CN112711837B - Anti-strong-interference wave beam forming method under low snapshot - Google Patents
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Abstract
The invention discloses a method for forming a strong interference resistant wave beam under low snapshot, which comprises the following steps when in application: setting the number N of constraint equations, and randomly assigning an initial value w to the weight coefficient w (0) (ii) a Iterative calculation is carried out on each weight coefficient variable by adopting an iterative formula of the weight coefficient; after one iteration operation is carried out, updating coefficients in an iteration equation according to the quantity of constraint equations, namely updating the expected signal d and the input signal x; carrying out the next iterative operation by using the updated coefficient reuse weight coefficient iterative formula; circularly executing the weight coefficient formula iteration and updating the coefficient until the data of the last snapshot is reached, and storing the finally calculated weight coefficient w (L) (L stands for fast beat number), look at w (L) The beamforming case of (1). The method has the advantages of high convergence speed, good real-time performance, strong anti-interference capability, capability of still keeping good performance in a low-snapshot environment, strong robustness, easiness in implementation and the like.
Description
Technical Field
The invention belongs to the technical field of array signal processing, relates to a strong interference resistant beam forming method under low snapshot, and particularly relates to a self-adaptive beam forming method based on a new steepest descent method.
Background
Array signal processing is widely applied to the fields of radar, sonar, wireless communication, space telemetering and the like. Beamforming, also known as spatial filtering, is the first step in array signal processing and is also representative of array signal processing. Beamforming is also widely used in many fields as the first step of array signal processing, and the performance of beamforming is directly related to the quality of subsequent signal processing. The main role of beamforming is to form a main beam in the target direction and form nulls in the interfering direction to reduce the effect of interference.
At present, the self-adaptive beam forming has the advantages that the main beam can be always aligned to a target and the null can be always aligned to interference due to the fact that the weight of each array element can be automatically adjusted along with the change of the environment, and great practical value is shown. Common adaptive beamforming algorithms are improved LMS-based, RLS-based and based on both algorithms. The LMS algorithm has the advantages of simplicity and easy implementation, but the convergence rate of the algorithm is slow, and the selection problem of the iteration step size needs to be considered. The LMS algorithm can show a good effect under the conditions of more snapshots and weaker interference signal strength, but when the interference signal strength is higher or the snapshots are fewer, the performance of the LMS algorithm is sharply reduced. Although the convergence rate of the RLS is faster than that of the LMS algorithm, the performance degradation is not as severe as that of the LMS when the number of snapshots decreases or the strength of the interference signal increases, but the influence is also large.
Therefore, a beam forming algorithm with fast convergence speed and good real-time performance, capable of resisting strong interference and still maintaining good performance under the condition of low snapshot number is needed at present. The beam forming method based on a new steepest descent method proposed by the present patent meets such a requirement.
Disclosure of Invention
The invention aims to provide a strong interference resistant wave beam forming method under low snapshot, which adopts a new steepest descent method to solve the optimal weight coefficient of each array element in an array, and aims to accelerate the convergence rate of self-adaptive wave beam formation, improve the anti-interference capability of the wave beam formation and keep the good performance of the self-adaptive wave beam formation under low snapshot number.
The technical scheme is as follows:
a wave beam forming method for resisting strong interference under low snapshot uses the minimum mean square error criterion, the signal processing mode is that the input signal is output after weighted by each array element in the array, the output signals of each array element are summed to be the output signal of the array, the mean square error of the array output signal and the expected signal is obtained, the new steepest descent method is used to obtain the weight coefficient added by each array element when the mean square error is minimum.
Assuming that the array is an M-element one-dimensional equidistant linear array, M represents the number of array elements, an input signal of the array is x (n), and a weight coefficient of each array element is w (θ), an output signal of the array is:
y(t)＝w H (θ)x(t)
in the above formula, d (n) is the desired signal, w H And (theta) represents the conjugate transpose of the array element weight coefficient w (theta). Then the mean square error function can be found as:
in the above formula, J (w) is the mean square error function, E | · + 2 ]Represents averaging over the square of the modulus.
The minimum mean square error criterion is to minimize the value of the mean square error function, i.e. to minimize the error between the output signal of the array and the desired signal by adjusting the weight coefficients of the individual array elements. And solving the weight coefficient of each array corresponding to the minimum mean square error by using a new steepest descent method. The solving process is as follows:
firstly, solving a mean square error function to obtain a first derivative and a second derivative:
in the above formula
Representing the first derivative of the mean square error function,
representing the second derivative, x, of the mean square error function H (n) denotes the conjugate transpose of the input signal x (n), d * (n) represents the conjugate of the desired signal d (n).
