A joint calculation method for radar transmit waveform and receive filter for extended targets

Abstract

This invention discloses a joint calculation method for radar transmit waveforms and receive filters for extended targets, belonging to the field of array radar signal processing. This invention jointly calculates radar transmit waveforms and receive filters with probabilistic robustness, thereby maximizing the probability that the radar output SINR is greater than a certain threshold when there are errors in the extended target's TIR. Compared with iterative calculation methods for transmit waveforms and receive filters, this invention solves for high-quality transmit waveforms and receive filters, significantly improving the radar output signal-to-interference-plus-noise ratio (SINR). Compared with maximizing the worst-case performance index, this invention considers the distribution of output SINR when the TIR follows a Gaussian distribution, resulting in transmit waveforms and receive filters with better probabilistic robustness.

Description

Technical Field

[0001] This invention belongs to the field of array radar signal processing. Specifically, it is a method that uses a mixed integer programming approach to calculate the radar transmit waveform and receive filter to maximize the probability that the output signal-to-interference-plus-noise ratio is greater than a certain threshold. Background Technology

[0002] Radar is ubiquitous in daily life and widely used in both military and civilian fields. With the development of electronic technology, radar range resolution has continuously improved, resulting in targets occupying multiple range resolution cells. To improve radar detection performance against such extended targets, the transmitter and receiver degrees of freedom are used to flexibly calculate the transmitted waveform and receiver filter, thereby improving the radar system's output signal-to-interference-plus-noise ratio (SINR). In recent decades, calculations of the joint transmitted waveform and receiver filter for extended targets have been conducted both domestically and internationally, but most methods employ iterative solutions to the transmitted waveform and receiver filter distribution, failing to obtain high-quality optimal solutions. Furthermore, due to errors in the target impulse response (TIR), the calculated transmitted waveform and receiver filter need to maximize the radar SINR under error conditions. This invention establishes a probabilistic robust model for extended target detection and uses a mixed-integer programming method to solve for the transmitted waveform and receiver filter, thereby obtaining the optimal solutions for both. Summary of the Invention

[0003] The purpose of this invention is to jointly calculate the probabilistically robust radar transmit waveform and receive filter, thereby maximizing the probability that the radar output SINR is greater than a certain threshold when there is an error in the extended target TIR.

[0004] To achieve the above objectives, the technical solution of the present invention is a method for jointly calculating radar transmit waveforms and receive filters for extended targets, comprising the following steps:

[0005] Step 1: Transmit signal Apply discrete phase constraints, defined as s = Dp, where D ∈ {0, 1} N×Q , The table lists the N-dimensional complex number set, {0, 1}. N×Q Let D1 represent the set of N×Q 0-1 matrices. Q =1 N p is a discrete phase vector. Q represents the number of discrete phases, 1 Q Describes a Q-dimensional all-one vector, 1 N This represents an N-dimensional all-one vector, where N is the dimension of the transmitted signal;

[0006] Step 2: According to s=Dp, the power of the echo signal received by the radar. Reconstructed into The constructed joint vector, with superscript This represents the conjugate transpose operation, T = T0 + T ε This represents the sum of the target reflection matrix and the target echo error matrix, and vec(.) represents the vectorization operation. T0 is the target reflection matrix, I N Let w represent the N×N identity matrix, w be the receiving filter, and the superscript T denote the transpose operation. The error vector... T ε Let G be the target echo error matrix; based on the distribution characteristics of error ε, construct δ to obtain the covariance matrix G of δ. δ ;

[0007] Step 3: Power of clutter and noise received by radar Reconstructed into C represents the clutter matrix;

[0008] Step 4: Since the noise signal v follows a zero mean and a variance of , The complex Gaussian distribution; using the above equivalent transformation formula and matrix Cholesky decomposition, the signal-to-interference-plus-noise ratio (SIR) of the radar receiver output is equivalent to:

[0009]

