A method for calculating LFMCW waveform of MIMO radar for detecting heart beat and breathing frequency

Abstract

The application provides a MIMO radar LFMCW waveform calculation method for detecting heartbeat and respiration frequency, belongs to the technical field of radar heartbeat and respiration measurement, and relates to the calculation of a Cramer-Rao bound (CRB) of a LFMCW radar heartbeat and respiration frequency estimation. The LFMCW radar waveform parameters at the time of minimum heartbeat and respiration frequency estimation CRB are calculated by solving the established mathematical model. Simulation experiments prove that the transmission of the LFMCW waveform obtained by using the waveform parameters of the optimization algorithm provided by the application can improve the estimation performance of the heartbeat and respiration frequency. Since the method takes the minimum heartbeat and respiration frequency estimation CRB as the objective function, according to the physical meaning of the CRB, the CRB describes the optimal performance of an unbiased estimation, and provides a strict bound for parameter estimation under a high signal-to-noise ratio, so that the LFMCW waveform setting designed by the method can improve the estimation performance of the heartbeat and respiration frequency.

Description

Technical Field

[0001] This invention belongs to the field of radar measurement of heart rate and respiration frequency. It relates to the calculation of the Cramer-Rao bound (CRB) for estimating heart rate and respiration frequency in LFMCW radar, modeling the LFMCW waveform design optimization problem, and solving the optimization problem using a genetic algorithm (GA) and a sequential quadratic optimization algorithm (SQP). The LFMCW waveform settings designed by this method can improve the estimation performance of heart rate and respiration frequency. Background Technology

[0002] With the continuous development of communication and sensor technologies, intelligent detection devices are gradually appearing in people's daily lives. Furthermore, with the advancement of sensing technology, radar has become increasingly smaller and more portable, expanding its application from military to civilian use, which has made it possible to use radar to detect life signals.

[0003] However, current technologies mainly focus on processing radar echo signals, with relatively little research on radar waveforms used for detecting heartbeats and respiration. Yet, the study of radar waveforms is a crucial area of ​​research in the radar field. MIMO radar employs multiple antennas to transmit various waveforms, allowing for dynamic adjustment of waveform parameters according to different mission requirements. This greater flexibility and potential for improving detection performance have been demonstrated in several studies. Reference 1 (He Q, Lehmann NH, Blum RS, et al. “MIMO radar application to moving target detection in homogenous clutter,” in IEEE Transactions on Aerospace and Electronic Systems, 2010, 1290-1301.) improves the accuracy of velocity estimation for slow-moving targets through waveform design. Reference 2 (Lehmann, NH, Haimovich, AM, Blum RS, et al. “High resolution capabilities of MIMO radar,” in 2006 Fortieth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2006: 25-30.) improves the accuracy of range-based target localization through radar waveform design. Reference 3 (Robey FC, Coutts S, Weikle D, et al. “MIMO radar theory and experimental results,” in Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2006: 25-30.) improves the accuracy of range-based target localization through radar waveform design. Grove, CA, USA, 2004: 300-304.) Improved the accuracy of target angle estimation through radar waveform design. Summary of the Invention

[0004] The technical problem addressed by this invention in response to the shortcomings of the prior art is to propose a mathematical model for MIMO radar waveform design that considers radar hardware limitations and experimental principles. By solving the established mathematical model, the LFMCW radar waveform parameters are calculated when estimating the minimum heart rate and respiratory rate (CRB).

[0005] This invention estimates the human heart rate and respiratory rate (CRB) using the LFMCW intermediate frequency signal. The CRB is used as the objective function, and the radar hardware is constrained by the feasible region of waveform parameters. Considering the working principle of radar detection of heart rate and respiratory rate, a nonlinear optimization problem expression is established. The optimization problem is solved using both GA and SQP methods to obtain the LFMCW waveform parameters with the minimum CRB. Therefore, this invention provides a method for calculating the LFMCW waveform of a MIMO radar for detecting heart rate and respiratory rate. This method includes:

[0006] Step 1: In the transmit segment of the MIMO radar system, the m-th transmit antenna transmits a chirp signal s. ch,m (t) is represented as:

[0007]

[0008] Among them, E m T represents the energy of the chirp signal transmitted by the m-th transmitting antenna. ch f represents the chirp signal width. c,m μ represents the starting frequency at which the m-th transmitting antenna transmits the chirp signal. m The frequency modulation slope of the chirp signal transmitted by the m-th transmitting antenna is represented by T; the time interval between adjacent chirps is T. rest This indicates that no signal is transmitted during this period to ensure that the initial phase of the next chirp is known; assume that different transmitted signals satisfy the following formula, i.e., condition 1:

[0009]

[0010] s ch,m' * (·) represents the conjugate of the signal transmitted by the m'-th transmitting antenna, τ m'n (t) represents the time delay under the m'n path, c m represents a constant, m and m' represent the transmitting antenna number, represents two different transmitting antennas, and n represents the receiving antenna number;

[0011] And the transmitted signals from different antennas are orthogonal to each other, i.e., condition 2:

[0012]

[0013] τ represents a constant. mn (t) represents the echo delay on the mn path, which contains heartbeat and breathing information;

[0014] Step 2: At the receiver of the MIMO radar system, the received signal r of the nth radar receiving antenna ch,n(t) is represented as:

[0015]

[0016] Where, α mn The complex reflection coefficient on the mn path is represented by μ, the frequency modulation slope of the LFM signal is represented by μ, and the number of transmit antennas in the MIMO system is represented by M. Let σ be the clutter noise of the nth receiver at time t, with a mean of zero and a variance of σ. 2 Both n and time t are independent and identically distributed complex Gaussian white noise;

[0017] Step 3: The intermediate frequency signal y after mixing and filtering ch,mn (t) is represented as

[0018]

[0019] r * ch,n (t) represents the conjugate of the signal received by the nth receiving antenna, E m' α represents the energy of the signal transmitted by the m'-th transmitting antenna. m'n Let s represent the reflection coefficient at the m'n path. ch,m' The conjugate of the signal transmitted by the m'-th transmitting antenna;

[0020] Since the transmitted signal satisfies conditions 1 and 2 above, the above equation can be expanded as follows:

[0021]

[0022] in, because s ch,m (t) is a known signal, so w mn (t) also follows a Gaussian distribution with a mean of zero and a variance of σ. mn 2 =s ch,m (t) 2 σ 2 =E m σ 2 , represented as CN~(0,σ 2 )

[0023] Step 4: Considering that the LFMCW signal has Q frames and each frame has P chirps, treat these chirp signals as a time-domain shift of a single chirp signal, and calculate the intermediate frequency signal y after the LFMCW signal has been mixed and filtered. mn,pq (t) is:

[0024]

[0025] Among them, Tfr T represents the frame width. chr Indicates the width of chirp, y ch,mn (·) indicates that the m-th transmitted signal is connected to the n-th receiver.

[0026] The intermediate frequency signal obtained after the received signal is mixed and filtered;

[0027]

[0028] x mn (t)=x r,mn (t)+x h,mn (t),

[0029]

[0030] A r,mn A represents the amplitude of thoracic cavity displacement caused by respiration along the mn pathway. h,mn f represents the amplitude of chest cavity displacement caused by heartbeat along the mn path. c,m,pq The starting frequency of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna is μ. m,pq d represents the frequency modulation slope of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna; 0,mn Let x be the distance between the human body and the radar along path mn. mn (t) Thoracic displacement as a function of time, x r,mn (t) represents the displacement of the thoracic cavity caused by human respiration, x h,mn (t) represents the displacement of the chest cavity caused by the human heartbeat, f r f represents respiratory rate. h The heart rate is represented by the initial phase, which is represented by the following: and

[0031] Step 5: At the receiver of the MIMO radar system, the LFMCW radar transmits a series of chirp signals, and the radar observation vector... Represented as:

[0032]

[0033] Let y be one of the elements. mn,pq ;

[0034] y mn,pq =[y mn,pq [1,1,1],...,y mn,pq [K 11 ,1,1],...,y mn,pq [K p1 ,P1,1],...,y mn,pq[K PQ ,P Q ,Q]],

[0035] K PQ P represents the number of sampling points for the P-th chirp in the Q-th frame. Q This represents the number of chirps in the Q-th frame;

[0036] Step 6: Likelihood function of LFMCW radar observation vector Represented as:

[0037]

[0038] in, Let θ represent the intermediate frequency signal vector, exp{·} represent the exponential operation, M represent the number of transmit antennas, and N represent the number of receive antennas.

