CN110927680A - Broadband receiving digital beam forming method based on digital deskew and frequency domain equalization - Google Patents

Broadband receiving digital beam forming method based on digital deskew and frequency domain equalization Download PDF

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CN110927680A
CN110927680A CN201911179026.6A CN201911179026A CN110927680A CN 110927680 A CN110927680 A CN 110927680A CN 201911179026 A CN201911179026 A CN 201911179026A CN 110927680 A CN110927680 A CN 110927680A
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deskew
phase
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CN110927680B (en
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蒋德富
钱荣
韩艳
蒋康辉
王松
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Hohai University HHU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/32—Shaping echo pulse signals; Deriving non-pulse signals from echo pulse signals
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a broadband receiving digital beam forming method based on digital deskew and frequency domain equalization, which is limited by FPGA clock frequency, carries out data rate conversion on a broadband intermediate frequency signal which is sampled and then sent into an FPGA, and divides the signal into multiphase representation; calculating the delay requirement of the corresponding array element according to the requirement of forming the pointing direction of the receiving wave beam, and dividing the delay into integer delay and fractional delay according to the sampling frequency of the signal; after integer time delay, the sampling signal adopts an orthogonal processing method based on multiphase interpolation filtering to realize the conversion from the intermediate frequency signal to the baseband signal; designing an equalization filter to realize the joint correction of transmitting and receiving channels, and solving a filter coefficient by adopting a frequency domain equalization method based on inverse Fourier transform; the orthogonal transformation outputs a fraction delay deskew local oscillator phase generated by an equalization filter and a plurality of accumulators, digital deskew processing and fraction delay compensation of echo signals after equalization processing are achieved by a CORDIC algorithm, and low side lobe and difference beams are formed by the CORDIC output through Taylor weighting and Bayliss weighting.

Description

Broadband receiving digital beam forming method based on digital deskew and frequency domain equalization
Technical Field
The invention relates to a broadband receiving digital beam forming method based on digital deskew and frequency domain equalization, and belongs to the technical field of array signal processing.
Background
The existing digital array radar adopting the broadband LFM signal generally adopts a receiving end analog deskewing processing method. The method is simple and efficient, and well solves the problem of receiving and processing the broadband LFM signal. On one hand, the method has the advantages that the receiving end carries out deskew receiving on the echo signals, so that the bandwidth of the received signals and the sampling rate of a system can be effectively reduced, and the acquisition difficulty and the data processing amount of echo data are reduced; on the other hand, because the deskew output is a single-frequency signal with the frequency being in direct proportion to the echo delay, the pulse compression of the signal can be realized only by one-time FFT, and compared with the traditional frequency domain matched filtering method which needs two-time FFT operation, the method greatly reduces the operation amount and the output delay.
However, the digital array radar adopting the analog deskew method has the disadvantages of complex system, high cost, high hardware overhead, and easy introduction of nonlinear errors, which results in difficult correction. In addition, the analog deskewing method is only applicable to LFM signals, which limits the use of other broadband signals, reduces the flexibility of the digital array radar system, and is not beneficial to the expansion or reconstruction of the digital array radar system. With the continuous development of digital integrated circuit technology and digital signal processing technology, digital deskewing methods are gaining more and more attention. Compared with an analog deskew method, the digital deskew method can realize deskew receiving of signals in a digital domain, not only saves complex analog equipment, reduces system complexity and cost, but also can avoid the problems of frequency modulation nonlinearity and amplitude phase inconsistency and the like of analog deskew local oscillators, improves the flexibility of a radar system, and is favorable for extension or reconstruction of the radar system.
Unlike transmit digital beamforming, which uses uniform weighting to obtain maximum transmit gain, receive digital beamforming typically uses Taylor weighting and Bayliss weighting to form low side lobes and difference beams, and for the side lobes of the sum and difference beams are both reference sum beam peaks, the low side lobes of the receive beams place higher requirements on the consistency between the receive channels. In addition, the mismatch in the receiving channel also affects the pulse compression performance of the received signal in the beam direction, so that the mismatch of the transmitting and receiving channels needs to be jointly corrected.
