CN111817765B - Generalized sidelobe cancellation broadband beam forming method based on frequency constraint - Google Patents

Generalized sidelobe cancellation broadband beam forming method based on frequency constraint Download PDF

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CN111817765B
CN111817765B CN202010571766.0A CN202010571766A CN111817765B CN 111817765 B CN111817765 B CN 111817765B CN 202010571766 A CN202010571766 A CN 202010571766A CN 111817765 B CN111817765 B CN 111817765B
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constraint
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auxiliary channel
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main channel
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CN111817765A (en
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谢菊兰
饶申宇
郭明宇
邓宇昊
冯雅栋
何子述
陈竹梅
胡瑞贤
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • 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
    • G01S7/292—Extracting wanted echo-signals
    • 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
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • G01S7/354—Extracting wanted echo-signals

Abstract

The invention provides a generalized sidelobe cancellation broadband beam forming method based on frequency constraint, which can enable an expected signal to pass through without distortion while interference is suppressed by carrying out new constraint on weight vectors of a main channel and an auxiliary channel of a GSC structure in a frequency domain. By controlling the array element numbers of the main channel and the auxiliary channel, the performance of the algorithm can be flexibly changed, the calculation amount of the algorithm can be reduced while the freedom degree is not wasted, and the practicability of the algorithm is further improved. The invention directly restrains the auxiliary channel weight vector through the restraint matrix, and the restraint matrix can change along with the difference of the target signal and the array, so the obtained auxiliary channel weight vector is most suitable for the current environment, which is also the premise of ensuring the high performance of the algorithm. The invention applies the idea of frequency domain constraint to the broadband beam forming method of generalized sidelobe cancellation without pre-delay, has low calculation cost and can inhibit interference and noise signals to the maximum extent.

Description

Generalized sidelobe cancellation broadband beam forming method based on frequency constraint
Technical Field
The invention belongs to the radar communication technology, and particularly relates to a generalized sidelobe canceling broadband beam forming technology.
Background
Broadband beam forming is an important array signal processing technology and is widely applied to the fields of radar, sonar, communication, seismology and the like. The generalized sidelobe canceling structure GSC (generalized sidelobe canceller) is one of the main structures of broadband beamforming, and the broadband beamforming algorithm based on the structure has good performance of suppressing interference and noise signals (see the documents: An alternative adaptive to linear constrained adaptive beamforming, L.Griffiths and C.Jim, IEEE Transactions on Antennas and processing, 1982,30(1): 27-34.). With the increasing bandwidth of processing signals, the GSC-based wideband beamforming method has attracted attention.
In practice, conventional GSCs require pre-delay processing in order to compensate for time delays due to inconsistencies in array geometry and viewing direction, as shown in fig. 2. However, accurate compensation of the pre-delay, whether analog or digital, cannot be achieved, and pre-delay compensation errors will cause severe degradation of the wideband beamforming performance; meanwhile, the time delay compensation of interference signals in different array elements is different, which will affect the effect of interference cancellation of the GSC main and auxiliary channels, so that it is important to find a method for eliminating the pre-delay. There is an algorithm for removing pre-delays by applying Convolution Constraints to the weights of an adaptive wideband beamformer (see the literature: constraint Constraints for Broadband Antenna Arrays, l.c. godara and m.r.s.jahromi, IEEE Transactions on Antennas and Propagation,2007,55(11):3146 and 3154.), but this method is more complex in terms of computation and algorithm structure and more complex to implement.
The generalized sidelobe canceling wideband beamforming algorithm without pre-delay does not need to pre-delay the received data first, thus saving the compensation unit and the phase compensation unit of the real-time delay line, and avoiding the error introduced by the pre-delay compensation (see the documents: adaptive wideband beamforming with robust estimation errors, Amr Ei Keyi, Thia Kirubabajan, Alex B.Gershman, IEEE Workshop on Sensor array and Multichannel Processing,2006: 1145.). The Broadband Beamforming algorithm without Pre-delay can be realized by directly applying constraint on the Frequency Domain (see the literature: interference of Pre-Steering delay in Space Time Broadband Beamforming Using Frequency Domain Constraints, Ebrahimi R, Seydnejad R, IEEE Communications letters,2013,17(4): 769-. Although not very stable, the wideband beamforming algorithm without pre-delay has a certain realizability, and the method can be used in GSC algorithm to suppress interference and noise signals (see Design of generated and received adaptive wireless beam former and past-sensing systems, K.Wu and T.Su., Electronics Letters,2016,52(3): 177-179.). The method constructs a new static weight and a blocking matrix to replace the pre-delay by utilizing the property of the kronecker product, proves that the non-pre-delay broadband beam forming algorithm based on the generalized steering vector is feasible, and verifies the effectiveness and the superiority of the method. However, the input of two channels in the GSC structure of this method is the same, resulting in poor output stability and higher requirement for the snapshot number of data.