[0039]

[0040] k pq p represents the k-th sample point of the p-th chirp in the q-th frame. q This represents the p-th chirp of a q-frame, indicated by the superscript. Indicates conjugate transpose, α MN,R α represents the real part of the reflection coefficient along the MN path. MN,I T represents the imaginary part of the reflection coefficient along the MN path. s Indicates the sampling interval;

[0041] Step 7: Log-likelihood function of LFMCW radar observation vector Represented as:

[0042]

[0043] K qp k represents the number of sampling points for the p-th chirp in the q-th frame. qp This represents the k-th sample point of the p-th chirp in the q-th frame;

[0044] Step 8: ML estimation of the unknown parameter vector θ for:

[0045]

[0046] Step 9: Since p(y; θ) is related to the time delay τ mn [k pq The function p(y; θ) represents the likelihood function of the LFMCW radar observation vector, y represents the intermediate frequency signal vector, and τ represents the IF signal vector. mn [·] represents the echo delay on the mn path; therefore, an intermediate variable Θ is introduced:

[0047] Θ=[τ 11 [1,1,1],...,τ 11 [K 11 ,1,1],...,τ 11 [K p1 ,P1,1],...,τ 11 [K PQ ,P Q ,Q],...,τ 1N [K PQ ,P Q ,Q]...τ 11 [1,1,1],...,τ 11 [K 11 ,1,1],...,τ 11 [K p1 ,P1,1],...,τ MN [K PQ ,P Q ,Q],...,τ 1N [K PQ ,P Q ,Q]α 11Re ,α 12Re ,...,α MNRe ,α 11Im ,α 12Im ,...,α MNIm ] T

[0048] Re denotes taking the real part, and Im denotes taking the imaginary part;

[0049] Step 10: Define the Fisher information matrix J(θ):

[0050]

[0051] Step 11: Calculate the gradient of Θ with respect to θ

[0052]

[0053] in,

[0054]

[0055] This indicates the initial phase of the chest cavity displacement caused by the heartbeat. Let θ represent the initial phase of the thoracic cavity displacement caused by respiration, and c represent the speed of light. Step 12: Calculate the Fisher information matrix J(θ), from which CRB can be obtained. CRB is represented as...

[0056]

[0057] The final estimated heart rate CRB is: Respiratory rate is estimated as CRB is

[0058] Step 13: Establish a mathematical model for LFMCW radar waveform design:

[0059]

[0060] stf c,pq,lb ≤f c,pq ≤f c,pq,ub

[0061] μ pq,lb ≤μ pq ≤μ pq,ub

[0062] T ch,pq,lb ≤T ch,pq ≤T ch,pq,ub

[0063]

[0064] μ pq T ch,pq <f c,pq,ub -f c,pq,lb

[0065] Where v1 is the CRB weight for heart rate estimation, v2 is the CRB weight for respiratory rate estimation, and μ pq The frequency modulation slope of the p-th chirp signal in the q-th frame is represented by f, CO_CRB represents the weighted sum of the heart rate and respiratory rate estimates CRB, and f c,pq f represents the starting frequency of the p-th chirp signal in the q-th frame. c,pq,lb f represents the lower bound of the starting frequency of the p-th chirp signal in the q-th frame. c,pq,ub This represents the upper bound of the starting frequency of the p-th chirp signal in the q-th frame, μ. pq,lb μ represents the lower bound of the frequency modulation slope of the p-th chirp signal in the q-th frame. pq,ub T represents the upper bound of the frequency modulation slope of the p-th chirp signal in the q-th frame. ch,pq,lb T represents the lower bound of the time width of the p-th chirp signal in the q-th frame. ch,pq T represents the time width of the p-th chirp signal in the q-th frame. ch,pq,ub This represents the upper bound of the time width of the p-th chirp signal in the q-th frame, [·]. 1,1 express The first row and first column of the matrix, [·] 2,2 express In the second row and second column of the matrix, according to the radar speed measurement principle, when the radar measures speed, the target motion needs to satisfy uniform acceleration motion within one frame of the signal; the chest cavity motion caused by heartbeat and breathing is regarded as uniformly accelerated linear motion, where a is the acceleration of uniformly accelerated linear motion;

[0066] Step 14: Calculate the LFMCW waveform parameter vector Ψ, represented as:

[0067]

[0068] in,

[0069] f represents the waveform parameter vector of the LFMCW signal transmitted by the m-th transmitting antenna. c,m =[f c,m,11 ,f c,m,21 ,...,f c,m,PQ ] represents the initial frequency vector, which is a 1×PQ dimensional vector, μ m =[μ m,11 ,μ m,21 ,...,μ m,PQ ] represents the frequency modulation slope vector, which is a 1×PQ dimensional vector, T ch,m =[T ch,m,11 ,T ch,m,21 ,...,T ch,m,PQ The chirp time-width vector is represented by ], which is a 1×PQ dimensional vector. The time-width of each frame is represented as a 1×Q dimensional vector T. fr,m =[T fr,m,1 ,T fr,m,2 ,...,T fr,m,Q ];

[0070] Step 15: Apply GA (Genetic Algorithm) and SQP (Quadratic Sequence Optimization) to solve the optimization problem and obtain the LFMCW parameter vector Ψ when the optimal CO_CRB is obtained.

