CN108259399B - Time domain equalizer and control method thereof - Google Patents

Abstract

The present invention provides a time domain equalizer for eliminating an echo signal in a received signal. The received signal includes an original signal and the echo signal. The time domain equalizer includes a time delay estimator, an amplitude magnification estimator, and a phase offset estimator. The time delay estimator finds a delay that can maximize a cost function as an estimated delay of the echo signal relative to the original signal. The amplitude magnification estimator determines an estimated amplitude magnification of the echo signal relative to the original signal based on the estimated delay. The phase offset estimator determines an estimated phase offset of the echo signal relative to the original signal based on the estimated delay.

Description

Time domain equalizer and control method thereof

technical field

The present invention is related to time-domain equalizers, and in particular to the way parameters are determined in time-domain equalizers.

Background technique

Orthogonal frequency-division multiplexing (OFDM) technology has been widely used in communication systems in recent years due to its advantages of high spectrum utilization and simple hardware architecture. The OFDM signal is composed of multiple symbols. In order to avoid intersymbol interference (ISI) caused by multipath (multipath), each symbol front end is provided with a guard interval (guard interval). However, in a more complex communication environment, there may still be a propagation delay that exceeds the length of the guard interval, thereby causing inter-symbol interference and reducing the overall performance of the system. This problem cannot be solved by frequency-domain equalization technology, but an additional time-domain equalizer must be set before the frequency-domain equalizer at the receiving end. Only by correctly estimating the arrival time delay, amplitude magnification and phase offset of each echo signal in the multiple propagation paths relative to the original signal, and setting the time domain equalizer accordingly, can it be effectively eliminated. Or try to reduce the interference of these echo signals to the original signal.

SUMMARY OF THE INVENTION

The present invention provides a time domain equalizer and a control method thereof. By defining an appropriate cost function as an evaluation basis, the time domain equalizer and control method according to the present invention can estimate the time delay of an echo signal relative to the original signal. Furthermore, according to the estimated delay amount, the amplitude magnification and phase offset of the echo signal relative to the original signal can also be determined.

An embodiment according to the present invention is a time domain equalizer for cancelling an echo signal in a received signal. The received signal includes an original signal and the echo signal. The time domain equalizer includes a time delay estimator, an amplitude magnification estimator, and a phase offset estimator. The time delay estimator first finds a delay that can maximize a cost function as an estimated delay of the echo signal relative to the original signal. The amplitude magnification estimator determines an estimated amplitude magnification of the echo signal relative to the original signal according to the estimated delay amount. The phase offset estimator determines an estimated phase offset of the echo signal relative to the original signal according to the estimated delay. The cost function is:

Among them, the symbol y represents the received signal, k represents a sampling index, the signal y[k+τ] represents a delayed signal generated by the received signal after a time delay of length τ, y ^* [k+τ] represents the The conjugate of the delayed signal.

Another specific embodiment according to the present invention is a control method applied to a time domain equalizer. The time domain equalizer is used to cancel an echo signal in a received signal. The received signal includes an original signal and the echo signal. First, a delay amount that can maximize a cost function is found as an estimated delay amount of the echo signal relative to the original signal. According to the estimated delay amount, an estimated amplitude magnification and an estimated phase offset of the echo signal relative to the original signal are determined. Then, the estimated delay amount, the estimated amplitude magnification and the estimated phase offset are used to set a filter condition that the time domain equalizer will apply to the received signal. The cost function is:

Among them, the symbol y represents the received signal, k represents a sampling index, the signal y[k+τ] represents a delayed signal generated by the received signal after a time delay of length τ, y ^* [k+τ] represents the The conjugate of the delayed signal.

Description of drawings

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of a time domain equalizer according to an embodiment of the present invention.

FIG. 2 is a flowchart of a time domain equalizer control method according to an embodiment of the present invention.

It should be noted that the drawings of the present invention include functional block diagrams showing various interrelated functional devices. These drawings are not detailed circuit diagrams, and the connecting lines are only used to represent signal flow. Various interactions between functional elements and/or programs are not necessarily achieved through direct electrical connections. In addition, the functions of individual elements do not have to be distributed as shown in the drawings, and the distributed blocks do not have to be implemented with distributed electronic elements.