Disclosure of Invention
The invention provides a broadband receiving digital beam forming method based on digital deskew and frequency domain equalization, which has the core technology that the conversion from an intermediate frequency signal to a baseband complex signal is realized by adopting digital orthogonal transformation based on multiphase interpolation filtering; channel mismatch correction is realized by adopting a frequency domain equalization algorithm; and (3) utilizing an accumulator to generate fractional delay deskew local oscillator phases, and combining a CORDIC algorithm to realize digital deskew and fractional delay compensation.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a broadband receiving digital beam forming method based on digital deskew and frequency domain equalization, which comprises the following steps:
step 1, multi-phase representation and integer time delay of a sampled echo signal are realized, and the method specifically comprises the following steps:
(1a) according to the band-pass sampling theorem, the bandwidth of an echo signal is B, the carrier frequency of an intermediate frequency is 3B, and the sampling frequency of the echo signal is 4B; the sampled echo signals are expressed in four phases, and the data rate of each phase is B;
(1b) determining the delay amount of each receiving unit relative to a reference unit according to the geometric structure of the antenna array, and decomposing the delay amount into an integer delay amount and a fractional delay amount according to the sampling frequency of the echo signal, specifically:
integral delay component T of the l receiving unit relative to the reference unitlAnd fractional delay component FlExpressed as:
Figure BDA0002290766230000021
Tl＝floor(τl/Ts)
Figure BDA0002290766230000022
where L is 0,1, …, L-1, L is the number of receiving units, τlFor the delay requirement of the ith receiving unit, thetatFor transmitting the beam direction, fcFor the radio frequency carrier frequency, Ts＝1/fsFor the sampling interval of the echo signal, floor (-) is rounded down;
(1c) carrying out data rearrangement and integer time delay processing on the sampled echo signals: the original q-th phase change of the sampled echo signal is the mod (q + T) th phase change after data rearrangement processinglAnd 4) after phase separation, performing integral time delay of
Figure BDA0002290766230000023
Obtaining a digital delay signal by integer delay processing, wherein q is 0,1, …,3, mod (·) is a remainder function;
step 2, orthogonal transformation and equalization processing of integer time delay signals, and the specific steps are as follows:
(2a) realizing orthogonal processing of integer delay signals by adopting a digital orthogonal transformation method based on multi-phase interpolation filtering;
(2b) equalizing the output of the step (2a) by adopting a frequency domain equalization filter;
step 3, digital deskew and sum-difference beam forming based on CORDIC algorithm, which comprises the following specific steps:
(3a) according to the fractional delay requirement, generating a fractional delay deskew local oscillator phase;
(3b) based on the output of the frequency domain equalization filter and the fractional delay deskew local oscillator phase generated in the step (3a), digital deskew processing and fractional delay compensation of the echo signal after equalization processing are realized by adopting a CORDIC algorithm;
(3c) and (4) forming low side lobe and difference beams by output of the step (3b) through Taylor weighting and Bayliss weighting.
As a further optimization scheme of the present invention, the digital orthogonal transformation based on the polyphase interpolation filtering in step (2a) specifically includes:
Figure BDA0002290766230000024
wherein h (4r + q ') is the coefficient of the q' th phase interpolation filter, xin(4p+q-4r-q ') is the q' th phase interpolation filter input, yout(4p + q) is the q-th phase output of the polyphase interpolation filter, q is 0,1,2,3, NhIs the number of filter coefficients.