For convenience of representation, let e (n) = x H (n)w-d * (n)
The iterative formula for obtaining the weight coefficient by applying the new steepest descent method is as follows:
in the above formula
And representing the value of the weight coefficient of the ith array element calculated by the kth iteration.
The steps based on a new steepest descent method can be summarized as follows:
a) Setting the number N of constraint equations, and randomly assigning an initial value w to the weight coefficient w (0) ；
b) Iterative formula using weight coefficients
Performing iterative computation on each weight coefficient variable;
c) After one iteration operation is carried out, updating coefficients in iteration equations according to the number of constraint equations, namely updating the expected signal d and the input signal x, wherein the updating process is to slide the expected signal and the input signal backwards by one bit in all the snapshot signals by using the number N of the constraint equations, namely updating the expected signal and the input signal by using the previous d (N) (N = k-N +1,k-N +2 … k) and x (N) (N = k-N +1,k-N +2 … k) into d (N) (N = k-N +2,k-N +3 … k + 1) and x (N) (N = k-N +2,k-N + … k + 1);
d) Re-performing the next iterative operation by using the updated coefficient, namely re-performing the step b);
e) Circularly executing the step b), the step c) and the step d) until the data of the last snapshot is processed, and storing the finally calculated weight coefficient w (L) (L represents fast beat number);
f) Coefficient of output weight w (L) I.e. the optimal weight coefficient, w (L) The beam directivity of the antenna array after weighting is the best, and the anti-interference capability is the strongest.
Compared with the prior art, the invention has the beneficial effects that:
the self-adaptive beam forming method based on the new steepest descent method mainly has the following advantages: (1) the convergence rate is high, and the real-time performance is good; (2) the anti-interference capability is strong, and as long as the maximum computing capability of hardware is not reached, a main beam can be formed in a target direction and formed in an interference direction; (3) the good performance can still be kept under the low-snapshot environment; (4) the robustness is strong; (5) the iterative operation mode is adopted, and the method is suitable for being realized by computers and programmable hardware and the like.
Drawings
FIG. 1 is a flow chart of the operation of an adaptive beamforming method based on a new steepest descent method;
FIG. 2 is a diagram of an array signal beamforming architecture;
fig. 3 is a diagram of an adaptive beamforming architecture;
fig. 4 is a beam direction diagram of an adaptive beamforming method based on a new steepest descent method.
Detailed Description
The technical solutions of the present invention will be described in further detail with reference to the accompanying drawings and the detailed description.
Principle of new steepest descent method
The new steepest descent algorithm firstly degrades a multivariate quadratic convex function into a unary quadratic function, the unary quadratic function is a parabola, the extreme value of the parabola is solved by utilizing the property of the parabola, and the solved result is converged to the extreme point of the convex function by adopting a circular iteration mode.
The properties of the parabola are: assume that the general form of a unary quadratic function is f (x) = ax 2 + bx + c, the position of the extreme point of the parabola is x = -b/2a, and b = f' x | x＝0 ，2a＝f″ xx Therefore, the position of the pole of the quadratic function can be obtained by calculating the first and second derivatives of the function to obtain x = -f' x | x＝0 /f″ xx 。
Assume the general form of a multivariate quadratic function as:
in the formula
In general form m represents the number of arguments in the function and n represents the number of constraint equations. The function may be extremized by the new steepest descent algorithm presented herein, which iterates as follows:
a) For random selection of values in the definition domain of variables
Assigning values to the m independent variables;
b) With x 1 As the independent variables of the multi-element function, the other independent variables are respectively assigned with values
The multivariate function becomes related to x 1 The unary quadratic function of (2) is parabolic, i.e. the extreme point can be obtained by using the property of the parabola
c) With x 2 As independent variable, the extreme point determined in step b) is used
Assigned to x 1 The other variables are assigned with initial values
The extreme point is also obtained by using the property of parabola
d) Repeating the steps b) to c), respectively calculating the extreme point of each variable
e) Assigning the extreme points obtained in the step d) to each variable, circularly obtaining the extreme points of each variable, and approaching the extreme points of each variable to the extreme points of the multivariate function more and more along with the increase of the iteration times.
The resulting iterative formula is as follows:
application of new steepest descent method in adaptive beam forming
This new steepest descent algorithm is next applied in adaptive beamforming.
