Adaptive Beamforming Method Based on Fractional Gradient in Impulse Noise Environment

Abstract

The present invention proposes an adaptive beamforming method based on fractional gradient in an impulsive noise environment, mainly solving the problem that the beamforming performance of existing adaptive beamforming methods severely degrades in a strong impulsive noise environment. The implementation scheme is as follows: parameter initialization; solving the weighted output of the sampled signal; constructing a cost function for adaptive beamforming using fractional lower-order moments; using the fractional gradient method to search for the minimum value of the cost function and iteratively updating the weight vector of adaptive beamforming; when the number of iterations reaches the preset weight value times, obtaining the final adaptive weight vector and simultaneously obtaining the output result of beamforming. The beamforming method provided by the present invention can provide better beamforming performance in a strong impulsive noise environment and has high robustness, and can be used in systems such as radar, communication, and sonar.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to an adaptive beamforming method, which can be used in radar, communication, and sonar systems in a complex noise environment, effectively suppressing the influence of impulse noise on beamforming and improving the robustness of the system. Background Art

[0002] Adaptive beamforming technology can adjust the array element weighting factors in real time according to the received signals, adaptively adjust the antenna pattern, increase the gain of the desired signal, and suppress interference signals. It is an important research content in the field of array signal processing. Currently, the commonly used optimization criteria in the field of adaptive beamforming are: the minimum mean square error (MMSE) criterion, the maximum signal-to-interference-plus-noise ratio (MSINR) criterion, and the minimum noise variance (MNV) criterion. To solve the adaptive weights according to the above optimization criteria, the echo signals or noise need to have finite second-order moments. However, in the actual outdoor environment, many noises exhibit significant spike pulse characteristics. Such noises belong to non-Gaussian noises, called impulse noises, and their statistical characteristics satisfy the α-stable distribution. Impulse noises have finite fractional lower-order moments (FLOM), but do not have finite second-order moments and higher-order moments. Therefore, the adaptive beamforming method based on second-order moments will degrade in performance in an impulse noise environment, and even obtain completely wrong results. In view of the limitations of existing algorithms, it is very necessary to study the adaptive beamforming method in an impulse noise environment.

[0003] Zhao Zhijin, Dong Kehai et al. disclosed a linear constraint adaptive beamforming method in their published paper "Linear Constraint Constant Modulus Blind Adaptive Beamforming Method Based on Fractional Lower-Order Statistics" (Journal of Circuits and Systems, Vol. 15, No. 2, 2010). This method introduces fractional lower-order statistics into the traditional linear constraint beamforming, changes the cost function, and derives the weight vector update formula. This method can achieve good beamforming results in a weak impulse noise environment. However, since the weight vector iteration formula contains the input signal, in a strong impulse noise environment, it is difficult for the weight vector iteration formula to approach the optimal weight vector, resulting in a decline in the algorithm performance; at the same time, since this method requires the step size factor to meet certain conditions for the weight vector to converge to the optimal value, and the conditions are related to the input signal, it is difficult to implement.

[0004] Qiu Tianshuang, Jin Fangxiao, etc. disclosed an adaptive beamforming method based on the maximum correlation entropy criterion in the patent document with the application number 2018101122396. The implementation steps are as follows: 1) Calculate the output and reference signal of each sampling point; 2) Estimate the exact cyclic frequency using the correlation function of the correlation entropy of the output signal; 3) Estimate the adaptive weight vector based on the maximum correlation entropy criterion; 4) Implement robust beamforming. This method applies the correlation entropy criterion to beamforming. Although it can improve the robustness of beamforming in a weak impulsive noise environment. However, since it uses the autocorrelation matrix of the input signal for iterative update of the adaptive weight vector, when the impulsive noise in the input signal is strong, it will lead to performance degradation and even failure. Summary of the Invention

[0005] The object of the present invention is to overcome the deficiencies of the prior art and provide an adaptive beamforming method based on fractional gradient in an impulsive noise environment to improve the beamforming performance and system robustness in a strong impulsive noise environment.

