1. A non-iterative DOA estimation method for discrete fourier transform interpolation of a wireless signal, comprising the steps of:

s1, the estimator utilizes the two highest amplitude Discrete Fourier Transform (DFT) coefficients of the input data and their two related adjacent bins to provide an accurate DOA estimate;

s2, analyzing the deviation and the mean square error of the DOA estimation;

and S3, verifying the correctness of theoretical derivation according to the simulation result.

2. The non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals according to claim 1, characterized in that: the specific steps of S1 are as follows:

a linear array is listed by discrete fourier transform, where there are N well-aligned, equally polarized sensors, where P uncorrelated, narrowband source targets hit from the far field,

the p-th target is called A_pFrom y_nThe observed single snapshot data for the nth sensor represented can be modeled as:

wherein theta is_pE [0 °,180 °) is the azimuth angle corresponding to the pth object, λ represents the wavelength, d is the distance between two adjacent sensors, with the value λ/2, q_nIs an independent identically distributed complex noise term with zero obedient mean and sigma variance²Unknown Gaussian distribution, according to the observed valueTo estimateIs provided withThe signal model in (1) can be rewritten as:

and theta_pIs a one-to-one mapping relation, and the DOA estimation task is converted into a slave observation valueFind out

Consider thatThe coefficient of the kth DFT is called Y_kExpressed as:

the signal component is given by:

wherein the content of the first and second substances,and Q_kIs the noise component associated with the DFT coefficient, let L_p(P is 1,2, …, P) isThe maximum amplitude peak index of P in (1),the true value of (d) is expressed as:

wherein-0.5. ltoreq. delta_pL is less than or equal to 0.5_pToThe amount of shift of the index is,is obtained according to DFT, and converts tasks into observed valuesTo estimateUsing equations (4) - (5), DFT coefficients S corresponding to the m-th (m ═ 1,2, …, P) peak and its neighboring peaks_kHaving the form:

wherein L is_pm＝L_p-L_mAnd a scalar product operator is represented by · and in a scene with a large number N, by using exp (pi (K + x)) sin (pi (K + x)) ═ exp (pi x) sin (pi x), it is possible to simplify (6) - (8) to (6) - (8)

The (9) to (11) can be simplified as follows:

according to the product-sum nature of the trigonometric function, there are three coefficients a₀,a₁And a₂So that

Let P be 2, let L be₁And L₂(0＜L₁＜L₂< N-1) isThe index of the largest two peaks in the middle,andis expressed as

Wherein-0.5 is not less than delta₁,δ₂Less than or equal to 0.5 respectively represents L₁And L₂Deviation between the true value and the bin value of, L₁And L₂Is obtained directly by DFT, the estimation task is converted to find delta₁And delta₂Let Δ δ be δ₂-δ₁，L＝L₂-L₁Considering the first two terms in (3),DFT of (1)Andwhere it reaches the peak value

The results of (18) and (19) show that,is simultaneously subjected toAndin the absence of the noise term Q_kIn the case of the first peak and its adjacent terms, Lth₁、(L₁-1)、(L₁+1) DFT coefficients are given by:

wherein:

at the same time(20) - (22) satisfy

L th₂The adjacent terms of the DFT coefficients satisfy the following relationship:

order toμ₁And mu₂Is real, the real part of the discrete Fourier transform coefficients being considered separately as

Using the product and formula of trigonometric functions from (25) to (26) to obtain

Where Re { x } represents the real part of x, in order to remove μ₁μ₂The term (27) can be simplified to two quadratic equations, one for each

Wherein

Solving (30) and (31) using the roots of the quadratic equations, estimating μ₁And mu₂I.e. byAndis composed of

Combinations of (27) to (40), on θ₁And theta₂Are respectively calledAndcomprises the following steps:

will delta₁Or delta₂The division into different sub-ranges divides the offset into three sub-ranges.

Sub-ranges with boundaries of 0.25 and-0.25 are selected, the three cases being

3. The non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals according to claim 1, characterized in that: the step S2 further includes the following steps:

s21, analysis of variance and deviationAnddeviation and variance of (c);

and S22, calculating complexity analysis and estimating NIFM.

