A local optimum-based MIMO radar true or false human body detection method

Abstract

The application discloses a local optimum-based MIMO radar real and false human body detection method and belongs to the field of human body target detection. The application is based on the local optimum detection theory, and the first-order Taylor expansion of a log-likelihood ratio function is calculated, so that the calculation complexity is reduced. Meanwhile, a calculation method of a detection probability corresponding to a known breathing frequency is given. With the aid of the detection probability, the influence of various parameters on the detection performance can be analyzed, and a parameter setting scheme for obtaining better MIMO radar real and false human body detection performance can be provided for technical personnel.

Description

Technical Field

[0001] This invention belongs to the field of human target detection, and specifically relates to a method for detecting weak respiratory movements and a method for calculating the detection probability. Background Technology

[0002] In modern society, the application of real and fake human body detection is increasing in both military and civilian fields. When electromagnetic waves emitted by radar irradiate a human body, a portion of the electromagnetic waves reflected by the surface of the human chest cavity is received by the radar receiving antenna. The main difference between a real and a fake human body lies in whether the target exhibits vital signs such as breathing. Human breathing causes periodic rises and falls in the human chest cavity, thus the time delay and phase in the radar echo corresponding to a real human body change over time, while the time delay and phase in the radar echo corresponding to a fake human body do not change over time.

[0003] Generally, the human body movement caused by breathing is relatively weak, so the detection of real and fake human bodies falls under the category of weak target detection. Weak target detection has always been a key and difficult problem in radar signal processing. MIMO radar has advantages such as waveform diversity, diversity gain, and geometric gain, and has the potential to improve target detection performance. In reference 1 (

[30] XZDai,J.Xu andY.N.Peng.A new method of improving the weak target detection performance based on the MIMO radar,2006CIE International conference on radar,pp.1-4,Oct2006), the authors proposed to use the spatial diversity characteristics of MIMO radar to improve the detection performance of weak targets in strong clutter. In reference 2 (

[32] X. Zhao, D. Xie, D. Jiang and J. Shen. Orthogonal polyphase code design for MIMO radar based on greedy algorithm, 2021 International Conference on Electronic Information Engineering and Computer Science (EIECS), pp. 119-122, Sep 2021), the authors proposed a MIMO radar orthogonal polyphase code waveform design method based on a greedy algorithm to improve the detection capability of weak targets in strong clutter backgrounds. Therefore, this invention applies MIMO radar technology to the problem of detecting real and fake human bodies to obtain detection performance superior to that of traditional radar.

[0004] In solving the problem of weak target or weak signal detection, Locally Optimal Detection (LOD), also known as Local Maximum Potential Test (LMPT), has advantages such as near-optimal detection performance and low mathematical computation. In Reference 3 (Zhu Z, Kay S, Raghavan R. Locally optimal radar waveform design for detecting doubly spread targets in colored noise[J]. IEEE Signal Processing Letters, 2018, 25(6): 833-837), the authors proposed using LOD-based waveform design to maximize detection performance for the problem of detecting doubly spread targets in colored noise. In Reference 4 (Routtenberg T, Concepcion R, Tong L. PMU-based detection of voltage imbalances with tolerance constraints[J]. IEEE Transactions on Power Delivery, 2017, 32(1): 484-494), the authors proposed using Generalized Local Maximum Potential Test (GLMPT) to solve the problem of detecting slight voltage imbalances in three-phase power systems. In reference 5 (Mohammadi A, Ciuonzo D, Khazaee A, et al. Generalized locally most powerful tests for distributed sparse signal detection[J]. IEEE Transactions on Signal and Information Processing over Networks, 2022, 8: 528-542.), the authors designed a generalized local maximum potential detector to improve the computational efficiency of the fusion center for the distributed sparse signal detection problem. This invention considers the situation where important parameters such as the amplitude of chest cavity fluctuations caused by breathing, respiratory frequency, and target reflection coefficient are unknown. It proposes a MIMO radar real / fake human detection method based on local optimum and analyzes the influence of human respiratory parameters and radar system parameters on local optimum detection performance, providing guidance for parameter optimization design. Summary of the Invention

[0005] This invention provides a MIMO radar method for detecting real and fake human bodies under the Neyman-Pearson (NP) criterion, using detection probability as the performance evaluation index. This method incorporates local optimum detection theory, using the subtle chest cavity fluctuations caused by human respiration as the independent variable. The log-likelihood ratio function can be approximated by a first-order Taylor expansion at the point where the independent variable equals zero. Furthermore, for cases where respiratory frequency and reflection coefficient are unknown, the maximum value of the first-order Taylor expansion within their domains is used as the detection statistic; this method is termed the generalized maximum potential test. The proposed method achieves superior detection performance and lower complexity when the difference between real and fake human bodies is small.

