RU2100822C1 - Rank adaptive serial signal finder - Google Patents

Abstract

FIELD: radio engineering, in particular, radars which detect signals of alternating power under combined effect of noise and sequence of jam pulses of unknown distribution function. SUBSTANCE: device estimates noise characteristics and use them for correction of signal-noise ratio. EFFECT: increased stability to noise. 7 dwg

Description

 The invention relates to radio engineering and can be used in radar devices for detecting signals with varying power under conditions of joint exposure to noise and a stream of non-synchronous impulse noise with an unknown distribution law.

на величину

и тем самым осуществить адаптацию рангового последовательного обнаружителя сигналов к совместному воздействию шума и потока несинхронных импульсных помех [3]
Технический результат заключается в увеличении помехозащищенности.An adaptable rank detector is known, comprising a matched filter and a detector sequentially connected, a multi-tap delay line, m outputs of which are connected to a rank calculating unit, the (m + 1) -th input of which is connected to the input of a multi-tap delay line, and a recirculation drive and an acceptance block connected in series solutions, an analog-to-digital converter connected between the detector and the delay line, a unit for measuring statistical characteristics, the first and second inputs of which are connected respectively with the first and last outputs of the multi-tap delay line, read-only memory, the first input of which is connected to the output of the rank calculation unit, the second input to the first, and the third to the second output of the statistical characteristics measurement unit, and the output of the read-only memory device is connected to the input of the recirculation drive, this unit of measurement of statistical characteristics contains the first and second quadrators, sequentially connected to the first recirculation drive and the first division unit, the follower the second recirculation drive and the third quadrator are turned on, the output of which is connected to the second input of the first division unit, as well as the counter, in addition, the output of the rank calculation unit is connected to the third input of the statistical characteristics measurement unit, the output of the decision unit is connected to the fourth input of the statistical measurement unit characteristics and the input of zeroing of the recirculation drive, and the unit for measuring statistical characteristics also contains the first and second units of subtraction and sequentially included in the numerator of the private evaluation of the signal, the first input of which is connected to the output of the first division unit, the third recirculation drive and the second division unit, the second input of which is connected to the output of the counter, while the outputs of the first and second quadrants are connected respectively to the first and second inputs of the first subtraction unit, the output which is connected to the input of the first recirculation drive, and the output of the second subtraction unit is connected to the input of the second recirculation drive, and the first, second, third and fourth inputs and The first and second outputs of the unit for measuring statistical characteristics, respectively, are the interconnected input of the first quadrator and the first input of the second subtraction unit, interconnected input of the second quadrator and the second input of the second subtraction unit, the second input of the private signal estimator, interconnected counter zeroing inputs, and the first, second and third recirculation drives and the outputs of the first and second division blocks, the decision block is made in the form of a first comparator and then the second comparator, the OR element, the decision counter and the third comparator, the output of which is connected to the input of the zeroing of the decision counter, the output of the first comparator connected to the second input of the OR element, and the input and output of the decision block, respectively, are interconnected inputs of the first and second comparators and the output of the third comparator, the rank calculation unit is made in the form of m comparators, the outputs of which are connected to the corresponding inputs of the adder, with m-inputs, (m + 1) -m input and output the rank calculation unit, respectively, are the first inputs of the comparators, the second inputs m of the comparators connected to each other and the output of the adder, the recirculation accumulator is made in the form of series-connected adder and a memory unit, the output of which is connected to the first input of the adder, and the input and input of zeroing and the output of the recirculation accumulator, respectively are the second input of the adder, the second input of the memory unit and the output of the adder [1]
The known device has low noise immunity, which is caused by a significant deterioration in the quality characteristics of an adaptive rank detector of signals with noise adaptation with an unknown distribution law under conditions of combined exposure to noise and a stream of non-synchronous impulse noise with an arbitrary statistical distribution law. The deterioration of the quality characteristics can be expressed in terms of the equivalent increment of the threshold signal-to-noise ratio Δa depending on the parameters of the impulse noise γ (probability of occurrence of an interference impulse in any range channel) and b (noise-to-noise ratio) [2] Measuring the interference parameters g, b and using the relationship between them and Da, we can introduce a correction in the measurement of the signal-to-noise ratio

by the amount

and thereby adapt the rank sequential detector of signals to the combined effects of noise and a stream of non-synchronous impulse noise [3]
The technical result consists in increasing the noise immunity.