The invention of application No. 202010418338.4 provides a wideband beamforming method without pre-delay, by performing a constraint on the weight vector in the frequency domain such that the desired signal passes through without distortion while interference is suppressed, comprising the steps of:
step 1, constructing a receiving signal model of each array element under a set array, wherein the array consists of M array elements;
step 2, down-conversion: the carrier removal processing is carried out on the received signals of all the array elements, and the received signals are converted into baseband analog signals;
step 3, A/D sampling: sampling the analog signal of the baseband, and converting the analog signal into a digital end for processing;
step 4, performing J-order Frost space-time processing on the baseband digital reception of the main channel to perform data recombination;
step 5, estimating an autocorrelation matrix of the received signal by using the received data after data recombination;
step 6, constructing a constraint matrix C and a constraint vector f according to the distortion-free condition;
and 7, under the linear constraint of the constraint matrix C and the constraint vector f, constructing an optimization problem with constraint by inhibiting other incoming interference and noise while realizing undistorted reception of the expected signal, and constructing a cost function according to the optimization problem to solve the optimal weight vector so as to obtain the final output of beam forming.
The method has low requirement on the fast beat number of the data and obtains good output performance with less calculation cost; the sensitivity to the time domain tap number, the frequency constraint point number and the received signal parameter is low, and the output stability is good.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a broadband beam forming method combining frequency domain constraint and generalized sidelobe cancellation without pre-delay.
The invention adopts the technical scheme that a generalized sidelobe canceling broadband beam forming method based on frequency constraint comprises the following steps:
step 1, constructing a receiving signal model of an array with an array element number of M, and using the M of the array1One array element forms a main channel, and the rest M2One array element forms an auxiliary channel, M is M1+M2，M1>M2；
Step 2, respectively carrying out down-conversion, A/D sampling and data recombination on the received data of the main channel and the auxiliary channel; wherein the data reassembly of the received data of the main channel employs J1A Frost space-time processor of order, and J is adopted for data recombination of the received data of the auxiliary channel2A front-order space-time processor;
step 3, estimating the autocorrelation matrix R of the auxiliary channel receiving signal by using the receiving data after data recombinationaaAnd cross-correlation matrix R of main and auxiliary channel receiving signalsam；
Step 4, constructing a constraint matrix and a constraint vector of the main channel under the condition of no distortion of the expected signal, wherein the constraint matrix and the constraint vector are respectively CmAnd fmThe constraint matrix of the auxiliary channel is Ca，CmHaving M1×J1Line Q1Column, CaHaving M2×J2Line Q2Column, Q1Number of frequency constraints, Q, for the main channel2The number of points is constrained for the frequency of the auxiliary channel;
step 5, according to the constraint matrix CmAnd a constraint vector fmSolving for the principal channel weight vector wq；
6, according to the autocorrelation matrix RaaCross correlation matrix RamA main channel weight vector wqAnd a constraint matrix CaSolving auxiliary channel weight vector wa，
wa＝Raa -1Ramwq-Raa -1Ca(Ca HRaa -1Ca)-1Ca HRaa -1Ramwq；
Step 7, utilizing the weight vector w of the main channelqWeighting the main channel receiving data of the generalized sidelobe cancellation structure GSC, and simultaneously utilizing an auxiliary channel weight vector waAnd weighting the auxiliary channel receiving data of the GSC, and canceling and outputting the weighted main channel receiving data and the weighted auxiliary channel receiving data by the GSC.
The invention can make the desired signal pass through without distortion while the interference is suppressed by carrying out a new constraint on the weight vector of the GSC structure main channel and the weight vector of the GSC structure auxiliary channel on the frequency domain. The GSC structure of the invention has different array element selection modes of the main channel and the auxiliary channel, which depends on different functions of the two channels. The main channel has the function of gaining the output of the expected signal, so that the array element number is generally more; the auxiliary channel is mainly used for suppressing interference, and the array element number of the auxiliary channel only needs to meet the degree of freedom of the interference number. By controlling the array element numbers of the main channel and the auxiliary channel, the performance of the algorithm can be flexibly changed, the calculation amount of the algorithm can be reduced while the freedom degree is not wasted, and the practicability of the algorithm is further improved. The GSC structure of the invention does not need the blocking matrix in the traditional GSC structure to block the expected signal from entering the auxiliary channel, but passes the constraint matrix CaDirect to auxiliary channel weight vector waMake a constraint, constraint matrix CaDepending on the desired signal orientation and the primary and secondary channel selection, this indicates the weight vector w for the secondary channelaThe constraints imposed will vary from target signal to target signal and from array to array, and the resulting auxiliary channel weight vector waThe method is most suitable for the current environment, and the premise for guaranteeing the high performance of the algorithm is also provided. Therefore, the method improves the performance and flexibility of the algorithm while avoiding blocking matrix solution.