[0006] The technical solution of this invention is: a method for detecting real and fake human bodies using MIMO radar based on local optima, the method comprising:

[0007] Step 1: Model the chest cavity rise and fall caused by human respiration as a sine function:

[0008] x(t)=A r sin(2πf r t) (1)

[0009] Among them, A r f is the amplitude of chest rise and fall caused by breathing. r Indicates respiratory rate, and A r and f r All are unknown;

[0010] Step 2: Consider a MIMO radar system with M single-antenna transmitters and N single-antenna receivers. Suppose there is a stationary human target (real or fake) within the range cell to be measured. Let d be the nominal distance at which the signal from the m-th single-antenna transmitter reaches the n-th single-antenna receiver after being reflected from the human target. nm If m = 1, ..., M, and n = 1, ..., N, then the receiver n in kT s The echo signal r received from the real human target at any time n [k] is:

[0011]

[0012] in, E is the low-pass equivalent signal transmitted by transmitter m. m For the transmitted signal energy, s m (·) satisfies the normalization condition. The basic waveform, T s Here, d is the sampling interval, k is the sampling sequence number (k = 1, ..., K), K is the total number of samples, and d is the sampling interval. nm For signal propagation distance, c represents the speed of light, fc It is the carrier frequency, ζ 1nm Let represent the reflection coefficient of a real human target on the nm-th path, and assume ζ. 1nm It is definitely unknown, w n [k] represents spatial and temporal clutter plus noise, and assumes w n [k] follows a mean of zero and a variance of σ. 2 The complex Gaussian distribution;

[0013] Step 3: For a dummy human target that is not breathing, let its reflection coefficient on the nm-th path be ζ. 0nm , and ζ 0nm If it is unknown, then receiver n in kT s The echo signal received at time is:

[0014]

[0015] It is worth noting that the signal propagation distance d corresponding to a real human target 1nm [k] and delay τ 1nm [k] all change with time, while the signal propagation distance d corresponding to the doid human target nm and latency None of them change over time;

[0016] Step 4: Based on equations (2) and (3), the problem of detecting real and fake human bodies can be transformed into a binary composite hypothesis testing problem:

[0017]

[0018] Where H1 hypothesis corresponds to a real human target, and H0 hypothesis corresponds to a fake human target;

[0019] Determination Furthermore, the reflectance coefficients of real and fake human targets are equal, and let ζ be... 1nm =ζ 0nm =ζ represents the unknown parameter;

[0020] The echo signal vector received by the receiver is:

[0021]

[0022] in This indicates transpose; therefore, the binary composite hypothesis problem of real and fake human bodies is:

[0023]

[0024] Among them 1 NM Describe an NM×1 dimensional matrix of all 1s, where i = 0 or 1.

[0025] S i =Diag{S i1 ,S i2 ,..,S iN} (7)

[0026] S i Represents the echo signal matrix.

[0027]

[0028]

[0029] The clutter plus noise vector is:

[0030]

[0031] in

[0032] Chest rise and fall amplitude A r respiratory rate f r The reflection coefficient ζ are both unknown parameters of the real scene. The composite hypothesis testing problem described by equation (6) can be rewritten in parametric form as follows:

[0033]

[0034] Where A under the H1 assumption r It is a one-sided unknown parameter;

[0035] The log-likelihood ratio function is:

[0036]

[0037] Among them, 1 NM Let N be an identity matrix of dimension NM;

[0038] Step 5: For f r For any value of ζ, in A r In the neighborhood of 0, the Taylor series of the log-likelihood ratio function (12) is:

[0039]

[0040] L(rζ,A r =0,f r ) represents L(r; ζ, A) r ,f r In A r The value at the position = 0, L(r; ζ, A) represents... r ,f r In A r =0 points about Ar The first partial derivative of A, due to the faintness of human respiration, i.e., A r Approaching 0, higher-order term o(A) r ) can be ignored, therefore, for f r For any value of ζ, A r The LMPT detection statistic within the =0 neighborhood is:

[0041]

[0042] Where the definition

[0043] T LMPT (r;ζ,f r ) is f r The function of f and ζ, the generalized local maximum potential test GLMPT is to use f as a function of ζ. r T within the two-dimensional domain of ζ LMPT (r;ζ,f r The maximum value of f is used as a new detection statistic; for any f r , making T LMPT (r;ζ,f r The largest value of ζ for

[0044]

[0045] use Replace T LMPT (r;ζ,f r From ζ in ) we can obtain

[0046]

[0047] Where |·| represents the modulus of the complex number; thus, we can obtain f r The estimated value for

[0048]

[0049] Therefore, the simplified GLMPT detection statistic is

[0050]

[0051] and define

[0052] Consider f r Given the ideal situation, at this time Both a and b become known, and the corresponding GLMPT detection statistics are:

[0053]

[0054] And T under the assumptions of dummy H0 and real person H1 KGLMPT (r) all follow a non-central chi-square distribution with 2 degrees of freedom, as follows:

[0055]

[0056]

[0057] in This indicates that the distribution follows a noncentral chi-square distribution with 2 degrees of freedom and a noncentral parameter λ.

[0058] When f r Given that a > 0, the simplified GLMPT detector becomes:

[0059]

[0060] in It is the first judgment threshold;

[0061] When f r Given that a < 0, the simplified GLMPT detector is:

[0062]

[0063] in It is the second judgment threshold;

[0064] Step 6: Select the detection probability to evaluate the performance of the MIMO radar human target GLMPT detector; based on the Neyman-Pearson NP criterion, the decision threshold γ GLMPT Based on false alarm probability Definition:

[0065]

[0066] This allows us to solve for the detection probability.

[0067]

[0068] in, This indicates that the probability density function is in the interval The points on the top

[0069] When f r Given that a > 0, the false alarm probability of the GLMPT detector shown in equation (22) is:

[0070]

[0071] Where Q(x,y) is the Marcum Q function. I0(·) represents the 0th-order modified Bessel function of the first kind, and the detection threshold is obtained. for:

[0072]

[0073] Q -1 (x,·) is the inverse function of Q(x,y), thus the detection probability is:

[0074]

[0075] Similarly, when f r Given that a < 0, the false alarm probability of the GLMPT detector shown in equation (23) is:

[0076]

[0077] Determine the judgment threshold for:

[0078]

[0079] Therefore, the detection probability is:

[0080]

[0081] This invention is based on the theory of local optimal detection and reduces computational complexity by calculating the first-order Taylor expansion of the log-likelihood ratio function. Simultaneously, it provides a method for calculating the detection probability corresponding to a known respiratory rate. Using this detection probability, the impact of various parameters on detection performance can be analyzed, providing technicians with parameter setting schemes to achieve better MIMO radar performance in detecting real and fake human bodies. Attached Figure Description

[0082] Figure 1 The graph shows the detection probability as a function of SCNR when M=2 and N=2.

[0083] Figure 2 For M=2, the effect of the number of receiving antennas on the detection probability;

[0084] Figure 3 To detect the change curve of probability with the amplitude of chest cavity rise and fall caused by respiration;

[0085] Figure 4 To detect the change curve of probability as a function of respiratory rate;

[0086] Figure 5 The curve shows the change in detection probability as a function of carrier frequency. Detailed Implementation

[0087] Human respiration causes periodic, subtle undulations on the surface of the chest cavity, which can be approximated as a sinusoidal vibration model.

[0088] x(t)=A r sin(2πf r t) (32)

[0089] Where A r f is the amplitude of chest rise and fall caused by breathing. r Let A represent the respiratory rate, and assume A... r and f r Both are known but unknown.

[0090] Consider a MIMO radar system with M single-antenna transmitters and N single-antenna receivers. The low-pass equivalent representation of the signal transmitted by the m-th (m = 1, ..., M) transmitter is: Where E m It is the transmitted signal energy, T s The sampling interval is k (k = 1, ..., K), the sampling number is k, and the total number of samples is K. The waveform is then normalized.