4. The non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals as recited in claim 1, whereinIn the following steps: x used in said formula (32)_sAnd Z_sThe method comprises the following steps:

wherein S is_lThe formula of (1) is:

wherein:

equations (46) to (47) satisfy:

using mu₁And mu₂And (28) - (29) and (50) - (51), yielding:

wherein:

to remove mu₁μ₂Using (44) - (45), (52) can be written as:

byTo obtain:

5. the non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals according to claim 1, characterized in that: the step S21 specifically includes: analysis ofAnddeviation and variance of (1), centered on δ₁,δ₂∈[-0.25,0.25]Within a sub-range δ₁,δ₂E-0.5, -0.25), two new variables are introduced according to the sub-range criterion in S2By passingAndto give a sum of₁,δ₂E-0.5, -0.25) corresponding toAndthe variance of (a) is determined,and andmay be determined byAndthe variance of (a) gives rise to,obtained by solving the following formula

WhereinAccording to the definitions in (32) to (38),

B＝AH+FA，C＝FAH, (57)

wherein

In combination with (57) to (58),is given by

Wherein, K ═ (. mu.) (₂I₃+F)A(μ₂I₃+H),I₃Representing a 3 x 3 identity matrix, accessible through TSEUpper calculationBias and MSE of (1):

wherein f' (μ)₂) Is f (mu)₂) At mu₂The first derivative of (c), and E {. cndot.) represents the desired operator.

Rewriting x and z in (32) as x ═ x_s+x_qAnd z ═ z_s+z_qWherein x is_sAnd z_sRepresents a signal portion, and x_qAnd z_qIs the noise part, x_qAnd z_qIs to have a variance σ²IID noise term of (1), (59), and f (μ)₂) Can be expressed as

According to the appendix, get

Using (25) - (26) and f (. mu.) (₂) Is defined by

Wherein tr {. cndot } represents a matrix trace, and

L＝A(μ₂I₃+H)+(μ₂I₃+F)A. (67)

according to (64) and (66), the result is (60)

With (61) and (65) to (66),is shown as

Has an offset and MSE of

Wherein

M＝G₁×D×G₂, (72)

T＝D×G₂+G₁×D. (73)

Wherein

According to the definitions of (41) to (42),andare respectively called MSEAnd MSEForm (1) of

6. The non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals according to claim 1, characterized in that: the NIFM estimating step in step S22 is as follows:

s221, calculating an observed Spectrum Using fast Fourier and using O (Nlog)₂(N)) flip-flops transform (FFT) and search for two amplitude peaks of o (N);

s222, estimating mu by using (39) and (40) twice₁And mu₂；

S223, estimating two DOA valuesAnd。

7. the non-iterative DOA estimation method for discrete Fourier transform interpolation of wireless signals according to claim 1, characterized in that: the step S3 further includes the following steps:

s31, verifying the performance of the interpolation formula, and performing computer simulation;

s32, researching the performance of the algorithm under different noise conditions;

s33, researching the relation between the root mean square error and the calculated amount and the number N of the sensors;

s34 test on L₁＝2，L₂Q is 6, SNR is 12dB₁And q is₂Estimates with different values are obtained;

s35, the estimated performance under different DOAs was studied.

Background

Direction of arrival (DOA) estimation can be applied in many areas, such as single-input single-output, multiple-input single-output radar/sonar range-doppler imaging and array processing, which refers to finding the position of a source accurately by parametric or non-parametric methods using a limited set of noisy observations. In the former method, the signal is assumed to be described as a known function, while in the latter method no assumptions are made about the signal. Parameterized algorithms generally allow the derivation of optimal estimates, but performance may deteriorate when the assumed signal model does not match the actual signal model. While non-parametric estimation may not provide optimal estimation performance, it can be used in more applications even without a priori knowledge of the signal. When the traditional estimator estimates the DOA, the steps are complex, the calculation complexity is very high, and the working efficiency is influenced.

Disclosure of Invention

It is an object of the present invention to provide a non-iterative DOA estimation method for discrete fourier transform interpolation of wireless signals to solve the problems set forth in the background above.

