阅读说明：本技术 基于双曲结构分数延时滤波器的发射数字波束形成方法 (Transmitting digital beam forming method based on hyperbolic structure fractional delay filter ) 是由 丁晓伟 蒋德富 何翱宇 付明星 于 2020-11-23 设计创作，主要内容包括：本发明公开了一种基于双曲结构分数延时滤波器的发射数字波束形成方法,具体包括对双曲函数进行幂级数的方式展开,对展开式中所涉及的子滤波器F(e～(jω))和G(e～(jω))进行系数求解,对求解出的子滤波器按照双曲分数延时滤波器的结构与加法器、乘法器组合起来实现分数延时滤波器,实现发射数字波束形成。本发明解决了现有的分数延时滤波器对宽带信号进行延时补偿精确不够和硬件资源消耗大的问题,并通过求解两种子滤波器的最佳系数来实现时钟分数倍的延时补偿,并利用设计出来的基于双曲结构的分数延时滤波器来实现发射数字波束形成。(The invention discloses a transmitting digital beam forming method based on a hyperbolic structure fractional delay filter, which specifically comprises the steps of expanding a hyperbolic function in a power series mode and expanding a sub-filter F (e) related in the expansion mode jω ) And G (e) jω ) And performing coefficient solving, combining the solved sub-filters with an adder and a multiplier according to the structure of the hyperbolic fractional delay filter to realize the fractional delay filter, and realizing the formation of the transmitting digital beam. The invention solves the problems of insufficient accuracy of delay compensation and high hardware resource consumption of the existing fractional delay filter on broadband signals, realizes delay compensation of the time fractional times by solving the optimal coefficients of two sub-filters, and realizes the formation of transmitting digital beams by utilizing the designed fractional delay filter based on a hyperbolic structure.)

1. A transmitting digital beam forming method based on a hyperbolic structure fractional delay filter is characterized by comprising the following specific steps:

and designing a hyperbolic structure fractional delay filter, and realizing the formation of a transmitting digital beam by using the designed fractional delay filter.

2. The method according to claim 1, wherein the hyperbolic fractional delay filter is designed as follows:

(1) expanding the hyperbolic function according to a power series mode;

(2) designing the frequency response of an ideal delay filter by utilizing a hyperbolic power series structure;

(3) setting sub-filter G (e)^jω) And F (e)^jω) And to two sub-filters G (e)^jω) And F (e)^jω) Designing;

(4) and (4) combining the two sub-filters obtained by the solution in the step (3) with an adder and a multiplier to realize the fractional delay filter.

3. The transmit digital beam forming method based on the hyperbolic structure fractional delay filter according to claim 2, wherein the step (1) expands the hyperbolic function according to a power series manner, which specifically includes:

(1.1) power series expansion of hyperbolic function:

(1.2) adding the power series expansions to obtain:

4. the method according to claim 3, wherein the step (2) of designing the frequency response of the ideal delay filter by using the hyperbolic structure fractional delay filter specifically comprises:

(2.1) setting x ═ -j ω p in step (1.2), yielding the expression:

in the formula: p is a delay amount; j is an imaginary unit; omega is angular frequency;

(2.2) Pre-M according to the expression in step (2.1)₁And (3) solving the frequency response approximate value of the ideal fractional delay filter:

in the formula: m₁Is the truncation order; h₁(omega, p) is the ideal fractional delay filter frequency response H_id(ω, p) approximation; h_id(ω, p) is the frequency response of the ideal fractional delay filter.

5. The hyperbolic fractional delay filter-based transmit digital beamforming method according to claim 4, wherein the sub-filter G (e) in step (3)^jω) And F (e)^jω) The design specifically comprises:

(3.1) setting the sub-filters while satisfying the following conditional expressions, obtaining a filter for the sub-filter G (e)^jω) And F (e)^jω) Expression (c):

in the formula: g (e)^jω) Is a sub-filter; f (e)^jω) Is a sub-filter;

wherein the condition is as follows:

(3.2)G(e^jω) With an ideal frequency response of (j ω)²According toFIR filter pair sub-filter G (e)^jω) Design is carried out and the sub-filter G (e) is solved^jω) The coefficient of (a);

(3.3)F(e^jω) Has an ideal frequency response of j ω according toOf the FIR filter pair of filters F (e)^jω) Design is carried out and the sub-filter F (e) is solved^jω) The coefficient of (a).