[0006] The key technology of the present invention is: constructing a cost function for adaptive beamforming with fractional lower-order moments and updating the adaptive weight vector through fractional gradients, so that the weight vector of beamforming continuously approaches the optimal weight value, obtaining better beamforming effects and better robustness in the case of strong impulsive noise. Its implementation steps include the following:

[0007] (1) Parameter initialization:

[0008] Set the fractional lower-order moment order p and the fractional gradient order r. The value range of p is (0, α), where α is the characteristic exponent of the stable distribution, and the value range is (0, 2]. The value range of r is (0, p);

[0009] Set the step size factor μ and the number of weight updates N I , where μ > 0, N I is a positive integer greater than 1000;

[0010] (2) Use the array antenna to receive the far-field echo signal s(t) and obtain the sampled array received signal X(k) through an analog-to-digital converter;

[0011] (3) Solve the weighted output y(k) of the sampled signal at time k:

[0012] y(k) = w H (k)X(k)

[0013] where w(k) is the adaptive weight vector at time k, X(k) represents the array received signal at time k, and H represents the vector transpose operation;

[0014] (4) Calculate the output error e(k) between the weighted output of the sampled signal at time k and the desired beamforming output:

[0015] e(k) = y(k) - d(k)

[0016] where d(k) represents the desired beamforming output at time k;

[0017] (5) Obtain the cost function J FLOM (w) based on the output error e(k);

[0018] (6) Use the fractional gradient method to search for the minimum value of the cost function J FLOM (w) and solve for the adaptive weight vector w(k + 1) at time k + 1:

[0019] (6a) Calculate the fractional gradient increment Δg(k) at time k;

[0020] Δg(k) = μ(-X(k)) r |e(k)| p-r conj[sign(e(k))]

[0021] where conj[·] is used to obtain the conjugate of a complex number, and sign(·) is the sign function;

[0022] (6b) Based on the fractional gradient increment Δg(k) at time k and the adaptive weight vector w(k) at time k, obtain the adaptive weight vector w(k + 1) at time k + 1:

[0023] w(k + 1) = w(k) - Δg(k);

[0024] (7) Determine whether the iteration count k of the adaptive weight vector at the current time is greater than the set weight update count N I :

[0025] If k ≥ N I , then export the weighted output of the sampled signal at all subsequent times as the final output result of beamforming;

[0026] Otherwise, return to step (3).

[0027] The present invention has the following advantages compared with the prior art:

[0028] 1) Considering the problem that the received signal in the actual outdoor environment may contain impulsive noise, the present invention constructs the cost function of adaptive beamforming using fractional lower-order moments, overcomes the problem that the cost function based on the second-order moment optimization criterion cannot obtain the optimal value in the impulsive noise environment, and expands the application range.

[0029] 2) The present invention uses a fractional gradient to optimize the cost function. Compared with the existing adaptive beamforming method based on integer gradient optimization, the influence of impulse noise intensity on the beamforming algorithm can be reduced by adjusting the order of the fractional gradient, and better beamforming effects and better robustness can be obtained in the case of strong impulse noise. Description of the Drawings

[0030] Figure 1 is the implementation flowchart of the present invention;

[0031] Figure 2 is the antenna pattern of a single beamforming of the present invention and the existing LMP adaptive beamforming method;

[0032] Figure 3 is the antenna pattern of five beamformings of the present invention and the existing LMP adaptive beamforming method. Specific Embodiment

[0033] The embodiments and effects of the present invention will be further described in detail below with reference to the drawings.

[0034] Refer to Figure 1 , and the implementation steps of the embodiments of the present invention are as follows:

[0035] Step 1, parameter initialization.

