Broadband digital beam forming method based on Farrow filter

Abstract

The invention discloses a broadband digital beam forming method based on a Farrow filter, and the method comprises the following steps: carrying out the DDC down-conversion and phase shift processing of a signal after the analog-to-digital conversion of a broadband signal is completed through an ADC; calculating the delay inequality of each array element signal relative to a reference array element, and decomposing the delay inequality into an integer sampling period and a fractional delay component; a fourth-order Lagrange type Farrow filter oriented to FPGA / DSP optimization is adopted to carry out fractional time delay compensation, and coefficients of the Farrow filter are dynamically adjusted through a polynomial expansion formula; and finally, performing complex weighted synthesis on each channel filtering signal to generate a directional wave beam. According to the method, high-precision fractional delay adjustment is achieved, the Farrow filter is adopted, the tedious process of recalculating coefficients can be omitted, only the P value is changed, and high-precision beam direction control can be achieved under the condition of low calculation amount.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to a broadband digital beamforming method based on a Farrow filter. Background Art

[0002] Digital array radar, by using digital beamforming technology, realizes the full-digital control of transmitting and receiving beams, and has advantages such as fast beam pointing, multi-target detection, and adaptive anti-interference. Its practical functions far exceed those of traditional radars. And its core digital beamforming technology is one of the important technologies in the fields of modern radar, wireless communication, and acoustic imaging. Compared with traditional analog beamforming, digital beamforming performs weighting and synthesis on received signals through digital signal processing technology to achieve flexible control and adaptive adjustment of signals in different directions, thereby improving the resolution, signal-to-noise ratio, and interference suppression ability of the system.

[0003] Digital beamforming can be divided into narrowband beamforming and broadband beamforming according to the ratio of the bandwidth to the center frequency. However, in order to obtain higher resolution, recognition, and anti-interference capabilities, arrays often need to process broadband signals with a relatively large bandwidth. There are usually two methods for broadband digital beamforming in the time domain and the frequency domain: In the time-domain method, the signals received by each array element channel are compensated for the time delay relative to the reference point through filters, and then the outputs of the filters are summed to obtain the time series of the broadband beam; in the frequency-domain method, the received signals are first subjected to discrete Fourier transform to obtain the narrowband signals corresponding to each frequency, then the narrowband beamforming algorithm is used for beamforming at this frequency point, and finally broadband synthesis is performed.

[0004] The real-time processing of broadband signals requires a relatively high computational complexity, and it is difficult for traditional FIR or IIR filters to efficiently achieve accurate interpolation of variable sampling rates. Using a high-order FIR filter for beam correction requires a large number of multiplication and accumulation operations, resulting in a relatively high occupation of FPGA or DSP resources.

[0005] Therefore, it is necessary to develop a broadband digital beamforming method based on a Farrow filter to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to propose a broadband digital beamforming method based on a Farrow filter for the problems existing in the above broadband digital beamforming method, to achieve high-precision time delay adjustment with a relatively low computational amount, and to improve the accuracy of beam pointing and the computational efficiency of the system.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A broadband digital beamforming method based on a Farrow filter, comprising the following steps:

[0009] Step 1: Convert the analog signal received by the antenna into a digital signal through an ADC chip ;

[0010] Step 2: In the phase shifter module, perform down-conversion processing to convert the signal from radio frequency to zero intermediate frequency through down-conversion;

[0011] Step 3: Calculate the difference between the time taken for the signal to reach each array element and the time taken for the reference array element according to the broadband array signal processing model, and then calculate the delay values of the integer multiple sampling period and the fractional multiple sampling period based on the difference value;

[0012] Step 4: Design the Farrow filter coefficients using an adaptive algorithm based on the required delay accuracy and the signal bandwidth size;

[0013] Step 5: In the time delay module, input the phase-shifted digital signal into the Farrow filter for filtering, which is used for fractional time delay compensation in broadband beamforming;

[0014] Step 6: In the summation module, synthesize the signals of each array element after filtering to achieve broadband beamforming.

[0015] Technical advantages of the present invention:

[0016] 1. High-precision fractional time delay adjustment: By using a Farrow filter, the cumbersome process of recalculating coefficients can be avoided, and only the P value needs to be changed. Moreover, high-precision beam direction control can be achieved with a relatively low computational load.

[0017] 2. Low computational complexity, suitable for FPGA / DSP implementation: Compared with traditional high-order FIR filters, this method can reduce the multiplication and accumulation operation amount and improve the computational efficiency.

[0018] 3. Applicable to broadband signal processing: Overcome the limitations of traditional narrowband beamforming and improve the beam pointing accuracy.