 To do this, in an adaptable rank detector containing a matched filter, a detector, an analog-to-digital converter and a multi-tap delay line and series-connected rank calculator, read-only memory unit, storage device, decision-making unit and statistical characteristics meter, the first and second outputs of which are connected respectively with the second and third inputs of the read-only memory block, while the m outputs of the multi-tap delay line are connected to the corresponding m inputs of the calculation rank, the (m + 1) -th input of which is connected to the output of the analog-to-digital converter, the output of the decision block is connected to the second input of the drive, and the first and last outputs of the multi-tap delay line are connected respectively to the second and third inputs of the meter of statistical characteristics, this rank calculator contains m comparators, the outputs of which are connected to the corresponding inputs of the adder, and m inputs, (m + 1) -th input and output of the rank calculator, respectively, are the first inputs of m comparators connected The second inputs of the comparators and the output of the adder are between themselves, the drive contains serially connected addition unit and a memory unit, the output of which is connected to the first input of the addition unit, while the first and second inputs and the output of the drive are respectively the second input of the addition unit, the zeroing input of the memory unit, and the output of the addition unit, the decision unit contains the first comparator and a second comparator, an OR element, a counter and a third comparator in series, the output of which is connected to the counter zeroing input, p In this case, the output of the first comparator is connected to the second input of the OR element, and the input and the first and second outputs of the decision block are respectively the inputs of the first and second comparators, the outputs of the third and first comparators, the statistical characteristics meter contains a first quadrator, a second quadrator connected in series , the first subtraction unit, the first drive and the first division unit, the second subtraction unit, the second drive and the third quadrator, the output of which with connected to the second input of the first division unit, the third drive and the first counter and the second division unit connected in series, while the input of the first quadrator is directly connected to the first input of the second subtraction unit, and the second quadrant input is connected to the second input of the first subtraction unit through the first quad the second input of the second subtraction unit, and the first, second and third inputs and the first output of the statistical characteristics meter, respectively, are interconnected zeroing inputs of the first, second of the third and third drives and the first counter, the input of the first quadrator, the input of the second quadrator and the output of the first division unit, a third subtraction unit, a first exponentiation unit and a weight unit, the output of which is connected directly to the first input of the first multiplexer, are inserted in series with the third subtraction unit and with the second input of the first multiplexer through a series-connected additional weighing unit and inverter, a third drive and a fourth unit connected in series Italy, the output of which is connected directly to the third input of the first multiplexer, and to the first and second control inputs of the first multiplexer through the first and second comparators, respectively, and the fourth quadrator connected in series, the input of which is connected to the output of the third drive, and the third division unit, the second input of which connected to the output of the first drive and the first input of the third subtraction unit, connected by its second input to the output of the third quadrator, while the output of the first multiplexer is connected is connected to the second input of the second division unit, the output of which is connected to the input of the third drive, the second inputs of the first and second comparators are connected respectively to the output of the weight unit and the output of the inverter, while the fourth input of the fourth characteristics unit is the second input of the fourth subtraction unit connected to the analog output -digital converter, K comparators connected by their first inputs to the input of the first quadrator, and outputs with the corresponding control inputs of the second multiplexer a, K inputs of which are connected to the corresponding second inputs K of comparators and to the corresponding outputs K of weight blocks, the second inputs of which are connected to the first input of the first division unit, the first control input of the second multiplexer is connected to the second input of the multiplication unit through the second counter connected in series, the zeroing input which is connected to the zero input of the first drive, and the fourth division unit, the first input of which is connected to the output of the first counter, while the output of the second multiplexer is connected with the input of the second exponentiation block, the output of which is connected to the first input of the multiplication block, connected by its output to the first input of the first addition block, the first addition block, the third exponentiation block, and the second addition block, the second input of which is connected to the output of the third block division, while the second output of the meter of statistical characteristics is the output of the second addition unit.

 Figure 1 shows the structural electrical diagram of the proposed device; in FIG. 2 structural electrical circuit of the meter of statistical characteristics; figure 3 is a structural electrical diagram of a decision block; figure 4 is a structural electrical circuit of the rank calculator; figure 5 structural electrical diagram of the drive; figure 6 - diagrams explaining the operation of the proposed device; 7 is a graph of the dependence of the parameter p on the size of the reference sample m.

 The rank adaptive serial signal detector contains a matched filter 1, detector 2, analog-to-digital converter 3, multi-tap delay line 4, rank 5 calculator, read-only memory block 6, drive 7, decision block 8, and statistical characteristics meter 9, which contains the first quadrator 10, the first subtraction block 11, the second quadrator 12, the first accumulator 13, the second subtraction block 14, the second accumulator 15, the third quadrator 16, the first division block 17, the third subtraction block 18, the first step raising block 19 n, weight unit 20, inverter 21, first multiplexer 22, first comparator 23, second comparator 24, fourth subtraction unit 25, third drive 26, second division unit 27, first counter 28, fourth quadrator 29, third division unit 30, additional weight block 31, K of comparators 32, K weight blocks 33, second counter 34, fourth division block 35, second multiplexer 36, second exponentiation block 37, multiplication block 38, first addition block 39, third exponentiation block 40 and second block 41 addition, decision block 8 contains the first, second the first and third comparators 42, 43 and 44, the OR element 45 and the counter 46, the rank 5 calculator contains m comparators 47 and the adder 48, the drives 7, 13, 15 and 26 contain an addition unit 49 and a memory unit 50.

 Rank adaptive serial signal detector works as follows.

). В результате на первый, второй и третий входы блока 6 постоянной памяти поступают соответственно значения ранга r $\genfrac{}{}{0ex}{}{\text{z}}{\text{n}}$ оценки отношения моментов

и параметра

.The input mixture of signal, noise and non-synchronous impulse noise after filtering in a matched filter 1 is detected in detector 2, converted to digital form in analog-to-digital converter 3, and fed to rank 5 calculator and multi-tap delay line 4, made, for example, on a multi-bit shift register moreover, the shift of information is carried out with a period equal to one resolution element in time. Rank calculator 5 calculates the rank of the sample of the tested channel relative to the samples of m neighboring channels, in which, with a significant asymmetry of the channel, there is practically only a mixture of noise and non-synchronous impulse noise. Rank r $\genfrac{}{}{0ex}{}{\text{z}}{\text{n}}$ (of the nth observation period, channel 2) is fed to the first input of the permanent memory block 6, in which the pre-calculated values of the logarithm of the likelihood ratio of rank λ, which is a function of the rank value, of the squared mathematical expectation of noise M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ to the noise power M ₂ and parameter a 'representing the adjusted (in the presence of non-synchronous impulse noise) estimate of the signal-to-noise ratio in terms of power. Ratio M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ is measured for the actual noise by the measuring instrument 9 of the statistical characteristics and is supplied to the second input of the permanent memory unit 6. Based on the statistical characteristics arriving at the fourth input of the meter 9, the reference values of the initial implementation of the mixture of signal, noise and impulse noise are corrected (taking into account impulse noise) the signal-to-noise value a 'is estimated in each of the studied channels. If the signal in the channel under study is absent, then a pseudo-estimate is formed, which tends to zero (

) As a result, the first, second and third inputs of the block 6 of read-only memory respectively receive values of rank r $\genfrac{}{}{0ex}{}{\text{z}}{\text{n}}$ assessment of the relationship of moments

and parameter

.