6. The hyperbolic fractional delay filter-based transmit digital beamforming method according to claim 5, wherein the sub-filter G (e) in step (3.2)^jω) The specific method for solving the coefficient of (1) is as follows:

(3.2.1) sub-filter G (e)^jω) Satisfies the even symmetry condition, the frequency response of G (z):

in the formula: g (k) is a sub-filter G (e)^jω) The coefficient of (a); g is the sub-filter G (e)^jω) G ═ g (0) g (1.) g (N)₂)]^T；r(ω)＝[1 2cos(ω) ... 2cos(N₂ω)]^T；N₂Is a sub-filter G (e)^jω) The order of (a);

(3.2.2) sub-filter G (e) designed using least squares quasi-quadratic^jω) The error function of the coefficient g is minimal:

wherein: e.g. of the type₂(g) Is a sub-filter G (e)^jω) An error function of the coefficient g;

(3.2.3) according to the error function e₂(g) Is the sub-filter G (e)^jω) Is squared to obtain the sub-filter G (e)^{j ω}) The optimal solution for the coefficients of (a) is:

g_opt＝U^-1u

in the formula: g_optIs a sub-filter G (e)^jω) Is determined by the optimal solution of the coefficients of (a).

7. The hyperbolic fractional delay filter-based transmit digital beamforming method according to claim 5, wherein the sub-filter F (e) in step (3.3)^jω) The specific method for solving the coefficient of (1) is as follows:

(3.3.1) sub-filter F (e)^jω) The coefficient f (k) of (a) satisfies the odd symmetry condition, and the frequency response of f (z) can be expressed as:

in the formula: f is the sub-filter F (e)^jω) F (1) f (2)₁)]^T；b(ω)＝-2[sin(ω) sin(2ω) ... sin(N₁ω)]^T；

(3.3.2) design of the sub-filter F (e) using the least squares criterion^jω) The error function of the coefficient f of (d) is minimal:

wherein: e.g. of the type₁(f) Is a sub-filter F (e)^jω) An error function of the coefficient f;

(3.3.3) according to the error function e₁(f) Is a sub-filter F (e)^jω) Is squared to obtain a sub-filter F (e)^{j ω}) The optimal solution for the coefficients of (a) is:

f_opt＝Q^-1q

in the formula: f. of_optIs a sub-filter F (e)^jω) Is determined by the optimal solution of the coefficients of (a).

Technical Field

The invention relates to the technical field of array signal processing, in particular to a transmitting digital beam forming method based on a hyperbolic structure fractional delay filter.

Background

There are two main methods for time domain beam forming, one is a narrowband beam forming method based on phase shift, and the other is a wideband beam forming method based on time delay. The beam forming method based on phase shift is also called as a conventional beam forming method, and the method has ideal effect on the narrow-band signals, so the method is mainly applied to the beam forming processing of the narrow-band signals. Conventional beamforming adds an extra phase shift to the received signal to offset the phase shift in the desired direction, so that the signals of different array elements are superimposed to obtain the maximum received power in the desired direction. The narrow-band signal approximately compensates the error caused by time delay by using a phase shifting method, and the phase shifting value is determined by the direction of the expected wave beam.

The direction matrix in the broadband signal receiving model is not only related to the direction of the incoming wave, but also related to the changed carrier frequency. If the broadband signal is still phase-shifted to perform beamforming, it is equivalent to replace the continuously varying frequency in the frequency band with a fixed signal center frequency to compensate the delay error, which will cause the beam pointing to shift, and the error will be more obvious when the signal bandwidth is larger. When a radar system uses a broadband signal, the aperture transit time of the antenna has a large influence. Since the direction of the incoming wave is time-varying, the aperture transit time is also varying, so that the phase shift value in the received signal array is also varying, which will greatly affect the broadband signal. Therefore, the wideband signal beamforming processing cannot be performed by the narrowband signal beamforming method based on phase shifting. Delay processing is introduced to accurately compensate for the delay of the received signal on the different elements of the array caused by the array.