In order to achieve the purpose, the invention provides the following technical scheme: a non-iterative DOA estimation method for discrete fourier transform interpolation of a wireless signal, comprising the steps of:

s1, the estimator utilizes the two highest amplitude Discrete Fourier Transform (DFT) coefficients of the input data and their two related adjacent bins to provide an accurate DOA estimate;

s2, analyzing the deviation and the mean square error of the DOA estimation;

and S3, verifying the correctness of theoretical derivation according to the simulation result.

Preferably, the specific step of S1 is:

a linear array is listed by discrete fourier transform, where there are N well-aligned, equally polarized sensors, where P uncorrelated, narrowband source targets hit from the far field,

the p-th target is called A_pFrom y_nOf the nth sensorThe observed single-shot data can be modeled as:

wherein theta is_pE [0 °,180 °) is the azimuth angle corresponding to the pth object, λ represents the wavelength, d is the distance between two adjacent sensors, with the value λ/2, q_nIs an independent identically distributed complex noise term with zero obedient mean and sigma variance²Unknown Gaussian distribution, according to the observed valueTo estimateIs provided withThe signal model in (1) can be rewritten as:

and theta_pIs a one-to-one mapping relation, and the DOA estimation task is converted into a slave observation valueFind out

Consider thatThe coefficient of the kth DFT is called Y_kExpressed as:

the signal component is given by:

wherein the content of the first and second substances,and Q_kIs the noise component associated with the DFT coefficient, let L_p(P is 1,2, …, P) isThe maximum amplitude peak index of P in (1),the true value of (d) is expressed as:

wherein-0.5. ltoreq. delta_pL is less than or equal to 0.5_pToThe amount of shift of the index is,is obtained according to DFT, and converts tasks into observed valuesTo estimateUsing equations (4) - (5), DFT coefficients S corresponding to the m-th (m ═ 1,2, …, P) peak and its neighboring peaks_kHaving the form:

wherein L is_pm＝L_p-L_mAnd a scalar product operator is represented by · and in a scene with a large number N, by using exp (pi (K + x)) sin (pi (K + x)) ═ exp (pi x) sin (pi x), it is possible to simplify (6) - (8) to (6) - (8)

The (9) to (11) can be simplified as follows:

according to the product-sum nature of the trigonometric function, there are three coefficients a₀,a₁And a₂So that

Let P be 2, let L be₁And L₂(0＜L₁＜L₂< N-1) isThe index of the largest two peaks in the middle,andis expressed as

Wherein-0.5 is not less than delta₁,δ₂Less than or equal to 0.5 respectively represents L₁And L₂Deviation between the true value and the bin value of, L₁And L₂Is obtained directly by DFT, the estimation task is converted to find delta₁And delta₂Let Δ δ be δ₂-δ₁，L＝L₂-L₁Considering the first two terms in (3),DFT of (1)Andwhere it reaches the peak value

The results of (18) and (19) show that,is simultaneously subjected toAndin the absence of the noise term Q_kIn the case of the first peak and its adjacent terms, Lth₁、(L₁-1)、(L₁+1) DFT coefficients are given by:

wherein:

at the same time(20) - (22) satisfy

L th₂The adjacent terms of the DFT coefficients satisfy the following relationship:

order toμ₁And mu₂Is real, the real part of the discrete Fourier transform coefficients being considered separately as

Using the product and formula of trigonometric functions from (25) to (26) to obtain

Where Re { x } represents the real part of x, in order to remove μ₁μ₂The term (27) can be simplified to two quadratic equations, one for each

Wherein

Solving (30) and (31) using the roots of the quadratic equations, estimating μ₁And mu₂I.e. byAndis composed of

Combinations of (27) to (40), on θ₁And theta₂Are respectively calledAndcomprises the following steps:

will delta₁Or delta₂The division into different sub-ranges divides the offset into three sub-ranges.

Sub-ranges with boundaries of 0.25 and-0.25 are selected, the three cases being

Preferably, the step S2 further includes the steps of:

s21, analysis of variance and deviationAnddeviation and variance of (c);

and S22, calculating complexity analysis and estimating NIFM.