As a further optimization scheme of the present invention, the design of the frequency domain equalization filter in step (2b) specifically includes:
setting the measurement frequency point of the channel frequency response as
Figure BDA0002290766230000031
x＝0,1,…,2K′-1，2K′Frequency response H of frequency domain equalization filter after equivalent interpolation for measuring number of frequency pointsR,l(Ix + i) is expressed as:
Figure BDA0002290766230000032
wherein I is 0,1, …, I-1, I is interpolation multiple, S'R,l,x(k) The measured baseband frequency response of the xth single-frequency signal injected for the ith receiving channel, k being 0,1, …,2K-2-1，2KThe number of sampling points of the signal during the frequency response measurement;
assuming that the number of coefficients of the equalization filter is M, the coefficient h of the frequency domain equalization filter of the ith receiving channell(m) is represented by:
Figure BDA0002290766230000033
Figure BDA0002290766230000034
hl(m)＝hR,l(m)
wherein M is 0,1, …, M-1, n is 0,1, …, i.2K′-1，IFFT[·]For inverse Fourier transform, w (n) is a Hamming window weighting function, hR,lAnd (n) is the impulse response of the frequency domain equalization filter.
As a further optimization scheme of the present invention, the generation of the fractional delay deskew local oscillation phase in step (3a) specifically includes:
assuming that the q-th phase output is taken as the orthogonal transformation output, the generation of the fractional delay deskew local oscillation phase is expressed as:
Figure BDA0002290766230000035
Figure BDA0002290766230000036
Figure BDA0002290766230000037
Figure BDA0002290766230000038
wherein q is 0,1,2,3, p is 0,1, …, BTp-1。
As a further optimization scheme of the invention, the polyphase interpolation Filter adopts a half-band Filter, the design of the half-band Filter is realized by a Filter Designer tool in MATLAB software, the sampling frequency is 4B, and the pass band width is
Figure BDA0002290766230000041
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1) the conversion from the intermediate frequency signal to the baseband signal is realized by utilizing an orthogonal transformation processing technology based on multiphase interpolation filtering;
2) the Hamming weighted frequency domain equalization technology is adopted to realize the mismatch correction of the transmitting and receiving channels;
3) the accumulator is used for generating fractional delay deskew local oscillator phases, digital deskew processing and fractional delay compensation are achieved by combining a CORDIC algorithm, and direct generation of digital deskew local oscillators and use of multipliers are avoided.
Drawings
FIG. 1 is a multiphase implementation of the integer delay of the present invention.
Fig. 2 is a diagram of the principle of the quadrature transform based on polyphase filtering according to the present invention.
Fig. 3 is a channel characteristic measurement scheme of the present invention.
Fig. 4 is a block diagram of a hardware implementation of the equalization filter of the present invention.
Fig. 5 is a block diagram of a digital deskew and sum difference beamforming hardware implementation of the present invention.
Fig. 6 shows the frequency response of the polyphase filter designed by the present invention for different quantization bit widths, where (a) is the amplitude response and (b) is the phase response.
FIG. 7 is the amplitude response of the output of the orthogonal transform of the present invention and the Hamming weighted pulse compression output, where (a) is the amplitude response and (b) is the pulse compression output (Hamming window weighted).
Fig. 8 is a graph showing the probability of the rms error of amplitude and phase measured by the measurement method of the present invention, wherein (a) is the probability of the rms error of amplitude and (b) is the probability of the rms error of phase.
Fig. 9 is a sum and difference beam pattern of the digital deskew output of the present invention, where (a) is the receive sum beam and (b) is the receive difference beam.
Fig. 10 shows the sum and difference beam patterns before and after filtering by the equalizer filter according to the present invention, wherein (a) is the sum beam and (b) is the difference beam.
FIG. 11 is a diagram of the filter front sum and difference beams PSL, difference beam null depth and angle measurement RMS error probability curves of the equalizer filter designed in accordance with the present invention, where (a) is the sum beam PSL probability curve, (b) is the difference beam PSL probability curve, (c) is the difference beam null depth probability curve, and (d) is the angle measurement RMS error probability curve.