The component numbers in the figure are explained as follows:

100: Time Domain Equalizer 11: Candidate Delay Generation Circuit

12: Time delay amount estimator 14: Amplitude magnification estimator

16: Phase Offset Estimator 18: Filter

S22～S26: Process steps

Detailed ways

In the signal model adopted in the present invention, the original signal sent by the transmitting end is represented by the symbol x, and the received signal received by the receiving end is represented by the symbol y. Without considering the symbol timing offset and frequency offset, after passing through multiple propagation paths, the received signal y can be expressed as follows:

Where k represents a sampling index, and P represents the total number of echo signals caused by the multiple propagation paths of the transmission channel between the transmitter and the receiver. It can be seen from equation 1 that the received signal y is the sum of the original signal x and P echo signals. Symbols a _p , θ _p,k , (M _p +Δ _p ) respectively represent the amplitude magnification, phase offset and arrival time delay of the p-th echo signal in the P echo signals relative to the original signal x Quantity (P is a positive integer, p is an integer index ranging from 1 to P). n[k] represents the noise signal. The arrival time delay amount (M _p +Δ _p ) contains two components, the symbol M _p is the approximate delay amount of the p-th echo signal, which can be known by the receiving end through the inverse fast Fourier transform, but the fine delay amount Δ _p is difficult to measure.

According to Equation 1, the conversion function between the original signal x and the received signal y received by the receiver can be defined as:

The design goal of the time domain equalizer provided by the present invention is to eliminate the echo signal in the signal y as much as possible, that is, to make the conversion function Z/X between the output signal z of the time domain equalizer and the original signal x close to 1. Therefore, it can be deduced that the ideal transfer function Z/Y should be:

Correspondingly, the ideal output signal z of the time domain equalizer is:

FIG. 1 is a functional block diagram of a time domain equalizer according to an embodiment of the present invention. The time-domain equalizer 100 estimates the arrival time delay, the amplitude magnification and the phase offset of each echo signal relative to the original signal x, which becomes the basis for adjusting the received signal y. As shown in FIG. 1 , the time domain equalizer 100 includes a candidate delay amount generating circuit 11, a time delay amount estimator 12, an amplitude magnification estimator 14, a phase offset amount estimator 16 and a filter 18; The operation of each circuit is described below.

该成本函数为：For an echo signal, the time delay estimator 12 first finds an arrival time delay that can maximize a cost function, as the estimated delay of the echo signal relative to the original signal x

The cost function is:

Where k represents a sampling index, and y[k] is the kth sample of the received signal y. The signal y[k+τ] represents a delayed signal generated by the signal y[k] after a time delay of length τ, and y ^* [k+τ] represents the conjugate signal of the delayed signal y[k+τ] . The delayed signal y[k+τ] is generated by the time delay amount estimator 12 from the signal y[k]; the delay amount τ is a variable that the time delay amount estimator 12 can control. The operation in Equation 5 can be regarded as calculating the correlation between the signal y[k] and its delayed signal y[k+τ], and accumulating the results of the correlation operation over a period of time. Theoretically, the closer the delay τ used by the time delay estimator 12 is to the actual delay of the echo signal, the higher the correlation between the signal y[k] and its delayed signal y[k+τ], and further The calculation result of Formula 5 is larger. In view of this, the time delay amount estimator 12 is designed to find the delay amount τ that maximizes the cost function C(τ) as the estimated delay amount of the echo signal relative to the original signal x

The candidate delay amount generating circuit 11 may preselect or instantly determine a plurality of candidate delay amounts, and provide them to the time delay amount estimator 12 . As described earlier, the rough delay amount M _p of the p-th echo signal is known by the inverse fast Fourier transform at the receiving end, but the fine delay amount _Δp is difficult to measure. For each echo signal, the candidate delay amount generating circuit 11 may first find out its approximate delay amount, and select the candidate delay amount from the adjacent range of the approximate delay amount. For example, if it is known that the adjacent range is (M _p -τ _min )～(M _p +τ _max ) and ten candidate delays τ ₀ ˜τ ₉ are to be selected, the candidate delay τ ₀ can be set equal to (M _p -τ _min ), let the candidate delay amount τ ₉ be equal to (M _p +τ _max ), and interpolate between the candidate delay amounts τ ₀ and τ ₉ to generate the other eight equidistantly spaced from small to large Candidate delay amounts τ ₁ to τ ₈ .

In practice, the time delay amount estimator 12 has various possible methods to find the delay amount τ that maximizes the cost function C(τ). Several embodiments are listed below, but the scope of the present invention is not limited thereto.