Preferably, X used in said formula (32)_sAnd Z_sThe method comprises the following steps:

wherein S is_lThe formula of (1) is:

wherein:

equations (46) to (47) satisfy:

using mu₁And mu₂And (28) - (29) and (50) - (51), yielding:

wherein:

to remove mu₁μ₂Using (44) - (45), (52) can be written as:

byTo obtain:

preferably, the step S21 specifically includes: analysis ofAnddeviation and variance of (1), centered on δ₁,δ₂∈[-0.25,0.25]Within a sub-range δ₁,δ₂E-0.5, -0.25), two new variables are introduced according to the sub-range criterion in S2By passingAndto give a sum of₁,δ₂E-0.5, -0.25) corresponding toAndthe variance of (a) is determined,andandmay be determined byAndthe variance of (a) gives rise to,by passingSolving the following equation to obtain

WhereinAccording to the definitions in (32) to (38),

B＝AH+FA，C＝FAH, (57)

wherein

In combination with (57) to (58),is given by

Wherein, K ═ (. mu.) (₂I₃+F)A(μ₂I₃+H),I₃Representing a 3 x 3 identity matrix, accessible through TSEUpper calculationBias and MSE of (1):

wherein f' (μ)₂) Is f (mu)₂) At mu₂The first derivative of (c), and E {. cndot.) represents the desired operator.

Rewriting x and z in (32) as x ═ x_s+x_qAnd z ═ z_s+z_qWherein x is_sAnd z_sRepresents a signal portion, and x_qAnd z_qIs the noise part, x_qAnd z_qIs to have a variance σ²IID noise term of (1), (59), and f (μ)₂) Can be expressed as

According to the appendix, get

Using (25) - (26) and f (. mu.) (₂) Is defined by

Wherein tr {. cndot } represents a matrix trace, and

L＝A(μ₂I₃+H)+(μ₂I₃+F)A. (67)

according to (64) and (66), the result is (60)

With (61) and (65) to (66),is shown as

Has an offset and MSE of

Wherein

M＝G₁×D×G₂, (72)

T＝D×G₂+G₁×D. (73)

Wherein

According to the definitions of (41) to (42),andare respectively called MSEAndform (1) of

Preferably, the NIFM estimating step in step S22 is as follows:

s221, calculating an observed Spectrum Using fast Fourier and using O (Nlog)₂(N)) flip-flops transform (FFT) and search for two amplitude peaks of o (N);

s222, estimating mu by using (39) and (40) twice₁And mu₂；

S223, estimating two DOA valuesAnd

preferably, the step S3 further includes the steps of:

s31, verifying the performance of the interpolation formula, and performing computer simulation;

s32, researching the performance of the algorithm under different noise conditions;

s33, researching the relation between the root mean square error and the calculated amount and the number N of the sensors;

s34 test on L₁＝2，L₂Q is 6, SNR is 12dB₁And q is₂Estimates with different values are obtained;

s35, the estimated performance under different DOAs was studied.

Compared with the prior art, the invention has the beneficial effects that: the calculation steps are simplified, and the operation efficiency is improved.

Drawings

FIG. 1 is a schematic view of a uniform linear array according to the present invention;

FIG. 2 is a graph of mean square error versus signal-to-noise ratio for the present invention;

FIG. 3 is a graph of absolute deviation versus signal-to-noise ratio for the present invention;

FIG. 4 is a schematic diagram of the relationship between the mean square error and the sensor number N according to the present invention;

FIG. 5 is a graph of the computation time for different N according to the present invention;

FIG. 6 is a graph illustrating the mean square error of the present invention compared to either θ 1 or θ 2;

FIG. 7 is a diagram of the mean square error and L of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1-7, the present invention provides a technical solution: a non-iterative DOA estimation method for discrete fourier transform interpolation of a wireless signal, comprising the steps of:

s1, the estimator utilizes the two highest amplitude Discrete Fourier Transform (DFT) coefficients of the input data and their two related adjacent bins to provide an accurate DOA estimate;

s2, analyzing the deviation and the mean square error of the DOA estimation;

and S3, verifying the correctness of theoretical derivation according to the simulation result.

