CN112882005A - OTFS radar target parameter estimation method based on Bayesian learning - Google Patents

OTFS radar target parameter estimation method based on Bayesian learning Download PDF

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CN112882005A
CN112882005A CN202110047037.XA CN202110047037A CN112882005A CN 112882005 A CN112882005 A CN 112882005A CN 202110047037 A CN202110047037 A CN 202110047037A CN 112882005 A CN112882005 A CN 112882005A
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CN112882005B (en
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刘升恒
黄永明
刘晨文
巩智含
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • 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
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • 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
    • G01S13/50—Systems of measurement based on relative movement of target
    • G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination 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
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention discloses an OTFS radar target parameter estimation method based on Bayesian learning, which comprises the following steps of obtaining a matrix Y of received symbols in a time delay-Doppler domain; expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y; calculating effective time delay unit M according to prior informationeffAnd an effective Doppler unit NeffObtaining a simplified estimation model; randomly selecting S rows from the vector y, and calculating to obtain a measurement matrix A under the same row index; sparse radar channel vector h obtained by using CPCSBL-GAMP algorithmest(ii) a Vector h of radar channelestReverting to matrix form HestFinding out the position of the non-zero element; and obtaining the estimated values of the target distance and the relative speed. The invention can solve the problem of the existing OTFS modulation radar target parameter estimation schemeThe method has the advantages of obviously reducing the computational complexity and having higher estimation precision and robustness.

Description

OTFS radar target parameter estimation method based on Bayesian learning
Technical Field
The invention relates to the technical field of digital signal processing, in particular to an OTFS radar target parameter estimation method based on Bayesian learning.
Background
In order to improve the positioning accuracy and the safety performance of an automatic driving automobile in a complex environment, the functions of radar sensing and wireless communication, namely a radar communication integrated system, need to be integrated on the automobile. The radar communication integrated system can solve the problem of shortage of current spectrum resources, and only one set of hardware equipment is needed in the integrated system, so that the size of the whole system can be greatly reduced, and the price can be reduced.
In recent years, radar communication integrated system design has attracted much attention. Generally, the existing integrated design schemes are mainly divided into two categories. The first category mainly adopts a resource sharing strategy, and time, frequency or space resources are respectively allocated to radar or a communication module for use. Because this type of method cannot fully utilize existing resources, radar and communication performance cannot be optimized simultaneously. The other type is mainly designed into an integrated waveform, namely, the radar and the communication system share one waveform. The method does not need to compromise radar and communication performance, so most documents design a radar communication integrated scheme from the angle.
OFDM modulation is often used in digital communications because of its high spectral efficiency and its ability to overcome inter-symbol interference. Moreover, as a vehicle-mounted radar waveform, the OFDM modulated signal does not have a range-doppler coupling problem compared to a chirped continuous wave signal. Therefore, many documents in the prior art use the OFDM modulated signal as a common waveform for the radar communication integrated system. However, the OFDM modulation signal itself is sensitive to doppler shift, so that the communication performance of the integrated system is seriously deteriorated in a fast time-varying channel.
In order to solve the above problems in OFDM modulation, a novel two-dimensional modulation technique, i.e., Orthogonal Time Frequency Space (OTFS) modulation, is proposed in the literature. From the communication perspective, many scholars design many low-complexity symbol detection algorithms based on OTFS modulation, and simulation verifies the superior error rate performance. However, in terms of radar target detection and parameter estimation based on OTFS modulation, corresponding research results are few, and at present, there are mainly two methods. One is to use the idea of maximum likelihood estimation to search all possible distance and speed combinations of the targets one by one and find out the combination that minimizes some cost function value. The other is to use a matched filtering method to convert the target parameter estimation into a vector estimation problem and multiply the received signal vector by a known matrix to counteract the effect of the transmitted communication symbols on the parameter estimation. Although the method can estimate a plurality of targets simultaneously, the complexity is still high, and especially when the number of subcarriers and the number of symbols modulated by the OTFS are large, the calculation complexity is also large.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides an OTFS radar target parameter estimation method based on Bayesian learning, and the method can reduce the complexity of radar target parameter estimation.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a bayesian learning-based OTFS radar target parameter estimation method, which comprises the following steps,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
and step 3: calculating effective time delay unit M according to prior informationeffAnd an effective Doppler unit NeffObtaining a simplified estimation model;
and 4, step 4: randomly selecting S rows from the vector y, and calculating to obtain a measurement matrix A under the same row index;
and 5: sparse radar channel vector h obtained by using CPCSBL-GAMP algorithmest；
Step 6: vector h of radar channelestReverting to matrix form HestFinding out the position of the non-zero element;
and 7: and obtaining the estimated values of the target distance and the relative speed.