на его выходе формируется значение логарифма функции правдоподобия, соответствующее этой комбинации параметров. В блоке 6 постоянной памяти записаны заранее рассчитанные значения λ для практически возможных комбинаций входных параметров. Для расчета значений l используется следующая методика:
1) по отношению моментов определяется параметр формы распределения Вейбулла d из соотношения

с учетом связи между моментами ν-го порядка и параметрами распределения Вейбулла
Mν = c^-ν/dГ(1+ν/d),
где Г(•) гамма-функция. Связь между отношением моментов M $\genfrac{}{}{0ex}{}{\text{2}}{\text{1}}$ /M₂ и параметром d, устанавливаемая этим соотношением, носит однозначный монотонный характер;
2) для фиксированного значения второго начального момента (обычно для M₂=2) определяется параметр масштаба с распределения Вейбулла из соотношения

3) производится расчет логарифма отношения правдоподобия по следующим соотношениям для всех значений ранга r 0 m

где G(t)=1-exp{-ct^d} распределение шума, аппроксимируемое распределением Вейбулла;

где F(t) распределение смеси сигнала с шумом; y переменная интегрирования; m размер опорной выборки.According to the parameter values received at the input of block 6 of permanent memory

at its output, the logarithm of the likelihood function corresponding to this combination of parameters is formed. In block 6 of read-only memory, pre-calculated values of λ for practically possible combinations of input parameters are recorded. The following procedure is used to calculate l values:
1) the parameter of the Weibull distribution form d is determined from the relation of moments from the relation

taking into account the relationship between the νth order moments and the Weibull distribution parameters
Mν = c ^{-ν / d} Г (1 + ν / d),
where Γ (•) is the gamma function. The relationship between the ratio of moments M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ and the parameter d, established by this relation, is of a monotonous character;
2) for a fixed value of the second initial moment (usually for M ₂ = 2), the scale parameter is determined from the Weibull distribution from the relation

3) the logarithm of the likelihood ratio is calculated using the following relationships for all values of rank r 0 m

where G (t) = 1-exp {-ct ^d } the noise distribution approximated by the Weibull distribution;

where F (t) is the distribution of the mixture of signal with noise; y integration variable; m is the size of the reference sample.

Although the given values of the logarithm of the likelihood ratio were calculated for a fixed value of M ₂ , they will have exactly the same value for other values of the second initial moment at fixed M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ and a '. The magnitude of the likelihood ratio logarithm is not affected by the absolute value of M ₂ , but by its relationship with the first initial moment and signal power.

Given that the relationship between the logarithms of the likelihood ratio λ, rank r, and adaptation parameters M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ and a 'is of a complex transcendental character, the determination of λ in a different way than using the block 6 of read-only memory is impractical and practically impossible. The issues of optimizing the quantitative organization of the likelihood ratio matrix (the number of quantization levels and the practical range of parameter changes) are investigated in detail. Recommended torque ratio M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ , the variation range of which is 0 1.0, quantize in increments of 0.1, and the signal-to-noise ratio a 'is quantized in increments of 0.25 0.5 within the expected range of values (usually 0.5 5). The losses in this case are about 10%. As an example, the table shows the logarithm of the likelihood ratio for various combinations of r and a 'at M $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ / M ₂ = 0.785, which corresponds to the coincidence of the Weibull distribution with the Rayleigh distribution (d = 2).

формально являются адресами, необходимыми для поиска ячейки, содержащей нужное значение λ. С выхода блока 6 постоянной памяти величина

соответствующая поступившим входным значениям, поступает в накопитель 7, где суммируется с ранее записанной суммой этих величин за предыдущие (n-1) периодов наблюдений в данном канале. Далее эта сумма в блоке 8 принятия решения испытывается на пороги A = ln[(1-β)/α] и B = ln[β/(1-α)] для вынесения решения по последовательному правилу, где α и β вероятности ложной тревоги и пропуска сигнала соответственно. После принятия решения во всех каналах на выходе блока 8 принятия решения формируется импульс сброса, который поступает на вход обнуления накопителя 7 и первый вход измерителя 9 статистических характеристик, устанавливая перечисленные блоки в исходное состояние. Этот же импульс поступает и во внешние синхронизирующие устройства. Выходом рангового адаптивного последовательного обнаружителя сигналов является выход первого компаратора 42 блока 8 принятия решения.This table is an element of a three-address cube of block 6 of read-only memory. The input values of the parameters r,

formally, they are the addresses needed to search for a cell containing the desired value of λ. From the output of block 6 of permanent memory value

corresponding to the received input values, it enters the accumulator 7, where it is summed with the previously recorded sum of these values for the previous (n-1) observation periods in this channel. Further, this amount in decision block 8 is tested on the thresholds A = ln [(1-β) / α] and B = ln [β / (1-α)] to make a decision according to the sequential rule, where α and β are the false alarm probabilities and signal skipping, respectively. After a decision is made in all channels at the output of decision block 8, a reset pulse is generated, which is fed to the input of zeroing of the drive 7 and the first input of the meter 9 of statistical characteristics, setting the listed blocks in the initial state. The same impulse enters the external synchronizing devices. The output of the rank adaptive serial signal detector is the output of the first comparator 42 of the decision block 8.

 The signal-to-noise ratio a, and then the corrected (taking into account the action of non-synchronous impulse noise) signal-to-noise ratio a 'are estimated using the statistical characteristics meter 9 as follows (Fig. 2).

где

и x_n значения оценки амплитуды сигнала и отсчета исходной реализации смеси сигнала и шума на n-м шаге наблюдений; l(x_n+1

) функция ограничения, определяемая как

где

k₁, K₂ некоторые коэффициенты.Initially, the signal amplitude is estimated. Taking into account the fact that rank detectors are designed to operate in an a priori indeterminate noise and noise environment, as well as asymmetry of the distribution density of the signal mixture with noise at small signals, a “robust” (stable to changing distributions) recursive estimation algorithm of the following form is used [ 3]

Where

and x _{n the} values of the estimation of the signal amplitude and the reference of the initial implementation of the mixture of signal and noise at the nth observation step; l (x _{n + 1}

) a restriction function defined as

Where

k ₁ , K _{2 are} some factors.

 The algorithm for estimating the signal amplitude is recurrent, which is important for sequential detection, when the estimate should be issued at any arbitrary time. Robustness is achieved by limiting extreme readings.