The specific steps of S1 are:

a linear array is listed by discrete fourier transform, where there are N well-aligned, equally polarized sensors, where P uncorrelated, narrowband source targets hit from the far field,

the p-th target is called A_pFrom y_nNth sensor of the representationThe observed single snapshot data of (a) can be modeled as:

wherein theta is_pE [0 °,180 °) is the azimuth angle corresponding to the pth object, λ represents the wavelength, d is the distance between two adjacent sensors, with the value λ/2, q_nIs an independent identically distributed complex noise term with zero obedient mean and sigma variance²Unknown Gaussian distribution, according to the observed valueTo estimateIs provided withThe signal model in (1) can be rewritten as:

and theta_pIs a one-to-one mapping relation, and the DOA estimation task is converted into a slave observation valueFind out

Consider thatThe coefficient of the kth DFT is called Y_kExpressed as:

the signal component is given by:

wherein the content of the first and second substances,and Q_kIs the noise component associated with the DFT coefficient, let L_p(P is 1,2, …, P) isThe maximum amplitude peak index of P in (1),the true value of (d) is expressed as:

wherein-0.5. ltoreq. delta_pL is less than or equal to 0.5_pToThe amount of shift of the index is,is obtained according to DFT, and converts tasks into observed valuesTo estimateUsing equations (4) - (5), DFT coefficients S corresponding to the m-th (m ═ 1,2, …, P) peak and its neighboring peaks_kHaving the form:

wherein L is_pm＝L_p-L_mAnd a scalar product operator is represented by · and in a scene with a large number N, by using exp (pi (K + x)) sin (pi (K + x)) ═ exp (pi x) sin (pi x), it is possible to simplify (6) - (8) to (6) - (8)

The (9) to (11) can be simplified as follows:

according to the product-sum nature of the trigonometric function, there are three coefficients a₀,a₁And a₂So that

Let P be 2, let L be₁And L₂(0＜L₁＜L₂< N-1) isThe index of the largest two peaks in the middle,andis expressed as

Wherein-0.5 is not less than delta₁,δ₂Less than or equal to 0.5 respectively represents L₁And L₂Deviation between the true value and the bin value of, L₁And L₂Is obtained directly by DFT, the estimation task is converted to find delta₁And delta₂Let Δ δ be δ₂-δ₁，L＝L₂-L₁Considering the first two terms in (3),DFT of (1)Andwhere it reaches the peak value

The results of (18) and (19) show that,is simultaneously subjected toAndin the absence of the noise term Q_kIn the case of the first peak and its adjacent terms, Lth₁、(L₁-1)、(L₁+1) DFT coefficients are given by:

wherein:

at the same time(20) - (22) satisfy

L th₂The adjacent terms of the DFT coefficients satisfy the following relationship:

order toμ₁And mu₂Is real, the real part of the discrete Fourier transform coefficients being considered separately as

Using the product and formula of trigonometric functions from (25) to (26) to obtain

Where Re { x } represents the real part of x, in order to remove μ₁μ₂The term (27) can be simplified to two quadratic equations, one for each

Wherein

Solving (30) and (31) using the roots of the quadratic equations, estimating μ₁And mu₂I.e. byAndis composed of

Combinations of (27) to (40), on θ₁And theta₂Are respectively calledAndcomprises the following steps:

will delta₁Or delta₂The division into different sub-ranges divides the offset into three sub-ranges.

Sub-ranges with boundaries of 0.25 and-0.25 are selected, the three cases being

Reduction of delta₁Or delta₂Will decrease the estimation rangeAndtable 1 and table 2 list details of the NIFM algorithm:

table 1: in three cases of theta₁Is estimated by the algorithm

Table 2: in three cases of theta₂Is estimated by the algorithm

The step S2 further includes the steps of:

s21, analysis of variance and deviationAnddeviation and variance of (c);

and S22, calculating complexity analysis and estimating NIFM.