[0010] Where v represents the noise signal, and L represents the noise signal. The matrix obtained after performing the Choliski decomposition satisfies

[0011] Step 5: In the Mixed Integer Programming (MIP) problem, due to the existence of nonlinear constraints... It cannot be solved directly; through linearization, the vector can be transformed. Transforming it into a linear constraint, we obtain a mixed integer programming problem;

[0012] Step 6: For a given signal-to-interference-plus-noise ratio (SINNR) threshold γ0, the probability that the output SINNR is greater than the threshold is expressed as: By performing relaxation operations and utilizing the properties of the Rayleigh distribution, its closed-form expression is obtained. Since the objective function of this problem is quasi-convex, the bisection method is used to solve the mixed integer programming problem to obtain the transmitted waveform and the receiving filter parameters.

[0013] Furthermore, the mixed-integer programming problem in step 5 is as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] D1 Q =1 N

[0022] ||f||≤1

[0023] D∈{0,1} N×Q

[0024] in, Represents the Kronecker product symbol, 1 NQ Describes an NQ-dimensional vector of all ones, 1 NQM Represents an NQM-dimensional all-one vector, 1 M Describes an M-dimensional vector of all ones, 1 N Let represent an N-dimensional vector of all ones, ||·|| denotes the L2 norm operation, Re{.} denotes the operation of taking the real part, Im{.} denotes the operation of taking the imaginary part, and a and b are given constants.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] 1) Compared with the iterative calculation method of the transmitted waveform and the received filter, the present invention solves for a high-quality transmitted waveform and the received filter, which significantly improves the radar output signal-to-interference-plus-noise ratio;

[0027] 2) Compared with maximizing the worst-case performance index, this invention considers the distribution of the output SINR when the TIR follows a Gaussian distribution, and the calculated transmit waveform and receive filter have better probabilistic robustness. Attached Figure Description

[0028] Figure 1 This is the overall flowchart of the present invention.

[0029] Figure 2 This is the output signal-to-interference-plus-noise ratio of the radar simulated multiple times in this invention.

[0030] Figure 3 It is a histogram showing the distribution of radar output signal-to-interference-plus-noise ratio under different error powers.

[0031] Figure 4 It is the probability value that the radar output signal-to-interference-plus-noise ratio (SIR) is greater than the threshold when different SIR thresholds γ0 are set.

[0032] Figure 5 It is the probability value that the radar output signal-to-interference-plus-noise ratio is greater than a certain threshold when different noise power settings are used. Detailed Implementation

[0033] Reference Figure 1 The specific implementation steps of this invention are as follows:

[0034] Step 1: Construct a joint calculation model for the probabilistic robust radar transmit waveform and receive filter.

[0035] 1a) Let the extended target impulse response be The clutter impulse response is M = L + N - 1. Then the TIR matrix and CIR matrix are expressed as follows:

[0036]

[0037]

[0038] Where i represents the discrete-time exponent, J i The transition matrix is ​​defined as follows:

[0039]

[0040] k1={1,...,M}, k2={1,...,N}.

[0041] Consider transmitting N snapshots of signal s, and receiving signal y as follows:

[0042] y = Ts + Cs + v

[0043] Where v represents a mean of zero and a variance of . Noise signals.

[0044] 1b) Since the target impulse response has an error signal ε, i.e. t = t0 + ε, and ε follows a complex Gaussian distribution. Therefore, the TIR matrix is ​​defined as

[0045] T = T0 + T ε

[0046] Among them, T0 and T ε Defined respectively and The output signal-to-interference-plus-noise ratio of the radar is then expressed as:

[0047]

[0048] 1c) Unlike the worst-case performance maximization method, the method proposed in this invention maximizes the probability that the radar output signal-to-interference-plus-noise ratio (SINNR) is greater than a certain threshold. Given that the transmitted signal is a discrete-phase signal, the problem model obtained in this invention is:

[0049]

[0050] sts(n)∈[1, e j2π / Q , ..., e j2π(Q1) / Q ]

[0051]

[0052] Step 2: Construct a joint solution model for the transmitted waveform and the received filter.

