CN111693976B - MIMO radar beam forming method based on residual error network - Google Patents
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Abstract
The invention belongs to the technical field of radars, and particularly provides a residual error network-based MIMO radar beam forming method, which is used for solving the contradiction that the performance of a directional diagram of a designed waveform has certain loss under the condition of absolute constant modulus or absolute constant modulus cannot be realized under the condition of better performance of the directional diagram in the existing method. The invention constructs a new optimization model, optimizes and separates the main lobe and the side lobe, and can flexibly fine-tune the performance of the main lobe and the performance of the side lobe by adjusting the size of a balance factor; meanwhile, the waveform in the optimization model is forced to be constant modulus, and good directional diagram optimization performance is realized; and simultaneously, optimizing the new optimization model by adopting a residual error network, constructing the residual error network, setting a target function in the optimization model as a loss function, and optimizing to obtain an optimal waveform.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a MIMO radar beam forming method based on a residual error network.
Background
The MIMO radar waveform design is a research hotspot in the radar field, and as a new radar technology, each antenna of the MIMO radar can emit different waveforms, so that compared with the traditional phased array radar, the MIMO radar has higher distance resolution and higher detection performance, and can realize a target meeting actual requirements through reasonable waveform design.
Due to different application scenes and actual requirements, the target functions of the MIMO radar waveform design are usually different; according to different target functions, the main MIMO radar waveform design methods can be divided into three categories: the first is to maximize the output SINR, and the method considers the case of transmit-receive integration, and jointly designs the transmit Waveform and the optimal filter weight vector, so as to maximize the output SINR after the receiving end filters, as in documents g.cui, h.li and m.rangmay, "MIMO radio wave Design With Signal modulation and precision Constraints," in IEEE Transactions on Signal Processing, vol.62, no.2, pp.343-353, jan.15,2014 "; the second category is the maximize MI method, which designs the Waveform by maximizing the Mutual Information of the target response and the received echo, so that there are more target characteristics in the echo, such as documents Y.Chen, Y.Nijsure, C.Yuen, Y.H.Chew, Z.Ding and S.Boussakta, "Adaptive Distributed MIMO radio wave Optimization Based on Multi Information," in IEEE T transmissions on Audio and Electronic Systems, vol.49, no.2, pp.1374-1385, APRIL 20; the third type is a beamforming method, which minimizes the error between the designed waveform pattern and the desired pattern to concentrate the MIMO Radar transmission energy in the spatial domain of interest, and at the same time, reduces the interference direction energy radiation, as in the documents p.st oica, j.li and y.xie, "On combining Signal Design For MIMO Radar," in IEEE transactions On Signal Processing, vol.55, no.8, pp.4151-4161, aug.2007 (hereinafter, referred to as document 1).
Among the above waveform design methods, the third type of beam forming method is particularly concerned; there are two main beamforming methods: one is a two-step method, that is, under the condition of constant modulus constraint, a waveform covariance matrix is solved first, and then a waveform corresponding to the covariance matrix is solved, as in document 1; another is a direct Design waveform, such as the documents Y.Wang, X.Wang, H.Liu and Z.Luo, "On the Design of Constant modules Signal for MIMO Radar," in IEEE transactions On Signal Processing, vol.60, no.8, pp.4432-4438, and Aug.2012 (hereinafter referred to as document 2). Document 1 proposes a method based on pattern template matching, which minimizes an error between a designed pattern of a waveform and a desired pattern, so that the transmission energy of the MIMO radar is concentrated in an interested space domain, and at the same time, cross-correlation side lobes are minimized; however, since this problem is a complicated non-convex optimization problem, document 1 merely designs an optimal covariance matrix R, and does not further design a MIMO radar waveform from R. Aiming at the problem, a cyclic iteration algorithm is further provided in a document P.Stoica, J.Li and X.Zhu, namely, a Waveform Synthesis for Diversity-Based Transmit Beampattern Design, an i n IEEE Transactions on Signal Processing, vol.56, no.6, pp.2593-2598, june 2008 (hereinafter referred to as document 3), so that an MIMO radar Waveform is further designed on the basis of an optimal covariance matrix R; however, this method has difficulty in obtaining a globally optimal solution. In order to solve the problem, documents j, lipor, s.ahmed and m.alouini, "Fourier-Based Transmit Beampattern Design Using MI MO Radar," in IEEE Transactions on Signal Processing, vol.62, no.9, pp.2226-2235, ma y1,2014 (hereinafter, referred to as document 4) propose a fast waveform covariance synthesis method Based on Fourier transform, which has slightly reduced performance when the number of antennas is small. Documents "z.cheng, z.he, s.zhang and j. Li," Constant module wave form Design for MIMO radius Transmit Beampattern, "in IEEE Transactions on Signal Processing, vol.65, no.18, pp.4912-4923,15sept.15,2017 (hereinafter referred to as document 5) further propose to directly Design an optimal Waveform by using the ADMM and DADMM methods, and the algorithm itself also has better convergence characteristics; however, under the constant modulus constraint, the method needs dozens of iterative computations to design a waveform close to the constant modulus, so that the practical application performance of the signal may be limited.