The invention has the beneficial effects that: the idea of frequency domain constraint is applied to a broadband beam forming method of generalized sidelobe cancellation without pre-delay, the calculation cost is low, and interference and noise signals can be inhibited to the maximum extent. According to the invention, through the mode of respectively selecting the array elements for the main channel and the auxiliary channel, the data dimension is reduced, meanwhile, the requirement on fast data beat is also reduced, and good output performance is obtained with lower calculation cost; the constraint matrix directly constrains the auxiliary channel weight vector, so that the dependence of the algorithm on an application environment is reduced, and the method is mainly characterized in that the sensitivity of the algorithm on the time domain tap number, the frequency constraint point number and the received signal parameter is low, so that the algorithm has good output stability.
Drawings
Fig. 1 is a flow chart of a generalized sidelobe canceling broadband beamforming method without pre-delay according to the present invention.
Fig. 2 is a schematic diagram of a conventional GSC structure.
Fig. 3 is a schematic diagram of a Frost space-time processor.
Fig. 4 is a schematic diagram of a GSC architecture without pre-delay.
Fig. 5 is a beam pattern after wideband beamforming in accordance with the present invention.
Fig. 6 is a top view of a beam pattern after broadband beamforming in accordance with the present invention.
Fig. 7 is a graph of the effect of input SNR on output SINR for different approaches.
Fig. 8 is a graph of the effect of low snapshot count on output SINR for different approaches.
Fig. 9 is a graph of the effect of high snapshot count on output SINR for different approaches.
Fig. 10 is a graph of the effect of the snapshot number on the output SINR for different time domain tap numbers.
Fig. 11 is a graph of the effect of snapshot number on output SINR for different signal parameters.
Detailed Description
For better description, the following definitions are first made:
broadband beamforming: a beam of broadband signals is transmitted to an antenna, and the beam is subjected to a series of processes at the receiving end of the antenna to direct the beam passing through the antenna in a desired direction, which is collectively referred to as broadband beamforming.
The desired signal: the desired signal, i.e., the signal that can pass through without distortion after beamforming.
Down conversion: in the process of reducing the rf signal to the baseband signal, the signal received by the antenna is generally the rf signal processed by the carrier, and if the original signal is to be processed, the carrier needs to be removed and the original signal is reduced to the baseband signal.
A/D sampling: the baseband analog signal is sampled according to a certain time interval to obtain a digital signal with discrete time and amplitude, the process of converting the analog signal into the digital signal is called A/D sampling, and the digital signal is more convenient to process.
Frost space-time processor: the delay circuit is composed of a delayer and a time domain tap, and the specific structure is shown in figure 3. Wherein x ism,k(n) and wm,k(M is 1,2, …, M; k is 1,2, …, J) are input data and applied weight value on J tap of M array element channel, y (n) is output signal of beam forming, J-1 is time delay number of space-time processor, n is digital time variable.
The cost function is: combining the constraint condition of the problem to be optimized to the objective function, constructing a function which meets the objective function and the constraint condition, and optimizing the function which is equivalent to solving the original optimization problem, so the function is called as a cost function.
The following describes an embodiment of the present invention in detail with reference to the drawings of the specification, and fig. 1 shows a flowchart of a generalized sidelobe canceling wideband beamforming method without pre-delay, which specifically includes the following steps:
step 1, constructing a receiving signal module of each array element under a set arrayType, M with the array1One array element forms a main channel, and the rest M2The array elements form an auxiliary channel.
Selecting a certain array element in the array as a reference array element, wherein a received signal of the certain array element is an original received signal; modeling the received signals of the other array elements according to the relative propagation delay of the array element and the reference array element, and specifically operating as follows:
selecting one array element in the array as a reference array element, marking as a 1 st array element, and setting a received signal of the array element as:
Figure GDA0002646581850000061
f0is the center frequency of the desired signal, and is also typically the carrier frequency of the received signal; s (t) is the complex envelope of the desired signal, t is an analog time variable. n is1And (t) is a noise signal (non-interference signal) or an interference plus noise signal (interference signal) received by the 1 st array element.