Анализ показывает, что при изменении отношения сигнал-шум a от 0,5 до 10 отношение k₂/k₁ принимает значения в пределах от 0,25 до 1,0 в зависимости от параметров формы d.In the above algorithm, an asymmetric limit of samples is used, expressed in the inequality of the coefficients k ₁ and k ₂ . The algorithm is adaptive and is designed for use in a non-stationary noise-noise situation. Adaptation to the noise level is carried out by the adjustment of the restriction levels, depending on the assessment of its rms value

The analysis shows that when changing the signal-to-noise ratio a from 0.5 to 10, the ratio k ₂ / k ₁ takes values in the range from 0.25 to 1.0, depending on the parameters of the form d.

. Так, при отношениях a 0,5 1,0 и числе наблюдений n=10 введение асимметричного ограничения при k₂/k₁=0,3 в релеевском шуме (d= 2) позволяет уменьшить величину относительной среднеквадратической ошибки δU на 40% Одновременно при этих же условиях уменьшается среднее относительное смещение оценки ΔU /U в два раза. Для наиболее характерных значений параметра формы d > 0,5 2,0 величина среднеквадратической ошибки оказывается еще меньшей.In view of the fact that the value of U is not known a priori, it makes sense to implement some average restriction, which would ensure, on average, a good estimation quality within the operating range of the signal-to-noise ratio a. With such an averaged value of the ratio k ₂ / k ₁ in the range a from 0 to 6, it is advisable to choose a value of 0.3 for

. So, for relations a 0.5 1.0 and the number of observations n = 10, the introduction of an asymmetric constraint for k ₂ / k ₁ = 0.3 in Rayleigh noise (d = 2) allows us to reduce the relative mean square error δU by 40% at the same time under the same conditions, the average relative bias of the ΔU / U estimate decreases by half. For the most characteristic values of the shape parameter d> 0.5 2.0, the value of the standard error is even smaller.

 An analysis of the quality of the algorithm showed that the algorithm ensures the stability of the estimate of the signal amplitude in an unsteady noise and noise environment and with other distributions. The analysis was carried out for distributions such as Rayleigh, Weibull, lognormal, etc.

 A significant deterioration in the quality characteristics of a rank sequential detector with noise adaptation when combined with noise and a stream of non-synchronous impulse noise with an arbitrary distribution law makes it necessary to create a rank sequential detector that adapts to these conditions.

при a₁=const для характеристик

(a). Она имеет вид [2]

где p параметр, величина которого зависит от m, как показано на фиг.7. Так, например, при m=20 значение параметра p=-1,1.An analysis of the quality characteristics of a rank sequential detector (the dependence of the probability of correct detection of the signal D and the average number of observations n on the signal-to-noise ratio a) under the combined influence of noise and impulse noise for various values of the parameters γ (the probability of the appearance of an interference pulse in some resolution element ( range channel)), b (noise-to-noise ratio), m (reference sample size), n (number of observations), a (probability of false alarm) allowed us to establish the dependence of the increment of the threshold ratio signal-to-noise Da in terms of D = D ₁ (calculated probability of correct detection) for a ₁ = const (a ₁ calculated signal-to-noise ratio) for detection characteristics D (a) and in level

when a ₁ = const for the characteristics

(a). It has the form [2]

where p is a parameter whose value depends on m, as shown in Fig.7. So, for example, with m = 20, the value of the parameter p = -1.1.

и далее использовать их для коррекции оценки отношения сигнал-шум по следующему алгоритму [3]

Оценка вероятности γ производится через относительную частоту превышения некоторого порогового уровня отсчетами смеси шума и импульсной помехи. Так как свойства несинхронной импульсной помехи не зависят от дальности, поэтому безразлично, на какой дальности оценивать g А поскольку отражения от местных предметов имеют место на малых дальностях, то оценки вероятности g будем производить на средних и больших дальностях. Так, при числе разрешаемых элементов 1024 отсчет превышений некоторого порогового уровня можно начинать с 513-го элемента дальности и продолжать до 1024-го элемента. По истечении всего периода (1024 элемента) получаем оценку g.Using dependence (1), it is possible, having only the quality characteristics of a rank sequential detector of signals in noise conditions, to obtain quality characteristics for the conditions of joint exposure to noise and the flow of impulse noise with arbitrary parameters γ and b. In other words, the presence of impulse noise with parameters g and b is equivalent to an increase in the threshold signal-to-noise ratio a by Da
Therefore, in order to adapt a rank sequential detector of signals in the conditions of joint action of noise and non-synchronous impulse noise, it is necessary to make estimates

continue to use them to correct the estimate of the signal-to-noise ratio according to the following algorithm [3]

The probability γ is estimated through the relative frequency of exceeding a certain threshold level by samples of a mixture of noise and impulse noise. Since the properties of non-synchronous impulse noise are independent of the range, it doesn’t matter at what range to evaluate g And since reflections from local objects take place at short ranges, we will estimate the probability g at medium and long ranges. So, with the number of allowed elements 1024, the countdown of excesses of a certain threshold level can be started from the 513rd element of the range and continue to the 1024th element. After the entire period (1024 elements), we obtain the estimate g.

в зависимости от того, какой из порогов превышен. Если имеет место только шум (ни один из порогов не превышен), то

0.The essence of estimating another parameter b is to compare the sample of the mixture of noise and impulse noise with quantization thresholds and to form estimates based on this

depending on which threshold is exceeded. If only noise occurs (none of the thresholds is exceeded), then

0.

[3] При расчетах принималась во внимание точность оценок параметров γ b, a и точность аппроксимации вида (1).The quality of adaptation of a rank sequential detector of signals in noise and non-synchronous impulse noise conditions is analyzed. For this, the standard deviations of the probability of correct detection (σ _ΔD ) and the average number of observations were estimated

[3] In the calculations, the accuracy of the estimates of the parameters γ b, a and the accuracy of the approximation of the form (1) were taken into account.

