CN109188366B - Broadband emission self-adaptive beam forming method based on subband maximum signal-to-noise ratio criterion - Google Patents

Broadband emission self-adaptive beam forming method based on subband maximum signal-to-noise ratio criterion Download PDF

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CN109188366B
CN109188366B CN201810895372.3A CN201810895372A CN109188366B CN 109188366 B CN109188366 B CN 109188366B CN 201810895372 A CN201810895372 A CN 201810895372A CN 109188366 B CN109188366 B CN 109188366B
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沈明威
王冠
李建峰
张琪
汪晨辉
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Hohai University HHU
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Abstract

The invention discloses a broadband emission self-adaptive beam forming method based on a subband maximum signal-to-noise ratio criterion, which comprises the following steps: designing a broadband transmitting antenna array, and calculating an output signal of the broadband array; step two, designing a sub-band filter bank; thirdly, completing sub-band division of the broadband signal by utilizing an analysis filter bank in a sub-band filter bank; step four, calculating the self-adaptive beam forming weight vector of each sub-band based on the sub-band maximum signal-to-noise ratio criterion; and step five, reconstructing the processed broadband signal by utilizing a comprehensive filter bank in the subband filter bank. The method can form the null with deep depth and direction not changing along with the frequency at the expected position, has small calculated amount and is beneficial to engineering realization.

Description

Broadband emission self-adaptive beam forming method based on subband maximum signal-to-noise ratio criterion
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a broadband emission adaptive beam forming method based on a subband maximum signal-to-noise ratio criterion.
Background
Adaptive arrays deployed in modern radar systems tend to place nulls at the receiving end that attenuate interfering signals, such as hostile interference, unintentional electromagnetic interference or environmental clutter, etc., and the antennas of such schemes typically transmit with uniform amplitude weighting over the aperture to maximize the main beam gain. Such signal processing techniques at the radar receiving end have been increasingly perfected, and it is increasingly difficult to improve the detection performance by optimizing the radar receiving signal processing algorithm, so that more and more recent research institutes have developed techniques for creating nulls at the radar transmitting end, which have the advantage that the antenna can apply significant bidirectional loss to the interference signals. Most transmit nulling algorithms developed to date are suitable for narrowband applications and assume infinite phase and amplitude accuracy.
Typically, the weights applied to each array element are calculated only at the center frequency of the array signal, corresponding to a half-wavelength spacing between array elements. In addition, the phase shifter behind each array element only corrects the center frequency of the signal. Therefore, the actual phase shift of the wideband signal transmitted by each array element will shift with the actual frequency, resulting in the nulls of the transmitted signal being shifted from the pointing direction over the entire signal bandwidth.
In order to solve the above problem, peter g.voras proposes a wideband array Robust Transmission Nulling (RTN) beamforming algorithm, which derives an SINR function with respect to frequency integration in order to maximize a signal-to-noise ratio (SINR) of a transmission signal, and solves the SINR function by a conjugate iterative algorithm, thereby obtaining an optimal tap delay line coefficient. Because the algorithm has some problems in setting the initial value of the conjugate iteration and the iteration step size is complex to calculate, in order to obtain the optimal solution, the conjugate iteration is often required for many times, so that the calculated amount is greatly increased, the load of the system is increased, and the engineering implementation is not facilitated.
Disclosure of Invention
The invention provides a broadband emission self-adaptive beam forming method based on a subband maximum signal-to-noise ratio criterion, wherein the emission beam can form a null with deep depth and direction unchanged along with frequency at an expected position, the calculated amount is small, and the engineering realization is facilitated.
In order to solve the technical problem, the following technical scheme is adopted:
the broadband emission self-adaptive beam forming method based on the subband maximum signal-to-noise ratio criterion comprises the following steps:
designing a broadband transmitting antenna array, and calculating an output signal of the broadband array;
step two, designing a sub-band filter bank;
thirdly, completing sub-band division of the broadband signal by utilizing an analysis filter bank in the sub-band filter bank;
step four, calculating the self-adaptive beam forming weight vector of each sub-band based on the sub-band maximum signal-to-noise ratio criterion;
and step five, reconstructing the processed broadband signal by utilizing a comprehensive filter bank in the subband filter bank.
