Improved adaptive pulse compression method based on MMSE criterion

Abstract

The invention discloses an improved adaptive pulse compression method based on an MMSE criterion, and is applied to the technical field of radar signal processing. The method comprises the following steps: firstly, establishing an echo signal model, and regarding an echo signal sequence corresponding to a certain distance unit as superposition of a signal component of a current distance unit, a signal component of an adjacent distance unit and noise; secondly, on the basis of the MMSE criterion, introducing a constraint term of a minimum filtering result of adjacent distance units, and establishing an improved filter cost function based on the MMSE criterion; performing optimization solution on the self-adaptive filter cost function to obtain an improved expression of an optimal filter based on an MMSE (Minimum Mean Square Error) criterion; and finally, solving an improved filter estimation value based on the MMSE criterion and a pulse compression result of an echo signal through an iterative operation method. According to the method, the distance side lobes of surrounding targets can be suppressed in a targeted manner in the pulse compression process, and the weak target detection capability of the radar is improved.

Description

Technical Field

[0001] The invention relates to the technical field of radar signal processing, and in particular to an improved adaptive pulse compression method based on a minimum mean-square error (MMSE) criterion. Background Art

[0002] Pulse compression technology is a key component in radar signal processing. It can expand the effective range of the signal and improve the range resolution, providing effective performance support for the radar system. The matched filter is currently the most widely used pulse compression method. It is an optimal linear filter based on the maximum output signal-to-noise ratio criterion. However, in practical applications, when there are multiple adjacent point targets in the range direction, the matched filter may have the phenomenon that the sidelobes of strong targets cover weak targets, resulting in the problem of weak target shielding.

[0003] In order to suppress the sidelobe effect of the matched filter, a variety of pulse compression methods have been proposed, such as the least squares (LS), mismatched filter, CLEAN algorithm, adaptive pulse compression method based on MMSE criterion and pulse compression repair (PCR). Among them, LS is the optimal filter in the sense of least mean square, but the filter is a filter with fixed weights determined by the transmitted signal, and does not take into account the influence of strong scattering points outside the processing window. The mismatched filter reduces the influence of the sidelobe to a certain extent at the cost of signal-to-noise ratio loss, but the sidelobe suppression effect is limited. The CLEAN algorithm removes large targets and their sidelobe responses in turn by estimating the location of the target, but the extraction effect of weak targets is not ideal.

[0004] Therefore, based on the shortcomings of non-adaptive pulse compression techniques, the MMSE-based adaptive pulse compression technique described in Reference 1 (Blunt SD, Gerlach K. Adaptive pulse compression via MMSE estimation [J]. IEEE Transactions on Aerospace and Electronic Systems, 2006, 42 (2): 572-584.) has attracted widespread attention. This method uses the non-adaptive pulse compression results as prior knowledge and obtains the optimal filter under the MMSE criterion through iterative adaptive means, which can better suppress the range sidelobe. For example, PCR described in Reference 2 (Gerlach K, Blunt SD. Radar pulse compression repair [J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43 (3): 1188-1195.) is a post-pulse compression method, which mainly performs adaptive pulse compression on the results of matched filtering, and can suppress the range sidelobe with fewer iterations. However, PCR is the same as the adaptive pulse compression technology based on the MMSE criterion. Both use the complete echo signal to construct the filter cost function, without considering the influence of surrounding pixels on the filtering result, and the range sidelobe suppression effect needs to be strengthened. Therefore, in order to more effectively suppress the range sidelobe and improve the detection capability of weak targets, it is necessary to improve the existing adaptive pulse compression method based on the MMSE criterion and further improve the effectiveness of the radar signal pulse compression results. Summary of the invention

[0005] Aiming at the existing pulse compression problem, the present invention provides an improved adaptive pulse compression method based on the MMSE criterion. Firstly, an echo signal model is constructed. Then, the suppression item of the filtering result of adjacent range units is combined with the MMSE criterion to construct a filter cost function. Finally, specific steps for optimizing the filter are given. The method can suppress the range sidelobe during the pulse compression process and improve the radar's detection capability for weak targets.