Further, in the present invention: the obtaining of the matrix Y may further comprise,
step 1-1: establishing a discrete radar channel model H (tau, ν) in a time delay-Doppler domain:
Figure BDA0002897701900000021
wherein, M and N respectively represent the number of delay units and the number of Doppler units in a delay-Doppler domain plane, τ and ν respectively represent round-trip delay and Doppler shift, Δ f is a subcarrier frequency interval, T is a time of a symbol, H [ k ', l' ] represents a target complex gain with a Doppler tap of k 'and a delay tap of l', and if there is no target at the position, the value of H [ k ', l' ] is 0, and δ (·) is a Dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbol X [ k, l ] and the received symbol Y [ k, l ] of the OFDM modulation system can be represented as:
Figure BDA0002897701900000022
wherein the content of the first and second substances,<·>Nand<·>Mrespectively representing modulo-N and modulo-M operations, k and l respectively representing the received symbols Y k, l in the delay-Doppler domain plane]The row and column indices of (a) and (b), l 'and k' represent the target delay tap length and the Doppler shift tap length, w [ k, l ], respectively]Is that the variance under the time delay-Doppler domain is sigma2Complex white gaussian noise, phase shift factor alphak,l[k′,l′]The expression of (a) is:
Figure BDA0002897701900000031
where L represents the length of the cyclic prefix.
Further, in the present invention: the column vector form y is:
Figure BDA0002897701900000032
wherein h is a radar signal vector, and the k 'M + l' element is h [ k ', l']Y is a received symbol vector, is a received symbol matrix Y [ k, l [ ]]Spread by rows, w is the noise vector, matrix
Figure BDA00028977019000000314
The (p, q) th element of (a) is:
Figure BDA0002897701900000033
further, in the present invention: the prior information comprises a maximum distance R of the actual targetmaxAnd a maximum relative velocity VmaxUnder this condition, the corresponding effective delay unit MeffAnd an effective Doppler unit NeffRespectively as follows:
Figure BDA0002897701900000034
Figure BDA0002897701900000035
wherein the content of the first and second substances,
Figure BDA0002897701900000036
represents rounding up, c0Is the speed of light, B is the bandwidth of the modulated signal, fcThe center frequency of the carrier.
Further, in the present invention: the acquisition of the measurement matrix A comprises the steps of randomly selecting S rows of a received symbol vector y to obtain a low-dimensional observation vector
Figure BDA0002897701900000037
According to the row index selected by the vector, calculating 11 the corresponding matrix
Figure BDA0002897701900000038
And recording the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
Figure BDA0002897701900000039
wherein the content of the first and second substances,
Figure BDA00028977019000000310
estimating a noise vector under a model for the compressed sensing signal, at an observation vector
Figure BDA00028977019000000311
And under the condition that the measurement matrix A is known, the sparse vector h can be estimated by the signal estimation modelest。
Further, in the present invention: the target distance and the relative speed are respectively as follows:
Figure BDA00028977019000000312
Figure BDA00028977019000000313
wherein R isestIs the target distance, VestIs the relative velocity.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the method provided by the invention utilizes a complex mode coupling sparse Bayesian learning algorithm and combines a generalized approximate message transfer algorithm, so that the computational complexity can be greatly reduced, the recovery performance of the algorithm can be improved, and the method has good robustness.