Furthermore, the broadband transmitting antenna array is a uniform linear array with the number of array elements being M, a Tapped Delay Line (TDL) equivalent to a discrete finite impulse response filter is arranged behind each array element, the TDL coefficient is J, and the lowest frequency of an original output signal x (n) of the broadband array is f L Maximum frequency of f H ，n＝0,±1,±2,…。
The response of the TDL array satisfies the following equation:
Figure BDA0001758002720000021
wherein j is an imaginary unit, θ 0 For the array signal transmission direction, ω is the digital frequency, w m [k]M =0,1, …, M-1, k =0,1, …, J-1,T for the weighting value of the k-th tap of the M-th array element s And phi is the sampling time interval of two adjacent taps, and phi is the phase difference of two adjacent array element transmission signals, and phi satisfies the formula:
Figure BDA0001758002720000022
wherein d is the array element spacing, f is the instantaneous frequency, and c is the speed of light.
To prevent spatial mixing, d = c/(2 f) is set H ) To avoid instantaneous mixing, T is set s ＝1/(2f H )。
The output signal of the m-th array element is:
Figure BDA0001758002720000023
wherein x is m And (n) is an output signal of the m-th array element, and x (n-k) represents that the input discrete signal x (n) is shifted to the left by k units.
Furthermore, the subband Filter Bank is a Discrete Fourier Transform Filter Bank (DFTFB), and the subband Filter Bank usually includes two groups of Filter banks, one of which is an analysis Filter Bank used for decomposing a broadband signal, and each path of subband after decomposition can be independently subjected to required signal processing; and the other group is a comprehensive filter group which is used for reconstructing the broadband signal, and an output signal processed by the system is obtained after reconstruction.
Furthermore, each array element is followed by Q sub-band processing channels, and each sub-band processing channel is provided with an analysis filter and a synthesis filter. The analysis filter in each sub-band channel is composed of a low-pass prototype filter H with length P 0 (z) obtained by translation at a sampling frequency f s Filter H of length P q (z) the wideband signal with bandwidth B may be filtered to a bandwidth f s Sub-band signal of/P, so the length of the filter P = f s /(B/M). The q-th subband analysis filter impulse response satisfies the following equation:
H q (z)＝H 0 (zW q+i ) (4)
H 0 (z)＝1+z -1 +…+z -(P-1) (5)
wherein H q (z) represents the z-transform of the impulse response of the qth channel analysis filter, Q =1 jω ，W＝e -j2π/P And q + i denotes the q-th subband analysis filter relative to the low-pass filter H 0 (z) frequency shift, and i = f L /(B/M)-0.5。
The impulse response of the q-th subband synthesis filter satisfies the following formula:
F q (z)＝W -(q+i) F 0 (zW q+i ) (6)
F 0 (z)＝1+z -1 +…+z -(P-1) (7)
wherein, F q (z) represents the z-transform of the impulse response of the qth channel synthesis filter.
It can be obtained from the above formula that each synthesis filter and the corresponding analysis filter have the same amplitude response, and if the broadband signal is only divided and reconstructed by sub-band without changing the frequency information of the original signal, the output signal obtained by sub-band division and reconstruction satisfies the formula:
y(n)＝Qx(n-Q+1) (8)
where y (n) is the subband divided and reconstructed output signal, and x (n-Q + 1) represents the discrete signal x (n) shifted to the right by Q-1 units.
Further, when the transmission direction of the broadband signal is theta 0 The array steering vector of the signal satisfies the formula:
v(θ 0 ,f)＝[1,exp(j2πfdsinθ 0 /c),…,exp(j2πfd(M-1)sinθ 0 /c)] T (9)
wherein [ ·] T For the transpose operator, v (θ) 0 And f) denotes the emission direction as θ 0 The array of signals of frequency f guides the vector.