В связи с тем, что оценка вероятности γ определяется как относительная частота некоторого события A (превышение порогового уровня), запишем [3]

где l число появлений события A (величина l имеет биномиальное распределение);
N общее число испытаний. Относительная частота

является несмещенной состоятельной оценкой для соответствующей вероятности, равной математическому ожиданию

[3] Дисперсия

определяется

Полагая, что N=512, получаем при

0,2 (одно из характерных значений вероятности появления импульса помехи)

При оценивании b используется разбиение на уровни квантования диапазона наиболее вероятных значений b. Шаг квантования принимается равным 0,5 В. Дисперсия

выражается [3]

где

0,5 В элементарный интервал.Estimates of the parameters gb, a and the approximation estimate are uncorrelated, therefore, we can write [3]

Due to the fact that the probability estimate γ is determined as the relative frequency of some event A (exceeding the threshold level), we write [3]

where l is the number of occurrences of event A (l has a binomial distribution);
N total number of tests. Relative frequency

is an unbiased consistent estimate for the corresponding probability equal to the mathematical expectation

[3] Dispersion

determined by

Assuming that N = 512, we obtain for

0.2 (one of the characteristic values of the probability of the appearance of an interference pulse)

In estimating b, a partition into the quantization levels of the range of the most probable values of b is used. The quantization step is taken equal to 0.5 V. Dispersion

expressed [3]

Where

0.5 V elementary interval.

где

20%
Аналогично выражается дисперсия оценки аппроксимации (1)

где, как показывают расчеты,
Δ_аппр (15-20)% (для расчетов берем Δ_аппр 20%).As indicated in [3], the maximum deviation of quality characteristics from potential characteristics due to adaptation of a rank sequential detector in terms of noise is 20%. Accepting the distribution law of the deviation normal, we find the variance

Where

twenty%
Similarly, the variance of the approximation estimate is expressed (1)

where, as calculations show,
Δ _appr (15-20)% (for calculations we take Δ _appr 20%).

(a) в условиях совместного действия шума и потока несинхронных импульсных помех [3] При этом полагаем, что частные производные приближенно равны отношению соответствующих приращений по уровню D= D₁= 0,9 при a₁=const (для производных из выражения (3)) и по уровню

при a₁=const (для производных из выражения (4)).The values of the partial derivatives in expressions (3), (4) are determined using the dependency graphs D (a) and

(a) under the conditions of the combined action of noise and the flow of non-synchronous pulsed noise [3] Moreover, we assume that the partial derivatives are approximately equal to the ratio of the corresponding increments in level D = D ₁ = 0.9 for a ₁ = const (for derivatives from expression (3 )) and by level

when a ₁ = const (for derivatives from expression (4)).

≈ 11%
Таким образом, применяя ранговый адаптивный последовательный обнаружитель сигналов в условиях совместного действия шума и потока несинхронных импульсных помех с неизвестным законом распределения, обеспечиваем тем самым хорошее соответствие показателей качества их потенциально достижимым значениям. Это удается осуществить, используя корректировку оценки отношения сигнал-шум согласно (2). При этом среднеквадратические отклонения от потенциально достижимых значений D и

как показывают расчеты, не превышают 10% и 11% соответственно.From expressions (3), (4) we finally obtain σ _ΔD ≈ 10%

≈ 11%
Thus, using a rank adaptive sequential detector of signals under conditions of the combined action of noise and a stream of non-synchronous impulse noise with an unknown distribution law, we thereby ensure good correspondence of quality indicators to their potentially achievable values. This can be done using the correction of the signal-to-noise ratio estimation according to (2). Moreover, the standard deviations from the potentially attainable values of D and

as calculations show, do not exceed 10% and 11%, respectively.

 The amplitude of the signal U and, subsequently, the signal-to-noise ratio a and the corrected (taking into account the action of non-synchronous impulse noise together with the noise), the signal-to-noise ratio a 'is estimated in the statistical characteristics meter 9, which operates as follows (see Fig. 2 )

Величины

являются оценками (с точностью до сомножителя (m-1)) среднего значения M₁ и мощности шума M₂. После возведения величины

(m-1) в квадрат в третьем квадраторе 16 и деления на

(m-1) в первом блоке 17 деления, на выходе первого блока 17 деления образуется величина

По поступающим на первый и второй входы третьего блока 18 вычитания значениям оценок

на выходе третьего блока 18 вычитания формируется разность

которая поступает далее в первый блок 19 возведения в степень, на выходе которого формируется оценка параметра σ служащего масштабом ограничения,

Полученная оценка поступает на первый вход весового блока 20, на выходе которого образуется произведение

которое поступает на первый (информационный) вход первого мультиплексора 22 и второй вход первого компаратора 23, а также поступает через последовательно включенные дополнительный весовой блок 31 и инвертор 21 на второй (информационный) вход первого мультиплексора 22 и второй вход второго компаратора 24.The input of the first drive 13 receives the difference between the squares of the noise signal present on the first and last taps of the multi-tap delay line 4 obtained with the help of the first and second quadrants 10, 12 and the first block 11 of subtraction. The input of the second drive 15 receives the difference of the noise signal obtained with the help of the second subtraction unit 14, which is present at the first and last taps of the multi-tap delay line 4. Thus, at the output of the second and first drives 15 and 13, we have, respectively, for the z-th channel

Quantities

are estimates (accurate to the factor (m-1)) of the average value of M ₁ and the noise power M ₂ . After raising the value

(m-1) squared in the third quadrator 16 and dividing by

(m-1) in the first division block 17, at the output of the first division block 17, a value

On arriving at the first and second inputs of the third block 18 of the subtraction of the values of the estimates

at the output of the third subtraction block 18, a difference is formed

which goes further to the first block 19 of raising to a power, the output of which forms an estimate of the parameter σ which serves as the scale of the constraint,

The resulting estimate goes to the first input of the weight unit 20, at the output of which a product is formed

which enters the first (information) input of the first multiplexer 22 and the second input of the first comparator 23, and also enters through the additional weight unit 31 and inverter 21 connected in series to the second (information) input of the first multiplexer 22 and the second input of the second comparator 24.