[0006] The improved adaptive pulse compression method based on MMSE criterion of the present invention comprises the following steps:

[0007] Step 1: Establish an echo signal model and regard the echo signal sequence y(l) corresponding to the lth distance unit as the echo signal component y of the current distance unit t (l) The echo signal component y with the adjacent distance unit c (l) and the superposition of noise n(l);

[0008] Step 2: Based on the MMSE criterion, the constraint term of the minimum filtering result of adjacent distance units is introduced to establish an improved filter cost function based on the MMSE criterion;

[0009] First, the filter cost function of the lth distance unit based on the MMSE criterion is constructed as follows:

[0010] P=E[x(l)-w(l) H y(l) 2 ];

[0011] Where x(l) is the impulse response of the sampled l-th distance unit, w(l) is the filter coefficient, the superscript H indicates the conjugate transpose, and E[·] indicates the expectation;

[0012] On the basis of MMSE criterion, the constraint term |w(l) of the minimum filtering result of adjacent distance units is introduced. H y c (l) 2 , add the constraint term to the filter cost function, and establish the improved filter cost function based on the MMSE criterion as follows:

[0013] J = E[x(l)-w(l) H y(l) 2 +λw(l) H y c (l) 2 ];

[0014] Where λ is a regularization parameter, which is used to control the degree of suppression of the filtering results of adjacent distance units;

[0015] Step 3: Optimize and solve the adaptive filter cost function J to obtain an improved expression of the optimal filter based on the MMSE criterion;

[0016] Step 4: Calculate the improved filter estimation value based on the MMSE criterion and the range pulse compression result through iterative calculation method.

[0017] In step 1, the radar transmission signal is assumed to be s=[s1 s2 … s N ] T , N is the signal length, and the superscript T indicates transposition; suppose that starting from the lth distance unit, the echo signal with a length of N is y(l) = [y(l)y(l+1)…y(l+N-1)] T ,l=1,2,…L, L is the number of sampling points of the distance scene; the specific expression of the echo signal is: y(l)=Sx(l)+n(l), where x(l) is the distance unit impulse response vector with a length of 2N-1, and x(l) is decomposed into:

[0018]

[0019] Among them, the lth distance unit is the current distance unit, x t (l) represents the impulse response of the lth distance unit, x c (l) represents the impulse response of the adjacent distance unit; then the echo signal y(l) can be decomposed into:

[0020] y(l)=S(x t (l)+x c (l))+n(l)=x(l)s+Sx c (l)+n(l)=y t (l)+y c (l)+n(l);

[0021] Among them, the matrix composed of the transmitted signal shift n(l) is the noise signal; y t (l) = x(l)s is the echo signal component on the lth distance unit, y c (l) = Sx c (l) is the echo signal component on the adjacent distance unit.

[0022] The step three includes: first, calculating the complex gradient of the filter coefficient w for the filter cost function J, as follows:

[0023]

[0024] make The expression for w is: w(l)={E[y(l)y H (l)+λy c (l)y c H (l)]} -1 E[y(l)x H (l)];

[0025] Then, y(l)=Sx(l)+n(l) is substituted into the expression of w. At the same time, assuming that the range impulse responses of each target are uncorrelated, and the noise is also uncorrelated with the range impulse response, the expression of the adaptive filter of the lth range unit is obtained as follows:

[0026] w(l)=ρ(l)[Sdiag(ρ c )S H +ρ(l)ss H +R] -1 s;

[0027] Among them, the power expectation of the impulse response of the lth distance unit ρ(l) =| x(l) 2 ; Power matrix ρ in the distance direction c =(1+λ)[ρ(l-N+1) … ρ(l-1) 0 ρ(l+1) … ρ(l+N-1)] T ; The correlation matrix of white noise is R = E[n(l)n(l) H ].

[0028] In the fourth step, an estimated value of w(l) is obtained by an iterative operation. During the iterative process, the value of λ is set from small to large, and the correlation matrix R of the calculated white noise is ignored. The iterative operation includes the following steps:

[0029] Step 1) Consider the radar transmission signal as the initial value of the filter: w i (l) = s, i = 1, where i is the number of iterations. The result of the matched filtering of the lth distance unit is The matched filtering results of each distance unit are regarded as the estimated values ​​of each distance unit:

[0030] Step 2) The estimated value of the distance unit of the i-th pulse compression is zero-filled and extended by a zero-value sequence with a length of N-1 before and after it: Calculate the corresponding power estimate On this basis, the adaptive filter value w is calculated at the i+1th iteration i+1 (l) and then update the estimate of the range cell using the new adaptive filter: Get the pulse compression results of each distance unit

[0031] Step 3) Repeat step 2 until a preset number of iterations or sidelobe suppression effect is achieved, terminate the iteration, and output the final adaptive filter coefficients and the estimated pulse compression results of each distance unit.