Drawings
FIG. 1 is a schematic overall flow chart of an OTFS radar target parameter estimation method based on Bayesian learning according to the present invention;
FIG. 2 is a block diagram of a radar system based on OTFS modulation according to the present invention;
FIG. 3 is a schematic diagram illustrating a comparison of an estimated target distance profile based on the method of the present invention and a conventional matched filtering scheme;
FIG. 4 is a schematic diagram illustrating a comparison of an estimated target relative velocity profile based on the method of the present invention and a conventional matched filtering scheme;
fig. 5 is a schematic diagram of the peak side lobe ratio of the method of the present invention and the conventional matched filtering scheme under different snr and different speed.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
As shown in fig. 1, an overall flow diagram of the OTFS radar target parameter estimation method based on bayesian learning proposed by the present invention specifically includes the following steps,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
specifically, in the OFDM modulation system, all transmitted information symbols are distributed in a time-frequency plane Λ { (nT, M Δ f), N ═ 0, …, N-1, M ═ 0, …, M-1}, where N and M respectively represent the number of OFDM symbols and the number of subcarriers in one frame signal, T is the duration of one OFDM symbol, Δ f is the frequency interval between adjacent subcarriers, and Δ f is 1/T. Therefore, the bandwidth of the OFDM modulation signal is B ═ M Δ f, and the OTFS modulation system is based on the OFDM modulation system, for which the information symbols are distributed in the delay-doppler plane Γ,
Figure BDA0002897701900000041
where k and l are the row and column indices of the delay-doppler plane Γ, respectively. Considering that the doppler shift of the target may be negative, the following operation is performed on k:
Figure BDA0002897701900000051
thus, the maximum measurable range of the target Doppler shift is (- Δ f/2, Δ f/2).
Further, the obtaining of the matrix Y further includes,
step 1-1: suppose there are Z targets in front of the radar, where the distance and relative speed between the ith target and the radar are RiAnd ViThen the round trip delay and Doppler shift of the target are respectively taui＝2Ri/c0And vi＝2Vifc/c0Wherein c is0Is the speed of light, fcIs the center frequency of the carrier. Thus, the discrete radar channel in the delay-doppler domain can be modeled as, and thus a model H (τ, ν) of the discrete radar channel in the delay-doppler domain can be established:
Figure BDA0002897701900000052
wherein τ and ν respectively represent round-trip delay and doppler shift, H [ k ', l' ] represents the target complex gain at doppler tap k 'and delay tap l', if there is no target at this position, the value of H [ k ', l' ] is 0, δ (·) is dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbol X [ k, l ] and the received symbol Y [ k, l ] of the OFDM modulation system can be represented as:
Figure BDA0002897701900000053
wherein the content of the first and second substances,<·>Nand<·>Mrespectively representing modulo-N and modulo-M operations, k and l respectively representing the received symbols Y k, l in the delay-Doppler domain plane]The row and column indices, l 'and k' represent the target delay tap length and doppler shift tap length respectively,w[k,l]is that the variance under the time delay-Doppler domain is sigma2Complex white gaussian noise, phase shift factor alphak,l[k′,l′]The expression of (a) is:
Figure BDA0002897701900000054
where L represents the length of the cyclic prefix.
Step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
specifically, the received symbols Y [ k, l ] and the radar channel matrix H [ k ', l' ] are arranged in rows, and the column vector form Y is obtained as:
Figure BDA0002897701900000055
wherein h is a radar signal vector, and the k 'M + l' element is h [ k ', l']Y is a received symbol vector, w is a noise vector, matrix
Figure BDA0002897701900000061
The (p, q) th element of (a) is:
Figure BDA0002897701900000062
and step 3: calculating effective time delay unit M according to prior informationeffAnd an effective Doppler unit NeffObtaining a simplified estimation model;
the prior information comprises a maximum distance R of the actual targetmaxAnd a maximum relative velocity VmaxThe prior information is determined by the working scene and the application range of the vehicle-mounted radar, is known information, and can reduce the dimensionality of a radar signal-to-reach vector h by utilizing the prior information, and the corresponding effective time delay unit M under the conditioneffAnd an effective Doppler unit NeffRespectively as follows:
Figure BDA0002897701900000063
Figure BDA0002897701900000064
wherein the content of the first and second substances,
Figure BDA0002897701900000065
represents rounding up, c0Is the speed of light, B is the bandwidth of the modulated signal, fcThe center frequency of the carrier.