[0091] Assume there is a stationary human target (real or fake) within the range measurement cell. Let d be the nominal distance at which the signal from the m-th transmitter reaches the n-th (n = 1, ..., N) receiver after being reflected from the human target. nm For a real human target that is breathing, the total time delay from transmitter m to receiver n is:

[0092]

[0093] Where c represents the speed of light, d 1nm (t)=d nm +2A r sin(2πf r t) represents the total propagation distance of the transmitted signal on the nm-th path after reflection from a real human target. Then, the receiver n in kT... s The echo signal received from the real human target at any given time can be written as:

[0094]

[0095] Where d 1nm [k] and τ 1nm [k] are respectively d 1nm (t) and τ 1nm (t) at kT s The sampled value at time f c It is the carrier frequency, ζ 1nmLet represent the reflection coefficient of a real human target on the nm-th path, and assume ζ. 1nm It is definitely unknown, w n [k] represents spatial and temporal clutter plus noise, and assumes w n [k] follows a mean of zero and a variance of σ. 2 The complex Gaussian distribution.

[0096] For a non-breathing dummy human target, assume its reflection coefficient on the nm-th path is ζ. 0nm , and ζ 0nm If it is a known unknown, then receiver n in kT s The echo signal received at any given time is

[0097]

[0098] Considering that the nominal distance of the radar transmission and reception path is much greater than the rise and fall of the human chest cavity (d), nm >>2A r sin(2πf r kT s It can be approximated as ), Meanwhile, considering that the reflectance coefficients of real and fake human targets are approximately equal and difficult to distinguish, to simplify the analysis, we assume ζ 1nm =ζ 0nm =ζ represents the unknown parameter.

[0099] Let the echo signal vector of receiver n be...

[0100]

[0101] in Let represent the transpose. Then the receive vectors of all receivers can be written as:

[0102]

[0103] The problem of detecting real and fake human bodies based on the presence or absence of respiratory movements can then be transformed into a binary composite hypothesis testing problem.

[0104]

[0105] Among them 1 NM Describe an NM×1 dimensional matrix of all 1s, where i = 0 or 1.

[0106] S i =Diag{S i1 ,S i2 ,..,S iN} (39)

[0107] Represents the echo signal matrix.

[0108]

[0109]

[0110] The clutter plus noise vector is

[0111]

[0112] in From equations (38) to (42), it can be seen that the main difference between the two hypotheses corresponding to the real and fake human targets lies in the amplitude of chest cavity rise and fall A caused by breathing. r The difference in the value of A. This article considers the amplitude of chest cavity movement A. r respiratory rate f r The reflection coefficient ζ are real-world scenarios where unknown parameters are determined. The composite hypothesis testing problem described by equation (38) can be rewritten in parametric form as follows:

[0113]

[0114] Since human respiration is usually weak, A under hypothesis H1 r It is a one-sided unknown parameter that tends to 0, and the difference between the H1 and H0 hypotheses may be small.

[0115] According to equation (38), the likelihood functions under the H1 and H0 hypotheses can be expressed as follows:

[0116]

[0117]

[0118] Furthermore, the log-likelihood ratio function can be expressed as:

[0119]

[0120] For f r For any value of ζ, in A r In the neighborhood of 0, the log-likelihood ratio function (46) can be written using a Taylor series as follows:

[0121]

[0122] Because A r Approaching 0, higher-order term o(A) r ) can be ignored, and thus we can obtain So regarding A r The LMPT detector can be represented as

[0123]

[0124] A again r >0, the LMPT detector can be further simplified to

[0125]

[0126] Therefore, for f r For any value of ζ, A r The LMPT detection statistic within the =0 neighborhood is

[0127]

[0128] in

[0129] Because of T LMPT (r;ζ,f r ) is f r The function of ζ can be used in f r T within the two-dimensional domain of ζ LMPT (r;ζ,f r The maximum value of ) is used as a new detection statistic, and this method is called GLMPT.

[0130] The following solution is used to make T LMPT (r;ζ,f r Maximize ζ and f r For any f r Calculate T LMPT (r;ζ,f r Take the partial derivative with respect to ζ and set it equal to 0.

[0131]

[0132] Then make T LMPT (r;ζ,f r The largest value of ζ for

[0133]

[0134] use Replace T LMPT (r;ζ,f r From ζ in ) we can obtain

[0135]

[0136] Where |·| represents the modulus of the complex number. Therefore, we can obtain f. r The estimated value for

[0137]

[0138] This expression has no closed-form solution. It needs to be solved using numerical methods.