которая поступает далее на третий (информационный) вход первого мультиплексора 22 и на первые входы первого и второго компараторов 23, 24, выходы которых соединены соответственно с первым и вторым управляющими входами первого мультиплексора 22. Поступающая на первые входы первого и второго компараторов 23, 24 разность

сравнивается в первом компараторе 23 с произведением

и во втором компараторе 24 с произведением

Если выполняется одно из соотношений

или

или

то на первом и втором управляющих входах первого мультиплексора 22, соответственно, принципиально возможны следующие состояния:
1) 00 соответствует значению функции ограничения

2) 10 соответствует значению функции ограничения

3) 01 соответствует значению функции ограничения

Полученное на выходе первого мультиплексора 22 значение функции ограничения

поступает далее на второй вход второго блока 27 деления. Первый счетчик 28 подсчитывает поступающие на его счетный вход из внешнего синхронизирующего устройства (на фиг.2 не показано) тактовые импульсы, соответствующие периоду повторения наблюдений. Результат подается на первый вход второго блока 27 деления, на выходе которого появляется величина

которая поступает в третий накопитель 26, где суммируется с накопленными за предыдущие периоды повторения значениями оценок амплитуды сигнала U данного элемента разрешения. Результирующая сумма

запоминается в третьем накопителе 26 и поступает на первый вход четвертого блока 25 вычитания и на вход четвертого квадратора 29, на выходе которого формируется величина

которая поступает далее на первый вход третьего блока 30 деления, на второй вход которого поступает значение оценки мощности шума

На выходе третьего блока 30 деления формируется оценка отношения сигнал-шум данного элемента разрешения

По поступающим на первые входы K компараторов 32 (число компараторов выбирается по количеству уровней квантования диапазона наиболее вероятных значений b(1 ≅ b ≅ 10) и, как показывают расчеты, равно 10) значениям отсчетов смеси шума и импульсной помехи Y_j, которые снимаются с первого отвода многоотводной линии 4 задержки, и поступающим на вторые входы компараторов 32 значениям порогов C₁, C₂, C₃, C_K, на выходах K компараторов 32 появляются логические единицы и нули. Логические единицы означают превышение порогов C₁, C₂, C₃, C_K (наличие импульсов помехи в соответствующих элементах разрешения). Логические нули свидетельствуют о том, что в соответствующих каналах присутствует только шум.According to the values of the reference sample of the initial implementation of the signal and noise mixture, which are generated at the output of the analog-to-digital converter 3 (Fig. 1), and the estimates of the amplitude of the initial implementation of the signal and noise mixture at the nth observation step accordingly, at the output of the fourth subtraction block 25, a difference is formed

which goes further to the third (information) input of the first multiplexer 22 and to the first inputs of the first and second comparators 23, 24, the outputs of which are connected respectively to the first and second control inputs of the first multiplexer 22. The difference arriving at the first inputs of the first and second comparators 23, 24

compared in the first comparator 23 with the product

and in the second comparator 24 with the product

If one of the relations

or

or

then on the first and second control inputs of the first multiplexer 22, respectively, the following states are fundamentally possible:
1) 00 corresponds to the value of the restriction function

2) 10 corresponds to the value of the restriction function

3) 01 corresponds to the value of the restriction function

Obtained at the output of the first multiplexer 22, the value of the restriction function

then goes to the second input of the second division unit 27. The first counter 28 counts the clock pulses arriving at its counting input from an external synchronizing device (not shown in FIG. 2) corresponding to the observation repetition period. The result is fed to the first input of the second division unit 27, the output of which appears

which enters the third drive 26, where it is summed up with the values of the signal amplitude U estimates of the given resolution element accumulated for the previous repetition periods. Resulting amount

stored in the third drive 26 and fed to the first input of the fourth block 25 subtraction and to the input of the fourth quadrator 29, the output of which is formed

which goes further to the first input of the third division unit 30, the second input of which receives the value of the noise power estimate

At the output of the third division unit 30, an estimate of the signal-to-noise ratio of this resolution element is formed

According to K comparators 32 arriving at the first inputs (the number of comparators is selected by the number of quantization levels of the range of the most probable values of b (1 ≅ b ≅ 10) and, as calculations show, is equal to 10) the values of the samples of the noise and impulse noise Y _j taken from the first tap of the multi-tap delay line 4, and the logic values and zeros appear on the outputs of the comparators 32 to the second inputs of the comparators 32 of the thresholds C ₁ , C ₂ , C ₃ , C _K. Logical units mean the thresholds C ₁ , C ₂ , C ₃ , C _{K are} exceeded (the presence of interference pulses in the corresponding resolution elements). Logical zeros indicate that only noise is present in the corresponding channels.

формируются в K весовых блоках 33 с использованием оценки второго начального момента

характеризующего мощность шума, которая поступает с выхода первого накопителя 13 на вторые входы К весовых блоков 33.Thresholds

are formed in K weight blocks 33 using an estimate of the second initial moment

characterizing the noise power that comes from the output of the first drive 13 to the second inputs K of the weight blocks 33.

Это число превышений подается на второй вход четвертого блока 35 деления, на первый вход которого поступает результат подсчета первым счетчиком 28 тактовых импульсов, соответствующих периоду повторения наблюдений. На выходе четвертого блока 35 деления получаем оценку

, которая поступает далее на второй вход блока 38 умножения.The results of comparison with the threshold C ₁ from the output of the first of K comparators 32 go to the second counter 34, which counts the number of excesses of the noise and impulse noise of the noise threshold C ₁ with the mixture

This number of excesses is fed to the second input of the fourth division block 35, the first input of which receives the result of counting by the first counter 28 clock pulses corresponding to the repetition period of the observations. At the output of the fourth division block 35 we get the estimate

which goes further to the second input of the multiplication unit 38.