The dimension of the radar signal arrival vector h is MeffNeffX 1, corresponding, matrix
Figure BDA00028977019000000611
Has dimension of MN × MeffNeffAnd matrix are
Figure BDA00028977019000000612
In the correlation calculation formula (k')NNeed to be replaced by
Figure BDA00028977019000000610
And the value ranges of k 'and l' are respectively [0, Neff-1]And [0, Meff-1]Due to the effective delay unit MeffAnd an effective Doppler unit NeffMuch smaller than M and N, so that the calculation matrix can be significantly reduced
Figure BDA0002897701900000069
And the complexity of subsequent parameter estimation.
And 4, step 4: randomly selecting S rows from the vector y, and calculating to obtain a measurement matrix A under the same row index;
in particular, in the delay-doppler domain, the radar channel vector h usually exhibits sparsity. Therefore, a radar channel vector h can be estimated by adopting a sparse recovery algorithm in the compressed sensing field, and then the distance and the speed value of the target can be calculated. In order to recover the vector with high efficiency, a complex mode coupling sparse Bayesian learning (CPCSBL) algorithm can be used to obtain the maximum posterior probability estimation result. In addition, matrix inversion operation in a complex mode coupling sparse Bayesian learning algorithm can be avoided by combining a Generalized Approximate Message Passing (GAMP) algorithm, so that the calculation complexity is further reduced.
Specifically, the obtaining of the measurement matrix A comprises randomly selecting S rows of the received symbol vector y, wherein the selected S satisfies S < MN, and obtaining a low-dimensional observation vector
Figure BDA0002897701900000066
According to the row index selected by the vector, the corresponding matrix is calculated
Figure BDA0002897701900000067
And recording the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
Figure BDA0002897701900000068
wherein the content of the first and second substances,
Figure BDA0002897701900000071
estimating a noise vector under the model for the compressed sensing signal, corresponding to selecting a vector w under the same row index, at the observation vector
Figure BDA0002897701900000072
And under the condition that the measurement matrix A is known, a sparse vector h can be estimated through the signal estimation model.
And 5: sparse radar channel vector h obtained by using CPCSBL-GAMP algorithmest；
Specifically, a complex mode coupling hierarchical model is constructed, and it is assumed that a vector h obeys the following prior distribution:
Figure BDA0002897701900000073
wherein the content of the first and second substances,
Figure BDA0002897701900000074
parameter h to be estimatednAnd a hyperparameter alphanRespectively represent the nth elements of the vectors h and alpha, beta represents a coupling coefficient, and the value range of beta is [0, 1%]，N(n)Representing four points adjacent to the point (k ', l') in the delay-Doppler plane, i.e.
Figure BDA0002897701900000075
Unlike the traditional SBL framework, the variance of each parameter in the complex mode coupling hierarchical model is not only determined by its corresponding hyper-parameter alphanDetermined by its neighboring hyper-parameter alphaiIt is decided to assign the hyperparametric vector a to obey a gamma distribution, i.e.
Figure BDA0002897701900000076
Where a and b are parameters in the gamma distribution, the hyperparameter α is selected if a suitable value is selected for a and bnCan be arbitrarily large, with variance close to 0. Thus, the parameter h to be estimatednAnd the surrounding points approach 0 with probability 1, so a sparse solution can be obtained. Similar to the above equation, it is assumed that the inverse γ of the noise variance also obeys the gamma distribution, γ ═ σ-2Wherein the gamma distribution parameters are denoted by c and d, respectively.