[0019] 4. Adaptive beam correction: Can dynamically adjust the beam direction in a complex channel environment and improve the robustness of the system. Description of the Drawings

[0020] The present invention will be described by way of examples with reference to the accompanying drawings, where:

[0021] Figure 1 is the flow chart of the present invention;

[0022] Figure 2 is the schematic diagram of a 4-element array in the embodiment of the present invention;

[0023] Figure 3 It is the farrow delay effect diagram in the embodiment of the present invention;

[0024] Figure 4 It is the broadband beam pattern of the farrow filter method in the embodiment of the present invention;

[0025] Figure 5 It is the signal comparison diagram after the delay compensation of the broadband digital beamforming FPGA in the embodiment of the present invention. Detailed implementation manners

[0026] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0027] As Figure 1 , 2 shown, a broadband digital beamforming method based on a farrow filter includes the following steps:

[0028] Step 1: Convert the analog signal received by the antenna into a digital signal through an ADC chip ;

[0029] Step 1.1: Define the broadband signal , frequency , and define the signal incident direction;

[0030] Step 1.2: Taking the first element of Figure 2 as a reference, the signals of the remaining elements are expressed by the formula ;

[0031] Step 1.3: Calculate the time difference between the signal arriving at the th element and the first element, which are respectively , where t n is the time difference between the nth element and the reference element, n is the nth element, d is the element spacing, c is the speed of light, is the sine value of the target direction;

[0032] Step 1.4: Calculate the signal of the th element in the FPGA as .

[0033] Step 2: In the phase shift module, perform DDC (down-conversion) processing to convert the signal from radio frequency to zero intermediate frequency through down-conversion, reduce the data volume, improve the sampling efficiency, and eliminate part of the interference;

[0034] Step 2.1: The signal carrier frequency is , and after down-conversion, is obtained;

[0035] Step 2.2: Perform phase shift processing in the FPGA, that is, multiply the above signal by a phase compensation factor .

[0036] As Figure 3 , 4 shown, the farrow filter coefficient calculation and filter performance simulation include the following steps:

[0037] Step 3: Calculate the difference between the time taken for the signal to reach each array element and the time taken for the reference array element according to the model of wideband array signal processing, and then calculate the delay values of the integer multiple sampling period and the fractional multiple sampling period based on the difference;

[0038] Step 3.1: Determine the sampling rate according to the radar system parameters , and obtain the sampling time ;

[0039] Step 3.2: Calculate the time difference between the signal reaching the th array element and the first array element, and obtain the time delay of the filter, , , where is the result of rounding to the nearest integer, representing the integer multiple of the time delay relative to the sampling time, represents the fractional multiple and .

[0040] Step 4: In the time delay module, design the farrow filter coefficients using an appropriate adaptive algorithm based on the required delay accuracy and the signal bandwidth size;

[0041] Step 4.1: is the sampling period corresponding to the sampling frequency , and the sampled pulse data string is , where m is the number of sampling points, obtained from the sampling theorem ;

[0042] Step 4.2: The continuous signal can be reconstructed from the ideal band-limited interpolation formula D / C as follows:

[0043]

[0044] where is the sampling angular frequency, m is the number of sampling points, T is the sampling period, and this reconstruction function is a sinc-form reconstruction;

[0045] Step 4.3: After the fractional multiple sampling period time delay processing, we get:

[0046]

[0047] where p is the calculated fractional part of the time delay;

[0048] Step 4.4: Finally, through sampling processing, we obtain:

[0049]

[0050] where n is the multiple by which the reconstructed signal needs to be multiplied;

[0051] Step 4.5: Because , the above equation can be simplified to:

[0052]

[0053] where * represents the convolution symbol;

[0054] Step 4.6: That is, the unit impulse response of the ideal fractional delay digital filter is:

[0055] ;

[0056] Step 4.7: The calculated ideal frequency response is:

[0057]

[0058] is the normalized angular frequency;

[0059] Step 4.8: Conduct pre-simulation of the processing effect of the Farrow filter, and take the lowest order that can achieve the ideal processing effect as the 4th order;

[0060] Step 4.9: Select Lagrange as the design method for the filter coefficients to approximate the ideal filter response;

[0061] Step 4.10: Calculate the Farrow filter coefficients. First, the basic form of the FIR filter coefficients calculated by the maximum flatness criterion approximation method is: , where is the time delay, is the order;

[0062] The frequency response of the Lagrange-type fractional delay filter is ;

[0063] Step 4.12: The Farrow filter coefficients can be derived from the FIR filter coefficients:

[0064] ;

[0065] where is the polynomial order;

[0066] Step 4.13: Substitute and calculate to obtain the frequency response of the Farrow filter:

[0067] .

[0068] As Figure 5 shown, the effect diagram of implementing the Farrow filter in the FPGA and completing broadband digital beamforming includes the following steps:

[0069] Step 5: Input the phase-shifted digital signal into the Farrow filter for filtering, which is used for fractional delay compensation in broadband beamforming;

[0070] Step 5.1: Perform integer multiple delay through the "beating" operation in the FPGA;

[0071] Step 5.2: Implement the four groups of FIR filters that make up the Farrow filter in the form of IP cores;

[0072] Step 5.3: Filter the delay by multiplying step by step and then adding.

[0073] Step 6: In the summing module, synthesize the signals of each array element after filtering processing to achieve broadband beamforming.

[0074] Step 6.1: Add the calculated real part and imaginary part respectively, and finally synthesize the broadband beam.