[0032] Compared with the prior art, the beneficial effect of the present invention is that the improved adaptive pulse compression method based on the MMSE criterion of the present invention first models the echo model, then introduces the minimum filtering result of the adjacent distance unit as a constraint item into the MMSE cost function, then optimizes and solves the cost function, and finally obtains the estimated value of the filter and the estimated value of the distance unit by an iterative update method. By introducing the minimum filtering value of the adjacent unit, the method of the present invention can suppress the distance sidelobes of the surrounding targets in a targeted manner, thereby improving the radar's detection capability for small and weak targets, and the core algorithm of the method of the present invention is simple to implement and has high practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1It is a flow chart of the implementation of the improved adaptive pulse compression method based on MMSE criterion of the present invention;

[0034] Figure 2 is a comparison result diagram of three target signals of equal strength using different pulse compression methods according to an embodiment of the present invention;

[0035] Figure 3 It is a comparison result diagram of the embodiment of the present invention using different pulse compression methods for echo signals with weak targets. DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0037] The present invention is an improved adaptive pulse compression method based on the MMSE criterion. Figure 1 As shown, the specific steps include the following steps 1 to 4.

[0038] Step 1: Construct the echo signal model. Assume that the radar transmission signal is s = [s1 s2 … s N ] T , N is the length of the radar transmission signal, and the impulse response of the distance scene is L sampling points x = [x(1) x(2) … x(L)] T The superscript T indicates transposition. The ideal radar echo range image length is L+N-1. Assuming that starting from the lth range unit, the radar echo vector of length N is y(l) = [y(l) y(l+1) … y(l+N-1)] T ,l=1,2,…L, the specific expression is: y(l)=Sx(l)+n(l). Where:

[0039] Noise component n(l) = [n(l-N+1) … n(l) … n(l+N-1)] T ;

[0040] The impulse response vector of the range cell x(l) = [x(l-N+1) …x(l) …x(l+N-1)] T ;

[0041] The matrix composed of the transmitted signal shift

[0042] By observing the impulse response vector x(l) of the range unit with a length of 2N-1, it can be seen that in addition to the impulse response x(l) of the lth range unit located at the center point, the impulse responses of the surrounding 2N-2 range units also participate in the construction of the echo signal. Therefore, x(l) is decomposed into x t (l) and x c (l) Two parts:

[0043] x(l)=[0 … 0 x(l) 0 … 0] T +[x(l-N+1) … x(l-1) 0 x(l+1) … x(l+N-1)] T

[0044] =x t (l)+x c (l)

[0045] Among them, the lth distance unit can be regarded as the current distance unit, x t (l) represents the impulse response of the current distance unit, x c (l) represents the impulse response of the adjacent distance unit.

[0046] The echo signal can be decomposed into:

[0047] y(l)=S(x t (l)+x c (l))+n(l)=x(l)s+Sx c (l)+n(l)=y t (l)+y c (l)+n(l);

[0048] Therefore, the echo signal y(l) can be regarded as the echo signal component y on the lth range unit t (l) = x(l)s and the interference signal component y on the adjacent distance unit c (l) = Sx c (l) and the superposition of the noise signal n(l).

[0049] Step 2: Establish an improved filter cost function based on the MMSE criterion.

[0050] The echo signal y(l) is pulse compressed, and the corresponding pulse compression in the lth range direction is: Where w(l)=[w(l) w(l+1) … w(l+N-1)] T are filter coefficients, the superscript H indicates conjugate transpose, is the estimate of the impulse response x(l) of the lth range unit.

[0051] Based on the MMSE criterion, the filter cost function of the lth distance unit can be constructed as:

[0052]

[0053] Where E[·] means to find the expectation.