The beam forming algorithm proposed by the invention is based on the minimum mean square error criterion, and the mean square error function between the array output signal and the expected signal is shown as follows:
the structure diagram of the array signal beam forming and the structure diagram of the adaptive beam forming are respectively shown in fig. 2 and fig. 3.
The mean square error function conforms to the general form of a multivariate quadratic function, so the extreme points of the mean square error function can be solved by adopting the new steepest descent algorithm proposed herein.
And (3) solving a first derivative and a second derivative of the formula mean square error function to obtain:
for convenience of representation, let e (n) = x H (n)w-d * (n)
Substituting the result of the above formula into an iterative formula derived from the new steepest descent algorithm, the iterative formula for obtaining the weight coefficient should be:
in summary, the steps of the adaptive beamforming algorithm based on the new steepest descent method can be summarized as follows:
a) Setting the number N of constraint equations, and randomly assigning an initial value w to the weight coefficient w (0) ；
b) Using a weight coefficient iterative formula
Performing iterative computation on each weight coefficient variable;
c) After one iteration operation is carried out, updating coefficients in iteration equations according to the number of constraint equations, namely updating the expected signal d and the input signal x, namely sliding the expected signal and the input signal backwards by one bit in all the snapshot signals by using the number N of the constraint equations as a group, namely updating the expected signal and the input signal into d (N) (N = k-N +1,k-N +2 … k) and x (N) (N = k-N +1,k-N +2 … k) and x (N) (N = k-N +2,k-N +3 … k + 1) and x (N) (N = k-N +2,k-N +3 … k + 1);
d) Re-performing the next iterative operation by using the updated coefficient, namely re-performing the step b);
e) Circularly executing the step b) step c) and the step d) until the data of the last snapshot is processed, and storing the finally calculated weight coefficient w (L) (L represents fast beat number);
f) Coefficient of output weight w (L) I.e. the optimal weight coefficient, w (L) The beam directivity of the antenna array after weighting is the best, and the anti-interference capability is the strongest.
And finally, converting the steps of the algorithm into a flow chart to obtain the operation flow chart of the adaptive beam forming method based on the new steepest descent method in the figure 1.
In the beam forming scene of a uniform linear array with the array element number of 16 and under the background of ultra-strong interference with the interference ratio (INR) of 1000dB, the target direction is set to 0 °, the interference direction is set to 50 °, the signal-to-noise ratio SNR =0dB, the snapshot number L =50, and the number N =5 of constraint equations, so as to obtain the beam directing graph of the adaptive beam forming method based on a new steepest descent method in fig. 4.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited thereto, and any simple modifications or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention are within the scope of the present invention.
Claims (1)
1. A method for forming a strong interference resistant wave beam under low snapshot is characterized by comprising the following steps:
a) Setting the number N of constraint equations, and randomly assigning an initial value w to the weight coefficient w (0) ；
b) Iterative formula using weight coefficients
Performing iterative computation on each weight coefficient variable;
in the formula:
representing the value of the weight coefficient of the 1 st array element calculated by the kth iteration;
representing the value of the weight coefficient of the 2 nd array element calculated by the kth iteration;
representing the value of the weight coefficient of the Mth array element calculated by the kth iteration;
representing the value of the weight coefficient of the 1 st array element calculated by the (k + 1) th iteration;
representing the value of the weight coefficient of the 2 nd array element calculated by the (k + 1) th iteration;
representing the value of the weight coefficient of the Mth array element calculated by the (k + 1) th iteration; d (n) represents a beamformed desired signal; e (a)n) represents the error between the beamformed output signal and the desired signal d (n);
c) After one iteration operation is carried out, updating coefficients in iteration equations according to the number of constraint equations, namely updating the expected signal d and the input signal x, wherein the updating process is to slide the expected signal and the input signal backwards by one bit in all the snap signals by using the number N of the constraint equations as a group, namely, the expected signal and the input signal are updated to d (N) by using the previous d (N), N = k-N +1,k-N +2 … k and x (N), N = k-N +1,k-N +2 … k, N = k-N +2,k-N +3 … k +1 and x (N), and N = k-N +2,k-N + … k +1;
d) Re-performing the next iterative operation by using the updated coefficient, namely re-performing the step b);
e) Circularly executing the step b) step c) and the step d) until the data of the last snapshot is processed, and storing the finally calculated weight coefficient w (L) L represents the number of fast beats;
f) Coefficient of output weight w (L) I.e. the optimal weight coefficient, w (L) The beam directivity of the antenna array after weighting is the best, and the anti-interference capability is the strongest.
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