When the desired signal incidence direction is (theta)0,φ0)，θ0And phi0The pitch angle and the azimuth angle of the desired signal are respectively, and the signal received by the mth array element is:
Figure GDA0002646581850000062
wherein n ism(t) is a noise signal (no interference signal) or an interference plus noise signal (interference signal) received by the mth array element; the relative delay of the mth array element and the reference array element for receiving the expected signal is as follows:
Figure GDA0002646581850000063
let the coordinates of the reference array element be (0,0,0), here (x)m,ym,zm) Is the three-dimensional spatial coordinate of the mth array element relative to the reference array element.
At GSC junctionsIn the structure, the front M of M array elements is set1One array element forms a main channel, and the rest M2(M1+M2M) array elements form auxiliary channels, and the specific GSC structure is shown in fig. 4.
Note that the expected signal received by the reference array element is:
Figure GDA0002646581850000064
the desired signal received by the corresponding mth array element is:
Figure GDA0002646581850000065
step 2, down-conversion: and (4) carrying out carrier removal processing on the received signals of all the array elements, and converting the received signals into baseband signals.
Multiplying the received signal of each array element by
Figure GDA0002646581850000066
The received signal of the mth array element is down-converted to be:
Figure GDA0002646581850000067
the desired signal received by the mth array element is down-converted into:
Figure GDA0002646581850000071
step 3, A/D sampling: and sampling the analog signal of the baseband, and converting the analog signal into digital end processing.
Sampling the received signal of each array element with a sampling period of TsIf the received signal of the mth array element is sampled, the baseband signal obtained by the sampling of the received signal of the mth array element is:
Figure GDA0002646581850000072
the baseband signal obtained by sampling the desired signal received by the mth array element is:
Figure GDA0002646581850000073
step 4, passing the baseband digital receiving signal of the main channel through J1Baseband digital received signal of order Frost space-time processor and auxiliary channel passes through J2And a front space-time processor of order for data recombination.
The baseband digital receiving signals of each array element of the main channel and the auxiliary channel respectively pass through a front space-time processor to realize the combination of a space domain and a time domain; adding the weight value before each tap, and further accumulating to obtain the output of the main channel and the auxiliary channel, wherein the specific operation is as follows:
the received signal of each array element generates corresponding time delay through a time delay unit of a Frost space-time processor, namely the baseband received signal at the kth tap of the mth array element should be:
rm,k(n)＝rm(n-(k-1)),m＝1,2,…,M；k＝1,2,…,J
the baseband expected signal at the kth tap of the mth array element should be:
Figure GDA0002646581850000074
if the desired signal of each array element channel passes through the Frost space-time structure in fig. 3 and is weighted, the following are:
Figure GDA0002646581850000081
the desired signal portion in the beamformed output is then:
Figure GDA0002646581850000082
in the GSC configuration of FIG. 4, the main channel takes the form of J1The order Frost space-time processor adopts J as the auxiliary channel2The order Frost space-time processor, assuming the number of sampling points (fast beat number) as N, then the equivalent received data of the main channel in the GSC structure is expressed as a matrix form as
Figure GDA0002646581850000083
Wherein r ism,k＝[rm,k(1) rm,k(2) … rm,k(N)],m＝1,2,…,M1,k＝1,2,…,J1。
The equivalent received data of the auxiliary channel in the GSC structure is expressed in a matrix form
Figure GDA0002646581850000084
Wherein r ism,k＝[rm,k(1) rm,k(2) … rm,k(N)],m＝M1+1,M1+2,…,M，k＝1,2,…,J2，
Figure GDA0002646581850000085
Representing a complex field.
Step 5, estimating the autocorrelation matrix R of the auxiliary channel receiving signal by using the receiving data after data recombinationaaCross correlation matrix R of received signals of main channel and auxiliary channelam。
Estimating a correlation matrix of the received signal using the snapshot data, and estimating an autocorrelation matrix R of the received signal of the auxiliary channelaaIs composed of
Figure GDA0002646581850000086
Figure GDA0002646581850000087
Representing a real number domain;
cross correlation matrix R of main and auxiliary channel receiving signalamIs composed of
Figure GDA0002646581850000091
Step 6, constructing a constraint matrix and a constraint vector of the main channel as C respectivelymAnd fmThe constraint matrix of the auxiliary channel is Ca，CmHaving M1×J1Line Q1Column, CaHaving M2×J2Line Q2And (4) columns.