[0054] Because the filter cost function based on MMSE only considers the true value x(l) and the estimated value of the l-th distance unit In order to achieve sidelobe suppression more effectively, the method of the present invention adds the minimum filtering result of adjacent distance units as a constraint item to the filter cost function, and establishes an improved filter cost function based on the MMSE criterion as follows:

[0055] J = E[x(l)-w(l) H y(l) 2 +λw(l) H y c (l) 2 ]

[0056] Where λ is a regularization parameter, which is used to control the degree of suppression of the filtering results of adjacent distance units.

[0057] As can be seen from the above formula, the cost function J proposed by the method of the present invention is composed of a data fidelity term based on MMSE and a filtering result suppression term of adjacent distance units. The purpose of this cost function is to suppress the influence of surrounding distance units on the filtering result while restoring the impulse response of the lth distance unit.

[0058] Step 3: Optimize and solve the filter cost function J to obtain the improved expression of the optimal filter based on the MMSE criterion.

[0059] First, find the complex gradient of w with respect to J:

[0060] make The expression for w is: w(l)={E[y(l)y H (l)+λy c (l)y c H (l)]} -1 E[y(l)x H (l)].

[0061] Substitute y(l)=Sx(l)+n(l) into the expression of w, assuming that the noise is uncorrelated with the range impulse response, and the range impulse responses of each target are also uncorrelated, then:

[0062] E[y(l)x H (l)] = ρ(l)S, where the power expectation of the impulse response of the lth range unit is: ρ(l) = |x(l)| 2 ;

[0063] E[y(l)y H (l)+λy c (l)y cH (l)] = Sdiag(ρ c )S H +ρ(l)ss H +R;

[0064] in:

[0065] Correlation matrix of white noise: R = E[n(l)n(l) H ];

[0066] Power matrix in the distance direction: ρ c =(1+λ)[ρ(l-N+1) … ρ(l-1) 0 ρ(l+1) … ρ(l+N-1)] T .

[0067] Therefore, the adaptive filter coefficient of the lth distance unit is obtained as:

[0068] w(l)=ρ(l)[Sdiag(ρ c )S H +ρ(l)ss H +R] -1 s;

[0069] Where diag represents the diagonal function.

[0070] Step 4: Calculate the improved filter estimation value based on the MMSE criterion and the range pulse compression result through iterative calculation method.

[0071] Since R is the correlation matrix of white noise, it cannot be obtained specifically during the calculation process, and ρ cThe power data contains noise components, so the calculation can be ignored in the specific process. At the same time, in the expression of the improved adaptive filter based on the MMSE criterion, because the impulse response of each distance unit is unknown, it is difficult to obtain accurate adaptive filter coefficients, so an iterative operation is used to obtain the estimated value of w(l). Because the pulse compression results of the N-1 distance units before and after the current range gate are needed in the calculation process of the filter w(l), the existing pulse compression results need to be zero-filled and expanded during the iteration process, that is, the head and tail of the existing pulse compression results are filled with a 0-value sequence of length N-1. During the iteration process, the value of λ represents the degree of suppression of the adjacent distance unit filtering results. The value range of λ is [0, ∞]. When the value of λ approaches 0, the degree of suppression of the adjacent distance unit filtering results is small. When the value of λ approaches infinity, the degree of suppression of the adjacent distance unit filtering results is large but may cause a decrease in the main lobe intensity. Therefore, during the iterative calculation process, the value of λ should be determined based on experience and increase with the increase in the number of iterations to gradually enhance the degree of suppression of the adjacent distance unit filtering results.

[0072] Step 1) Consider the radar transmission signal as the initial value of the filter: w i (l) = s, i = 1, where i is the number of iterations. The result of the matched filtering of the lth distance unit is The matched filtering results of each distance unit are regarded as the estimated values ​​of each distance unit:

[0073] Step 2) The estimated value of the distance unit of the i-th pulse compression is zero-filled and extended by a zero-value sequence with a length of N-1 before and after it: Calculate the corresponding power estimate On this basis, the adaptive filter value w at the i+1th iteration is calculated according to the formula obtained in step 3. i+1 (l) and then update the estimate of the range cell using the new adaptive filter: Get the pulse compression results of each distance unit

[0074] Step 3) Repeat step 2 until a preset number of iterations or sidelobe suppression effect is achieved, terminate the iteration, and output the final adaptive filter coefficients and the estimated pulse compression results of each distance unit.