Fig. 12 shows the sum and difference beam PSL, difference beam null depth and angle measurement root mean square error probability curves after filtering by the equalizer filter according to the present invention, where (a) is the sum beam PSL probability curve, (b) is the difference beam PSL probability curve, (c) is the difference beam null depth probability curve, and (d) is the angle measurement root mean square error probability curve.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the invention provides a broadband receiving digital beam forming method based on digital deskew and frequency domain equalization, which comprises the following concrete implementation steps:
step 1, multi-phase representation and integer time delay of a sampling signal are realized, and the method specifically comprises the following steps:
(1a) according to the band-pass sampling theorem, the signal bandwidth is B, the intermediate frequency carrier frequency is 3B, the sampling frequency of the echo signal is 4B, the sampling frequency is limited by the clock frequency of the FPGA, the sampling data is sent to the FPGA to be represented by four phases, and the data rate of each phase is B;
(1b) the delay amount of each receiving unit relative to the reference unit is determined according to the geometry of the antenna array and is decomposed into an integer delay amount and a fractional delay amount according to the sampling frequency of the signal.
Assuming that the number of receiving units is L, the integer delay and the fractional delay of the ith receiving unit can be expressed as:
Figure BDA0002290766230000051
Tl＝floor(τl/Ts)
Figure BDA0002290766230000052
wherein L is 0,1, …, L-1, taulFor the delay requirement of the ith receiving unit, thetatFor transmitting the beam direction, fcFor the radio frequency carrier frequency, Ts＝1/fsFor signal sampling intervals, TlIs an integer time delay component, FlFor fractional delay components, floor (-) is rounded down;
(1c) data rearrangement and integer time delay processing are carried out on the four-phase data, and the original q-th-phase data of the sampling signal is changed into the mod (q + T) after rearrangement processingl4) phase data with an integer delay of
Figure BDA0002290766230000053
Where q ═ 0,1, …,3, mod (·) is a remainder function, and integer delay is implemented by registers, with specific implementation referring to fig. 1.
Step 2, orthogonal transformation and equalization processing of integer time delay signals, and the specific steps are as follows:
(2a) the digital orthogonal transformation method based on the multiphase interpolation filtering is adopted to realize the orthogonal processing of the integer time delay signal, and as the bandwidth of the integer time delay signal is B, the requirement can be met by only taking one phase of four-phase complex data, so that the hardware multiplier resource can be saved, and the specific implementation is shown in FIG. 2;
assume that the ADC input analog intermediate frequency signal is:
Figure BDA0002290766230000061
where a (t) is the envelope of the signal,
Figure BDA0002290766230000062
is a phase modulation of the signal, fIFIs the signal intermediate frequency carrier frequency.
Get
Figure BDA0002290766230000063
For the above-mentioned letterThe number is sampled, the sequence of sampled digital signals can be represented as:
Figure BDA0002290766230000064
in the formula (I), the compound is shown in the specification,
Figure BDA0002290766230000065
is the in-phase component of the signal,
Figure BDA0002290766230000066
for the quadrature component of the signal, s (k) is expressed in four phases, which can be further abbreviated as:
s(4p+0)＝sI(4p+0)
s(4p+1)＝(-1)x+1sQ(4p+1)
s(4p+2)＝-sI(4p+2)
s(4p+3)＝(-1)xsQ(4p+3)
it should be noted that the sampling frequency of each phase signal is only the original sampling frequency
Figure BDA0002290766230000067
Looking at the above equation, it can be seen that the if signal can be represented by the baseband signal without distortion, and the sign of the quadrature component is related to the value of x, which is generally equal to 1. However, the in-phase component and the quadrature component are different by half a sampling point in time, and delay compensation is required in the time domain, and the delay compensation can be realized by a branch filter of a multi-phase interpolation filter with an interpolation factor of 4.