Based on the complex mode coupled hierarchical model described above, the MAP estimation result of the vector can be generally obtained iteratively through an expectation-maximization algorithm. For step E in the expectation-maximization algorithm, the posterior probability of the vector h, given the hyperparameters α and γ, follows a Gaussian distribution with a mean and a variance, respectively
Figure BDA0002897701900000077
And
Σ＝(γAHA+D)-1
wherein, (.)HWhich represents the transpose of the conjugate,
Figure BDA0002897701900000078
when the iteration process is stopped, the MAP estimation result of the vector h is the mean value μ of the gaussian distribution. Since each iteration process requires the inverse of the matrix to be calculated, the complexity is
Figure BDA0002897701900000079
This complexity is still large in practical applications. Therefore, the invention utilizes the GAMP algorithm with low complexity to approximate the posterior probability distribution of the vector h, thereby designing the high-efficiency CPCSBL-GAMP algorithm which can be directly applied to complex-valued signals, and the pseudo code of the specific realization process is as follows:
Figure BDA0002897701900000081
the parameter epsilon in the end-of-pseudocode condition is a threshold value predetermined by a person skilled in the art, which determines the error margin. In fact, the maximum number of iterations N is also setiterAs another termination condition, the algorithm is guaranteed to terminate after the number of iterations is reached. The 3-1) step to the 3-4) step of the pseudo code is the E step in the expectation-maximization algorithm implemented by the GAMP algorithm, wherein
Figure BDA0002897701900000082
And
Figure BDA0002897701900000083
respectively representing the mean and variance, a, of the nth element of the vector h in the current iterationmnThe (m, n) th element of the measurement matrix A, (-)*Representing a conjugate operation. In addition, a noise-free output variable is defined
Figure BDA0002897701900000084
It obeys an average value of
Figure BDA0002897701900000085
Variance of
Figure BDA0002897701900000086
A Gaussian distribution of wherein
Figure BDA0002897701900000087
Is the mth row of the measurement matrix a. Steps 3-5) of the pseudo code are the updating process of the hyper-parameters α and γ, corresponding to the M steps in the expectation maximization algorithm. Will omeganIs defined as:
Figure BDA0002897701900000088
wherein the content of the first and second substances,
Figure BDA0002897701900000091
representing the expectation of the posterior probability distribution p (h | y, α, γ). In a similar manner, the first and second substrates are,<|ym-zm|2>can be expressed as
Figure BDA0002897701900000092
In the step, the finally obtained vector h is the radar channel vector hest。
Step 6: vector h of radar channelestReverting to matrix form HestFinding out the position of the non-zero element;
specifically, vector H is restored to matrix Hest[k′,l′]And find out matrix Hest[k′,l′]Position of non-zero element (k'est,l′est)。
And 7: and obtaining the estimated values of the target distance and the relative speed.
Specifically, the obtained target distance and the obtained relative speed are respectively as follows:
Figure BDA0002897701900000093
Figure BDA0002897701900000094
wherein R isestIs the target distance, VestIs the relative velocity.
Further, in order to verify the beneficial effects of the method provided by the invention, the following simulation experiment is carried out: simulation parameters of the OTFS-based modulation vehicle-mounted millimeter wave radar communication integrated system in the experiment are shown in the following table 1:
TABLE 1 vehicle-mounted radar communication integrated system parameters
Figure BDA0002897701900000095
Figure BDA0002897701900000101
While QPSK modulation is selected as the communication modulation scheme, the target complex gain is set to 1 for simplicity. In the CPCSBL-gam algorithm, the parameters controlling the gamma distribution of the hyper-parameters α and γ are respectively set as: a is 0.1, b is 10-10；c＝1，d＝10-10。
Target parameter estimation is performed, as shown in FIG. 2, on QPSK modulated communication symbols
Figure BDA0002897701900000102
Distributed in a time delay-Doppler plane, and subjected to inverse finite cosine Fourier transform to obtain a time-frequency domain signal matrix
Figure BDA0002897701900000103
And then carrying out Heisebarg transformation on the time-frequency domain signal to obtain a time domain emission signal s (t). For a radar receiving end, the reverse operation is carried out on a received signal r (t), namely a receiving symbol matrix of a time delay-Doppler domain is obtained through finite symplectic Fourier transform and Virger transform
Figure BDA0002897701900000104
Wherein the relationship between the (k, l) th element of the matrix Y and the respective elements of the matrix X is referred to the above system's relationship between the transmitted symbol and the received symbol.