[0075] Example

[0076] In order to verify the effectiveness of the method of the present invention in sidelobe suppression, this embodiment conducts a pulse compression experiment under multiple targets and compares it with the existing matched filtering method (MF), MMSE method and PCR method.

[0077] Assuming that the transmitted signal is a linear frequency modulation signal with a signal bandwidth of 50MHz, a time width of 1μs, and a sampling rate of 150MHz, there are three equally strong target signals with a spacing of 5 range gates in the radar echo. The pulse compression results using different methods are as follows: Figure 2 The result of using the matched filter method to compress the signal pulse is shown in Figure 2 As shown by the black solid line in the middle, it can be seen that the matched filter can obtain the main lobes of the three target signals, but due to the large amplitude of the side lobes of the distance targets at each point, the main lobes of the three targets are not well distinguished. The PCR method is used to compress the echo signal to obtain the result as shown in the figure. Figure 2 As shown by the green solid line, it can be seen that the PCR method can effectively distinguish the main lobes of the three target signals, and the main-side lobe ratio is reduced to 107dB. The echo signal is compressed by adaptive pulse compression based on MMSE, and the result is as follows: Figure 2 As shown by the blue solid line, the method is iterated twice. It can be seen that the MMSE-based adaptive pulse compression method can compress the main lobes of the three target signals well, and the main-side lobe ratio is reduced to 151 dB. The improved MMSE-based adaptive pulse compression method of the present invention is used for pulse compression, and the filter is iterated twice. The values ​​of λ in the two iterations are 100 and 500 respectively. The results are shown in FIG. Figure 2 As shown by the red solid line in the figure, the main-to-sidelobe ratio is 198 dB. It can be seen that compared with the matched filtering, MMSE and PCR methods, the method of the present invention can more effectively suppress the target sidelobe while detecting the target signal strength.

[0078] Assume that there are two targets with a distance of 3 range gates in the radar echo, but the target echo energy differs by 20dB. Use each method to perform pulse compression on the radar echo with weak targets. The results are as follows: Figure 3 The result of matched filtering is shown in Figure 3 As shown by the black solid line in , it can be seen that due to the large sidelobe amplitude of the strong point target, the weak target signal is masked by the range sidelobe of the strong target signal, so the information of the weak target signal cannot be effectively detected. The results of the PCR pulse compression method are shown in Figure 3 As shown by the green solid line, it can be seen that the PCR method can effectively detect the main lobe of weak targets, and its main-to-side lobe ratio is reduced to 134dB. The filtering results of the adaptive pulse compression method based on MMSE are shown in Figure 3As shown by the blue solid line, the method is iterated twice. It can be seen that the method can compress the main lobe of the weak target signal well, and the main-to-side lobe ratio is reduced to 137dB. The improved adaptive pulse compression method based on MMSE criterion of the present invention is used for pulse compression. The filter is iterated twice. The values ​​of λ in the two iterative updates are 5 and 1000 respectively. The results are shown in FIG. Figure 3 As shown by the red solid line in the figure, the main-to-sidelobe ratio is 173 dB. It can be seen that compared with the matched filtering, MMSE and APC methods, the method of the present invention can more effectively suppress the range sidelobe of the strong point target while detecting the signal strength of the weak target, thereby improving the radar's detection capability for the weak target.

[0079] Therefore, through the pulse compression experimental results of multi-target strong point signals and the pulse compression experimental results with weak targets, it can be proved that the method of the present invention is a pulse compression method that effectively suppresses range side lobes and detects target signals.

[0080] Except for the technical features described in the specification, all of them are known technologies to those skilled in the art. The present invention omits the description of known components and known technologies to avoid redundancy and unnecessary limitation of the present invention. The implementation methods described in the above embodiments do not represent all implementation methods consistent with the present application. On the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative labor are still within the protection scope of the present invention.