[0139] Due to σ 2 It is a constant that does not affect the likelihood ratio test; the GLMPT test statistic can be simplified to:

[0140]

[0141] Therefore, the MIMO radar real / fake human body GLMPT detector can be represented as

[0142]

[0143] Among them, the judgment threshold γ GLMPT Constraint P can be given according to the NP criterion. FA Find ≤α.

[0144] Next, consider f. r The known ideal situation. When f r When known, the GLMPT detector based on equation (55) can be expressed as:

[0145]

[0146] in It is the judgment threshold. r Given, then Given that a and b are known, respectively, detector (57) can be further simplified by defining a new detection statistic T. KGLMPT (r)

[0147]

[0148] When a > 0, the simplified GLMPT detector becomes

[0149]

[0150] in It is the corresponding judgment threshold.

[0151] When a < 0 The simplified GLMPT detector then becomes

[0152]

[0153] in It is the corresponding judgment threshold.

[0154] Under both H0 and H1 assumptions, r follows a covariance matrix σ. 2 The complex Gaussian distribution of I, therefore under the assumptions of H0 and H1 All are complex Gaussian variables with a variance of 2, and their specific distributions are as follows:

[0155]

[0156]

[0157] Furthermore, we can obtain T under the assumptions of H0 and H1. KGLMPT (r) all follow a non-central chi-square distribution with 2 degrees of freedom, which can be specifically expressed as

[0158]

[0159]

[0160] in This indicates that the distribution follows a noncentral chi-square distribution with 2 degrees of freedom and a noncentral parameter λ.

[0161] The detection probability is used as a performance evaluation metric for the MIMO radar human target GLMPT detector. The NP criterion is adopted, based on the false alarm probability. Definition

[0162]

[0163] Solving for the decision threshold γ GLMPT Then the detection probability can be calculated.

[0164]

[0165] When f r Given that T is assumed by H1 and H0 KGLMPT (r) all follow a non-central chi-square distribution with 2 degrees of freedom, and according to equations (20) and (21), the probability density functions under the assumptions H1 and H0 can be expressed as follows:

[0166]

[0167]

[0168] Where I0(·) represents the 0th order modified Bessel function of the first kind.

[0169] Based on equations (67) and (68), when f r Given that a > 0, the false alarm probability of the GLMPT detector (22) is:

[0170]

[0171] Where Q(x,y) is the Marcum Q function. Therefore, the detection threshold can be obtained. for

[0172]

[0173] Q -1 (x,·) is the inverse function of Q(x,y). Therefore, the detection probability can be calculated as follows:

[0174]

[0175] Similarly, when f r Given that a < 0, the false alarm probability of the GLMPT detector (60) is:

[0176]

[0177] The decision threshold can be derived. for

[0178]

[0179] Therefore, the detection probability can be written as

[0180]

[0181] The effectiveness and feasibility of the method of the present invention will be illustrated through simulation. In the simulation, the low-pass equivalent signal selected for the m-th transmitter is...

[0182]

[0183] Where T = 5s is the signal duration, f Δ =100Hz is the frequency interval between two adjacent transmitted signals. The sampling frequency is set to f. s =800Hz, carrier frequency is f c =30GHz, the energy of the signals transmitted by each transmitter is the same: E1 = ... = E M =E / M, E=10 2 In a two-dimensional Cartesian coordinate system, assume that all single-antenna transmitters and receivers are 10m away from the reference point (0,0)m, and that the transmitters are uniformly distributed on arcs with angles [π / 5, 5π / 18], and the receivers are uniformly distributed on arcs with angles [π / 6, π / 3]. Therefore, the position angles of the m-th transmitter and the n-th receiver are respectively...

[0184]

[0185]

[0186] Assume the location of the human target to be identified as real or fake is (0,0)m, the reflection coefficient ζ=0.1, and the amplitude of chest rise and fall A caused by the breathing of the real human target. r =1.5cm, respiratory rate is f r =0.3Hz. The signal-to-clutter-plus noise ratio (SCNR) is defined as...