Deducing the relation between the output of the signal through the Frost space-time processor and the original received signal in the frequency domain, and establishing a transmission function H (f, theta)0,φ0) (ii) a According to the condition of no distortion
Figure GDA0002646581850000092
And constructing a constraint matrix of the main channel and the auxiliary channel and a constraint vector of the main channel. The specific operation is as follows:
assuming that the fourier transform of the signal S (n) is S (ω), where ω is the digital angular frequency, the baseband desired signal x at the kth tap of the mth array elementm,k(n) Fourier transform:
Figure GDA0002646581850000093
setting the baseband analog frequency of the desired signal to
Figure GDA0002646581850000094
B is the bandwidth of the desired signal; 2 pi fTsTherefore, Xm,k(ω) the corresponding baseband analog frequency domain is represented as
Figure GDA0002646581850000095
Fourier transform of the desired signal portion y' (n) in the beamformed output:
Figure GDA0002646581850000096
the transfer function is denoted as H (f, θ)0,φ0) The calculation formula is:
Figure GDA0002646581850000097
wherein:
Figure GDA0002646581850000101
wk＝[w1,k w2,k … wM,k]T
for undistorted output of the desired signal, the frequency domain of the desired signal output may be made such that the amplitude gain is constant, the phase and the frequency are linear, i.e. the transfer function is:
Figure GDA0002646581850000102
where K is an amplitude gain coefficient, and is generally taken as K1; d is the relative time delay of the output expected signal and the input expected signal, and the value range of D belongs to [1, J-1 ]]To do so
Figure GDA0002646581850000103
The best effect of beam forming is achieved.
The main channel in the GSC structure has the function of ensuring that the expected signal passes through without distortion, and a constraint matrix C of the main channel is constructedmAnd a constraint vector fmSo that the condition that the desired signal is free from distortion is met, namely:
Figure GDA0002646581850000104
wherein
Figure GDA0002646581850000105
Order to
Figure GDA0002646581850000106
Figure GDA0002646581850000107
Wherein Q is1The number of frequency constraint points of the main channel is generally not less than the constraint matrix CmThe rank of (c) may be such that,
Figure GDA0002646581850000108
q＝1,2,…,Q1。
Figure GDA0002646581850000109
expressed as a space-domain steering vector a (θ)0,φ0,fq) And time domain steering vector at(fq) Kronecker product of (a):
Figure GDA00026465818500001010
space domain steering vector a (theta)0,φ0,fq) And time domain steering vector at(fq) Respectively as follows:
Figure GDA00026465818500001011
Figure GDA0002646581850000111
likewise, constructing a constraint matrix C of GSC structure auxiliary channelsaComprises the following steps:
Figure GDA0002646581850000112
wherein Q is2The number of frequency constraint points for the auxiliary channel is generally not less than the constraint matrix CaThe rank of (c) may be such that,
Figure GDA0002646581850000113
p＝1,2,…,Q2。
Figure GDA0002646581850000114
denoted as space-domain steering vector a' (θ)0,φ0,fp) And time domain steering vector at′(fp) Kronecker product of (a):
Figure GDA0002646581850000115
space domain steering vector a' (θ)0,φ0,fp) And time domain steering vector at′(fp) Comprises the following steps:
Figure GDA0002646581850000116
Figure GDA0002646581850000117
step 7, according to the constraint matrix CmAnd a constraint vector fmSolving for the principal channel weight vector wq。
In a constraint matrix CmAnd a constraint vector fmUnder the linear constraint of (3), establishing a constraint condition of the main channel, and solving a weight vector w of the main channelq. The specific operation is as follows:
in the GSC structure, the transmission function of the main channel needs to satisfy the condition of
Figure GDA0002646581850000118
Equivalence ofGround, main channel weight vector wqThe constraint condition to be satisfied is
Cm Hwq＝fm
Direct utilization of Cm HIs solved for wqIs composed of
wq＝(Cm H)+fm＝Cm(Cm HCm)-1fm
Wherein, the operation symbol (·)+To solve a generalized inverse matrix of a matrix, (-)-1The inverse of the matrix is calculated.