Processing radar signals, firstly, expanding a matrix Y according to rows to obtain column vectors
Figure BDA0002897701900000105
The relationship between the matrix Y and the vector Y may be expressed as Y ═ vec (Y)T) (ii) a Calculate the matrix
Figure BDA0002897701900000106
And according to the maximum distance R of the targetmaxAnd a maximum relative velocity VmaxCalculating the effective time delay unit MeffAnd an effective Doppler unit Neff(ii) a Then, S rows of the vector y are randomly selected to obtain a low-dimensional observation vector
Figure BDA0002897701900000107
And slave matrix
Figure BDA0002897701900000108
Selecting the same row to obtain a measurement matrix A; then, according to the set parameters, the CPCSBL-GAMP algorithm is utilized to iteratively estimate the radar channel vector
Figure BDA0002897701900000109
Finally by the vector hestRestacking into a matrix
Figure BDA00028977019000001010
And find out HestOf non-zero elements (k'est,l′est) And calculating the distance and relative velocity values of each target.
Referring to fig. 3 and 4, a distance profile and a velocity profile based on a conventional single-target matched filtering scheme and the scheme of the present invention are shown, respectively. Wherein the distance and the relative speed of the object are set to R, respectively90m and V59.45 m/s, the matched filtering scheme is performed by left-multiplying the received symbol vector y by a matrix
Figure BDA00028977019000001011
Thereby directly obtaining the estimation result of the vector h. It can be seen that the distance and relative velocity values of the target can be accurately estimated under both schemes, but the peak-to-side lobe ratio of the method at the position of the estimated target is obviously higher than that of the traditional scheme, because a sparse Bayesian learning algorithm can obtain a more sparse estimation result, in practical application, the interference during multi-target detection can be reduced, thereby realizing higher robustness.
Referring to the schematic diagram of fig. 5, which is a schematic diagram of peak side lobe ratio between the method of the present invention and the conventional matched filtering scheme under different signal-to-noise ratios and different speeds, it can be seen that the PSLR under the method of the present invention is significantly better than the conventional matched filtering scheme under any given signal-to-noise ratio; furthermore, PSLR is independent of the relative velocity of the target when the signal-to-noise ratio is sufficiently large (typically greater than 0dB), and some attenuation of PSLR occurs when the relative velocity of the target increases in the case of low signal-to-noise ratio because the non-zero elements of the vector to be recovered eventually become zero after iterative estimation through sparse bayes learning in the case of low signal-to-noise ratio.
The calculation amount of the method provided by the invention is mainly concentrated in the CPCSBL-GAMP algorithm, and the calculation amount of each iteration of the algorithm is O (SM)effNeff) Therefore, the overall computational complexity of the method of the present invention is at most O (N)iterSMeffNeff) Much less than the computational complexity O (M) of conventional matched filtering schemes2N2)。
It should be noted that the above-mentioned examples only represent some embodiments of the present invention, and the description thereof should not be construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, various modifications can be made without departing from the spirit of the present invention, and these modifications should fall within the scope of the present invention.

Claims (6)

1. An OTFS radar target parameter estimation method based on Bayesian learning is characterized in that: comprises the following steps of (a) carrying out,
step 1: acquiring a matrix Y of received symbols in a delay-Doppler domain;
step 2: expanding the matrix Y according to rows to obtain a column vector form Y of the matrix Y;
and step 3: calculating effective time delay unit M according to prior informationeffAnd an effective Doppler unit NeffObtaining a simplified estimation model;
and 4, step 4: randomly selecting S rows from the vector y, and calculating to obtain a measurement matrix A under the same row index;
and 5: sparse radar channel vector h obtained by using CPCSBL-GAMP algorithmest；
Step 6: vector h of radar channelestReverting to matrix form HestAnd find out matrix Hest[k′,l′]Position of non-zero element (k'est,l′est)；
And 7: and obtaining the estimated values of the target distance and the relative speed.
