results of calculating the normalized energy spectrum of the estimate for the relatively difficult operating conditions of the matrix filter shown in FIG. 2

;

give a fairly good agreement of the energy spectra of the concentrated noise and its estimates. We emphasize that these results relate to the device of FIG. 1 are obtained under the assumption that the correlation function of the process ξ (t) is known.

и зависит от r₀ и дисперсии

оценки

, формируемой на выходе блока 6 усреднения. Выберем K₀ в виде

,
где

.We will use the estimate obtained by the matrix filter (FIG. 2) in the filtration scheme shown in FIG. 4. The thickened arrow characterizes the transmission of the set of samples {r _k }, calculated by expression (17), to the block 5 for calculating the control coefficients of adaptive filters. Unit 5 for calculating the control coefficients of adaptive filters operates according to the least squares algorithm with a known interference correlation function [1]. The multiplication coefficient K _{0 of the} scale block 7 determines the necessary scale for the presentation of the estimate

and depends on r ₀ and variance

assessments

formed at the output of block 6 averaging. We choose K ₀ in the form

,
Where

.

Аналогично формулам (7) и (8) можно записать

При использовании ранее введенных обозначений выражения G_{ш вых.} ( ω ) и G_{S вых.} ( ω ) можно привести к виду

В формулах (26) и (27) введены обозначения
P₁(ω) = W₁(ω)K₀;
P₂(ω) = W₂(ω)K₀;

;

Сравним эффективность подавления сосредоточенной помехи в схеме фиг. 1 (или схеме фиг. 2 без знания корреляционной функции помехи) и предлагаемом устройстве (схема фиг. 4.).Let us evaluate the quality of filtration in the upper channel of the proposed device, the output signal of which is

Similarly to formulas (7) and (8), we can write

When using the previously introduced notation of the expression G _{w o.} (ω) and G _{S o} (ω) can be reduced to

In formulas (26) and (27), the notation
P ₁ (ω) = W ₁ (ω) K ₀ ;
P ₂ (ω) = W ₂ (ω) K ₀ ;

;

Let us compare the concentrated noise suppression efficiency in the circuit of FIG. 1 (or the diagram of FIG. 2 without knowing the correlation function of the interference) and the proposed device (the diagram of FIG. 4.).

As the analysis of formula (27) for the above example shows, the energy spectrum of the signal at the output of the proposed device is practically not distorted in comparison with the spectrum at the input for small values of R _K (R _K ≤ 0.3). Calculations show that the noise at the output is determined by the weakly correlated spectral components of the signal, and takes on the greatest value at frequencies near the maximum of the concentrated interference spectrum. The difference between R _L from 1 and R _K from 0 leads to a small decrease in the energy gain η.

Comparison of the dependence of η on the signal-to-noise ratio at the input assuming its identity for both diversity branches shows that in the case when the diversity condition does not strictly fulfill the condition R _L = 1 and R _K = 0, the proposed device is 2 times more efficient than the prototype ( Fig. 2.). If you neglect the "white" noise and (P _c / P _W ) _VH. = 1, R _L = 0.8; R _K = 0.2, the proposed device provides η = 5, while the prototype has η = 2.5.

 Computer simulations have confirmed the findings regarding the effectiveness of suppressing correlated interference by the proposed device for any form of interference energy spectrum.

 All entered blocks (5-9) can be performed on the same elemental base as the prototype blocks. In addition, the modern level of development of digital signal processing processors (DSPs) in combination with fast-acting ADCs and DACs makes it relatively easy to implement all operations on analog signals and discrete sequences described in the materials presented.

LITERATURE
1. Widrow B., Stearns S. Adaptive signal processing: Per. from English - M.: Radio and communications, 1989 .-- 440 p.

 2. Sosulin Yu.G. The theory of detection and estimation of stochastic signals. - M .: Owls. Radio, 1978.- 320 s.

 3. Land mobile radio: In 2 kn. Prince 1. Fundamentals of the theory / I.M. Pyshkin, I.I. Duty, R.T. Pantikyan et al .: Ed. V.S. Semenikhina and I.M. Pyshkina. - M.: Radio and Communications, 1990. - 340 p.

 4. Turkin A.I. Recurrent reception of complex signals. - M .: Radio and communications, 1988 .-- 248 p.

 5. Bykov VV Digital modeling in statistical radio engineering. - M.: Sov. Radio, 1971. - 328 p.

Claims (1)

 An adaptive interference suppression device comprising first and second adaptive filters and an adder, adaptive filter outputs connected to the first and second adder inputs, characterized in that a correlation function calculation unit, adaptive filter control coefficient calculation unit, averaging unit, scale unit, first are introduced and the second adders, and the inputs of the device are the first and second inputs of the block for calculating the samples of the correlation function, the first output of which is connected to the input of the second adaptive filter and to the first input of the first adder, the second output of the correlation function sample calculation unit is connected to the input of the first adaptive filter and the first input of the second adder, the third output of the correlation function sample calculation unit is connected to the third input of the scale unit and the first input of the adaptive filter control coefficient calculation unit the second input of which is connected to the output of the adder, and the output is connected to the control inputs of the first and second adaptive filters, the output of the adder is connected to the first the input of the scale unit, and through the averaging unit, with the second input of the scale unit, the output of which is connected to the second inputs of the first and second adders, the outputs of which are the outputs of the entire device.

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