Step 8, constructing an optimization problem with constraint and a cost function based on a linear constraint non-minimum variance criterion, and constructing the cost function according to an autocorrelation matrix RaaCross correlation matrix RamA main channel weight vector wqAnd a constraint matrix CaSolving auxiliary channel weight vector wa。
Constructing an optimization problem with constraints by suppressing other incoming interference and noise while realizing undistorted reception of the expected signal; establishing a cost function according to the optimization problem and solving the optimal weight vector wa. The specific operation is as follows:
in the GSC architecture of FIG. 4, the final output signal data y is represented as
Figure GDA0002646581850000121
In the auxiliary channel of the GSC structure, the desired signal is not allowed to enter the auxiliary channel, i.e. the desired signal does not appear in the output of the auxiliary channel, while the constraint matrix CaIs the space-time steering vector of the expected signal at different frequency points, therefore, the weight vector w of the auxiliary channelaShould satisfy
Ca Hwa＝0
Under the minimum mean square error criterion, constructing the optimization problem of restraining other coming interference and noise while realizing the undistorted receiving of the expected signal into a band constraint
Figure GDA0002646581850000122
st.Ca Hwa＝0
Constructing a real-valued cost function as follows:
Figure GDA0002646581850000123
wherein Re {. is a real part,
Figure GDA0002646581850000124
is the lagrange multiplier vector; rmmAnd RaaAutocorrelation matrices, R, for the signals received in the main and auxiliary channels, respectivelyamThe cross-correlation matrix of the signals received by the auxiliary channel and the main channel is obtained by estimating sampling snapshot data.
Then with respect to the above formula with respect to waGradient and make it equal to zero vector
Figure GDA0002646581850000125
Obtaining an auxiliary channel weight vector waIs optimally solved as
Figure GDA0002646581850000131
Will be the above formula waoInto Ca Hwa0 is got
λ＝2(Ca HRaa -1Ca)-1Ca HRaa -1Ramwq
Bringing the above into
Figure GDA0002646581850000132
Get it solved
wao＝Raa -1Ramwq-Raa -1Ca(Ca HRaa -1Ca)-1Ca HRaa -1Ramwq
The final output of the GSC structure is then:
Figure GDA0002646581850000133
in order to make the purpose, technical scheme and technical effect of the invention clearer, the invention is further described in detail through simulation experiments.
Simulation experiment conditions I: the experiment is simulated aiming at the generalized sidelobe cancellation method without pre-delay. In the simulation, the array is a uniform linear array, and the array element spacing is half of the wavelength corresponding to the highest frequency. Number of main channel array elements M 120, time-domain tap number J1Number of frequency discrete points Q of 17114; number of auxiliary channel array elements M2Time-domain tap number J ═ 52Number of frequency discrete points Q of 17214. The array receives three far-field broadband signals and sets the incidence angle theta of the expected signals0At-30 deg. center frequency f01GHz, bandwidth B300 MHz, signal-to-noise ratio SNR 0; interference signal 1: incident angle theta 030 °, center frequency f00.99GHz, bandwidth B300 MHz, dry-to-noise ratio INR 120 dB; interference signal 2: incident angle theta 05 °, center frequency f01.01GHz, bandwidth B300 MHz, dry-to-noise INR 220 dB. Sampling frequency fs600MHz, fast sampling N3000, amplitude gain K1, relative delay
Figure GDA0002646581850000134
The simulation results are shown in fig. 5 and 6.
Fig. 5 shows a beam pattern after broadband beamforming according to the invention, and fig. 6 is a top view of fig. 5. As can be seen from fig. 5 and 6, the output beam is directed in the direction of the set desired signal, and at the same time, deep nulls are formed in two interference directions, which indicates that the method achieves passing the desired signal without distortion while suppressing other incoming interference signals.
Simulation experiment conditions II: the experiment is carried out by simulating the influence of the input signal-to-noise ratio SNR on the output signal-to-interference noise ratio SINR under the simulation condition of the experiment I. The expected signal input signal-to-noise ratio SNR is-30, -15, …,20dB, the number of monte carlo trials is 500, and the other experimental conditions are consistent with the one of the simulated experimental conditions. In order to embody the performance of the algorithm of the invention, a conventional pre-delay generalized sidelobe cancellation broadband beam forming method (referred to as conventional GSC for short) and an existing pre-delay-free generalized sidelobe cancellation method (referred to as pre-delay-free GSC for short) are compared and simulated. The simulation results are shown in fig. 7. As can be seen from fig. 7, the output SINR for different methods changes towards increasing and then towards stabilizing, which also conforms to the theoretical relationship between the output SINR and the input SNR; the output SINR of the new method is higher than that of the conventional GSC method and the pre-delay-removed GSC method under the same input SNR, which also proves that the interference suppression performance of the algorithm of the present invention is better than that of other methods.
And (3) simulation experiment conditions are as follows: the experiment is carried out by simulating the influence of the data sampling fast beat number on the output signal to interference plus noise ratio (SINR) under the simulation condition of the experiment I. The experiment is divided into two parts, namely, low sampling fast beat number and high sampling fast beat number are simulated respectively. The low-sampling snapshot simulation is taken as N50, 50, … and 500, the high-sampling snapshot simulation is taken as N1000, … and 10000, the Monte Carlo test times are 500, and other test conditions are consistent with the first simulation test condition. The simulation results are shown in fig. 8 and 9.