The input signal of the polyphase interpolation filter with an interpolation factor of 4 is assumed to be xin(4p + q), then the filter output yout(4p + q) can be expressed as:
Figure BDA0002290766230000068
wherein h (4r + q ') is the coefficient of the q' th phase interpolation filter, xin(4p + q-4r-q ') is the q' th phase interpolation filter inputIn, yout(4p + q) is the q-th phase output of the polyphase interpolation filter, q is 0,1,2,3, NhIs the number of filter coefficients. The polyphase interpolation Filter adopts a half-band Filter, the Filter design is realized by a Filter Designer tool in MATLAB software, the sampling frequency is 4B, and the pass band width
Figure BDA0002290766230000069
(2b) Performing equalization processing on the output in the step (2a) by adopting a frequency domain equalization filter to realize joint correction of mismatch of transmitting and receiving channels;
the conventional channel characteristics are generally measured by injecting an LFM signal, but this method requires a high signal-to-noise ratio of the input signal. Considering that the amplitude and phase distortion varies slowly with frequency within the operating bandwidth, it is considered here to improve the measurement accuracy by measuring the amplitude and phase errors of a plurality of single-frequency signals of different frequencies, and then to fit the frequency response of the actual channel by means of equivalent interpolation.
Designing the measurement scheme of the channel frequency response as shown in fig. 3, assuming that the number of the measurement frequency points is 2K′Setting the measurement frequency points as follows:
Figure BDA0002290766230000071
wherein x is 0,1, …,2K′-1。
Will have a frequency fxThe single-frequency signal is sent to the transmitting channels, and the synthesized coupling output signals of the L transmitting channels can be expressed as:
Figure BDA0002290766230000072
in the formula, AT(fx) And thetaT(fx) Are respectively synthesized for L transmitting channels at frequency point fxAmplitude response and phase response.
sT(t) after passing through the power divider, the signals are coupled into all the receiving channels, and then the output signal of the ith receiving channel can be expressed as:
Figure BDA0002290766230000073
wherein n is 0,1, …,2K-1，2KFor the number of valid points of the sampled data, AR,l(f) And thetaR,l(f) At frequency f for the l-th receiving channel respectivelyxThe amplitude and phase response of (a) and (b),
Figure BDA0002290766230000074
output signal s of the l-th receiving channelR,l,x(n) the 0 th phase output after the orthogonal transform process can be expressed as:
Figure BDA0002290766230000075
wherein k is 0,1, …,2K-2-1。
To s'R,l,x(k) By taking the fourier transform, the equivalent interpolated equalizer filter frequency response can be expressed as:
Figure BDA0002290766230000076
wherein I is 0,1, …, I-1, I is interpolation multiple, S'R,l,x(k) The baseband frequency response of the x-th single-frequency signal injected for the l-th receiving channel, k being 0,1, …,2K-2-1。
Assuming that the number of coefficients of the equalization filter is M, the coefficient h of the frequency domain equalization filter of the ith receiving channell(m) is represented by:
Figure BDA0002290766230000081
Figure BDA0002290766230000082
hl(m)＝hR,l(m)
wherein M is 0,1, …, M-1, n is 0,1, …, i.2K′-1，IFFT[·]For inverse Fourier transform, w (n) is a Hamming window weighting function, hR,lAnd (n) is the impulse response of the frequency domain equalization filter, and the implementation of the equalization filter specifically refers to fig. 4.
Step 3, digital deskew and sum-difference beam forming based on CORDIC algorithm, specifically implementing the specific steps with reference to fig. 5:
(3a) and according to the fractional delay requirement, generating fractional delay deskew local oscillator phases through a plurality of accumulators.
In view of the fact that the receiving process of each array element is the same, the received echo signal process of the ith array element is taken as an example here. Consider ideal reception, assume θtIf there is a stationary target with a distance R in the direction (element 0 is the reference), the ideal echo signal received by the ith element can be expressed as:
Figure BDA0002290766230000083
in the formula, ARIn order to be the scattering coefficient of the target,
Figure BDA0002290766230000084
C＝3×108m/s，fcfor the radio frequency carrier frequency, TpIs the signal pulse width.