[0036] In this embodiment, a fractional lower-order moment is used to construct an adaptive beamforming cost function in an impulse noise environment. On this basis, a fractional gradient is introduced to optimize the iterative formula of the adaptive weight vector, so that the adaptive weight vector continuously approaches the optimal weight vector, and finally the adaptive beamforming in the impulse noise environment is completed. The specific implementation is as follows:

[0037] Set the order p of the fractional lower-order moment and the order r of the fractional gradient. The value range of p is (0, α), where α is the characteristic exponent of the stable distribution, and the value range is (0, 2]. The value range of r is (0, p);

[0038] Set the step factor μ and the weight update times N in the iterative formula of the adaptive weight vector I , where μ > 0, N I is a positive integer greater than 1000.

[0039] Step 2, use the array antenna to receive the far-field echo signal s(t), and obtain the sampled array received signal X(k) through the analog-to-digital converter.

[0040] (2.1) Use a uniform linear array containing M array elements to construct an array signal model X(t) for adaptive beamforming:

[0041]

[0042] where x i (t) represents the received signal of the i-th array element, and s i (t) represents the echo signal received by the i-th array element, and n i (t) represents the impulse noise received by the i-th array element, and the value range of i is from 1 to M, where M is the number of array elements;

[0043] This impulse noise has spike characteristics, and its probability density function has heavy-tail characteristics and follows the alpha-stable distribution. The characteristic function of the stable distribution is expressed as:

[0044]

[0045] where exp(·) is the exponential function with base e, δ is the location parameter, usually set to 0, γ > 0 is called the scale parameter, -1 ≤ β ≤ 1 is called the skewness parameter, which determines the symmetry degree of the distribution, sign(·) is the sign function, and ω(t, α) is defined as:

[0046]

[0047] tan(·) is the tangent function, log(·) is the logarithm function with base e, and |·| is the modulus function;

[0048] (2.2) Samples the array signal model X(t) through an analog-to-digital converter. The array received signal X(k) at time k after sampling is expressed as:

[0049]

[0050] where x i (k) represents the received signal of the i-th array element at time k, and s1(k) represents the echo signal received by the first array at time k; e (·) is the exponential function with base e, D represents the spacing between adjacent array elements, θ represents the incident signal angle, c represents the electromagnetic wave propagation speed; n i (k) represents the impulse noise received by the i-th array element at time k.

[0051] Step 3: Calculate the error e(k) between the weighted output y(k) of the sampled signal and the desired beamforming output d(k) according to the sampled array received signal X(k) and the adaptive weight vector w(k).

[0052] (3.1) Calculate the weighted output y(k) of the sampled signal at time k

[0053] The weighted output of the sampled signal is the result of multiplying and adding the multi-channel received signals corresponding to the adaptive weight vector. The calculation formula for the weighted output y(k) of the sampled signal at time k is as follows:

[0054] y(k) = w H (k)X(k)

[0055] where w(k) is an M×1 dimensional adaptive weight vector at time k, and H represents the vector transpose operation;

[0056] (3.2) Calculate the desired beamforming output d(k) at time k:

[0057] d(k) = Ms1(k)

[0058] (3.3) Calculate the error signal e(k) at time k based on the weighted output y(k) of the sampled signal at time k and the desired beamforming output d(k):

[0059] e(k) = y(k) - d(k).

[0060] Step Four, obtain the cost function J FLOM (w) based on the error signal e(k).

[0061] J FLOM (w) = E[|e(k)| p

[0062] where E[·] is used to calculate the mean value.

[0063] Step Five, use the fractional gradient method to search for the minimum value of the cost function J FLOM (w) and solve for the adaptive weight vector w(k + 1) at time k + 1.