то на первом, втором, третьем, K-м управляющих входах второго мультиплексора 36 соответственно принципиально возможны следующие состояния: 1) 111. 1; 2) 111.10; 3) 111.100; K) 100.0; K+1) 000.0. Состояния 1 K соответствуют наличию шума и импульсной помехи, а для состояния K+1 характерно присутствие только шума. Если на управляющих входах второго мультиплексора 36 появляется состояние K+1, то на выходе его формируется псевдооценка отношения помеха-шум, которая стремится к нулю (

0). Для состояний 1 K на управляющих входах 1, 2, 3, K второго мультиплексора 36 характерны значения оценок

соответственно.The first, second, third, K-th control inputs of the second multiplexer 36 receive the results of comparing the samples of the mixture of noise and impulse noise with thresholds C ₁ , C ₂ , C ₃ , C _K, respectively, and the first, second, third, K-th (information) inputs of the second multiplexer 36 receives the values of these thresholds. If one of the K + 1 relations holds:

then at the first, second, third, K-th control inputs of the second multiplexer 36, respectively, the following states are fundamentally possible: 1) 111. 1; 2) 111.10; 3) 111.100; K) 100.0; K + 1) 000.0. The 1 K states correspond to the presence of noise and impulse noise, while the K + 1 state is characterized by the presence of only noise. If the state K + 1 appears at the control inputs of the second multiplexer 36, then a pseudo-estimate of the noise-noise ratio is formed at its output, which tends to zero (

0). For states 1 K at the control inputs 1, 2, 3, K of the second multiplexer 36, characteristic values of estimates

respectively.

поступает во второй блок 37 возведения в степень, на выходе которого формируется величина

, поступающая затем на первый вход блока 38 умножения, где имеем

. Далее полученное значение поступает на первый вход первого блока 39 сложения, на выходе которого образуется

. Полученная сумма подается на первый вход третьего блока 40 возведения в степень, на выходе которого имеем величину

, которая поступает на первый вход второго блока 41 сложения, на второй вход которого поступает оценка отношения сигнал- шум

, сформированная третьим блоком 30 деления без учета влияния несинхронной импульсной помехи. На выходе второго блока 41 сложения формируется скорректированная (с учетом совместного действия шума и несинхронной импульсной помехи) оценка отношения сигнал-шум

которая в условиях только шума равна

В вычислителе 5 ранга (фиг. 4) сравнивается исследуемый отсчет x_i с опорными помехошумовыми сигналами Y_j с помощью компараторов 47. Результаты сравнения (инверсии)

суммируются в сумматоре 48. Результирующая сумма

, появляющаяся на выходе сумматора 48, является рангом исследуемого отсчета.With the output of the second multiplexer 36 evaluation

enters the second block 37 of raising to a power, at the output of which the value is formed

, then arriving at the first input of the multiplication block 38, where we have

. Next, the obtained value goes to the first input of the first addition unit 39, at the output of which is formed

. The resulting amount is fed to the first input of the third block 40 of raising to a power at the output of which we have the value

, which goes to the first input of the second addition unit 41, the second input of which receives the signal-to-noise ratio estimate

formed by the third division unit 30 without taking into account the influence of non-synchronous impulse noise. At the output of the second addition unit 41, an adjusted (taking into account the combined action of noise and non-synchronous impulse noise) estimate of the signal-to-noise ratio is formed

which in conditions of noise alone is equal to

In the rank 5 calculator (Fig. 4), the studied sample x _{i is} compared with the reference noise-noise signals Y _j using comparators 47. Comparison (inversion) results

summarized in adder 48. The resulting amount

appearing at the output of the adder 48, is the rank of the studied sample.

 Drives 7, 13, 15 and 26 (figure 5) work as follows.

 From the output of the corresponding block, the signal is supplied to the second input of the addition unit 49. At the same time, the value accumulated for the previous (n-1) observations of the signal is supplied to the first input of the addition unit 49. As a result, the sum of n signal values is formed at the output of addition block 49. The installation of the block 50 of the memory in the initial state occurs in the case of a decision in all the analyzed channels using a pulse received at the input of zeroing of the block 50 of the memory from the output of block 8 decision.

 In the process, the address, third, input of the memory unit 50 receives synchronization signals in accordance with the viewed range channels.

 Block 8 decision (figure 3) works as follows.

сравнивается в первом компараторе 42 с порогом A и во втором компараторе 43 с порогом B. Если выполнится одно из соотношений Λ_n≥ A или Λ_n≅ B то на выходах соответствующих компараторов 42 и 43 появятся логические единицы (второй компаратор 43 имеет инверсный выход), что означает принятие решения соответственно об обнаружении или необнаружении цели. Сигналы, свидетельствующие о принятии решения, поступают через элемент ИЛИ 45 на счетчик 46, где число их подсчитывается и затем сравнивается в третьем компараторе 44 с числом анализируемых каналов. При достижении равенства на выходе третьего компаратора 44 возникает импульс, который поступает на вход обнуления счетчика 46, устанавливая его в исходное состояние, также является сигналом сброса для других блоков рангового адаптивного последовательного обнаружителя сигналов.The statistics received at the input of decision block 8

in the first comparator 42 is compared with threshold A and in the second comparator 43 with threshold B. If one of the relations Λ _n ≥ A or Λ _n ≅ B is satisfied, then logical units will appear at the outputs of the respective comparators 42 and 43 (the second comparator 43 has an inverse output) , which means deciding accordingly whether the target is detected or not. The signals indicating the decision are received through the OR element 45 to the counter 46, where their number is calculated and then compared in the third comparator 44 with the number of analyzed channels. When equality is reached, a pulse arises at the output of the third comparator 44, which is fed to the input of zeroing the counter 46, setting it to its initial state, is also a reset signal for other blocks of a rank adaptive serial signal detector.

 In FIG. 6, A, B, C are plots describing the type of clock signals that synchronize the operation of individual blocks of the proposed device (the synchronizer in figure 1 is not shown).

 Diagram A shows the type of pulses, the repetition period of which is equal to the repetition period of the observations. These pulses are supplied from the synchronizer to the counting input of the first counter 28 of the observation repetition periods (Fig. 2), as well as to the reset input of the second counter 34 and the reset input of the counter 46 (Fig. 3), resetting the second counter 34 and the counter 46 by the trailing edge end of each observation period.

 Diagram B shows the type of clock pulses, the repetition period of which is equal to the duration of the resolution interval. These pulses are used to synchronize the analog-to-digital Converter 3 and the multi-tap delay line 4.

 The diagrams C depict a set of pulses characterizing the change in address (numbers in binary code) in accordance with the analyzed resolution elements. The address code arrives at the address inputs of the memory unit 50 of the drives 7, 13, 15, and 26 and synchronizes them.