[0071] The LFMCW parameter vector Ψ calculated using the above steps, with its optimal CO_CRB, can be used to guide the radar waveform parameter settings when conducting experiments using LFMCW radar to detect human heartbeat and respiration. Since this method uses the minimum heartbeat and respiration frequency estimation of CRB as the objective function, and based on the physical meaning of CRB, CRB describes the optimal performance of unbiased estimation, providing a strict bound for parameter estimation at high signal-to-noise ratios, the LFMCW waveform settings designed in this method can improve the estimation performance of heartbeat and respiration frequencies. Attached Figure Description

[0072] Figure 1 This is a schematic diagram showing the results of ML estimation of the heartbeat and respiratory frequency of the SISO radar system under different SNR conditions.

[0073] Figure 2 This is a schematic diagram showing the results of ML estimation of the heartbeat and breathing frequency of a MIMO radar system under different SNR conditions.

[0074] Figure 3 This is a schematic diagram showing the results of estimating heart rate and respiratory rate using MIMO radar when setting LFMCW parameters, as shown in Table 2.

[0075] Figure 4 This is a schematic diagram showing the results of estimating heart rate and respiratory rate using MIMO radar when setting LFMCW parameters, as shown in Table 5. Detailed Implementation

[0076] Consider a MIMO radar system with M transmitters and N receivers, where the transmitting antenna transmits LFMCW signals.

[0077] Step 1: In the transmit segment of the MIMO radar system, a chirp signal transmitted by the m-th transmit antenna is represented as:

[0078]

[0079] Among them, T ch f represents the chirp signal width. c,m μ represents the starting frequency at which the m-th transmitting antenna transmits the chirp signal. m Let T represent the frequency modulation slope of the chirp signal transmitted by the m-th transmitting antenna. The time interval between adjacent chirps is T. rest This indicates that no signal is transmitted during this period to ensure that the initial phase of the next chirp is known. This phase control is to ensure the coherence of the radar, thereby obtaining the changes in the Doppler frequency of the intermediate frequency signal caused by the target.

[0080] Step 2: At the receiver of the MIMO radar system, the received signal of the nth radar receiving antenna is represented as...

[0081]

[0082] Where α mn τ represents the complex reflection coefficient along the mn path. mn (t) represents the echo delay on the mn path, which contains heartbeat and breathing information. Let σ be the clutter noise of the nth receiver at time t, with a mean of zero and a variance of σ. 2 Both n and time t are independent and identically distributed complex Gaussian white noise.

[0083] Step 3: The intermediate frequency signal after mixing and filtering is represented as follows:

[0084]

[0085] Assume that the transmitted signals from different transmitting antennas satisfy

[0086]

[0087] The transmitted signals from different antennas are orthogonal to each other, that is...

[0088]

[0089] From equations (4) and (5), it can be seen that time delay and Doppler frequency shift do not affect orthogonality. Therefore, equation (3) can be expressed as follows:

[0090]

[0091] Where E m Let m represent the energy of the chirp signal transmitted by the m-th transmitting antenna. Expanding equation (3) yields... because s ch,m (t) is a known signal, so w mn (t) also follows a Gaussian distribution with a mean of zero and a variance of σ. mn 2 =|s ch,m (t)| 2 σ 2 =E m σ 2 .

[0092] Step 4: The transmitted signal after mixing and filtering of the LFMCW signal is represented as follows:

[0093]

[0094] Where T per =T ch +T rest T rest This represents the idle time between chirps in each frame. The LFMCW radar transmit signal for continuously transmitting Q frames is represented as follows:

[0095]

[0096] Where T fr This represents the duration of one frame. Substituting equation (7) into equation (8), the LFMCW transmit signal is expressed as...