[0064] Using the fractional gradient to update the adaptive beamforming weight vector will continuously reduce the error e(k) between the weighted output y(k) of the sampled signal and the desired beamforming output d(k). Perform an adaptive weight iteration for each sampling time. When the iteration number k reaches the set weight update number N I , the error reaches the minimum. At this time, the optimal adaptive weight vector w(k) and the final beamforming output result are obtained. The specific implementation is as follows:

[0065] (5.1) Calculate the fractional gradient increment Δg(k) at time k;

[0066] Δg(k) = μ(-X(k))r|e(k)p - rconj[sign(e(k))]

[0067] where conj[·] is used to calculate the conjugate of a complex number;

[0068] ​(5.2) Obtain the adaptive weight vector w(k + 1) at time k + 1 based on the fractional gradient increment Δg(k) at time k and the adaptive weight vector w(k) at time k;

[0069] w(k + 1) = w(k) - Δg(k).

[0070] Step six, obtain the final output of beamforming.

[0071] Judge whether the iteration times k of the adaptive weight vector at the current moment is greater than the set weight update times N I :

[0072] If k ≥ N I , then export the weighted output of the sampling signals at all moments after this moment as the final output result of beamforming;

[0073] Otherwise, return to step three.

[0074] The following further illustrates the effect of the present invention in combination with simulation experiments.

[0075] 1. Simulation conditions:

[0076] The simulation running system is the Windows 10 64-bit operating system, and the compilation environment is MATLAB 2019a.

[0077] The simulation parameters are as follows:

[0078] The number of simulation array elements is 16, the array element type is a uniform linear array, the array element spacing is λ / 2, λ is the wavelength corresponding to the signal center frequency, and the desired beam angle is 30°;

[0079] The starting frequency of the echo signal is 15 MHz, the bandwidth is 10 MHz, the pulse width is 10 μs, the sampling frequency is 100 MHz, and the GSNR is 10 dB;

[0080] Set the parameters of the pulse noise to α = 1.1, γ = 0.1, β = 0, δ = 0;

[0081] Set the fractional lower-order moment order p = 0.8 and the fractional gradient order r = 0.7 of the present invention;

[0082] Set the fractional lower-order moment order p = 1.05 of the existing LMP adaptive beamforming method;

[0083] The weight update times N I = 1000, the step size factor μ = 0.001, and the number of Monte Carlo times is 200 times.

[0084] 2. Simulation experiment content:

[0085] Simulation 1: Under the above simulation conditions, the single beamforming experiment was carried out in a strong impulse noise environment using the present invention and the existing LMP adaptive beamforming method respectively, and the corresponding antenna patterns were plotted. The beamforming performance of the two methods was evaluated by the main beam pointing, sidelobe suppression and main beam width in the antenna pattern. The results are as Figure 2 shown, Figure 2 where the horizontal axis represents the beam angle in degrees; the vertical axis is the spatial response in dB.

[0086] It can be Figure 2 seen that the present invention has a narrower main beam width and stronger sidelobe suppression ability than the existing technology, indicating that the beamforming effect of the present invention is significantly better than the existing method in a strong impulse noise environment.

[0087] Simulation 2: Under the above simulation conditions, the five beamforming experiments were carried out in a strong impulse noise environment using the present invention and the existing LMP adaptive beamforming method respectively, and the corresponding antenna patterns were plotted. The robustness of the two methods was evaluated according to the fluctuations of the antenna patterns obtained from the five experiments. The results are as Figure 3 shown, where Figure 3 (a) is the result of five experiments of the LMP method, Figure 3 (b) is the result of five experiments of the present invention. Figure 3 The horizontal axis represents the beam angle in degrees; the vertical axis is the spatial response in dB.

[0088] Figure 3 (a) and Figure 3 (b) both have five curves, where the curve corresponding to the first line type represents the result of the first experiment, the curve corresponding to the second line type represents the result of the second experiment, and so on.

[0089] It can be Figure 3 seen from (a) and Figure 3 (b) that in the case of multiple experiments, the antenna pattern of the present invention does not change significantly, while the antenna pattern obtained by the existing LMP method fluctuates greatly, indicating that the present invention has better robustness than the existing method in a strong impulse noise environment.