From the above, the existing beamforming method has two design difficulties: 1. the performance of a directional diagram of the designed waveform is better, but the waveform is not absolute constant modulus; based on the method, the invention provides a MIMO radar beam forming method based on a residual error network.
Disclosure of Invention
The invention aims to provide a MIMO radar beam forming method based on a residual error network, so that a directional diagram corresponding to a designed waveform is fitted with an expected directional diagram as much as possible, and meanwhile, cross-correlation side lobes are reduced; the invention uses the residual error neural network for MIMO radar waveform design, so that the performance of beamforming is further improved on the basis of absolute constant modulus of the designed waveform.
In order to achieve the purpose, the invention adopts the technical scheme that:
a MIMO radar beam forming method based on a residual error network comprises the following steps:
the residual error network comprises 5 residual error blocks which are connected in sequence, and each residual error block consists of two layers of neural networks; wherein the content of the first and second substances,
the first layer in the first residual block is a neural network with a weight matrix dimension of ML xJ and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J xJ and a neuron number of J;
each layer of the second to fourth residual blocks is a neural network with the dimension of a weight matrix of J multiplied by J and the number of neurons of J;
the first layer in the fifth residual block is a neural network with a weight matrix dimension of J multiplied by J and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J multiplied by ML and a neuron number of ML;
a layer of neural network with the weight matrix dimension of ML multiplied by J and the number of neurons of J is arranged between the input and the output of the first residual block, and a layer of neural network with the weight matrix dimension of Jmultiplied by ML and the number of neurons of ML is arranged between the input and the output of the last residual block, so as to realize dimension matching;
setting x = [ x (1), x (2), …, x (ML) ] as the input of a residual error network, wherein x (i) ∈ [0,1] and is a random number, i =1,2, …, ML and M are the number of transmitting antennas of a MIMO radar transmitting array, and L is a snapshot number;
the residual error network output is
The loss function is:
the first method comprises the following steps:
loss 1 ＝F 1 +F 2 +F 3
wherein:
n 1 number of mesh points, η, representing main lobe region 1 A balance factor representing a main lobe region;
ε k ＝|u opt d(θ k )-P(θ k )| 2 ，
a t (θ k ) Denotes theta k The direction vector of the direction is,
representation matrix
The first column of (a) is,
and reducing the matrix into a matrix with M rows and L columns;
|P(θ p ,θ q )| 2 ＝Re(P(θ p ,θ q )) 2 +Im(P(θ p ,θ q )) 2 ，
and the second method comprises the following steps:
loss 2 ＝F 4 +F 5 +F 6
wherein, F 4 ＝F 1 ，F 6 ＝F 3 ；
Step 3. Calculating
And restoring S into a transmitting waveform matrix S, namely completing beam forming and realizing directional diagram matching.
The invention has the following beneficial effects:
the invention provides a MIMO radar beam forming method based on a residual error network, which has the following advantages:
and optimizing the model based on a residual error network to solve the beamforming problem based on the optimized model
1. Constructing a new optimization model; in the existing method, a main lobe part and a side lobe part of a directional diagram are always optimized together; because the energy of the main lobe and the energy of the side lobes are different, the unified optimization of the main lobe and the side lobes can bring certain influence on the performance of the algorithm; based on the method, a new optimization model is constructed, the optimization of the main lobe and the side lobe is separated, and the performance of the main lobe and the performance of the side lobe can be flexibly adjusted by adjusting the size of the balance factor; meanwhile, the waveform in the optimization model is forced to be constant modulus, good directional diagram optimization performance is realized, and the contradiction that the directional diagram performance has certain loss under the condition of absolute constant modulus or absolute constant modulus cannot be realized under the condition of better directional diagram performance of the designed waveform in the existing method is effectively overcome;
2. the invention optimizes the new optimization model by adopting a residual error network, constructs the residual error network, sets a target function in the optimization model as a loss function, and optimizes to obtain the optimal waveform.