Considering the ideal receiving channel characteristic, the channel gain is 1, and the broadband intermediate frequency signal after mixing, filtering and amplifying can be expressed as:
Figure BDA0002290766230000085
at a sampling frequency fs4B to s _ rIF,l(t) sampling,. tau.lTime delay divided into integers
Figure BDA0002290766230000091
And fractional delay
Figure BDA0002290766230000092
Then sampleThe latter signal can be expressed as:
Figure BDA0002290766230000093
for s _ rIF,l(k) Carry out TlAn integer delay, where the delay output can be expressed as:
Figure BDA0002290766230000094
to s _ r'IF,l(k) Performing the ideal orthogonal transform processing, the output baseband signal can be expressed as:
Figure BDA0002290766230000095
in the formula (I), the compound is shown in the specification,
Figure BDA0002290766230000096
assuming that the q-th phase output is taken as the orthogonal transformation output, the fractional delay deskewing local oscillation phase required to be generated can be expressed as:
Figure BDA0002290766230000097
wherein q is 0,1,2,3, p is 0,1, …, BTp-1. As can be seen from the above equation, the phase (4 a)lThe +8qb +16b) p generation can be achieved by a single accumulator, phase
Figure BDA0002290766230000101
The generation of (2) may be implemented by 2 accumulators, with specific implementation referring to fig. 5.
(3b) And (4) outputting the equalization filter and the fractional delay deskew local oscillator phase generated in the step (3a), and realizing digital deskew processing and fractional delay compensation of the echo signal by adopting a CORDIC algorithm.
The CORDIC algorithm is an algorithm that can solve operations such as trigonometric functions, exponential functions and the like by simply performing shift addition operation, and can perform operations in three rotational coordinate systems, namely a circular coordinate system, a linear coordinate system and a hyperbolic coordinate system. Under each coordinate system, the CORDIC algorithm has two working modes, namely a rotation mode and a vector mode, and the equation of each iteration of the circular rotation mode CORDIC algorithm is expressed as follows:
x(i′+1)＝x(i′)-di′(2-i′y(i′))
y(i′+1)＝y(i′)+di′(2-i′x(i′))
z(i′+1)＝z(i′)-di′θ(i′)
in the formula, x(i′),y(i′),z(i′)Represents the data before the i' +1 iteration; x is the number of(i′+1),y(i′+1),z(i′+1)Represents the data after the i' +1 iteration; theta(i′)＝arctan(2-i′) Arctan () represents an arctangent function; symbol di′Is a decision operator for determining the direction of rotation, and
Figure BDA0002290766230000102
after X iterations we obtain:
x(M)＝KX(x(0)cos z(0)-y(0)sin z(0))
y(M)＝KX(y(0)cos z(0)+x(0)sin z(0))
in the formula, KXIs the scaling factor of the signal to be transmitted,
Figure BDA0002290766230000103
(3c) and (3b) outputting and forming low side lobe and difference beams through Taylor weighting and Bayliss weighting.
The algorithm and the processing method of the invention have passed verification, and have achieved satisfactory application effect:
1. the experimental conditions are as follows: the signal form is LFM signal, ADC quantization bit width takes 14bits, signal bandwidth B400 MHz, time width Tp20.48us, sampling rate fs1600MHz, radio frequency carrier frequency fc15GHz, intermediate frequency fIF1200 MHz; the channel characteristic measurement is that K is 16, K' is 6, the interpolation multiple I is 128 when the channel characteristic is fitted, and the number of equalizing filter coefficients M is 13. Assume a target direction of 300The number of array elements L is 32.
2. Simulation content:
simulation 1: designing an interpolation filter, wherein the filter adopts a half-band filter and is based on the following parameters: the cut-off frequency of the passband is 200MHz, the sampling frequency is 1600MHz, and the fluctuation of the passband is 0.01 dB; fig. 6 (a) and (b) show the frequency response of the designed filter for different quantization bit widths.