After the analysis filter divides the sub-band, the tap sampling frequency of the TDL is reduced to the original 1/Q, and the sub-band TDL delay chain vector meets the formula:
Figure BDA0001758002720000048
the space-time pilot vector related to the signal frequency satisfies the formula:
Figure BDA0001758002720000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001758002720000042
kronecker product, V, representing a vector st (θ 0 And f) denotes the emission direction as θ 0 Space-time pilot vector of frequency f.
Further, if the analysis filter divides the bandwidth of the broadband signal into K frequency points uniformly, there are { f } 1 ,f 2 ,...,f K }∈[f L ,f H ]The signal variance matrix and the interference noise covariance matrix satisfy the following formula:
Figure BDA0001758002720000043
Figure BDA0001758002720000044
wherein [ ·] H For the transposed conjugate operator, R st-q Is the signal variance matrix of the q-th subband signal, N st-q Is the interference noise covariance matrix of the q-th subband signal, K is the total number of frequency points, V st-q (θ 0 ,f l ) Representing a frequency f l Space-time pilot vector of time, H q (f l ) Representing a frequency of f l Frequency response of the q-th subband analysis filter, F q (f l ) Representing a frequency f l The frequency response of the q-th subband synthesis filter, beta being the power of the interference signal, sigma 2 Is the power of the zero-mean additive white noise Gaussian process, I is the identity matrix, θ 0 Is the main lobe direction, theta 1 Is the direction in which the formation of the null is desired, f l ∈{f 1 ,f 2 ,...,f K And l =1,2.
Further, the signal-to-noise ratio SINR of the q sub-band signal q Satisfies the formula:
Figure BDA0001758002720000045
wherein, W q Is NJx 1-dimensional TDL weight vector of the q-th sub-band signal, when SINR q And when the maximum value is reached, obtaining the optimal solution of the weight vector:
Figure BDA0001758002720000046
wherein, W opt-q Is the sub-band optimal TDL weight vector, λ max Is that
Figure BDA0001758002720000047
Maximum eigenvalue, W opt-q Is λ max The corresponding feature vector.
Further, according to the reconstruction of the synthesis filter bank, after the transmission adaptive beam forming, the frequency domain expression of the signal output by the m-th array element is:
Figure BDA0001758002720000051
wherein, Y m (e jω ) Frequency domain, w, representing the signal output by the m-th array element qm [k]A k tap weight, X (e), representing the q subband of the m array element jω ) Representing the frequency domain of the original wideband signal, H q (e jω ) Representing the frequency response of the analysis filter of the q-th sub-band, F q (e jω ) Representing the frequency response of the synthesize filter for the q-th subband.
Further, the antenna directional pattern of the broadband output signal transmitting beam after the reconstruction of the comprehensive filter bank is as follows:
Figure BDA0001758002720000052
wherein P (θ, f) represents a broadband signal transmission beam antenna pattern, v st (theta, f) represents space-time pilot vector when the transmission direction of broadband signal is theta and the frequency is f, H q (f) Representing the frequency response of the q-th subband analysis filter at frequency F, F q (f) Representing the frequency response of the q-th subband synthesis filter at frequency f.
Through the technical means, the following technical effects can be obtained:
the invention discloses a broadband emission self-adaptive beam forming method based on a subband maximum signal-to-noise ratio criterion, which solves the optimal TDL weight vector based on a maximum signal-to-interference-and-noise ratio (MSNR) criterion through a full-bandwidth covariance matrix and an interference noise covariance matrix of a maximum likelihood estimation (MEL) broadband signal, thereby greatly reducing the operation amount of the method and having good performance. Through sub-band division processing, deeper zero notch can be formed in an expected direction, interference suppression effect is stronger, tap sampling frequency of TDL is reduced, and engineering realization is facilitated
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a processing structure of the broadband array TDL of the present invention.
FIG. 3 is a schematic diagram of the subband partition-based array processing structure according to the present invention.
Fig. 4 is a wideband RTN algorithm transmit beam antenna pattern.
Fig. 5 is a subband RTN algorithm wideband transmit beam antenna pattern.
FIG. 6 is a diagram of wideband transmit adaptive beamforming based on the wideband MSNR algorithm for an undivided subband according to the present invention; wherein, (a) is the antenna direction of the transmitting beam of the wideband MSINR algorithm, and (b) is the graph of the null direction of the wideband MSINR algorithm with the change of frequency.