Drawings
Fig. 1 is a schematic diagram of a residual error network structure according to the present invention.
Figure 2 is a graph comparing the performance of an embodiment of the present invention with the prior art scheme.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the following embodiments and the accompanying drawings.
For convenience of description, the following definitions are first made:
setting a transmitting array of a co-located MIMO radar as a uniform linear array consisting of M transmitting antennas; let L, L =1,2,3, the emission waveform of L snapshots be s l ＝[s 1 (l),s 2 (l),…,s M (l)] T Then the transmit waveform matrix is:
the composite beam emitted by all antennas in the theta direction is:
wherein, a t (θ) represents an M-dimensional direction vector:
a t (θ)＝[1,e -j2πνsinθ/λ ,…,e -j2π(M-1)νsinθ/λ ] T (3)
v is the spacing between array elements, and lambda is the signal wavelength;
let y = [ y (1), y (2), …, y (L)] T A vector of synthesized signals representing L snapshots, then:
wherein, I L An identity matrix of dimension L, S = vec (S);
the directional pattern of the beam in the θ direction is:
wherein the content of the first and second substances,
and then, defining the cross-correlation side lobes in different directions as follows:
wherein the content of the first and second substances,
the goal of beam forming is to enable the directional diagram of the designed waveform to approach the expected directional diagram as much as possible at all angles, and simultaneously to reduce the cross-correlation side lobe as much as possible; based on this goal, two existing optimization problem models are as follows:
wherein K is the number of grid points of the direction angle,
the number of grid points with high cross correlation is shown, and u is a scaling factor; omega k 、ω c Are all weight factors, ω k Weight of the waveform at the kth angle, ω c Weights for the cross-correlation side lobes; d (theta) k ) Representing a desired waveform; the difference between the two objective functions is that the first terms of the two objective functions are absolute error and mean square error, respectively;
in the above optimization problem, the reason for adding the constant modulus constraint is to avoid distortion of the transmit signal in the nearly saturated operating mode of the high frequency amplifier while reducing the operating pressure of the digital-to-analog converter (DAC) as much as possible.
The working principle of the invention is as follows:
definition of n 1 The number of mesh points of the main lobe part, and therefore the number of mesh points of the side lobe part is n 2 ＝K-n 1 ；
Reissue to order
Being the grid points of the main lobe portion,
grid points that are side lobe portions; to this end, θ of the main lobe and the side lobe k I.e. are separated;
due to d (θ) in the formula (7) and the formula (8) k ) The main lobe and the side lobe of the beam pattern are included; on the other hand, since the desired pattern of the side lobe portion is set to 0 according to the setting in the conventional method, for example, in documents 1 and 5:
d(θ k )＝0，k＝n 1 +1,n 1 +2,…,K (9)
in the formula (7), absolute errors are added to the main lobe and the side lobe part, in the invention, the mean square error is added to the main lobe, and the absolute error is also adopted to the side lobe; the new optimization problem is then constructed as follows:
for the optimization problem shown in equation (8), the mean square error is used for both the main lobe and the side lobe part in the present invention; thus, another objective function is constructed as follows:
according to documents 1 and 5, ω in the main lobe region k All are equal, ω in the side lobe region k Are also equal; thus, it is possible to provide
Order to
(to distinguish from the description of the weighting factors, we call η 1 、η 2 、η 3 Balance factors of a main lobe area, balance factors of a side lobe area and balance factors of cross-correlation side lobe items are respectively); then the equations (10) and (11) are converted as follows:
the scaling factor u and the waveform s in the above formulas (12) and (13) are variables to be optimized, and the variables have a theoretically optimal analytical solution; in order to reduce the computational complexity, the analytical solution of the variable u is further solved below to improve the optimization performance; under the condition that s is given, the optimal solution of u can be obtained, the obtained optimal solution is substituted into the original objective function, and the optimization problem is converted into a univariate optimization problem only related to s;
order type(12) The partial derivative of the objective function in (1) with respect to u is
Then there are:
order to
Can be solved to obtain:
the optimization problem shown in equation (12) then translates into:
the partial derivative of the objective function in equation (13) with respect to u is also u opt Therefore, the optimization problem shown in (13) translates into:
in document 5, a designed waveform is made to approximate a constant modulus signal by iteration, and thus the designed signal is only an approximate constant modulus, not an absolute constant modulus signal; in contrast, in the solution of the present invention, the designed signal is directly forced to be
i =1,2, … ML, wherein,
the absolute constant modulus of the signal is realized by designing the phase of the signal for the phase of each component of the signal to be designed.