X used in formula (32)_sAnd Z_sThe method comprises the following steps:

wherein S is_lThe formula of (1) is:

wherein:

equations (46) to (47) satisfy:

using mu₁And mu₂And (28) - (29) and (50) - (51), yielding:

wherein:

to remove mu₁μ₂Using (44) - (45), (52) can be written as:

byTo obtain:

step S21 specifically includes: analysis ofAnddeviation and variance of (1), centered on δ₁,δ₂∈[-0.25,0.25]Within a sub-range δ₁,δ₂E-0.5, -0.25), two new variables are introduced according to the sub-range criterion in S2By passingAndto give a sum of₁,δ₂E-0.5, -0.25) corresponding toAndthe variance of (a) is determined,andandmay be determined byAndthe variance of (a) gives rise to,obtained by solving the following formula

WhereinAccording to the definitions in (32) to (38),

B＝AH+FA，C＝FAH, (57)

wherein

In combination with (57) to (58),is given by

Wherein, K ═ (. mu.) (₂I₃+F)A(μ₂I₃+H),I₃Representing a 3 x 3 identity matrix, accessible through TSEUpper calculationBias and MSE of (1):

wherein f' (μ)₂) Is f (mu)₂) At mu₂The first derivative of (c), and E {. cndot.) represents the desired operator.

Rewriting x and z in (32) as x ═ x_s+x_qAnd z ═ z_s+z_qWherein x is_sAnd z_sRepresents a signal portion, and x_qAnd z_qIs the noise part, x_qAnd z_qIs to have a variance σ²IID noise term of (1), (59), and f (μ)₂) Can be expressed as

According to the appendix, get

Using (25) - (26) and f (. mu.) (₂) Is defined by

Wherein tr {. cndot } represents a matrix trace, and

L＝A(μ₂I₃+H)+(μ₂I₃+F)A. (67)

according to (64) and (66), the result is (60)

With (61) and (65) to (66),is shown as

Has an offset and MSE of

Wherein

M＝G₁×D×G₂, (72)

T＝D×G₂+G₁×D. (73)

Wherein

According to the definitions of (41) to (42),andare respectively called MSEAndform (1) of

The NIFM estimation step in step S22 is as follows:

s221, calculating an observed Spectrum Using fast Fourier and using O (Nlog)₂(N)) flip-flops transform (FFT) and search for two amplitude peaks of o (N);

s222, estimating mu by using (39) and (40) twice₁And mu₂；

S223, estimating two DOA values by the table 1 and the table 2And

the step S3 further includes the steps of:

s31, verifying the performance of the interpolation formula, and performing computer simulation;

s32, researching the performance of the algorithm under different noise conditions;

s33, researching the relation between the root mean square error and the calculated amount and the number N of the sensors;

s34 test on L₁＝2，L₂Q is 6, SNR is 12dB₁And q is₂Estimates with different values are obtained;

s35, the estimated performance under different DOAs was studied.

In particular, in use, the estimator utilizes the two highest amplitude Discrete Fourier Transform (DFT) coefficients of the input data and their two associated adjacent bins to provide an accurate DOA estimate, analyzes the DOA estimate for bias and mean square error, bias and variance analysis, and analyzesAnddeviation and variance of, computational complexity analysis, and for NIFM estimation, the use of fast Fourier to compute the observed spectra uses O (Nlog)₂(N)) triggers are transformed (FFT) and search for two amplitude peaks of O (N), and two estimates of μ are obtained using (39) and (40)₁And mu₂Estimating two DOA valuesAndthe simulation result verifies the correctness of theoretical derivation, verifies the performance of an interpolation formula, carries out computer simulation, researches the performance of the algorithm under different noise conditions, and researches the performance of the algorithm under different noise conditionsThe relation between the square root error and the calculated amount and the number N of the sensors is tested in L₁＝2， L₂Q is 6, SNR is 12dB₁And q is₂And the estimation performance under different DOA conditions is researched by taking different values for estimation.

In the description of the present invention, it is to be understood that the terms "coaxial", "bottom", "one end", "top", "middle", "other end", "upper", "one side", "top", "inner", "front", "center", "both ends", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, and do not indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.

Furthermore, the terms "first", "second", "third", "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated, whereby the features defined as "first", "second", "third", "fourth" may explicitly or implicitly include at least one such feature.

In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "disposed," "connected," "secured," "screwed" and the like are to be construed broadly, e.g., as meaning fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; the terms may be directly connected or indirectly connected through an intermediate, and may be communication between two elements or interaction relationship between two elements, unless otherwise specifically limited, and the specific meaning of the terms in the present invention will be understood by those skilled in the art according to specific situations.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.