для обнаружителя с адаптацией в условиях только шума в 3,3 6,0 раза и 7,0 9,1 раза соответственно (m 20 30, α 10^-6 10^-12, a₁ 1,0, D₁ 0,9, g 0,05 0,25, b 5 10). Дальнейшее увеличение параметров помехи g, b приводит к еще более сильному увеличению по D и уменьшению по

. Кроме того, применение предлагаемого рангового адаптивного последовательного обнаружителя сигналов обеспечивает хорошее соответствие показателей качества их потенциально достижимым значениям в условиях совместного воздействия шума и потока несинхронных импульсных помех с произвольными параметрами γ и b (среднеквадратические отклонения от потенциально достижимых D и

не превышают 10 и 11% соответственно).A comparative analysis of the known and proposed devices showed that the use of the proposed rank adaptive sequential detector of signals provides an increase in noise immunity, expressed in an increase in the probability of correct detection and a decrease in the average number of observations relative to the calculated values of the characteristics D and

for a detector with adaptation in conditions of noise only, 3.3 6.0 times and 7.0 9.1 times, respectively (m 20 30, α 10 ^-6 10 ^-12 , a ₁ 1.0, D ₁ 0.9, g 0.05 0.25, b 5 10). A further increase in the interference parameters g, b leads to an even stronger increase in D and a decrease in

. In addition, the use of the proposed rank adaptive sequential detector of signals ensures good compliance of the quality indicators with their potentially achievable values under the combined influence of noise and a stream of non-synchronous impulse noise with arbitrary parameters γ and b (standard deviations from potentially attainable D and

do not exceed 10 and 11%, respectively).

Sources of information
1. USSR author's certificate N 995042, cl. G 01 S 7/292, priority 03/27/81 (prototype).

 2. Biryukov MN Quality characteristics of nonparametric serial detectors under noise and unsteady noise flow with arbitrary distribution laws. Murom, 1996, 28 p. Dep. in VINITI 05.24.96, N 1894-B96.

 Z. Biryukov MN A rank sequential detector of signals with adaptation in conditions of noise and a stream of non-synchronous impulse noise with arbitrary parameters. Murom, 1996, 12 p. Dep. VINITI 06/24/96, N 1695-B96.

Claims (1)

 A rank adaptive serial signal detector containing a matched filter, a detector, an analog-to-digital converter, and a multi-tap delay line, and a series-rank calculator, a read-only memory unit, a drive, a decision-making unit, and a statistic meter, the first and second outputs of which are connected respectively to the second and third inputs of the read-only memory block, with m outputs of the multi-tap delay line connected to the corresponding m input by a rank calculator, the (m + 1) -th input of which is connected to the output of the analog-to-digital converter, the output of the decision block is connected to the second input of the drive, and the first and last outputs of the multi-tap delay line are connected respectively to the second and third inputs of the statistical characteristics meter, wherein the rank calculator contains m comparators, the outputs of which are connected to the corresponding inputs of the adder, the m inputs, the (m + 1) -th input and output of the rank calculator, respectively, are the first inputs of m comparators, with interconnected second inputs of m comparators and the output of the adder, the drive contains serially connected addition unit and a memory unit, the output of which is connected to the first input of the addition unit, while the first and second inputs and outputs of the drive are respectively the second input of the addition unit, the input of zeroing the memory unit and the output of the addition unit, the decision unit contains a first comparator and a second comparator, an OR element, a counter and a third comparator, the output of which is connected to the zero input, in series I am the counter, while the output of the first comparator is connected to the second input of the OR element, and the input and the first and second outputs of the decision block are respectively the inputs of the first and second comparators, the outputs of the third and first comparators, the statistical characteristics meter contains the first quadrator, in series the second quadrator included, the first subtraction unit, the first drive and the first division unit, the second subtraction unit, the second drive and the third quadrator connected in series, out which is connected to the second input of the first division block, the third drive and the first counter and the second division block are connected in series, while the input of the first quadrator is connected directly to the first input of the second subtraction unit and the second quadrant input to the second input of the first subtraction block connected to the second input of the second subtraction unit, and the first, second and third inputs and the first output of the statistical characteristics meter, respectively, are interconnected zeroing inputs the first, second and third drives and the first counter, the input of the first quadrator, the input of the second quadrator and the output of the first division unit, characterized in that a third subtraction unit, a first exponentiation unit and a weight unit, the output of which is connected to the statistical characteristics meter, are introduced with the first input of the first multiplexer directly, and with the second input of the first multiplexer through a series-connected additional weight unit and inverter, connected in series to the three the first drive and the fourth subtraction unit, the output of which is connected directly to the third input of the first multiplexer, and to the first and second control inputs of the first multiplexer through the first and second comparators, respectively, the fourth quadrator connected in series, the input of which is connected to the output of the third drive, the third division unit, the second input of which is connected to the output of the first drive and the first input of the third subtraction unit, connected by its second input to the output of the third quadrator, while the output the first multiplexer is connected to the second input of the second division unit, the output of which is connected to the input of the third drive, the second inputs of the first and second comparators are connected respectively to the output of the weight unit and the output of the inverter, while the fourth input of the fourth subtraction unit connected to the fourth input of the statistical characteristics meter with the output of an analog-to-digital converter, K comparators, connected by their first inputs to the input of the first quad, and the outputs with the corresponding control the inputs of the second multiplexer, the K inputs of which are connected to the corresponding second inputs K of the comparators and the corresponding outputs K of the weight blocks, the second inputs of which are connected to the first input of the first division unit, the first control input of the second multiplexer is connected to the second input of the multiplication unit through the second counter connected in series, the zeroing input of which is connected to the zeroing input of the first drive, and the fourth division unit, the first input of which is connected to the output of the first counter, while the output to The next multiplexer is connected to the input of the second exponentiation block, the output of which is connected to the first input of the multiplication unit, connected by its output to the first input of the first addition block, the first addition block, the third exponentiation block, and the second addition block, the second input of which is connected with the output of the third division block, while the second output of the statistical characteristics meter is the output of the second addition block.

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