RU2788589C1 - Method for adapting an antenna array by a gradient procedure with variable pitch - Google Patents

Abstract

FIELD: communication.

SUBSTANCE: invention relates to the field of communication, in particular, to radio engineering wireless communication systems; more specifically, to methods for processing signals in adaptive antenna arrays (AAA). Method for adapting an antenna array by a gradient procedure with a variable pitch consists in selecting the initial conditions for the gradient procedure in the form of zero values of the weight vector and a single instantaneous estimation of the input signal matrix in a certain way, and subsequently iteratively calculating the value of the output signal, error signal, and the gain factor of the linear recurrence filter. Introduced is a variable vector of gain factors, depending on the forgetting factor and taking into account the previous counts of the input signal in criteria with the exponentially decreasing weight; also calculated is the instantaneous estimation value of the input signal matrix and the weight vector determining the instantaneous directivity pattern of the antenna array, with account to the forgetting factor selected from the condition of attribution to the zero to one range when calculating the gain factor and the instantaneous estimation value of the input signal matrix.

EFFECT: higher rate of convergence of the antenna array adaptation procedure due to the reduced number of iterations.

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Description

The invention relates to the field of communications, in particular to radio wireless communication systems, and more specifically to methods for signal processing in adaptive antenna arrays (ARs).

Adaptive antennas (in foreign literature sometimes "smart antenna") are a type of antenna systems whose parameters change automatically in order to provide the best conditions for receiving a useful signal against the background of changing interfering external influences [1-3].

The main elements of an adaptive antenna are: an antenna array, a beam-forming circuit, and a block for adaptive control of the directivity pattern (DN) [3]. The signals received by the individual antennas of the system pass through devices that regulate their amplitude and phase and are added in an adder, each with its own weighting factor (w ₁ , w ₂ , w _n ). The DP adaptive control unit adjusts the weight coefficients in the diagram-forming circuit. In the adaptive processor, in turn, there is a signal processor and a device that implements the control procedure. For each antenna with a given signal-interference situation, there is an optimal vector of weight coefficients (W _opt ) (VVK), uniquely associated with the formed AP AR [1-3].

One of the main characteristics of the adaptive array that determines the quality of signal processing is the type and parameters of the adaptive procedure for generating IVC. Since the nature of the received signals and the direction of arrival are usually not known in advance, the adaptive processor must automatically adjust to any changes in the signal reception conditions. The main task of the adaptive processor is to adjust the weight coefficients, at which a certain efficiency criterion is optimized, and the required RP AR is formed.

The adaptive processor adjusts the VVC for each element of the AP. The change in IVC from the initial value to the optimal one can occur along various trajectories, the form of which depends on many factors, first of all, on the chosen criterion of the quality of adaptation and the method of searching for the extremum.

There are various technical solutions with gradient methods for processing heterogeneous input parameters.

Thus, the patent of the Russian Federation for the invention No. 2325044 (IPK G06K 9/46, published on May 20, 2008) “Gradient method for selecting the contours of objects on a matrix of a halftone raster image” is known. The gradient method of selecting the contours of objects on a matrix of a halftone raster image consists in the fact that for all pixels of a raster image, the norm or square of the norm of the gradient of their brightness change is calculated according to a pre-selected method, then all elements are selected on a new black-and-white monochrome matrix in black on a white background , for which the value of the norm or the square of the norm of the gradient is greater than a certain threshold value, and connected configurations of black elements are taken as the contours of objects on a monochrome matrix. For the chosen method for calculating the gradient, the coefficient is experimentally determined, then the threshold value of the square of the gradient norm is calculated as the product of this coefficient by the sum of the squares of the average values of the modules for changing the brightness of neighboring pixels in rows and columns, for which the values exceed the total average levels of non-zero changes, respectively, in rows and columns, and among the connected configurations of black elements on a monochrome matrix, configurations are immediately discarded, in which the number of incoming elements is less than 5-7 elements, for the remaining configurations, the average degree of neighborhood is calculated - the quotient of dividing the sum over all elements of the configuration of elements adjacent to it by the sum of the elements in the configuration , and those configurations in which the average degree of neighborhood is less than 3 are discarded as recognition errors, and the remaining ones are taken as the desired object contours.

There is a gradient method for selecting the contours of objects on a matrix of a halftone bitmap image [Andreev A.L. Automated television surveillance systems. Part P. Arithmetic and logical foundations and algorithms. Uch. allowance. SPb, SPbGUITMO, 2005, p. 35-38. http://window.edu.ru/window/library], which consists in the fact that for all pixels of a raster image, according to a pre-selected method, the norm or square of the norm of the gradient of their brightness change is calculated, then on a new black-and-white monochrome matrix in black white background allocate all the elements for which the value of the norm or the square of the norm of the gradient is greater than a certain threshold value, and connected configurations of black elements are taken as the contours of objects on a monochrome matrix.