[0053] The constrained transmitted signal is represented as s = Dp, where D satisfies D1 Q =1 N Then the output signal-to-interference-plus-noise ratio is reconstructed as follows:

[0054]

[0055] Therefore, the problem of jointly solving the probabilistic robust joint transmit waveform and receive filter is re-expressed as follows:

[0056]

[0057]

[0058] D1 Q =1N

[0059] ||f||≤1

[0060] D∈{0,1} N×Q

[0061] Step 3, Mixed Integer Constraint Linearization

[0062] 3a) Incorporate nonlinear constraints Transformed into the following linear constraints

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Where R is a very large positive number, and a and b are real numbers, which restrict the range of values ​​for the real and imaginary parts of f.

[0070] 3b) Based on 3a), the joint solution problem of the probabilistic robust transmit waveform and the receive filter is expressed as:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] D1 Q =1 N

[0079] ||f||≤1

[0080] D∈{0,1} N×Q

[0081] Step 4: Solve for the closed-form expression of the probability objective function.

[0082] 4a) Based on the triangle inequality and the properties of probability, we can obtain...

[0083]

[0084] because The real and imaginary parts of follow Gaussian distributions, therefore Following a Rayleigh distribution, we obtain

[0085]

[0086] in, Let be the covariance matrix of the error δ. In practical applications, this invention generates a large number of error vectors based on the distribution of the error vector ε, thereby constructing δ and calculating its covariance matrix. Then, the objective function for jointly solving the probabilistic robust joint transmit waveform and receive filter problem is re-expressed as: Using arbitrary rotation Given the phase of the objective function and its invariant value, the objective function of the original problem can be expressed as:

[0087] 4b) Since the objective function is a quasi-convex problem, this invention uses a bisection method for solving it. The following problem is reconstructed and solved using the bisection method to obtain the optimal transmit waveform and receive filter.

[0088] find f, D, w

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] D1 Q =1 N

[0097] ||f||≤1

[0098]

[0099] D∈{0,1} N×Q

[0100] in, Its upper and lower bounds can be determined based on probability. The value of τ is calculated between [0, 1]. Through calculation, it is found that τ does not have a strict upper bound, but generally setting τ to 10 makes the probability value very close to 1. Therefore, in practical applications, this invention sets τ∈[0, 10].

[0101] Simulation conditions and simulation data processing

[0102] 1. Simulation conditions

[0103] The simulation parameters are set as shown in Table 1:

[0104] Table 1 Simulation Parameters

[0105] System parameters symbol Parameter value Operating frequency / GHz <![CDATA[f0]]> 3 Pulse duration is / ns 10 Radar range resolution / m 1.5 Target length / m 15 Number of transmitted pulse points N 7 Number of distance units occupied by the target L 10 Number of discrete transmitted signals Q 2

[0106] For convenience, this invention considers the error matrix. Extended target TIR information is defined as

[0107]

[0108] Clutter CIR matrix is ​​defined as

[0109]

[0110] in and These represent the power of TIR and CIR respectively, and are set.

[0111] 2. Simulation Data Processing

[0112] Simulation 1, setting noise power Error Power This invention underwent 5000 Monte Carlo simulations, and the output signal-to-noise ratio performance of the two methods for radar was compared. Figure 2 The information is provided in the text.

[0113] Figure 2 It can be seen that the proposed methods significantly improve the output signal-to-noise ratio (SNR) of the radar. Specifically, compared with the continuous phase case, the method proposed in this invention improves the output SNR performance by approximately 10 dB. This is because the method of this invention can directly solve for the joint vector of the transmitted signal and the receiving filter, obtaining a high-quality optimal solution for both. Furthermore, this invention constrains the transmitted signal to be selected only from the discrete phase set, which avoids the performance loss caused by phase discretization.