[0097]

[0098] Step 5: The intermediate frequency signal after mixing and filtering of the LFMCW signal is represented as follows:

[0099]

[0100] Among them, f c,m,pq The starting frequency of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna is μ. m,pq Let represent the frequency modulation slope of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna. The echo delay τ along the mn path. mn (t) The distance d between the human body and the radar along path mn. 0,mn 1. Time-varying thoracic displacement x mn (t) and the speed of light c are jointly determined:

[0101]

[0102] Thoracic displacement is the thoracic displacement caused by human respiration. r,mn (t) and displacement x caused by heartbeat h,mn (t) is composed of, therefore, thoracic displacement can be expressed as

[0103] x mn (t)=x r,mn (t)+x h,mn (t) (12)

[0104] Suppose that x r,mn (t) and x h,mn (t) represent frequencies f r and f h The initial phases are respectively and The sine function is expressed as

[0105]

[0106] Where A r,mn and A h,mn These represent the amplitude of thoracic cavity movement caused by respiration and heartbeat along the mn pathway, respectively. Here, we assume a respiratory rate f. r and heart rate f h To simplify the analysis and without loss of generality, we assume the initial phase of the periodic motion is unknown.

[0107] For ease of calculation, the reflection coefficient is represented in two parts: real and imaginary.

[0108] α mn =α mn,R +jα mn,I (15)

[0109] Represent all unknown parameters as a (2+2MN)×1 vector.

[0110]

[0111] To represent the transpose sign, let t' = t - qT fr -pT ch Then t = t' + pT ch +qT fr T s This represents the fast time sampling interval. Equation (10) can be further written as follows:

[0112]

[0113] Step 6: LFMCW Radar Observation Vector Represented as

[0114]

[0115] Where y mn,pq =[y mn,pq [1,1,1],...,y mn,pq [K 11 ,1,1],...,y mn,pq [K p1 ,P1,1],...,y mn,pq [K PQ ,P Q The intermediate frequency signal obtained after mixing the m-th transmitted signal and the n-th received signal and passing it through a low-pass filter is represented as follows:

[0116]

[0117] Where w mn,qp [k qp ,p q ,q]~CN(0,E m σ 2 ),

[0118]

[0119] Step 6: LFMCW radar observation vector The likelihood function is expressed as

[0120]

[0121] Step 7: LFMCW radar observation vector The log-likelihood function is expressed as:

[0122]

[0123] Step 8: The ML estimate of the unknown parameter vector θ is as follows

[0124]

[0125] Step 9: Since p(y; θ) is related to the time delay τ mn [k pq The function is called ], therefore, an intermediate variable is introduced.

[0126]

[0127] Step 10: Define the Fisher information matrix J(θ)

[0128]

[0129] The gradient operation is as follows:

[0130] Step 11: Calculate the gradient of Θ with respect to θ

[0131]

[0132] in

[0133]

[0134] Step 12: Calculate the Fisher information matrix J(Θ)

[0135] Consider the ij-th element of Θ in the formula, when i,i'∈[1,2,...,ZMN]

[0136]

[0137] in For ease of expression, equation (27) will be represented as J. τ . When i∈[1,2,...,KN], i'∈[KN+1,...,KN+MN] or i∈[KN+1,...,KN+MN], i'∈[1,2,...,KN]

[0138]

[0139] When i,i'∈[ZMN+MN+1,...,ZMN+2MN],

[0140]

[0141] To solve for the Cramer-Rao lower bound matrix, we need to solve for the inverse of the Fisher information matrix. The lower bound for the estimated parameter, heart rate, is expressed as... The lower bound of respiratory rate is expressed as

[0142] Step 13: Establish a mathematical model for LFMCW radar waveform design:

[0143]

[0144] stf c,pq,lb ≤f c,pq ≤f c,pq,ub

[0145] μ pq,lb ≤μ pq ≤μ pq,ub

[0146] T ch,pq,lb ≤T ch,pq ≤T ch,pq,ub

[0147]

[0148] μ pq T ch,pq <f c,pq,ub -f c,pq,lb ,

[0149] Where v1 is the CRB weight for heart rate estimation, v2 is the CRB weight for respiratory rate estimation, and c is the speed of light. According to the principle of radar velocity measurement, when radar measures velocity, the target motion must satisfy the assumption of uniformly accelerated motion within one frame of the signal. The chest cavity motion caused by heartbeat and respiration is regarded as uniformly accelerated linear motion, where a is the acceleration of uniformly accelerated linear motion.