举例而言，若C(τ₃)为成本函数运算结果C(τ₀)～C(τ₉)中最大的一个成本函数运算结果，时间延迟量估计器12便可选择延迟量τ₃作为估计延迟量

In one embodiment, the time delay amount estimator 12 can respectively generate ten kinds of delayed signals of the received signal y according to the candidate delay amounts τ ₀ ˜τ ₉ , and generate ten costs according to the ten kinds of delayed signals and the received signal y. Function operation results C(τ ₀ ) to C(τ ₉ ). Then, according to the cost function operation results C(τ ₀ )˜(τ ₉ ), the time delay amount estimator 12 selects a candidate delay amount that can produce a maximum cost function operation result as the estimated delay amount

For example, if C(τ ₃ ) is the largest cost function operation result among the cost function operation results C(τ ₀ )˜C(τ ₉ ), the time delay amount estimator 12 can select the delay amount τ ₃ as the estimation delay amount

换句话说，若C′(τ₃)为偏微分运算结果C′(τ₀)～C′(τ₉)中最接近零的一个偏微分运算结果，时间延迟量估计器12便可选择延迟量τ₃作为估计延迟量

In another embodiment, a partial differential function C′(τ) generated by applying a partial differential to the cost function C(τ) with the delay amount τ as the partial derivative is provided in advance. The time delay amount estimator 12 respectively substitutes multiple candidate delay amounts into the partial differential function C'(τ) to generate multiple partial differential operation results, such as C'(τ ₀ )˜C'(τ ₉ ). Then, the time delay amount estimator 12 selects, as the estimated delay amount, a candidate delay amount that can produce a partial differential operation result closest to zero

In other words, if C'(τ ₃ ) is a partial differential operation result closest to zero among the partial differential operation results C'(τ ₀ )-C'(τ ₉ ), the time delay estimator 12 can select the delay The amount τ ₃ is used as the estimated delay amount

(必然邻近于该初步估计延迟量)。以延迟量τ₃被选择作为该初步估计延迟量为例，时间延迟量估计器12会将初步估计延迟量τ₃代入偏微分函数C′(τ)，以产生一第一偏微分结果C′(τ₃)。假设候选延迟量τ₀～τ₉是由小到大依序排列。可理解的是，若第一偏微分结果C′(τ₃)为大于零，能最大化成本函数C(τ)的延迟量(亦即可令其偏微分结果大致为零的延迟量)很可能是出现在候选延迟量τ₃、τ₄之间，且候选延迟量τ₄对应的偏微分结果C′(τ₄)很可能小于零。相对地，若第一偏微分结果C′(τ₃)小于零，能最大化成本函数C(τ)的延迟量(亦即可令其偏微分结果大致为零的延迟量)则很可能出现在候选延迟量τ₂、τ₃之间，且候选延迟量τ₄对应的偏微分结果C′(τ₄)很可能大于零。因此，根据第一偏微分结果C′(τ₃)的正负号，时间延迟量估计器12可自多个候选延迟量τ₀～τ₉中再选择另一个参考延迟量。举例而言，若第一偏微分结果C′(τ₃)为大于零，时间延迟量估计器12便可选择候选延迟量τ₄作为另一个参考延迟量，并将参考延迟量τ₄代入偏微分函数C′(τ)，以产生一第二偏微分结果C′(τ₄)。随后，时间延迟量估计器12可根据第一偏微分结果C′(τ₃)与第二偏微分结果C′(τ₄)内插产生令偏微分结果大致为零的延迟量，作为估计延迟量

In another embodiment, similarly, a partial differential function C′(τ) generated by applying a partial differential to the cost function C(τ) with the delay amount τ as the partial derivative is provided in advance. First, the time delay amount estimator 12 respectively substitutes a plurality of candidate delay amounts into the cost function C(τ) to generate a plurality of cost function operation results, such as C(τ ₀ )˜C(τ ₉ ). Then, according to the cost function operation results C(τ ₀ )˜C(τ ₉ ), the time delay amount estimator 12 selects a candidate delay amount that can generate a maximum cost function operation result as a preliminary estimated delay amount, and further Infer a more accurate estimate of the delay amount