Simulation 2: the quantization bit width of the filter is 16bits, based on the filter designed above, orthogonal transformation is carried out, and with an ideal baseband signal as a reference object, (a) and (b) in fig. 7 show the amplitude response of the output result of the orthogonal transformation and Hamming weighted pulse compression output of the orthogonal transformation output in the patent. In the figure, LPG represents the loss of the signal-to-noise ratio of pulse compression, and PSL represents the peak-to-side lobe ratio of the pulse compression output.
Simulation 3: assuming that the snr of the input signal is 20dB when the channel characteristics are measured, and the conventional measurement method is used as a reference object, (a) and (b) in fig. 8 show the probability curves of the rms error of the amplitude and phase measured by the measurement method proposed in this patent.
Simulation 3: with the ideal reception sum and difference beams as reference objects, the sum and difference beam patterns of the digital deskew output with the reference direction of 300 are given by (a) and (b) in fig. 9, where PSL represents the peak side lobe ratio of the beam patterns.
And (4) simulation: the root mean square error of the amplitude between the receiving channels is 1dB, the root mean square error of the phase is 20 degrees, the fluctuation of the amplitude in the band is 1dB, the fluctuation of the phase in the band is 10 degrees, and the sum and difference beam patterns before and after the equalization are given in (a) and (b) in fig. 10.
And (5) simulation: in order to avoid the contingency, 100 times of simulation statistical analysis is performed, and (a) to (d) in fig. 11 give curves of the sum and difference beams PSL, the difference beam null depth, and the angle-measuring root mean square error probability, and (a) to (d) in fig. 12 give curves of the sum and difference beams PSL, the difference beam null depth, and the angle-measuring root mean square error probability after the equalization.
3. And (3) simulation result analysis:
from (a) and (b) in fig. 7, it can be seen that the orthogonal transform output of the present patent is substantially consistent with the performance of an ideal baseband signal.
From the observations of (a) and (b) in fig. 8, it can be seen that the root mean square error of the amplitude and phase measurements can be significantly reduced compared to the conventional measurement method in the case of low signal-to-noise ratio.
From the observations of (a) and (b) in fig. 9, the PSL of the sum and difference beams is negligible compared to the ideal case, the peak loss of the sum beam is around-0.38 dB, and the null depth of the difference beam is around-56.42 dB, which is substantially consistent with the ideal and difference beam performance.
As can be seen from (a) and (b) in fig. 10, and (a) to (d) in fig. 11, and (a) to (d) in fig. 12, the beam performance is greatly improved after the equalization filter designed by the present patent, which is substantially consistent with the performance of fig. 8, and the loss of the beam performance is negligible.
Simulation results show the effectiveness of the broadband receiving digital beam forming method based on digital deskew and frequency domain equalization.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. The broadband receiving digital beam forming method based on digital deskew and frequency domain equalization is characterized by comprising the following steps of:
step 1, multi-phase representation and integer time delay of a sampled echo signal are realized, and the method specifically comprises the following steps:
(1a) according to the band-pass sampling theorem, the bandwidth of an echo signal is B, the carrier frequency of an intermediate frequency is 3B, and the sampling frequency of the echo signal is 4B; the sampled echo signals are expressed in four phases, and the data rate of each phase is B;
(1b) determining the delay amount of each receiving unit relative to a reference unit according to the geometric structure of the antenna array, and decomposing the delay amount into an integer delay amount and a fractional delay amount according to the sampling frequency of the echo signal, specifically:
integral delay component T of the l receiving unit relative to the reference unitlAnd fractional delay component FlExpressed as:
Figure FDA0002290766220000011
Tl＝floor(τl/Ts)
Figure FDA0002290766220000012