The invention provides a solving method based on a depth residual error network, which comprises the following steps:
the essence of the above equations (16) and (17) is to design the constant modulus signal
Phase of
i =1,2, …, ML; in the present invention, the residual network is used for design
The input of each training of the residual error network is a normalized random vector, and the output is the waveform phase designed by the invention;
fig. 1 shows the optimization model based on the residual error network, which includes: input, forward propagation, output, loss function calculation, optimizer;
1) Input and output design:
order to
Represents the input of the n-th training, where x n (i)∈[0,1]I =1,2, …, ML; we turn x 1 As the input of the first forward propagation module, the initial value is a normalized random sequence; in the present invention, the input for each training is equal, x 1 ＝x 2 ＝…＝x n ；
Next, x 1 The value range of (c) needs to be determined; since sigmoid function is selected as the activation function in the present invention, the nonlinear range of the function is about [ -1.7,1.7]Within the interval, the direct input interval is [0,2 pi]The values in between may affect network performance, so the present invention normalizes the input to [0,1 [ ]]I.e. x 1 (i)∈[0,1],i＝1,2,…,ML；
The output of the forward propagation module is the normalized phase vector of the waveform designed by the present invention
Wherein
Represents the output of the nth training;
2) Forward propagation design:
the residual error network comprises 5 residual error blocks which are connected in sequence, and each residual error block consists of two layers of neural networks; wherein the content of the first and second substances,
the first layer in the first residual block is a neural network with a weight matrix dimension of ML xJ and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J xJ and a neuron number of J;
each layer of the second to fourth residual blocks is a neural network with the dimension of a weight matrix being J multiplied by J and the number of neurons being J;
the first layer in the fifth residual block is a neural network with a weight matrix dimension of J multiplied by J and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J multiplied by ML and a neuron number of ML;
a layer of neural network with the weight matrix dimension of ML multiplied by J and the number of neurons of J is arranged between the input and the output of the first residual block, and a layer of neural network with the weight matrix dimension of Jmultiplied by ML and the number of neurons of ML is arranged between the input and the output of the last residual block, so as to realize dimension matching;
in the forward propagation process, each two layers of networks form a residual block, and the total number of the residual blocks is 5; the residual error network defines that the output of each layer of residual error block is obtained by adding the input of the first layer network and the output of the second layer network in the residual error block, so that the condition that the dimension of the input of the first layer network and the dimension of the output of the second layer network are not matched possibly needs to be considered; in practical network architectures, this situation can only occur for the first residual block at the input and the last residual block close to the output of the entire residual network; taking an input end as an example, when ML is not equal to J, if a common residual block is directly adopted for construction, the output dimension of the second layer network of the first residual block is J, the input dimension of the first layer network is ML, the dimensions of the two are not equal, and the two dimensions cannot be added; therefore, a layer of network is additionally built between the input and the output of the first residual block, the dimension of the weight matrix of the network is ML multiplied by J, and therefore, the number of the neurons is also J; thus, after the input passes through the layer network from above, the dimension is converted into J; similarly, the dimension transformation is also needed to be carried out on the output end, so that a network layer containing ML neurons is built between the input and the output of the residual block of the output end by using the same idea; thus, dimension matching in the forward propagation process of the whole network structure is realized.