(necessarily adjacent to this preliminary estimated delay). Taking the delay amount τ ₃ selected as the preliminary estimated delay amount as an example, the time delay amount estimator 12 will substitute the preliminary estimated delay amount τ ₃ into the partial differential function C′(τ) to generate a first partial differential result C′ (τ ₃ ). It is assumed that the candidate delay amounts τ ₀ to τ ₉ are arranged in ascending order. It can be understood that if the first partial differential result C'(τ ₃ ) is greater than zero, the delay amount that can maximize the cost function C(τ) (that is, the delay amount that can make its partial differential result approximately zero) is very high. It may appear between the candidate delay amounts τ ₃ and τ ₄ , and the partial differential result C′(τ ₄ ) corresponding to the candidate delay amount τ ₄ is likely to be less than zero. Conversely, if the first partial differential result C'(τ ₃ ) is less than zero, the delay that can maximize the cost function C(τ) (that is, the delay that makes the partial differential result approximately zero) is likely to occur. Between the candidate delay amounts τ ₂ and τ ₃ , the partial differential result C′(τ ₄ ) corresponding to the candidate delay amount τ ₄ is likely to be greater than zero. Therefore, according to the sign of the first partial differentiation result C'(τ ₃ ), the time delay amount estimator 12 can select another reference delay amount from the plurality of candidate delay amounts τ ₀ -τ ₉ . For example, if the first partial differential result C'(τ ₃ ) is greater than zero, the time delay estimator 12 can select the candidate delay τ ₄ as another reference delay, and substitute the reference delay τ ₄ into the partial Differentiate the function C'(τ) to generate a second partial differential result C'(τ ₄ ). Then, the time delay amount estimator 12 can generate a delay amount that makes the partial differential result approximately zero by interpolation according to the first partial differential result C′(τ ₃ ) and the second partial differential result C′(τ ₄ ), as the estimated delay quantity

It should be noted that, in practical applications, the above-mentioned candidate delay amount does not necessarily correspond to an integer sampling index k, for example, it may correspond to a sampling index k=1.5 or k=1.75. More specifically, if a non-integer sampling index k is to be generated, the candidate delay amount used by the time delay amount estimator 12 may be generated by one-stage or multi-stage interpolation according to several delay amounts corresponding to the integer sampling index k. An example of a two-stage interpolation generating candidate delay amounts is presented below.

First, the first-stage interpolation is to generate a plurality of preliminary interpolation results y(k+t _j ). For example, five preliminary interpolation results y(k+t _j ) can be obtained by linearly combining the received signals y corresponding to each of the five initial delay amounts t ₀ -t ₄ :

为权重系数，各延迟量t_j的权重系数皆不同；M_j为一基本延迟量(与t_j无关)。where j is an integer index ranging from 0 to 4;

is a weight coefficient, and the weight coefficients of each delay amount t _j are different; M _j is a basic delay amount (independent of t _j ).

Next, the second-stage interpolation is to generate a plurality of second-stage interpolation results y(k+τ _i ). For example, eleven second-stage interpolation results y(k+τ _i ) can be generated by re-interpolation using y(k+t _j ) obtained according to Equation 6:

为权重系数，各延迟量t_j的权重系数皆不同。where i is an integer index ranging from 0 to 10,

is a weight coefficient, and the weight coefficient of each delay amount t _j is different.

Combining Equation 6 and Equation 7, the cost function C(τ _i ) can be expanded as follows:

in,

According to Equation 8 and Equation 9, the partial differential function C′(τ _i ) can be derived:

和

都可以预先计算并储存在存储器中作为参考资料，供时间延迟量估计器12使用。Among them, _Ak,I and _Ak,Q correspond to the in-phase component and quadrature-phase component of the signal, respectively. In practice, the coefficient

and

can be pre-computed and stored in memory as reference data for the time delay amount estimator 12 to use.

之后，振幅放大倍率估计器14便根据估计延迟量

决定该回波信号相对于原始信号x的估计振幅放大倍率

于一实施例中，振幅放大倍率估计器14根据下列运算式决定该估计振幅放大倍率：An estimated delay amount is generated for an echo signal at the time delay amount estimator 12

After that, the amplitude magnification estimator 14 estimates the delay amount according to the

Determines the estimated amplitude magnification of the echo signal relative to the original signal x

In one embodiment, the amplitude magnification estimator 14 determines the estimated amplitude magnification according to the following formula:

代表时间延迟量估计器12产生的该估计延迟量，μ代表时域均衡器100所属的接收端施于接收信号y的快速傅立叶变换的长度。实务上，式十一中的数值

可能稍早已由时间延迟量估计器12产生，可直接提供给振幅放大倍率估计器14使用。where k∈GI means that the estimated amplitude magnification is calculated by selecting the sampling result within a guard interval corresponding to the original signal x,

represents the estimated delay amount generated by the time delay amount estimator 12, and μ represents the length of the fast Fourier transform applied to the received signal y by the receiving end to which the time domain equalizer 100 belongs. In practice, the numerical value in Equation 11

It may be generated earlier by the time delay amount estimator 12 and may be directly supplied to the amplitude magnification estimator 14 for use.