FIG. 7 is a diagram of the present invention for partitioning sub-bands based on the sub-band MSINR algorithm wideband transmit adaptive beamforming; wherein, (a) is the subband MSINR algorithm transmitting beam antenna direction, and (b) is a graph of subband MSINR algorithm null direction versus frequency.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
a method for forming a wideband transmit adaptive beam based on a subband maximum signal-to-interference-and-noise ratio criterion, as shown in fig. 1, mainly includes the following steps:
step one, designing a broadband transmitting antenna array and calculating an output signal of the broadband array. Signal x output by mth array element m (n) satisfies the formula:
Figure BDA0001758002720000061
wherein x (n-k) refers to the output discrete signal x (n) shifted to the left by k units, w m [k]The weighting values for the k tap of the M-th array element are referred to, M =0,1, …, M-1, k =0,1, …, J-1,M is the total number of array elements, and J is the tapped delay line coefficient.
And designing a sub-band filter bank, wherein the sub-band filter bank can be divided into an analysis filter bank and a synthesis filter bank, the analysis filter bank is used for sub-band division of the broadband signal, the synthesis filter bank is used for signal reconstruction, and the discrete Fourier transform filter bank is selected by the sub-band filter bank.
And step three, completing the sub-band division of the broadband signal by utilizing an analysis filter bank in the sub-band filter bank. Assuming that Q sub-band processing channels are arranged behind each array element, the broadband signal bandwidth is uniformly divided into K frequency points by the analysis filter, and the signal variance matrix and the interference noise covariance matrix meet the following formula:
Figure BDA0001758002720000062
Figure BDA0001758002720000063
wherein [ ·] H For the transposed conjugate operator, R st-q Is the signal variance matrix of the q-th subband signal, N st-q Is the interference noise covariance matrix of the q-th subband signal, K is the total number of frequency points, V st-q (θ 0 ,f l ) Representing a frequency f l Space-time pilot vector of time, H q (f l ) Representing a frequency f l Frequency response of the q-th subband analysis filter, F q (f l ) Representing a frequency f l The frequency response of the q-th subband synthesis filter, beta being the power of the interference signal, sigma 2 Is the power of the zero-mean additive white noise Gaussian process, I is the identity matrix, θ 0 Is the main lobe direction, theta 1 Is the direction in which the formation of the null is desired, f l ∈{f 1 ,f 2 ,...,f K And l =1,2.
And step four, calculating the self-adaptive beam forming weight vector of each sub-band based on the sub-band maximum signal-to-noise ratio criterion. Signal to noise ratio SINR of the q-th subband signal q Satisfies the formula:
Figure BDA0001758002720000071
wherein, W q Is an NJ × 1 dimensional TDL weight vector of the qth subband signal. When the SINR is q At maximum, the optimal solution of the weight vector can be obtained:
Figure BDA0001758002720000072
wherein, the sub-band optimal TDL weight vector W opt-q Is that
Figure BDA0001758002720000073
Maximum eigenvalue λ max The corresponding feature vector.
And step five, reconstructing the processed broadband signal by utilizing a comprehensive filter bank in the subband filter bank. And (3) solving the optimal TDL weight vector of each sub-band, and performing transmission adaptive beam forming according to the reconstruction of the comprehensive filter bank, wherein the frequency domain expression of the signal output by the mth array element is as follows:
Figure BDA0001758002720000074
wherein, Y m (e jω ) Frequency domain, w, representing the signal output by the m-th array element qm [k]A k tap weight, X (e), representing the q subband of the m array element jω ) Representing the frequency domain of the original wideband signal, H q (e jω ) Representing the frequency response of the analysis filter of the q-th sub-band, F q (e jω ) Representing the frequency response of the synthesis filter for the q-th subband.
The main lobe direction of the final output is theta 0 The broadband signal transmitting beam antenna pattern is as follows:
Figure BDA0001758002720000075
wherein P (θ, f) represents a broadband signal transmission beam antenna pattern, v st (theta, f) represents space-time pilot vector when the transmission direction of broadband signal is theta and the frequency is f, H q (f) Denotes the frequency response of the q-th subband analysis filter at frequency F, F q (f) Representing the frequency response of the q-th subband synthesis filter at frequency f.