However, in the broadband signal beam forming, if only the delay compensation of the integral multiple of the clock is performed on the signal, a large delay error will be generated, so that it is necessary to perform the delay compensation accurately, and in order to implement the delay compensation of the integral multiple of the clock, a fractional delay filter is needed. The fractional delay filter can be realized by the windowing method, and the structure of the realization is simpler, but the windowing method is not suitable for being applied to actual work because the structure cannot be flexibly adjusted according to the actual delay amount, namely, the filter needs to be redesigned when the delay amount is changed. The sub-filter coefficient of the Farrow structure fractional delay filter is irrelevant to the delay amount, so that the delay amount can be flexibly adjusted, and the Farrow structure fractional delay filter is widely applied, but the Farrow structure fractional delay filter needs more hardware resources. The coefficients of the sub-filters of the hyperbolic fractional delay filter are also irrelevant to the delay amount, and the hyperbolic fractional delay filter only comprises two sub-filters, so that the coefficients of the two filters only need to be stored in a memory, and the hardware resource consumption is greatly saved.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problems, the invention provides a transmitted digital beam forming method based on a hyperbolic structure fractional delay filter, which utilizes a hyperbolic function Taylor expansion to approach a system function of an ideal fractional delay filter to realize delay compensation of clock fractional times, and utilizes the designed hyperbolic structure fractional delay filter to realize transmitted digital beam forming.

The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a transmitting digital beam forming method based on a hyperbolic structure fractional delay filter comprises the following specific steps:

designing a hyperbolic structure fractional delay filter, and realizing the formation of a transmitting digital beam by using the designed fractional delay filter;

the specific design method of the hyperbolic power series fractional delay filter is as follows:

(1) expanding the hyperbolic function according to a power series mode, which specifically comprises the following steps:

(1.1) power series expansion of hyperbolic function:

(1.2) adding the power series expansions to obtain:

(2) the method for designing the frequency response of the ideal delay filter by utilizing the hyperbolic power series structure specifically comprises the following steps:

(2.1) letting x ═ -j ω p in step (1.2), the expression is obtained:

in the formula: p is a delay amount; omega is angular frequency;

(2.2) Pre-M according to the expression in step (2.1)₁And (3) solving the frequency response approximate value of the ideal fractional delay filter:

in the formula: m₁Is the truncation order; h₁(omega, p) is the ideal fractional delay filter frequency response H_id(ω, p) approximation; h_id(ω, p) is the frequency response of the ideal fractional delay filter;

(3) setting sub-filter G (e)^jω) And F (e)^jω) And to two sub-filters G (e)^jω) And F (e)^jω) The design is carried out by the following specific method:

(3.1) setting the sub-filters while satisfying the following conditional expressions, obtaining a filter for the sub-filter G (e)^jω) And F (e)^jω) Expression (c):

in the formula: g (e)^jω) Is a sub-filter; f (e)^jω) Is a sub-filter;

wherein the condition is as follows:

(3.2)G(e^jω) With an ideal frequency response of (j ω)²According toFIR filter pair sub-filter G (e)^jω) Design and solve the sonFilter G (e)^jω) The specific method is as follows:

(3.2.1) sub-filter coefficients g (k) satisfy the even symmetry condition, frequency response of g (z):

in the formula: g (k) is a sub-filter G (e)^jω) A coefficient; g is a sub-filter coefficient, g ═ g (0) g (1)₂)]^T；r(ω)＝[1 2cos(ω)...2cos(N₂ω)]^T；N₂Is a sub-filter G (e)^jω) The order of (a);

(3.2.2) minimizing the error function of the designed filter coefficients g using a least squares criterion:

wherein: e.g. of the type₂(g) Is a sub-filter G (e)^jω) An error function of the coefficient g;

(3.2.3) according to the error function e₂(g) Is a squared function of the coefficient G, resulting in a sub-filter G (e)^jω) The optimal solution for the coefficients of (a) is:

g_opt＝U^-1u

in the formula: g_optIs a sub-filter G (e)^jω) The optimal solution of the coefficients of (a);