之后，相位偏移量估计器16便根据估计延迟量

决定该回波信号相对于原始信号x的估计相位偏移

于一实施例中，相位偏移量估计器16找出运算结果

的相位角(或称幅角)，作为该估计相位偏移

实务上，运算结果

稍早已由时间延迟量估计器12产生，可直接提供给相位偏移量估计器16使用。In addition, the time delay amount estimator 12 generates an estimated delay amount for an echo signal

Then, the phase offset estimator 16 estimates the delay according to

Determines the estimated phase offset of this echo signal relative to the original signal x

In one embodiment, the phase offset estimator 16 finds the result of the operation

The phase angle (or argument) of , as the estimated phase offset

In practice, the result of the operation

It is generated earlier by the time delay estimator 12 and can be directly supplied to the phase offset estimator 16 for use.

估计振幅放大倍率

与估计相位偏移

来设定将施加于接收信号y的过滤条件。须说明的是，如何根据各回波信号的估计延迟量

估计振幅放大倍率

与估计相位偏移

来设定适当的过滤条件以滤除这些回波信号为本发明所属技术领域中的技术人员所知，于此不赘述。Finally, the filter 18 is based on the estimated delay of each echo signal

Estimated amplitude magnification

offset from the estimated phase

to set the filter conditions that will be applied to the received signal y. It should be noted that how to estimate the delay according to the echo signal

Estimated amplitude magnification

offset from the estimated phase

It is known to those skilled in the art to which the present invention pertains to set appropriate filtering conditions to filter out these echo signals, and details are not described herein.

Those skilled in the art to which the present invention pertains can appreciate that there are various circuit configurations and components that can implement the candidate delay amount generating circuit 11, the time delay amount estimator 12, and the amplitude magnification estimator without departing from the spirit of the present invention 14. Phase offset estimator 16, eg fixed and programmable logic circuits, eg programmable logic gate arrays, application specific integrated circuits, microcontrollers, microprocessors, digital signal processors. In addition, these estimators can also be designed to complete their computing tasks by executing processor instructions stored in memory.

Another specific embodiment of the present invention is a control method applied to a time-domain equalizer, the flowchart of which is shown in FIG. 2 . The time domain equalizer is used to cancel an echo signal in a received signal. The received signal includes an original signal and the echo signal. First, step S22 is to find a delay that can maximize a cost function as an estimated delay of the echo signal relative to the original signal. In step S24, according to the estimated delay amount, an estimated amplitude magnification and an estimated phase offset of the echo signal relative to the original signal are determined. Then, in step S26, the estimated delay amount, the estimated amplitude magnification and the estimated phase offset are used to set a filter condition that the time domain equalizer will apply to the received signal. In step S22, the cost function is:

Among them, the symbol y represents the received signal, k represents a sampling index, the signal y[k+τ] represents a delayed signal generated by the received signal after a time delay of length τ, y ^* [k+τ] represents the The conjugate of the delayed signal.

Those skilled in the art to which the present invention pertains can understand that the various operation changes described in the introduction of the time domain equalizer 100 can also be applied to the control method in FIG. 2 , and details thereof will not be repeated.

It should be noted that the mathematical expressions herein are used to illustrate the principles and logics related to the embodiments of the present invention, and do not limit the scope of the present invention unless otherwise specified. Those skilled in the art to which the present invention pertains can understand that there are various techniques for realizing the physical representations corresponding to these mathematical formulas.

Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the present invention The scope of protection shall be defined by the claims.

Claims (8)

1. A time domain equalizer for eliminating an echo signal in a received signal, the received signal comprising an original signal and the echo signal, the time domain equalizer comprising: a time delay estimator to find a delay that maximizes a cost function as an estimated delay of the echo signal relative to the original signal; an amplitude magnification estimator for determining an estimated amplitude magnification of the echo signal relative to the original signal according to the estimated delay; and a phase offset estimator for determining an estimated phase offset of the echo signal relative to the original signal according to the estimated delay; where the cost function is:

Among them, the symbol y represents the received signal, k represents a sampling index, the signal y[k+τ] represents a delayed signal generated by the received signal after a time delay of length τ, y ^* [k+τ] represents the The conjugate signal of the delayed signal; The amplitude magnification estimator determines the estimated amplitude magnification according to the following formula:

where k∈GI represents the sampling result within a guard interval corresponding to the original signal,

represents the estimated delay generated by the time delay estimator, and μ represents the length of a fast Fourier transform; The phase offset estimator finds the result of the operation