[0114] Simulation 2, setting noise power Error Power The distribution histograms of SINR output from 5000 Monte Carlo trials using two different methods were simulated.

[0115] from Figure 3 It can be seen that the probabilistic robust calculation method proposed in this invention can reduce the variance of the output SINR. Furthermore, by jointly calculating the transmit code and the receive filter, high-quality optimal solutions for both are obtained, thus improving output performance.

[0116] Simulation 3, setting error power Noise power This invention evaluated the probability that the output signal-to-interference-plus-noise ratio (SIR) exceeds the threshold when different SIR thresholds are set. The obtained optimal probability and the actual Monte Carlo probability value are as follows: Figure 4 As shown.

[0117] from Figure 4It can be seen that the Monte Carlo simulation using the solved optimal transmit code and receive filter yields a higher probability than the actual optimal solution. This is due to the relaxation process applied when solving the closed-form probabilistic expression. Furthermore, when γ0 exceeds a certain threshold, both probability values ​​become zero. This is because, given the input signal power and clutter power, it is impossible to solve for a transmit waveform and receive filter that would make the radar output SINR greater than this threshold; therefore, the probability value is zero.

[0118] Simulation 4, Error Power γ0 = 0 dB. This invention evaluates the detection probability performance of the present invention combined with the robust joint calculation method. The present invention defines a stable detection probability as...

[0119]

[0120] Where N m N represents the number of Monte Carlo simulations. r This represents the number of times the event Pr{γ(w,s)≥γ0} occurs.

[0121] Figure 5 The stable detection probability of the present invention and the robust joint calculation method under different noise power conditions is given. It can be seen that the method of the present invention can significantly improve the stable detection probability of radar.

Claims

1. A method for jointly calculating radar transmit waveforms and receive filters for extended targets, comprising the following steps: Step 1: Transmit signal Apply discrete phase constraints, defined as ,in , express A set of complex numbers of dimension 1 express A set of 0-1 matrices of dimension, satisfying , For discrete phase vectors, , Indicates the number of discrete phases. express One-dimensional vector express One-dimensional vector It is the dimension of the transmitted signal; Step 2: According to The power of the echo signal received by the radar Reconstructed into ; For the constructed joint vector, the superscript This indicates the conjugate transpose operation. This represents the sum of the target reflection matrix and the target echo error matrix. Indicates vectorization operation, , For the target reflection matrix, express 3D identity matrix For the receiving filter, the superscript T indicates the transpose operation, and the error vector... , The target echo error matrix; based on the error The distribution characteristics, construct ,get covariance matrix ; Step 3: Power of clutter and noise received by radar Reconstructed into , , Represents the clutter matrix; Step 4: Due to noise signals It follows a zero mean and has a variance of . The complex Gaussian distribution; using the equivalent transformation formula and matrix Cholesky decomposition, the signal-to-interference-plus-noise ratio (SIR) of the radar receiver output is equivalent to: ； in Indicates noise signal, Indicates to The matrix obtained after performing the Choliski decomposition satisfies ; Step 5: Through linearization, the vector can be transformed... Transforming it into a linear constraint, we obtain a mixed integer programming problem; The mixed integer programming problem is: ； ； ； ； ； ； ； ； ； ； in, Represents the Kronecker product symbol. express A one-dimensional vector express A one-dimensional vector express A one-dimensional vector express A one-dimensional vector This represents the L2 norm operation. This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part. and For a given constant; Step 6: For a given signal-to-interference-plus-noise ratio (SINR) threshold The probability that the output signal-to-interference-plus-noise ratio (SIR) is greater than this threshold is expressed as: By performing relaxation operations and utilizing the properties of the Rayleigh distribution, its closed-form expression is obtained. Since the objective function of this problem is quasi-convex, a bisection method is used to solve the mixed-integer programming problem, yielding the transmitted waveform and the receiver filter parameters. For error The covariance matrix.

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