2. The OTFS radar target parameter estimation method based on bayesian learning of claim 1, wherein: the obtaining of the matrix Y may further comprise,
step 1-1: establishing a discrete radar channel model H (tau, ν) in a time delay-Doppler domain:
Figure FDA0002897701890000011
wherein, M and N respectively represent the number of delay units and the number of Doppler units in a delay-Doppler domain plane, τ and ν respectively represent round-trip delay and Doppler shift, Δ f is a subcarrier frequency interval, T is a time of a symbol, H [ k ', l' ] represents a target complex gain with a Doppler tap of k 'and a delay tap of l', if there is no target at the position, the value of H [ k ', l' ] is 0, τ (·) is a Dirichlet function;
step 1-2: in the delay-doppler domain, the transmitted symbol X [ k, l ] and the received symbol Y [ k, l ] of the OFDM modulation system can be represented as:
Figure FDA0002897701890000012
wherein the content of the first and second substances,<·>Nand<·>Mrespectively representing modulo-N and modulo-M operations, k and l respectively representing the received symbols Y k, l in the delay-Doppler domain plane]The row and column indices of (a) and (b), l 'and k' represent the target delay tap length and the Doppler shift tap length, w [ k, l ], respectively]Is that the variance under the time delay-Doppler domain is sigma2Complex white gaussian noise, phase shift factor alphak,l[k′,l′]The expression of (a) is:
Figure FDA0002897701890000013
where L represents the length of the cyclic prefix.
3. The OTFS radar target parameter estimation method based on bayesian learning according to claim 2, characterized by: the column vector form y is:
Figure FDA0002897701890000021
wherein h is a radar signal vector, and the k 'M + l' element is h [ k ', l']Y is a column vector form of the received symbol, and is a matrix of received symbols Y [ k, l ]]Spread by rows, w is the noise vector, matrix
Figure FDA0002897701890000022
The (p, q) th element of (a) is:
Figure FDA0002897701890000023
4. the OTFS radar target parameter estimation method based on bayesian learning of claim 3, wherein: the prior information comprises a maximum distance R of the actual targetmaxAnd a maximum relative velocity VmaxUnder this condition, the corresponding effective delay unit MeffAnd an effective Doppler unit NeffRespectively as follows:
Figure FDA0002897701890000024
Figure FDA0002897701890000025
wherein the content of the first and second substances,
Figure FDA0002897701890000026
represents rounding up, c0Is the speed of light, B is the bandwidth of the modulated signal, fcThe center frequency of the carrier.
5. The Bayesian learning-based OTFS radar target parameter estimation method of claim 4, wherein: the acquisition of the measurement matrix A comprises the steps of randomly selecting S rows of a received symbol vector y to obtain a low-dimensional observation vector
Figure FDA0002897701890000027
According to the row index selected by the vector, the corresponding matrix is calculated
Figure FDA0002897701890000028
And recording the obtained result as a measurement matrix A, and then the signal estimation model based on compressed sensing is as follows:
Figure FDA0002897701890000029
wherein the content of the first and second substances,
Figure FDA00028977018900000210
estimating a noise vector under a model for the compressed sensing signal, at an observation vector
Figure FDA00028977018900000211
And under the condition that the measurement matrix A is known, the sparse vector h can be estimated by the signal estimation modelest。
6. The OTFS radar target parameter estimation method based on bayesian learning of claim 5, wherein: the target distance and the relative speed are respectively as follows:
Figure FDA00028977018900000212
Figure FDA00028977018900000213
wherein R isestIs the target distance, VestIs the relative velocity.
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