Fig. 8 shows a graph of the effect of low-sample fast-beat numbers on the output signal-to-interference-and-noise ratio SINR, and fig. 9 shows a graph of the effect of high-sample fast-beat numbers on the output signal-to-interference-and-noise ratio SINR. As can be seen from fig. 8: when the number of snapshots reaches 100, the output SINR of the new method and the conventional GSC method tends to be stable, and under the same number of snapshots, the output SINR of the new method is obviously higher than that of the conventional GSC method; the output SINR of the pre-delay-free GSC method is very low at low snapshot numbers, which indicates that the interference suppression performance of the method is not good at low snapshot numbers. As can be seen from fig. 9: under the condition that the number of snapshots is increased, the output SINR of the new method and the conventional GSC method is kept stable; the output SINR of the pre-delay-free GSC method is also increased with the increase of the number of fast beats, which indicates that the method needs to pay a large amount of calculation to obtain higher interference suppression performance. In conclusion, experiment three again proves that the interference suppression performance of the novel calculation method is superior to that of other methods, and the requirement on the snapshot number is low.
The performance of the existing cancellation wideband beam forming method (the cancellation pre-delay GSC method) without pre-delay generalized sidelobe is greatly influenced by the number of time-domain taps, the number of frequency discrete points and the parameters of received signals, but the new method of the invention has good stability, and in order to embody the superiority of the method of the invention, the simulation is carried out by changing the number of time-domain taps, the number of frequency discrete points and the incident angle of the received signals.
And (4) simulation experiment conditions are as follows: in the experiment, under the condition of changing the number of time domain taps and the number of frequency discrete points, the influence of the data sampling fast beat number of the novel method and the pre-delay GSC method on the output SINR is compared and simulated. The experiment considers that the time domain tap number and the frequency discrete point number of the main channel are the same as those of the auxiliary channel, and four different time domain tap numbers and frequency discrete point numbers are simulated. Here take J1＝ J 27,11,20,30, corresponding to Q1＝Q2The other experimental conditions are consistent with the high sampling fast-beat experiment of the third simulation experimental condition 7,11,17 and 30. The simulation results are shown in fig. 10. It can be seen from fig. 10 that, when the number of snapshots is constant and the number of time-domain taps and the number of frequency discrete points are changed, the variation range of the output SINR of the novel method of the present invention is within 0.5dB, while the variation range of the output SINR of the pre-delay removing GSC method exceeds 3dB, which shows that the sensitivity of the novel method of the present invention to the number of time-domain taps and the number of frequency discrete points is significantly lower than that of the pre-delay removing GSC method.
And (5) simulation experiment conditions are as follows: the experiment is carried out under the condition of changing the incident angle of the received signalThe method mainly aims at the comparison and simulation of the influence of the data sampling fast beat number of the novel method and the pre-delay GSC method on the output SINR. The experiment only simulates the positive and negative conditions of the incident angle of the expected signal, namely the incident angle of the received signal is theta0＝30°,θ1＝10°,θ2-20 ° and angle of incidence of received signal θ0＝-30°,θ1＝30°,θ2The other experimental conditions are consistent with the high sampling fast-beat number experiment of the third simulation experimental condition. The simulation results are shown in fig. 11. As can be seen from fig. 11, when the number of snapshots is constant and the signal incidence angles are different, the difference in output SINR of the novel method of the present invention is small, while the difference in output SINR of the pre-delay GSC method is large, which indicates that the sensitivity of the novel method of the present invention to the received signal incidence angle is significantly lower than that of the pre-delay GSC method. From the simulation results of experiment four and experiment five, the sensitivity of the new method of the invention to the time domain tap number, the frequency discrete point number and the received signal parameter is lower, which shows that the method of the invention has good output stability.
The invention obtains the condition that the received signal passes through without distortion by deducing the relation between the output of the received signal through a Frost space-time processor and the original received signal on a frequency domain, constructs the constraint matrix and the constraint vector of a main channel and an auxiliary channel of a GSC structure by adopting a method of directly constraining in the frequency domain, and constructs an optimization problem to ensure that the expected signal is received without distortion, and simultaneously inhibits interference and noise signals to the maximum extent. The method has low requirement on the fast beat number of the data and obtains good output performance with less calculation cost; the sensitivity to the time domain tap number, the frequency constraint point number and the received signal parameter is low, and the output stability is good.