RF patent for invention No. 2695417 (MPK G06K 9/48, published on 07/23/2019) "Method for noise-resistant gradient selection of object contours in digital halftone images". A method for noise-resistant gradient extraction of object contours on digital halftone images, in which two matrices and a brightness gradient component are formed at each point of the image, the module of the brightness gradient is determined at each point of the image, the contours of the object are formed by thresholding the module of the brightness gradient, during which on a new white elements are highlighted in black in the matrix, the gradient modulus for which in the corresponding image coordinates exceeds the transformation threshold. Before the formation of the matrices and components of the brightness gradient, taking into account the level of image noise, a smoothing coefficient is selected and the coefficients of smoothing cubic B-splines along each row and each column of the image are calculated, and two matrices and a component of the brightness gradient at each point of the image are formed by summing the smoothing parabolic B-splines with the previously found coefficients of smoothing cubic B-splines for rows and columns, respectively.

A method is known for noise-resistant gradient selection of object contours on digital halftone images (RF patent No. 2648954, IPC G06K 9/48, publ. 08/15/2017), which consists in the fact that first a direct wavelet transform of rows and columns of a digital halftone image is calculated, and then two matrices and a component of the brightness gradient at each point of the image are formed by inverse wavelet transformation, in which analytical functions are used as the transformation kernel, describing the derivatives of the used inverse transformation wavelets with respect to the corresponding coordinates. After that, the module of the brightness gradient is determined at each point of the image, and the contours of the object are formed by threshold transformation of the module of the brightness gradient, during which elements are highlighted in black on the new white matrix, the gradient module for which in the corresponding image coordinates exceeds the transformation threshold.

The disadvantage is that calculating the direct wavelet transform of the rows and columns of a digital grayscale image is computationally expensive. In addition, the known method demonstrates poor resistance to impulse noise.

One of the most common methods for processing heterogeneous input parameters of adaptive antenna arrays in radio engineering wireless communication systems is the method of optimal by the criterion of minimum mean square error (MSE) between the received and reference (reference) signal [1-3]. To carry out the normal operation of the adaptation loop, the task arises of setting or extracting the reference signal that is closest, for example, in some metric to the useful one, which is solved either by using synchronization methods or by extracting the reference signal from the useful one, if the useful signal has a complex structure (such solutions are known for phase-shift keyed signals with pseudo-random sequences, signals with pseudo-random tuning of the operating frequency, and some others) [4].

. Вектор w находится в результате решения оптимизационной задачи - поиска минимума целевой функции F₁(k, w), зависящей от времени. Для поиска минимума функции F₁(k, w) наиболее часто используют градиентный метод (метод наискорейшего спуска) - итерационную процедуру, определяющую траекторию пошагового приближения к минимуму, где шагам итерации соответствуют моменты дискретного времени к. На каждом шаге итерации оценивается вектор

, смещаемый относительно вектора

на величину, пропорциональную градиенту функции F₁(k, w) в точке k.The ISCED method implements recurrent calculation of IVC estimates

. The vector w is found as a result of solving the optimization problem - finding the minimum of the objective function F ₁ (k, w), which depends on time. To find the minimum of the function F ₁ (k, w), the gradient method (the steepest descent method) is most often used - an iterative procedure that determines the trajectory of stepwise approximation to the minimum, where iteration steps correspond to discrete time moments k. At each iteration step, the vector is estimated

, shifted relative to the vector

by a value proportional to the gradient of the function F ₁ (k, w) at the point k.

A well-known method using an iterative procedure for calculating estimates of AR parameters according to the MSCED criterion includes the following steps:

;step 1 - assign k=0 and set the initial values of the AR parameter estimates

;

step 2 - calculate the values of the output signal y _k and the error signal

; e_k=d_k - y_k;

; e _k =d _k - y _k ;

;step 3 - update parameter estimates

;

step 4 - assign k=k+1;

step 5 - repeat the procedure for calculating the estimates of the AR parameters: go to step 2-4.