where L is 0,1, …, L-1, L is the number of receiving units, τlFor the delay requirement of the ith receiving unit, thetatFor transmitting the beam direction, fcFor the radio frequency carrier frequency, Ts＝1/fsFor the sampling interval of the echo signal, floor (-) is rounded down;
(1c) carrying out data rearrangement and integer time delay processing on the sampled echo signals: the original q-th phase change of the sampled echo signal is the mod (q + T) th phase change after data rearrangement processinglAnd 4) after phase separation, performing integral time delay of
Figure FDA0002290766220000013
Obtaining a digital delay signal by integer delay processing, wherein q is 0,1, …,3, mod (·) is a remainder function;
step 2, orthogonal transformation and equalization processing of integer time delay signals, and the specific steps are as follows:
(2a) realizing orthogonal processing of integer delay signals by adopting a digital orthogonal transformation method based on multi-phase interpolation filtering;
(2b) equalizing the output of the step (2a) by adopting a frequency domain equalization filter;
step 3, digital deskew and sum-difference beam forming based on CORDIC algorithm, which comprises the following specific steps:
(3a) according to the fractional delay requirement, generating a fractional delay deskew local oscillator phase;
(3b) based on the output of the frequency domain equalization filter and the fractional delay deskew local oscillator phase generated in the step (3a), digital deskew processing and fractional delay compensation of the echo signal after equalization processing are realized by adopting a CORDIC algorithm;
(3c) and (4) forming low side lobe and difference beams by output of the step (3b) through Taylor weighting and Bayliss weighting.
2. The wideband reception digital beamforming method based on digital deskew and frequency domain equalization according to claim 1, wherein the digital orthogonal transformation based on polyphase interpolation filtering in step (2a) is specifically:
Figure FDA0002290766220000021
wherein h (4r + q ') is the coefficient of the q' th phase interpolation filter, xin(4p + q-4r-q ') as the q' th phase interpolation filter input, yout(4p + q) is the q-th phase output of the polyphase interpolation filter, q is 0,1,2,3, NhIs the number of filter coefficients.
3. The wideband receiving digital beamforming method based on digital deskew and frequency domain equalization according to claim 1, wherein the frequency domain equalization filter in step (2b) is specifically designed as follows:
setting the measurement frequency point of the channel frequency response as
Figure FDA0002290766220000022
2K′Frequency response H of frequency domain equalization filter after equivalent interpolation for measuring number of frequency pointsR,l(Ix + i) is expressed as:
Figure FDA0002290766220000023
wherein I is 0,1, …, I-1, I is interpolation multiple, S'R,l,x(k) The measured baseband frequency response of the xth single-frequency signal injected for the ith receiving channel, k being 0,1, …,2K-2-1，2KThe number of sampling points of the signal during the frequency response measurement;
assuming that the number of coefficients of the equalization filter is M, the coefficient h of the frequency domain equalization filter of the ith receiving channell(m) is represented by:
Figure FDA0002290766220000024
Figure FDA0002290766220000025
hl(m)＝hR,l(m)
wherein M is 0,1, …, M-1, n is 0,1, …, i.2K′-1，IFFT[·]For inverse Fourier transform, w (n) is a Hamming window weighting function, hR,lAnd (n) is the impulse response of the frequency domain equalization filter.
4. The method for forming a wideband receiving digital beam based on digital deskew and frequency domain equalization according to claim 1, wherein the generation of the fractional delay deskew local oscillator phase in step (3a) is specifically:
assuming that the q-th phase output is taken as the orthogonal transformation output, the generation of the fractional delay deskew local oscillation phase is expressed as:
Figure FDA0002290766220000031
Figure FDA0002290766220000032
Figure FDA0002290766220000033
Figure FDA0002290766220000034
wherein q is 0,1,2,3, p is 0,1, …, BTp-1。
5. The method of claim 2, wherein the polyphase interpolation Filter is a half-band Filter, and the design is implemented by a Filter Designer tool in MATLAB software, with a sampling frequency of 4B and a pass-band width
Figure FDA0002290766220000035
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