Claims

1. An improved adaptive pulse compression method based on MMSE criterion, characterized in that: The following steps are involved: Step 1: Establish an echo signal model and regard the echo signal sequence y(l) corresponding to the current l-th distance unit as the echo signal component y of the current distance unit t (l) The echo signal component y with the adjacent distance unit c (l) and the superposition of the noise signal n(l); Step 2: Based on the MMSE criterion, the constraint term of the minimum filtering result of adjacent distance units is introduced to establish an improved filter cost function based on the MMSE criterion; First, the filter cost function of the lth distance unit based on the MMSE criterion is constructed as follows: P=E[|x(l)-w(l) H y(l)| 2 ]; where w(l) is the filter coefficient, x(l) is the impulse response of the l-th distance unit, the superscript H represents the conjugate transpose, and E[·] represents the expectation; Then the constraint term |w(l) of the minimum filtering result of the adjacent distance unit is H y c (l)| 2 Add it to the filter cost function to establish an improved filter cost function based on the MMSE criterion: J = E[|x(l)-w(l) H y(l)| 2 +λ|w(l) H y c (l)| 2 ], where λ is a regularization parameter used to control the degree of suppression of the filtering results of adjacent distance units; Step 3: Optimize and solve the adaptive filter cost function J to obtain an improved expression of the optimal filter based on the MMSE criterion; Step 4: derive the improved filter estimation value based on the MMSE criterion and the pulse compression result of the echo signal through an iterative calculation method; Here, MMSE stands for minimum mean square error.

2. The method according to claim 1, characterized in that In the step 1, the radar transmission signal is represented by s=[s1 s2 … s N ] T , N is the signal length, and the superscript T indicates transposition; let the echo signal of length N starting from the lth range unit be y(l) = [y(l) y(l+1) … y(l+N-1)] T ,l=1,2,…L, L is the number of sampling points of the distance scene, and the echo signal is expressed as: y(l)=Sx(l)+n(l); Matrix composed of radar transmission signal shifts The impulse response vector of the range cell is x(l) = [x(l-N+1) … x(l) … x(l+N-1)] T ; Noise component n(l) = [n(l-N+1) … n(l) … n(l+N-1)] T ; The impulse response vector x(l) of the distance unit with the lth distance unit located at the center and a length of 2N-1 is decomposed into the impulse response x of the lth distance unit t (l) and the impulse response component x of the adjacent 2N-2 distance units c (l); then the echo signal y(l) = S(x t (l)+x c (l))+n(l)=x(l)s+Sx c (l)+n(l)=y t (l)+y c (l)+n(l).

3. The method according to claim 1 or 2, characterized in that: The step three comprises: First, the complex gradient of the filter coefficient w is calculated for the filter cost function J as follows: make The expression for w is: w(l)={E[y(l)y H (l)+λy c (l)y c H (l)]} -1 E[y(l)x H (l)]; Then, y(l)=Sx(l)+n(l) is substituted into the expression of w. At the same time, assuming that the range impulse responses of each target are uncorrelated, and the noise is also uncorrelated with the range impulse response, the expression of the adaptive filter of the lth range unit is obtained as follows: w(l)=ρ(l)[Sdiag(ρ c )S H +ρ(l)ss H +R] -1 s; Where diag represents the diagonal function; the power expectation of the impulse response of the lth distance unit is ρ(l) = |x(l) 2 ; Power matrix ρ in the distance direction c =(1+λ)[ρ(l-N+1) … ρ(l-1) 0 ρ(l+1) … ρ(l+N-1)] T ; The correlation matrix of white noise is R = E[n(l)n(l) H ].

4. The method according to claim 3, characterized in that In the fourth step, an estimated value of w(l) is obtained by iterative operation. During the iteration process, the value of λ is set from small to large, and the correlation matrix R of the white noise is ignored. The iterative operation includes the following steps: Step 1) Consider the radar transmission signal s as the initial value of the filter coefficient: w i (l) = s, i = 1, where i is the number of iterations. The result of the matched filtering of the lth distance unit is The result of matched filtering of each distance unit is regarded as the estimated value of the distance unit: Step 2) The estimated value of the distance unit of the i-th pulse compression is zero-filled and extended by a zero-value sequence with a length of N-1 before and after it: Calculate the corresponding power estimate Then calculate the adaptive filter coefficient w at the i+1th iteration i+1 (l), and then use the new adaptive filter coefficients w i+1 (l) Update the estimated value of the distance unit: Get the pulse compression results of each distance unit Step 3) Repeat step 2 until a preset number of iterations or sidelobe suppression effect is achieved, terminate the iteration, and output the final adaptive filter coefficients and the estimated pulse compression results of each distance unit.

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