[0075] The present invention innovatively combines the Farrow filter structure with broadband beamforming, reducing the multiplication and accumulation operation amount by more than 60% compared with the traditional FIR filter, achieving a directional error of 0.01° under the time delay accuracy of 0.1 times the sampling period, and supporting the processing of instantaneous bandwidth above 500 MHz. Adaptive delay compensation is realized through configurable polynomial coefficients, greatly improving the anti-interference ability and moving target resolution of the digital array radar, and is especially suitable for complex electromagnetic environments with multipath effects and rapid interference changes.

[0076] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A broadband digital beamforming method based on Farrow filter, comprising the following steps: Step 1: Convert the analog signal received by the antenna into a digital signal through the ADC chip ; Step 2: In the phase shift module, perform down-conversion processing to convert the signal from radio frequency to zero intermediate frequency through down-conversion; Step 3: Calculate the difference between the time taken for the signal to reach each array element and the time taken for the reference array element according to the model of broadband array signal processing, and then calculate the delay values of integer multiple sampling periods and fractional multiple sampling periods based on the difference; Step 4: Design the coefficients of the Farrow filter using an adaptive algorithm based on the required delay accuracy and the size of the signal bandwidth; Step 5: In the time delay module, input the phase-shifted digital signal into the Farrow filter for filtering, which is used for fractional time delay compensation in broadband beamforming; Step 6: In the summation module, synthesize the signals of each array element after filtering to achieve broadband beamforming.

2. The broadband digital beamforming method based on a Farrow filter according to claim 1, characterized in that The specific steps of Step 1 are as follows: Step 1.1: Define the broadband signal , frequency , and define the signal incident direction; Step 1.2: Using the first array element as a reference, the signals of the remaining array elements are expressed by the formula ; Step 1.3: Calculate the time differences between the signal arriving at the th array element and the first array element, which are respectively , where t n is the time difference between the nth array element and the reference array element, n is the nth array element, d is the array element spacing, c is the speed of light, is the sine value of the target direction; Step 1.4: Calculate the signal of the th array element in the FPGA, which is .

3. A broadband digital beamforming method based on a Farrow filter according to claim 2, characterized in that, The specific steps of Step 2 are as follows: Step 2.1: The signal carrier frequency is , and after down-conversion, is obtained; Step 2.2: Perform phase shift processing in the FPGA, that is, multiply the above signal by the phase compensation factor .

4. A broadband digital beamforming method based on a Farrow filter according to claim 3, characterized in that, The specific steps of Step 3 are as follows: Step 3.1: Determine the sampling rate according to the radar system parameters , and obtain the sampling time ; Step 3.2: Calculate the time difference between the signal arriving at the th array element and the first array element, which is , to obtain the time delay of the filter. , where is the result of rounding to the nearest integer, representing the integer multiple of the time delay relative to the sampling time, and represents the fractional multiple and .

5. A broadband digital beamforming method based on a Farrow filter according to claim 4, characterized in that, The specific steps of Step 4 are as follows: Step 4.1: is the sampling frequency The corresponding sampling period, and the sampled pulse data string is , where m is the number of sampling points, obtained from the sampling theorem ; Step 4.2: The continuous signal can be reconstructed from D / C by the ideal band-limited interpolation formula: ， where is the sampling angular frequency, m is the number of sampling points, T is the sampling period, and this reconstruction function is a sinc-form reconstruction; Step 4.3: After fractional multiple sampling period time delay processing, we get: ； where p is the calculated fractional part of the time delay; Step 4.4: Finally, after sampling processing, we get: ； where n is the multiple that the reconstructed signal needs to be multiplied by; Step 4.5: Since , the above equation can be simplified to: ； where * represents the convolution symbol; Step 4.6: That is, the unit impulse response of the ideal fractional time delay digital filter is: ； Step 4.7: Calculate the ideal frequency response: ； is the normalized angular frequency; Step 4.8: Conduct pre-simulation on the processing effect of the Farrow filter, and take the lowest order that can achieve the ideal processing effect as the 4th order; Step 4.9: Select Lagrange as the design method for the filter coefficients to approximate the ideal filter response; Step 4.10: Calculate the Farrow filter coefficients. First, the basic form of the FIR filter coefficients calculated by the maximally flat criterion approximation method is: , where is the time delay, is the order; Step 4.11: The frequency response of the Lagrange type fractional delay filter is ; Step 4.12: The coefficients of the Farrow filter can be derived from the coefficients of the FIR filter: ； Among them is the polynomial order; Step 4.13: Substitute and calculate to obtain the frequency response of the Farrow filter: 。 6. A broadband digital beamforming method based on a Farrow filter according to claim 5, characterized in that, The specific steps of Step 5 are as follows: Step 5.1: Perform integer multiple time delay through "beating" operation in the FPGA; Step 5.2: Each of the four groups of FIR filters that make up the Farrow filter is implemented in the form of an IP core; Step 5.3: The time delay is filtered by the method of successive multiplication and addition.

7. A broadband digital beamforming method based on a Farrow filter according to claim 6, characterized in that The specific steps of Step 6 are as follows: Step 6.1: Add the calculated real part and imaginary part respectively, and finally synthesize the broadband beam.

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