[0090] In summary, in a strong impulse noise environment, the present invention has better beamforming effect and better robustness than the existing method.

Claims

1. An adaptive beamforming method based on fractional gradient in an impulse noise environment, characterized in that, It includes the following steps: (1) Parameter initialization: Set the fractional lower-order moment order p and the fractional gradient order r. The value range of p is (0, α), where α is the characteristic exponent of the stable distribution and its value range is (0, 2]. The value range of r is (0, p); Set the step size factor μ and the number of weight update times N I , where μ > 0, N I is a positive integer greater than 1000; (2) Use the array antenna to receive the echo signal s(t) in the far field, and obtain the sampled array received signal X(k) through the analog-to-digital converter; (3) Solve the weighted output y(k) of the sampled signal at time k: y(k) = w H (k)X(k) where w(k) is the adaptive weight vector at time k, X(k) represents the array received signal at time k, and H represents the vector transpose operation; (4) Calculate the output error e(k) between the weighted output of the sampled signal at time k and the desired beamforming: e(k) = y(k) - d(k) where d(k) represents the desired beamforming output at time k; (5) Obtain the cost function \(J\) based on the fractional lower-order moment according to the output error \(e(k)\). FLOM (w); (6) Search for the minimum value of the cost function J FLOM (w) using the fractional gradient method, and solve for the adaptive weight vector w(k + 1) at time k + 1: (6a) Calculate the fractional gradient increment Δg(k) at time k; Δg(k) = μ(-X(k)) r |e(k)| p-r conj[sign(e(k))] where conj[·] is used to obtain the conjugate of a complex number, and sign(·) is the sign function; (6b) According to the fractional gradient increment Δg(k) at time k and the adaptive weight vector w(k) at time k, obtain the adaptive weight vector w(k + 1) at time k + 1: w(k + 1) = w(k) - Δg(k); (7) Determine whether the number of iterations k of the adaptive weight vector at the current moment is greater than the set number of weight updates N I : If k ≥ N I , then the weighted output of the sampling signals at all times after this moment is derived as the final output result of beamforming; Otherwise, return to step (3).

2. The method according to claim 1, wherein The echo signal s(t) in the step (2) is expressed as follows: s(t) = Acos[2πf(t - τ)] where A represents the signal amplitude, f represents the signal frequency, and τ represents the delay between signal transmission and reception.

3. The method according to claim 1, wherein The implementation of obtaining the sampled array received signal X(k) through the analog-to-digital converter in the step (2) is as follows: (2a) Use a uniform linear array containing M array elements to construct the array signal model X(t) of adaptive beamforming; where x i (t) represents the received signal of the i-th array element, and s i (t) represents the echo signal received by the i-th array element, and n i (t) represents the impulse noise received by the i-th array element, and the value range of i is from 1 to M, where M is the number of array elements; (2b) Sample X(t) through the analog-to-digital converter. The array received signal X(k) at time k after sampling is expressed as: where x i (k) represents the received signal of the i-th array element at time k, and s1(k) represents the echo signal received by the first array at time k; e (·) is the exponential function with base e, D represents the spacing between adjacent array elements, θ represents the incident signal angle, c represents the electromagnetic wave propagation speed; n i (k) represents the impulse noise received by the i-th array element at time k.

4. The method according to claim 1, characterized in that, The desired beamforming output d(k) at time k in the step (4) is expressed as follows: d(k) = Ms1(k) where M is the number of array elements, and s1(k) represents the echo signal received by the first array element at time k.

5. The method according to claim 1, characterized in that The cost function J FLOM (w) obtained in the step (5) is expressed as follows:​ J FLOM (w) = E[|e(k)| p ​ where E[·] is used to obtain the mean value, |·| is the modulus function, e(k) is the output error between the weighted output of the sampled signal at time k and the desired beamforming, p is the lower-order moment order, and the value range of p is (0, α), where α is the characteristic exponent of the stable distribution and its value range is (0, 2].

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