The phase angle of , as the estimated phase offset,

represents the estimated delay amount produced by the delay amount estimator. 2. The time domain equalizer of claim 1, wherein the delay estimator is used to: respectively substituting a plurality of candidate delay amounts into the cost function to generate a plurality of cost function operation results; and According to the plurality of cost function calculation results, a candidate delay amount that can generate a maximum cost function calculation result is selected as the estimated delay amount. 3. The time domain equalizer according to claim 1, wherein a partial differential function generated by applying a partial differential to the cost function with the delay amount τ as a partial derivative is provided in advance; the delay amount estimator is provided by Use to: respectively substituting a plurality of candidate delay amounts into the partial differential function to generate a plurality of partial differential operation results; and Based on the plurality of partial differential operation results, a candidate delay amount that can produce a partial differential operation result closest to zero is selected as the estimated delay amount. 4. The time domain equalizer according to claim 1, wherein a partial differential function generated by applying a partial differential to the cost function with the delay amount τ as a partial derivative is provided in advance; the delay amount estimator is provided by Use to: Substitute multiple candidate delay amounts into the cost function respectively to generate multiple cost function operation results; According to the plurality of cost function operation results, a candidate delay amount that can generate a maximum cost function operation result is selected as a preliminary estimated delay amount; Substituting the preliminary estimated delay amount into the partial differential function to generate a first partial differential result; selecting a reference delay amount from the plurality of candidate delay amounts according to the sign of the first partial differentiation result; Substituting the reference delay amount into the partial differential function to generate a second partial differential result; and The estimated delay amount is generated by interpolation according to the first partial differential result and the second partial differential result. 5. A control method applied to a time-domain equalizer, the time-domain equalizer being used to eliminate an echo signal in a received signal, the received signal comprising an original signal and the echo signal, the control method comprising : (a) finding a delay that can maximize a cost function as an estimated delay of the echo signal relative to the original signal; (b) determining an estimated amplitude magnification and an estimated phase offset of the echo signal relative to the original signal according to the estimated delay; and (c) setting a filter condition that the time domain equalizer will apply to the received signal according to the estimated delay amount, the estimated amplitude magnification and the estimated phase offset; where the cost function is:

Among them, the symbol y represents the received signal, k represents a sampling index, the signal y[k+τ] represents a delayed signal generated by the received signal after a time delay of length τ, y ^* [k+τ] represents the The conjugate signal of the delayed signal; Step (b) includes determining the estimated amplitude magnification according to the following formula:

where k∈GI represents the sampling result within a guard interval corresponding to the original signal,

represents the estimated delay amount generated in step (a), and μ represents the length of a fast Fourier transform; Step (b) includes: find the result of the operation

The phase angle of , as the estimated phase offset,

represents the estimated delay amount produced by step (a). 6. The control method of claim 5, wherein step (a) comprises: respectively substituting a plurality of candidate delay amounts into the cost function to generate a plurality of cost function operation results; and According to the plurality of cost function calculation results, a candidate delay amount that can generate a maximum cost function calculation result is selected as the estimated delay amount. 7. The control method of claim 5, wherein a partial differential function generated by applying the partial differential to the cost function with the delay amount τ as the partial derivative is provided in advance, and step (a) comprises: respectively substituting a plurality of candidate delay amounts into the partial differential function to generate a plurality of partial differential operation results; and Based on the plurality of partial differential operation results, a candidate delay amount that can produce a partial differential operation result closest to zero is selected as the estimated delay amount. 8. The control method of claim 5, wherein a partial differential function generated by applying the partial differential to the cost function with the delay amount τ as the partial derivative is provided in advance, and step (a) comprises: Substitute multiple candidate delay amounts into the cost function respectively to generate multiple cost function operation results; According to the plurality of cost function operation results, a candidate delay amount that can generate a maximum cost function operation result is selected as a preliminary estimated delay amount; Substituting the preliminary estimated delay amount into the partial differential function to generate a first partial differential result; selecting a reference delay amount from the plurality of candidate delay amounts according to the sign of the first partial differentiation result; Substituting the reference delay amount into the partial differential function to generate a second partial differential result; and The estimated delay amount is generated by interpolation according to the first partial differential result and the second partial differential result.

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