[0187]

[0188] like Figure 1 The figure shows the curve of the detection probability of the GLMPT detector as a function of SCNR when M=2 and N=2. The figure considers ζ and A. r and f r Both determine the unknown true situation and ζ, A r Determine the unknown and f r The known ideal situation. As can be seen from the figure, the detection probability of the GLMPT detector increases with increasing SCNR in both cases, and the curves for both cases show two SCNR thresholds, one low and one high. r It is known that the corresponding SCNR left and right thresholds are both less than f. r The corresponding left and right thresholds for SCNR are unknown, which indicates that compared to f r Unknown, f r This situation is known to allow the GLMPT detector to effectively detect real and fake human bodies at lower SCNR, and also to achieve near-error-free detection of real and fake human bodies at even lower SCNR. Meanwhile, given the false alarm probability and the SCNR within the left and right threshold intervals, f r The detection probability under known conditions is greater than f r Detection probability under unknown conditions. The above phenomenon indicates that increasing the number of unknown parameters leads to a loss of detection performance in the GLMPT detector. Although f r Given and f r The unknown parameters correspond to different detection performances of the GLMPT detector, but the detection probability of the GLMPT detector changes with SCNR and false alarm probability in the same way. This indicates that the number of unknown parameters affects the detection performance of the GLMPT detector, but does not affect the overall trend of its detection performance. Therefore, f can be considered as... r The known analysis results are extended to f r Unknown situation.

[0189] like Figure 2 The figure shows f rThe graph compares the detection probability of the GLMPT detector with SCNR when the number of transmitting antennas M=2 and the number of receiving antennas N=8, N=14, and N=20. As shown in the graph, for a given false alarm probability and SCNR, the number of receiving antennas corresponding to the decreasing detection probability is: N=20, N=14, and N=8. This indicates that increasing the number of receiving antennas can improve the detection performance of the GLMPT detector.

[0190] like Figure 3 The figure shows the detection probability of the GLMPT detector as a function of the amplitude of chest cavity fluctuation A caused by respiration. r The curve shows the change in SCNR, where SCNR = -10dB, M = 2, and N = 2. The graph shows that the detection performance of the GLMPT detector changes with A. r The increase is due to the increase of A, and A r Even a slight increase in the carrier frequency can lead to a significant increase in the detection probability, because a larger carrier frequency amplifies A. r The impact on signal phase increases the degree of difference between the two hypotheses, making it easier for the GLMPT detector to capture the respiratory information of real human targets from the echo signal, and its detection performance is improved accordingly.

[0191] like Figure 4 The figure shows the detection probability of the GLMPT detector as a function of respiratory rate f. r The curve shows the change, where SCNR = -10dB, M = 2, and N = 2. As can be seen from the graph, the detection probability of the GLMPT detector changes with f. r The increase in respiratory rate leads to a higher limit, which is because an increase in respiratory rate means that the changes in chest cavity movement caused by human breathing are faster. Correspondingly, the difference between the two hypotheses also increases, and the GLMPT detector is more likely to capture the respiratory information of the real human target from the echo signal, thus improving its detection performance.

[0192] like Figure 5 The figure shows the detection probability of the GLMPT detector as a function of carrier frequency f. c The curve shows the change, where SCNR = -10dB, M = 2, and N = 2. As can be seen from the graph, from f... c Starting at 100MHz, as the carrier frequency increases, the detection probability of the GLMPT detector initially remains approximately equal to the false alarm probability. Then, the detection probability gradually increases to 1 and remains constant. When the carrier frequency exceeds 3.1GHz, the detection probability of the GLMPT detector decreases with the increase of the carrier frequency until it approaches 0 and then remains essentially constant.