(3.3)F(e^jω) Has an ideal frequency response of j ω according toOf the FIR filter pair of filters F (e)^jω) Design is carried out and the sub-filter F (e) is solved^jω) The specific method is as follows:

(3.3.1) the filter coefficients f (k) satisfy the odd symmetry condition, and the frequency response of f (z) can be expressed as:

in the formula: f is the sub-filter F (e)^jω) F (1) f (2)₁)]^T；b(ω)＝-2[sin(ω) sin(2ω) ... sin(N₁ω)]^T；

(3.3.2) minimizing the error function of the designed filter coefficients f using a least squares criterion:

wherein: e.g. of the type₁(f) Is a sub-filter F (e)^jω) An error function of the coefficient f;

(3.3.3) according to the error function e₁(f) Is a squared function of the coefficient F, resulting in a sub-filter F (e)^jω) The optimal solution for the coefficients of (a) is:

f_opt＝Q^-1q

in the formula: f. of_optIs a sub-filter F (e)^jω) Is determined by the optimal solution of the coefficients of (a).

(4) And (4) combining the two sub-filters obtained by the solution in the step (3.2) and the step (3.3) with an adder and a multiplier to realize the fractional delay filter.

Has the advantages that: the hyperbolic structure-based fractional delay filter only needs to design a sub-filter, has a reliable design principle and a simple structure, is fixed in structure and is irrelevant to delay, and the delay is only one input quantity of a filter module; in addition, the method consumes less resources than a common Farrow structure filter and has wide application prospect.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a block diagram of the hyperbolic power series delay filter of the present invention;

FIG. 3 is a graph of the amplitude-frequency response of a hyperbolic structure sub-filter of the present invention;

FIG. 4 is a graph of the amplitude-frequency response of the hyperbolic power series structure of the present invention;

FIG. 5 is a time delay test chart of hyperbolic power series structure of the present invention;

figure 6 is a graph of the digital delay versus digital phase shifted beamforming of the present invention.

Detailed Description

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

The technical scheme adopted by the invention is as follows: a transmitting digital beam forming method based on a hyperbolic structure fractional delay filter comprises the following specific steps:

designing a hyperbolic structure fractional delay filter, and realizing the formation of a transmitting digital beam by using the designed fractional delay filter;

the specific design method of the hyperbolic power series fractional delay filter is as follows:

(1) expanding the hyperbolic function according to a power series mode, which specifically comprises the following steps:

(1.1) power series expansion of hyperbolic function:

(1.2) adding the power series expansions to obtain:

(2) the method for designing the frequency response of the ideal delay filter by utilizing the hyperbolic power series structure specifically comprises the following steps:

(2.1) letting x ═ -j ω p in step (1.2), the expression is obtained:

in the formula: p is a delay amount; omega is angular frequency;

(2.2) Pre-M according to the expression in step (2.1)₁And (3) solving the frequency response approximate value of the ideal fractional delay filter:

in the formula: m₁Is the truncation order; h₁(omega, p) is the ideal fractional delay filter frequency response H_id(ω, p) approximation; h_id(ω, p) is the frequency response of the ideal fractional delay filter;

(3) setting sub-filter G (e)^jω) And F (e)^jω) And to two sub-filters G (e)^jω) And F (e)^jω) The design is carried out by the following specific method:

(3.1) setting the sub-filters while satisfying the following conditional expressions, obtaining a filter for the sub-filter G (e)^jω) And F (e)^jω) Expression (c):

in the formula: g (e)^jω) Is a sub-filter; f (e)^jω) Is a sub-filter;

wherein the condition is as follows:

(3.2)G(e^jω) With an ideal frequency response of (j ω)²According toFIR filter pair sub-filter G (e)^jω) Design and solve the sub-filter G (e)^jω) The specific method is as follows:

(3.2.1) filter coefficients g (k) satisfy the even symmetry condition, frequency response of g (z):

in the formula: g (k) is a sub-filter G (e)^jω) A coefficient; g is a sub-filter coefficient, g ═ g (0) g (1)₂)]^T；r(ω)＝[1 2cos(ω)...2cos(N₂ω)]^T；N₂Is a sub-filter G (e)^jω) The order of (a);

(3.2.2) minimizing the error function of the designed filter coefficients g using a least squares criterion:

wherein: e.g. of the type₂(g) Is a sub-filter G (e)^jω) An error function of the coefficient g;

(3.2.3) according to the error function e₂(g) Is the sub-filter G (e)^jω) The square function of the coefficient G, resulting in a sub-filter G (e)^jω) The optimal solution for the coefficients of (a) is:

g_opt＝U^-1u

in the formula: g_optIs a sub-filter G (e)^jω) The optimal solution of the coefficients of (a);

(3.3)F(e^jω) Has an ideal frequency response of j ω according toOf the FIR filter pair of filters F (e)^jω) Design is carried out and the sub-filter F (e) is solved^jω) The specific method is as follows:

(3.3.1) the filter coefficients f (k) satisfy the odd symmetry condition, and the frequency response of f (z) can be expressed as:

in the formula: f is the sub-filter F (e)^jω) F (1) f (2)₁)]^T；b(ω)＝-2[sin(ω) sin(2ω) ... sin(N₁ω)]^T；

(3.3.2) minimizing the error function of the designed filter coefficients f using a least squares criterion:

wherein:

(3.3.3) according to the error function e₁(f) Is a squared function of the coefficient F, resulting in a sub-filter F (e)^jω) The optimal solution for the coefficients of (a) is:

f_opt＝Q^-1q

in the formula: f. of_optIs a sub-filter F (e)^jω) The optimal solution of the coefficients of (a);

(4) and (4) combining the two sub-filters obtained by the solution in the step (3.2) and the step (3.3) with an adder and a multiplier to realize the fractional delay filter.

The effect of the method for forming the transmitted digital beam based on the hyperbolic fractional delay filter of the invention is further explained below;

1. the experimental conditions are as follows:

the invention uses bandwidth B asLFM (linear frequency modulation) with the pulse width T of 200us at 32MHz is used as an input signal, and the sampling rate is divided into the sampling rate f used by a reference signal_sLow sampling rate f for 2GHz and artificial signals_s1200MHz, 0.3f is selected as the delay amount_s1。

2. And (3) simulation results:

simulation 1: designing an all-pass filter to set the frequency range of the filter to 0,0.9 pi]Two sub-filters F (e)^jω) And G (e)^jω) Are respectively N₁＝40、N₂20; referring to fig. 3, the condition is satisfied by the amplitude-frequency response of the sub-filter.

Simulation 2: according to the coefficient of the sub-filter and the sub-filter group M of the hyperbolic power series structure₁Let the delay amount be-0.5, -0.4,. times.0.5, set to 4; referring to fig. 4, the amplitude-frequency response of the fractional delay filter is obtained, the amplitude-frequency response of the hyperbolic power series fractional delay filter corresponding to the delay amount is observed, and the passband range reaches the designed [0,0.9 pi ]]And the ripple is stable.

Simulation 3: LFM with bandwidth B of 32MHz and pulse width T of 200us is used as an input signal, and the sampling rate is divided into the sampling rate f adopted by a reference signal_sLow sampling rate f for 2GHz and artificial signals_s1200MHz, 0.3f is selected as the delay amount_s1Carrying out simulation; referring to fig. 5, it is observed that the signal data points passing through the hyperbolic power series fractional delay filter can fall on the "delayed reference signal" line through mathematical computation, that is, the hyperbolic power series fractional delay filter can accurately delay the signal.

And (4) simulation: setting signal parameters as follows: sampling rate f_s200MHz, 16 mus pulse width T bandwidth B80 MHz, radio frequency f_RF1 GHz; the array element parameters are set as follows: the number M of array elements is 128, the distance between the array elements is half wavelength corresponding to the center frequency, and the target beam direction theta_B15 °; referring to fig. 6, the design of the hyperbolic power series structure-based digital delay module meets the design requirements of beam forming.