к оптимальным параметрам w_opt, получаемым из винеровского решения [1-3], сводится к выбору величины шага адаптации μ, гарантирующему сходимость результатов. Под сходимостью в известном способе понимается приближение значений оценок параметров

к значениям w_opt. В процессе адаптации они будут флюктуировать относительно значений w_opt, хаотично приближаясь к ним, но никогда не достигнут этих значений, даже при k → ∞. Поэтому, при выборе шага адаптации μ анализируется сходимость средних (математических ожиданий) и средних квадратов (дисперсий) значений вектора

, которые сводятся к соответствующим значениям вектора w_opt. В первом случае, говорят о сходимости в среднем, а во втором - в среднем квадрате. В режиме дисперсии сигнала ошибки АР с процедурой МСКО будет больше минимального достижимого в фильтре Винера, т.к. значения вектора

не достигают значений вектора w_opt, и ее значение будет зависеть от шага адаптации. Поэтому, шаг адаптации выбирается из компромиссных соображений: чем больше μ, тем выше скорость сходимости; чем больше μ., тем больше дисперсия сигнала ошибки (по сравнению с фильтром Винера). Обычно значение μ равняется половине максимального шага 1/NP. В случае если мощность сигнала Р невозможно оценить заранее, или оно меняется в процессе обработки сигнала, применяют нормированную процедуру МСКО (NLMS) с шагом адаптации, нормированным к входному. Процедура NLMS имеет меньший уровень средней ошибки по сравнению с обыкновенной процедурой МСКО.Despite the simplicity of the known method, the convergence analysis of parameter estimates

to the optimal parameters w _opt obtained from the Wiener solution [1-3] is reduced to the choice of the adaptation step μ, which guarantees the convergence of the results. Convergence in the known method is understood as the approximation of the values of parameter estimates

to the values of w _opt . In the process of adaptation, they will fluctuate relative to the values of w _opt , randomly approaching them, but will never reach these values, even for k → ∞. Therefore, when choosing the adaptation step μ, the convergence of the mean (mathematical expectations) and mean squares (variances) of the vector values is analyzed

, which are reduced to the corresponding values of the vector w _opt . In the first case, they speak of convergence on the average, and in the second - in the mean square. In the error signal dispersion mode, the AR with the MMSE procedure will be greater than the minimum achievable in the Wiener filter, because vector values

do not reach the values of the w _opt vector, and its value will depend on the adaptation step. Therefore, the adaptation step is chosen from compromise considerations: the larger μ, the higher the convergence rate; the larger μ, the greater the dispersion of the error signal (compared to the Wiener filter). Usually the value of μ is equal to half of the maximum step 1/NP. If the signal power P cannot be estimated in advance, or it changes during signal processing, the normalized MMSE procedure (NLMS) is used with an adaptation step normalized to the input. The NLMS procedure has a lower level of mean error compared to the ordinary ISCE procedure.

The technical problem in this area is the low rate of convergence of the AR adaptation procedure. In the proposed solution, this problem is solved by reducing the iterations required for the procedure to converge to a steady state. To do this, in the gradient adaptation procedure, a variable vector of gain factors is introduced, which depends on the forgetting factor.

The technical result of the proposed solution is to increase the rate of convergence of the antenna array adaptation procedure by reducing iterations.

The technical result is achieved by the fact that in the proposed method of adapting the antenna array by a gradient procedure with a variable step, in which the initial conditions for the gradient procedure are selected in a certain way in the form of zero values of the weight vector and a single instantaneous estimate of the matrix of input signals, followed by iterative calculation of the output signal, signal error, gain factor of the linear recurrent filter, according to the invention, a variable vector of gain factors is introduced, depending on the forgetting factor, taking into account the previous samples of the input signal in the criterion with exponentially decreasing weight. In addition, the instantaneous value of the estimate of the matrix of input signals and the weight vector that determines the instantaneous radiation pattern of the antenna array are calculated, taking into account the forgetting coefficient selected from the condition of belonging to the range from zero to one, when calculating the gain and the instantaneous value of the estimate of the matrix of input signals.

In the method that implements the RLS procedure (Recursive Least Squares, recursive method according to the least squares criterion), which is the closest to the proposed method, respectively, taken as a prototype [5, p. 478-484], the recursive calculation of the optimal parameters of the weight coefficients W _k is implemented in the steady state. The minimum sum of squares error signal e _k is used as the best approximation of the output signal y _k to the reference d _k

,

,

where L is the length of the input signal X _k , w is the vector of weights. The vector w is found as a result of solving the optimization problem - finding the minimum of the objective function F ₂ (W), which does not depend on time:

.

.

The minimum of the function F ₂ (w) is achieved when the partial derivatives with respect to all w _n are equal to zero at time k. Their totality can be written as a system of linear algebraic equations of the following form:

.

.

Let's replace n with m outside the brackets and divide both sides of the equality by 2:

.

.

After transferring the sum with unknown parameters w _n to the left side and changing the order of summation, we get:

.

.