3) And (3) calculating a loss function: the normalized phase calculated by the residual error network will be used in the following
Calculating a loss function;
let the original signal formed by the nth output be
Then
Wherein the content of the first and second substances,
and is provided with
Based on the inverse of the column vectorization in equation (5), we can direct the vector to the target vector
Rearranged to a matrix similar to formula (1) and then derived from column I
From the foregoing analysis, the loss function in the present invention is set as the objective function in the optimization problem of the above equations (16) and (17); because the residual error network can not directly process the complex problem, some algebraic transformations need to be carried out on the original objective function;
calculating two target functions respectively; for convenience of description, we call the calculation of the first loss function algorithm 1, and the calculation of the second loss function algorithm 2:
for algorithm 1, first, a decomposition is performed on the objective function in (16); let loss 1 For the designed objective function:
wherein:
for F 1 Due to the fact that
Wherein the content of the first and second substances,
i =1,2, …, ML, transformed by the euler equation as follows:
further, in the present invention,
is shown as
Wherein the content of the first and second substances,
to represent
The real part of (a) is,
is that
An imaginary part;
by the formula (2), y (l) is at theta k The resultant signal of direction is:
wherein the content of the first and second substances,
respectively correspond to
The phase of each component of (a);
from (20) obtained:
further, in the present invention,
y (k) ＝[y (k) (1),y (k) (2),…,y (k) (L)] T (22)
obtained by the following formulae (5) (21) (22):
from formula (15), u opt It can be calculated that:
and then ordering: epsilon k ＝|u opt d(θ k )-P(θ k )| 2 Thus:
in summary, F 1 The specific calculation flow of (2) is shown in table 1:
TABLE 1
For F 2 Note that the grid point at this time is n 1 +1 to K; by and F 1 In the same calculation steps (19) to (23), the energy value P (θ) at each grid point can be obtained k )：
For F 3 Similarly to the formula (5), from the formula (6), we have the following equations:
by the same method as in the above formula (20) and formula (21), respectively
And
the real and imaginary parts of (c); thus, there are:
thus obtaining P (theta) p ,θ q ) The real part of (c):
and P (theta) p ,θ q ) Imaginary part of (c):
thus, there are:
|P(θ p ,θ q )| 2 ＝Re(P(θ p ,θ q )) 2 +Im(P(θ p ,θ q )) 2 (30)
further, there are obtained:
to this end, F 1 ,F 2 ,F 3 The calculation work of (2) is completed; finally, we will F 1 、F 2 、F 3 The calculation results of (2) are added, the first Loss function Loss 1 The calculation is completed.
For algorithm 2, we also decompose the objective function in (17) in a similar way, let loss 2 For the designed objective function, then
Wherein, the first and the second end of the pipe are connected with each other,
note F 4 ＝F 1 ，F 6 ＝F 3 Therefore, only F needs to be calculated 5 Then the method is finished; it is to be noted that,
while
The former differs from the latter only in that the former uses squares and the latter absolute values; therefore, P (θ) is calculated from (23) k ) (i.e. the
Then, the square of the grid is directly solved (note that the grid point at this time is n) 1 +1 to K, but the calculation method is the same); namely, it is
Finally, we will F 4 ，F 5 ，F 6 Add to obtain loss 2 。
4) Optimizing network weights via ADAM optimizer
Setting a loss function, and optimizing a weight matrix W in the network by adopting an ADAM deep learning optimizer; because the AD AM algorithm is based on the python 3.6 environment in the simulation experiment, and the library function package of the sensor Flow is called for optimization; therefore, after the network is built, the whole optimization process is automatically completed by a computer.
Examples
The simulation of this example was performed by comparing the existing scheme (document 3) of the present invention; the simulation scenes are uniformly set as follows:
setting a transmission antenna M =10 of a co-located MIMO radar of a uniform linear array, setting a sampling number L =32 of a pulse, and setting an array element interval as a half wavelength; the range of the direction angle is (-90 degrees, 90 degrees),the grid point spacing is 1 DEG, K =1,2, …, K, eta 1 ＝1，η 3 =0 (i.e. ω) c =0, same as in the prior art);
for the number J of neurons in each layer of the residual error network, J =128 is adopted in this embodiment, and the training times are all 2000.
Two desired patterns are considered, the first one being a desired pattern with three main lobes whose main lobe centers are at respective angles θ 1 ＝40°、θ 2 ＝0°、θ 3 =40 °, the width of each main lobe is 20 °, which is represented by the following equation:
the second is the desired pattern with only one main lobe, with a main lobe center of 0 ° and a main lobe width of 60 °, represented by:
after practical test, when eta 2 When the value is more than or equal to 50, the value change has little influence on the algorithm; therefore, in this embodiment, η is taken 2 =100; FIG. 2 shows the performance comparison analysis of the two algorithms of the present invention and the prior art scheme 1, in which the expected directional diagram in FIG. 2 (b) is a main lobe (d) 2 (theta)), the directional diagram matching performance of the algorithm 1 is obviously superior to that of the existing scheme no matter in the main lobe area or the side lobe area, and the algorithm 2 is obviously superior to that of the existing scheme in the main lobe area and the edge area close to the side lobe; it is worth mentioning that the invention can flexibly adjust eta according to actual requirements 2 If the performance of the main lobe is required to be fitted better, eta can be properly improved 2 Taking the value of (A); in FIG. 2 (a), the desired pattern is three main lobes (d) 1 (theta)), the two algorithms of the invention have better pattern matching performance than the prior scheme no matter in the main lobe area or the side lobe area, so the algorithm provided by the invention is also superior to the prior scheme 1.