The key elements of the present invention are based on techniques that do not require pre-delay and directly establish constraints on frequency, and are not limited to the foregoing embodiments; the optimal weight vector solving method is not limited to the direct solving method, and may be other means such as a least mean square algorithm (LMS) or a Recursive Least Squares (RLS). The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.

Claims (3)

1. A generalized sidelobe cancellation broadband beam forming method based on frequency constraint is characterized by comprising the following steps:
step 1, constructing a receiving signal model of an array with an array element number of M, and using the M of the array1One array element forms a main channel, and the rest M2One array element forms an auxiliary channel, M is M1+M2，M1>M2；
Step 2, respectively carrying out down-conversion, A/D sampling and data recombination on the received data of the main channel and the auxiliary channel; wherein the data reassembly of the received data of the main channel employs J1A Frost space-time processor of order, and J is adopted for data recombination of the received data of the auxiliary channel2A front-order space-time processor;
step 3, estimating the autocorrelation matrix R of the auxiliary channel receiving signal by using the receiving data after data recombinationaaAnd cross-correlation matrix R of main and auxiliary channel received signalsam；
Step 4, constructing a constraint matrix and a constraint vector of the main channel under the condition of no distortion of the expected signal, wherein the constraint matrix and the constraint vector are respectively CmAnd fmThe constraint matrix of the auxiliary channel is Ca，CmHaving M1×J1Line Q1Column, CaHaving M2×J2Line Q2Column, Q1Number of frequency constraints, Q, for the main channel2The number of points is constrained for the frequency of the auxiliary channel;
constructing a constraint matrix C of a main channel according to an expected signal undistorted conditionmAnd a constraint vector fmThe specific method comprises the following steps:
Figure FDA0003268504140000011
Figure FDA0003268504140000012
wherein the content of the first and second substances,
Figure FDA0003268504140000013
representing a complex field, fqIndicating the frequency of the qth frequency constraint point on the main channel, Q being 1,2, …, Q1；θ0And phi0Pitch and azimuth, respectively, of the desired signal, D1Is the relative delay of the output desired signal and the input desired signal on the main channel,
Figure FDA0003268504140000014
Figure FDA0003268504140000015
the space domain steering vector a (theta) expressed as the main channel0,φ0,fq) And the time domain steering vector a of the main channelt(fq) Kronecker product of (a):
Figure FDA0003268504140000016
Figure FDA0003268504140000017
Figure FDA0003268504140000021
wherein f is0Is the center frequency, τ, of the desired signalm(θ0,φ0) For the relative delay of receiving the desired signal for the mth array element and the reference array element, M is 1,2, …, M1，TsIs a sampling period;
step 5, according to the constraint matrix CmAnd a constraint vector fmSolving for the principal channel weight vector wq；
6, according to the autocorrelation matrix RaaCross correlation matrix RamA main channel weight vector wqAnd a constraint matrix CaSolving auxiliary channel weight vector wa：
wa＝Raa -1Ramwq-Raa -1Ca(Ca HRaa -1Ca)-1Ca HRaa -1Ramwq；
Step 7, utilizing the weight vector w of the main channelqWeighting the main channel receiving data of the generalized sidelobe cancellation structure GSC, and simultaneously utilizing an auxiliary channel weight vector waAnd weighting the auxiliary channel receiving data of the GSC, and canceling and outputting the weighted main channel receiving data and the weighted auxiliary channel receiving data by the GSC.
2. The method of claim 1 wherein the principal channel weight vector wqComprises the following steps: w is aq＝Cm(Cm HCm)-1fm(ii) a Wherein, (.)-1The inverse of the matrix is calculated.
3. The method of claim 1, wherein the constraint matrix C of the auxiliary channel is constructed in step 4 according to the undistorted condition of the desired signalaThe specific method comprises the following steps:
Figure FDA0003268504140000022
wherein the content of the first and second substances,
Figure FDA0003268504140000023
representing a complex field, fpFrequency representing the p-th frequency constraint point on the auxiliary channel, p ═ 1,2, …, Q2；θ0And phi0Pitch and azimuth angles of the desired signal, respectively;
Figure FDA0003268504140000024
denoted as the auxiliary channel up-space steering vector a' (θ)0,φ0,fp) And time domain steering vector a 'on auxiliary channel't(fp) Of Crohn's rubber
Figure FDA0003268504140000025
Figure FDA0003268504140000026
Figure FDA0003268504140000027
Wherein f is0Is the center frequency, τ, of the desired signalm’ (θ0,φ0) For the M' th element relative delay of receiving the desired signal with respect to the reference element, M ═ M1+1,M1+2,…,M，TsIs the sampling period.
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