Assuming the initial conditions to be zero (X _kn =0, k - n < 0), we write (*) in matrix form the left side:

and similarly on the right:

Then:

Let us determine the value of the vector w _k at time k:

where matrix X _k and vector d _k are calculated on the current interval [0; k]. For the next point in time (k+1):

In this case, an additional column x _k+1 will appear in the matrix X _k :

In the vector d _k is an additional element d _k+1 , this allows you to establish a recursive connection between the product X _k+1 X' _k+1 and the product X _k X' _k :

as well as the recurrent connection of the product X _k+1 d _k+1 with the product X _k d _k :

Let's introduce a variable:

Then, given the new variable:

The result of performing operations in square brackets is a scalar, for which the inversion operation corresponds to raising to the minus first power:

Taking into account the designation P _k+1 :

Taking into account w _k =P _k X _k d _k :

The expression in square brackets is the error signal e _k+1 :

The multiplier in front of this signal is a vector of gains:

Then the recursive formula in the RLS procedure can be represented as:

The RLS procedure includes the following steps:

1. Set the initial (usually zero) values of the AR parameters (W _-1 ).

2. Set the initial values for the elements of the matrix P-1. It is recommended to use the identity matrix.

3. Assign k=0.

4. Calculate the values of the output signal y _k and the error signal e _k :

5. Calculate the value of the gain vector K _k :

6. Update the matrix P _k taking into account the vector of weight coefficients:

7. Update the value of the weight vector W _k :

8. Assign k=k+1.

9. Repeat paragraphs. 4 - 8.

Using the proposed method, we modify the well-known criterion by adding a forgetting factor λ selected from the range 0<λ≤1, which allows taking into account the previous samples of the input signal in the criterion with an exponentially decreasing weight:

Then:

The method for adapting an antenna array by a gradient procedure with a variable step consists in the fact that the initial conditions for the gradient procedure are chosen in a certain way in the form of zero values of the weight vector and a single instantaneous estimate of the matrix of input signals, followed by iterative calculation of the output signal, error signal, linear recurrent gain filter. A variable vector of gain factors is introduced, which depends on the forgetting factor, taking into account the previous samples of the input signal in the criterion with an exponentially decreasing weight, in addition, the instantaneous value of the estimate of the matrix of input signals and the weight vector that determines the instantaneous radiation pattern of the antenna array are calculated, taking into account the value chosen from the condition of belonging to the range from zero to unity of the forgetting factor, when calculating the gain factor and the instantaneous value of the evaluation of the matrix of input signals.

The proposed method is illustrated by the graphic material presented in Fig. 1-3, from which it can be seen that the RLS procedure, according to the proposed method, provides faster convergence of results compared to the classical one, however, it has a larger error signal dispersion, so the forgetting factor λ is chosen from compromise solutions:

- with an increase in λ, the noise dispersion decreases, and at the limit value λ=1, the modified procedure is reduced to the classical one;

- when λ decreases, the rate of convergence of results increases.

Thus, with the help of the proposed method, the number of iterations, which ensure the convergence of the results, is almost halved, which makes it possible to use the method of adapting the antenna array by a gradient procedure with a variable step in a rapidly changing signal-interference environment in radio engineering information transmission systems, with increased convergence rate of the antenna array adaptation procedure.

Literature

1. Monzingo R.A., Miller T.W. Adaptive antenna arrays. Introduction to theory. - M.: Radio and communication, 1986. - 448 p.

2. Widrow B., Stearns S. Adaptive signal processing. - M.: Radio and communication, 1989. - 440 p.

3. Pistolkors A.A., Litvinov O.S. Introduction to the theory of adaptive antennas - M.: Nauka, 1991. - 200 p.

4. Dzhigan V.I. Adaptive filtering of signals: theory and algorithms. - M.: Technosfera, 2013. - 528 p.

5. Solonin A.I. Digital signal processing in Matlab mirror. St. Petersburg: BHV. 2018.

Claims (2)

A method for adapting an antenna array by a gradient procedure with a variable step, in which the initial conditions for the gradient procedure are chosen in a certain way in the form of zero values of the weight vector and a single instantaneous estimate of the matrix of input signals, followed by iterative calculation of the values of the output signal, the error signal, the gain of the linear recurrent filter, characterized in that a variable vector of gain factors is introduced, depending on the forgetting factor, taking into account the previous samples of the input signal in the criterion with an exponentially decreasing weight, in addition, the instantaneous value of the estimate of the matrix of input signals and the weight vector that determines the instantaneous radiation pattern of the antenna array are calculated, taking into account the selected from the condition of belonging to the range from zero to one of the forgetting factor when calculating the gain and the instantaneous value of the evaluation of the matrix of input signals.

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