Claims

1. A method for detecting real and fake human bodies using MIMO radar based on local optima, the method comprising: Step 1: Model the chest cavity rise and fall caused by human respiration as a sine function: x(t)=A r sin(2πf r t) (1) Among them, A r f is the amplitude of chest rise and fall caused by breathing. r Indicates respiratory rate, and A r and f r All are unknown; Step 2: Consider a MIMO radar system with M single-antenna transmitters and N single-antenna receivers. Suppose there is a stationary human target (real or fake) within the range cell to be measured. Let d be the nominal distance at which the signal from the m-th single-antenna transmitter reaches the n-th single-antenna receiver after being reflected from the human target. nm If m = 1, ..., M, and n = 1, ..., N, then the receiver n in kT s The echo signal r received from the real human target at any time n [k] is: in, E is the low-pass equivalent signal transmitted by transmitter m. m For the transmitted signal energy, s m (·) satisfies the normalization condition. The basic waveform, T s Here, d is the sampling interval, k is the sampling sequence number (k = 1, ..., K), K is the total number of samples, and d is the sampling interval. nm For signal propagation distance, c represents the speed of light, f c It is the carrier frequency, ζ 1nm Let represent the reflection coefficient of a real human target on the nm-th path, and assume ζ. 1nm It is definitely unknown, w n [k] represents spatial and temporal clutter plus noise, and assumes w n [k] follows a mean of zero and a variance of σ. 2 The complex Gaussian distribution; Step 3: For a dummy human target that is not breathing, let its reflection coefficient on the nm-th path be ζ. 0nm , and ζ 0nm If it is unknown, then receiver n in kT s The echo signal received at time is: It is worth noting that the signal propagation distance d corresponding to a real human target 1nm [k] and delay τ 1nm [k] all change with time, while the signal propagation distance d corresponding to the doid human target nm and latency None of them change over time; Step 4: Based on equations (2) and (3), the problem of detecting real and fake human bodies can be transformed into a binary composite hypothesis testing problem: Where H1 hypothesis corresponds to a real human target, and H0 hypothesis corresponds to a fake human target; Determination Furthermore, the reflectance coefficients of real and fake human targets are equal, and let ζ be... 1nm =ζ 0nm =ζ represents the unknown parameter; The echo signal vector received by the receiver is: in This indicates transpose; therefore, the binary composite hypothesis problem of real and fake human bodies is: Among them 1 NM Describe an NM×1 dimensional matrix of all 1s, where i = 0 or 1. S i =Diag{S i1 ,S i2 ,..,S iN } (7) S i Represents the echo signal matrix. The clutter plus noise vector is: in Chest rise and fall amplitude A r respiratory rate f r The reflection coefficient ζ are both unknown parameters of the real scene. The composite hypothesis testing problem described by equation (6) can be rewritten in parametric form as follows: A under the H1 assumption r It is a one-sided unknown parameter; The log-likelihood ratio function is: Among them, 1 NM Let N be an identity matrix of dimension NM; Step 5: For f r For any value of ζ, in A r In the neighborhood of 0, the Taylor series of the log-likelihood ratio function (12) is: L(r|ζ,A r =0,f r ) represents L(r; ζ, A) r ,f r In A r The value at the position = 0, L(r; ζ, A) represents... r ,f r In A r =0 points about A r The first partial derivative of A, due to the faintness of human respiration, i.e., A r Approaching 0, higher-order term o(A) r ) can be ignored, therefore, for f r For any value of ζ, A r The LMPT detection statistic within the =0 neighborhood is: Where the definition T LMPT (r;ζ,f r ) is f r The function of f and ζ, the generalized local maximum potential test GLMPT is to use f as a function of ζ. r T within the two-dimensional domain of ζ LMPT (r;ζ,f r The maximum value of f is used as a new detection statistic; for any f r , making T LMPT (r;ζ,f r The largest value of ζ for use Replace T LMPT (r;ζ,f r From ζ in ) we can obtain Where |·| represents the modulus of the complex number; thus, we can obtain f r The estimated value for Therefore, the simplified GLMPT detection statistic is and define Consider f r Given the ideal situation, at this time Both a and b become known, and the corresponding GLMPT detection statistics are: Furthermore, under the assumptions of dummy H0 and real person H1, T KGLMPT (r) all follow a non-central chi-square distribution with 2 degrees of freedom, as follows: in This indicates that the distribution follows a noncentral chi-square distribution with 2 degrees of freedom and a noncentral parameter λ. When f r Given that a > 0, the simplified GLMPT detector becomes: in It is the first judgment threshold; When f r Given that a < 0, the simplified GLMPT detector is: in It is the second judgment threshold; Step 6: Select the detection probability to evaluate the performance of the MIMO radar human target GLMPT detector; based on the Neyman-Pearson NP criterion, the decision threshold γ GLMPT Based on false alarm probability Definition: This allows us to solve for the detection probability. in, This indicates that the probability density function is in the interval The points on the top When f r Given that a > 0, the false alarm probability of the GLMPT detector shown in equation (22) is: Where Q(x,y) is the Marcum Q function. I0(·) represents the 0th-order modified Bessel function of the first kind, and the detection threshold is obtained. for: Q -1 (x,·) is the inverse function of Q(x,y), thus the detection probability is: Similarly, when f r Given that a < 0, the false alarm probability of the GLMPT detector shown in equation (23) is: Determine the judgment threshold for: Therefore, the detection probability is:

Images