In this particular embodiment, the effectiveness of the method is further verified by computer simulation and compared to the algorithm of the present invention using the RTN beamforming algorithm of Peter g. The parameter settings of this simulation experiment are shown in table 1:
TABLE 1 System simulation parameters
Parameter name Value of parameter
Array element number (M) 32
Number of sub-band channels (Q) 5
Signal center frequency (fc) 1250MHz
Signal bandwidth (B) 500MHz
Array element spacing (d) 0.1m
Main beam direction (theta) 0 ) 0°
Direction of interference (theta) 1 ) 20°
Original tap sampling frequency (Ts) 3000MHz
Dividing number of frequency points (K) 96
In addition, in order to ensure that the time domain broadband when the sub-band is not divided is the same as the time domain width after the sub-band is divided, the TDL order J when the sub-band is not divided is 15, and the TDL order J when the sub-band is divided is 5, fig. 2 is a schematic diagram of a TDL processing structure of the broadband array of the present invention.
The array processing structure of the simulation based on sub-band division is shown in fig. 3, a broadband signal x (n) passes through an analysis filter, each divided sub-band is subjected to TDL processing independently, the processed signal is reconstructed through a synthesis filter, and a final processed output signal y is obtained m (n)。
According to theoretical analysis and simulation experiments, the RTN algorithm can form deep nulls in the specified direction of the broadband emission beam, and the null direction does not change along with the frequency. The transmission beam antenna pattern of the wideband RTN algorithm and the transmission beam antenna pattern of the subband RTN algorithm are shown in fig. 4 and 5, respectively, and it can be seen that the subband RTN algorithm can obtain deeper nulls compared with the wideband RTN algorithm.
A beam antenna pattern based on the wideband MSINR wideband transmit adaptive beamforming algorithm without subband division is shown in (a) of fig. 6, and its null direction varies with frequency as shown in (b) of fig. 6, and a beam antenna pattern based on the subband MSINR wideband transmit adaptive beamforming algorithm with subband division is shown in (a) of fig. 7, and its null direction varies with frequency as shown in (b) of fig. 7. As can be seen from both (b) in fig. 6 and (b) in fig. 7, when the angle is 20 °, i.e. the interference direction, it is a vertical line, which shows that both the wideband MSINR algorithm and the subband MSINR algorithm can suppress the aperture transit effect, and the null steering formed on the wideband transmit beam does not vary with frequency.
The ratio of the depth of the null obtained by different algorithm simulation experiments is shown in table 2:
TABLE 2 different algorithms to form the null depth contrast (dB)
Algorithm Most preferably Center of a ship Highest point of the design
Broadband RTN algorithm 36.4 41.8 42.6
Subband RTN algorithm 33.2 45.9 38.4
Wideband MSNR algorithm 57.6 73.0 66.2
Subband MSNR algorithm 76.2 86.6 69.7
As can be seen from table 2, the depth of the null formed based on the MSINR criterion algorithm is significantly deeper than that of the RTN algorithm, and the subband division wideband transmit adaptive beamforming algorithm based on the MSINR criterion has the strongest performance. The beam null depth formed by the broadband MSNR algorithm is improved by about 20dB at the lowest frequency, the central frequency and the highest frequency, the depth can reach 73dB at the central frequency, and the performance is obviously superior to that of the RTN algorithm. Meanwhile, compared with a broadband MSNR algorithm, the subband MSNR algorithm has the advantages that the null depth is further improved, the central frequency null depth reaches 86.2dB, the interference suppression performance is further enhanced, and compared with the broadband MSNR algorithm, the tap sampling frequency of the TDL is reduced to 1/5 of the original frequency, so that the subband MSNR algorithm is more beneficial to engineering implementation.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (6)

1. The broadband emission self-adaptive beam forming method based on the subband maximum signal-to-noise ratio criterion is characterized by comprising the following steps of:
designing a broadband transmitting antenna array, and calculating an output signal of the broadband array;
step two, designing a sub-band filter bank;
thirdly, completing sub-band division of the broadband signal by utilizing an analysis filter bank in a sub-band filter bank;
step four, calculating the self-adaptive beam forming weight vector of each sub-band based on the sub-band maximum signal-to-noise ratio criterion;
step five, reconstructing the processed broadband signal by utilizing a comprehensive filter bank in a sub-band filter bank;
wherein, the broadband transmitting antenna array in the step oneThe array is a uniform linear array with the array element number of M, a tapped delay line equivalent to a discrete finite impulse response filter is arranged behind each array element, the coefficient of the tapped delay line is J, and the lowest frequency of an output signal x (n) of the broadband array is f L Maximum frequency of f H N =0, ± 1, ± 2, …; signal x output by mth array element m (n) satisfies the formula:
Figure FDA0003945907110000011
wherein x (n-k) refers to the output discrete signal x (n) shifted to the left by k units, w m [k]A weighted value referring to the kth tap of the mth array element, M =0,1, …, M-1, k =0,1, …, J-1;
q sub-band processing channels are arranged behind each array element, and each sub-band processing channel is internally provided with an analysis filter and a synthesis filter;
the analysis filter for each sub-band channel is composed of a low-pass prototype filter H with length P 0 (z) obtained by translation at a sampling frequency f s When, P = f s (B/M), wherein B is the bandwidth of the signal in the sub-band channel, and M is the total number of array elements; the analysis filter satisfies the following formula:
H q (z)＝H 0 (zW q+i )
H 0 (z)＝1+z -1 +…+z -(P-1)
wherein H q (z) represents the z-transform of the impulse response of the qth channel analysis filter, Q =1 jω ，W＝e -j2π/P Q + i denotes the q-th subband analysis filter relative to the low-pass filter H 0 Frequency shift of (z), i = f L /(B/M)-0.5，f L Is the lowest frequency of the wideband signal.
2. The method of claim 1, wherein the subband maximum snr criterion based wideband transmit adaptive beamforming is selected from the group consisting of discrete fourier transform (dft) filterbanks.
3. The method of claim 1, wherein the synthesize filter satisfies the following formula:
F q (z)＝W -(q+i) F 0 (zW q+i )
F 0 (z)＝1+z -1 +…+z -(P-1)
wherein, F q (z) denotes the z-transform of the qth channel synthesis filter.
4. The method of claim 1, wherein the subband maximum snr criterion-based wideband transmit adaptive beamforming is satisfied by a subband maximum snr criterion weight vector W opt-q Satisfies the formula:
Figure FDA0003945907110000021
wherein λ is max Is that
Figure FDA0003945907110000022
Maximum eigenvalue, R st-q Is the signal variance matrix of the q-th subband signal, N st-q Is the interference noise covariance matrix of the qth subband signal.
5. The method of claim 1, wherein the frequency domain expression of the signal output by the m-th array element after the reconstruction of the synthesis filter bank is:
Figure FDA0003945907110000023
wherein, Y m (e jω ) Representing the frequency domain of the signal output by the mth array element, Q is the total number of subband processing channels,j is the tapped delay line coefficient, Q = 1.., Q, k =0,1, …, J-1,w qm [k]A k tap weight, X (e), representing the q subband of the m array element jω ) Representing the frequency domain of the original wideband signal, H q (e jω ) Representing the frequency response of the analysis filter of the q-th sub-band, F q (e jω ) Representing the frequency response of the synthesize filter for the q-th subband.
6. The method of claim 5, wherein the antenna pattern of the wideband transmit output signal transmit beam reconstructed by the synthesis filter bank is:
Figure FDA0003945907110000024
where P (θ, f) represents a broadband signal transmit beam antenna pattern, v st (theta, f) represents space-time pilot vector when the transmission direction of the broadband signal is theta and the frequency is f, W opt-q Is the optimal weight vector, H q (f) Representing the frequency response of the q-th subband analysis filter at frequency F, F q (f) Representing the frequency response of the q-th subband synthesis filter at frequency f.
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