In this embodiment, MSE is defined as:
the indicator is the overall performance indicator of the pattern matching algorithm, P (theta) k ) Is a normalized desired pattern; as the results in table 2 show, the MSE of our proposed method is lower than that of prior art scheme 1.
TABLE 2
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.
Claims (2)
1. A MIMO radar beam forming method based on a residual error network comprises the following steps:
step 1, constructing a residual error network;
the residual error network comprises 5 residual error blocks which are connected in sequence, and each residual error block consists of two layers of neural networks; wherein the content of the first and second substances,
the first layer in the first residual block is a neural network with a weight matrix dimension of ML xJ and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J xJ and a neuron number of J;
each layer of the second to fourth residual blocks is a neural network with the dimension of a weight matrix being J multiplied by J and the number of neurons being J;
in the fifth residual block, the first layer is a neural network with a weight matrix dimension of J multiplied by J and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J multiplied by ML and a neuron number of ML;
a layer of neural network with the weight matrix dimension of ML multiplied by J and the number of neurons of J is arranged between the input and the output of the first residual block, and a layer of neural network with the weight matrix dimension of Jmultiplied by ML and the number of neurons of ML is arranged between the input and the output of the last residual block, so as to realize dimension matching;
setting x = [ x (1), x (2), …, x (ML) ] as the input of a residual error network, wherein x (i) ∈ [0,1] and is a random number, i =1,2, …, ML and M are the number of transmitting antennas of a MIMO radar transmitting array, and L is a snapshot number;
the residual error network output is
Step 2, setting a loss function, and optimizing the residual error network in the step 1 by adopting an ADAM deep learning optimizer; obtaining the output of the last training after the optimization
The loss function is:
loss 1 ＝F 1 +F 2 +F 3
wherein:
n 1 number of mesh points, η, representing main lobe region 1 A balance factor representing a main lobe region;
ε k ＝|u opt d(θ k )-P(θ k )| 2 ，
a t (θ k ) Denotes theta k The direction vector of the direction is,
representation matrix
The first column of (a) is,
and reducing the matrix into a matrix with M rows and L columns;
|P(θ p ,θ q )| 2 ＝Re(P(θ p ,θ q )) 2 +Im(P(θ p ,θ q )) 2 ，
step 3. Calculating
S is restored to the transmit waveform matrix S.
2. A MIMO radar beam forming method based on a residual error network comprises the following steps:
step 1, constructing a residual error network;
the residual error network comprises 5 residual error blocks which are connected in sequence, and each residual error block consists of two layers of neural networks; wherein the content of the first and second substances,
the first layer in the first residual block is a neural network with a weight matrix dimension of ML xJ and a neuron number of J, and the second layer is a neural network with a weight matrix dimension of J xJ and a neuron number of J;
each layer of the second to fourth residual blocks is a neural network with the dimension of a weight matrix being J multiplied by J and the number of neurons being J;
the first layer in the fifth residual block is a neural network with the dimension of a weight matrix of J multiplied by J and the number of neurons of J, and the second layer is a neural network with the dimension of the weight matrix of J multiplied by ML and the number of neurons of ML;
a layer of neural network with the weight matrix dimension of ML multiplied by J and the number of neurons of J is arranged between the input and the output of the first residual block, and a layer of neural network with the weight matrix dimension of Jmultiplied by ML and the number of neurons of ML is arranged between the input and the output of the last residual block, so as to realize dimension matching;
setting x = [ x (1), x (2), …, x (ML) ] as the input of a residual error network, wherein x (i) ∈ [0,1] and is a random number, i =1,2, …, ML and M are the number of transmitting antennas of a MIMO radar transmitting array, and L is a snapshot number;
the residual error network output is
Step 2, setting a loss function, and optimizing the residual error network in the step 1 by adopting an ADAM deep learning optimizer; obtaining the output of the last training after the optimization
The loss function is:
loss 2 ＝F 4 +F 5 +F 6
wherein:
n 1 number of mesh points, η, representing main lobe region 1 A balance factor representing a main lobe region;
ε k ＝|u opt d(θ k )-P(θ k )| 2 ，
a t (θ k ) Denotes theta k The direction vector of the direction is the direction vector,
representation matrix
The first column of (a) is,
and reducing the matrix into a matrix with M rows and L columns;
|P(θ p ,θ q )| 2 ＝Re(P(θ p ,θ q )) 2 +Im(P(θ p ,θ q )) 2 ，
step 3. Calculating
S is restored to the transmit waveform matrix S.
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