[0150] Step 14: The LFMCW waveform parameter vector is represented as follows:

[0151]

[0152] in,

[0153] f represents the waveform parameter vector of the LFMCW signal transmitted by the m-th transmitting antenna. c,m =[f c,m,11 ,f c,m,21 ,...,f c,m,PQ ] represents the initial frequency vector, which is a 1×PQ dimensional vector, μ m =[μ m,11 ,μ m,21 ,...,μ m,PQ ] represents the frequency modulation slope vector, which is a 1×PQ dimensional vector, T ch,m =[T ch,m,11 ,T ch,m,21 ,...,T ch,m,PQ ] The chirp time-width vector is a 1×PQ dimensional vector, and the time-width of each frame is represented as a 1×Q dimensional vector T. fr,m =[T fr,m,1 ,T fr,m,2 ,...,Tfr,m,Q ].

[0154] Step 15: Apply GA and SQP to solve the optimization problem to obtain the LFMCW parameter vector Ψ when the optimal CO_CRB is obtained.

[0155] Working principle of the invention

[0156] Transmit a linear frequency modulated continuous wave signal, and the intermediate frequency signal y is obtained by mixing and filtering the signals received by the m-th antenna and the n-th receiving antenna. mn [k], whose expression is

[0157]

[0158] For ease of analysis, let k qp =k, meaning the number of sampling points per chirp is k. The signal-to-noise ratio (SNR) is defined as the sum of the ratios of the intermediate frequency signal after mixing and filtering for each chirp to the noise energy, expressed in dB as:

[0159]

[0160] In numerical simulations, the signal-to-noise ratio (SNR) is changed by adjusting the noise variance.

[0161] The simulation considers two systems: Single Input Single Output (SISO) radar and MIMO radar. To compare the estimation performance of the heartbeat and breathing frequency of the two radar systems, the MIMO radar system transmits the same waveform through different antennas. The specific parameter settings of the waveform are shown in Table 1.

[0162] Table 1 Simulation parameter settings

[0163]

[0164] Figure 1 , Figure 2 These are heart rate monitoring systems for both SISO and MIMO. h and respiratory rate f r The curves showing the mean squared error (RMSE) and CRB as a function of SNR are shown. The red dashed line represents the RMSE as a function of SNR, and the black solid line represents the CRB as a function of SNR. Asterisks and circles represent heart rate (f), respectively. h and respiratory rate f rThe estimation results show that when the SNR is between -40 and -20 dB, the slope of the RMSE curve changes drastically. When the SNR is above -20 dB, the RMSE curve begins to decline slowly, and the ML estimation performance tends to stabilize. The figure also shows that the RMSE and CRB values ​​for heart rate estimation are higher than those for respiratory rate estimation. This is because the chest cavity fluctuation caused by heartbeat is much smaller than the chest cavity amplitude caused by respiration, and the heart rate is numerically larger than the respiratory rate, making heart rate estimation more difficult. Furthermore, the data at SNR = 10 dB in the figure indicates that the CRB value for heart rate and respiratory rate estimation by the MIMO radar system is an order of magnitude smaller than that by the SISO radar system. This suggests that using MIMO radar for heart rate and respiratory rate estimation yields more accurate results.

[0165] The LFMCW radar waveform design for heartbeat and breathing frequency estimation was simulated using the GA and SQP algorithms. The weights for the heartbeat and breathing CRB were set to v1 = 0.01 and v2 = 1, respectively. The key radar parameters were set in the same way as in the previous chapter, as shown in Table 1.

[0166] First, the total duration of the chirp signal within a frame is fixed, allowing for variations in the chirp signal duration within a single frame. Optimization results of the waveform parameters show that different chirp durations result in lower CRB (Cost Per Frame). To verify this, a control group is set up where the chirp signal duration within a frame is the same, and other waveform parameters are set identically to the experimental group. This section considers both SISO and MIMO radar systems to verify that different chirp signal durations within a frame can achieve lower CRB under both radar systems.

[0167] Table 2 shows the optimization results for a MIMO radar system with a fixed total chirp duration within a frame and varying chirp durations. The results indicate that the CRB result is smaller when the chirp signal durations within a frame vary. Table 3 shows the calculation results of chirp-related parameters when the chirp duration is optimized. Table 4 shows the numerical calculation results of CRB-HR, CRB-RR, and CO-CRB when the chirp durations within a frame are the same. The results in Tables 2 and 3 show that in a MIMO radar system, when the total chirp duration within a frame is fixed but the chirp durations vary, the values ​​of CRB_HR, CRB_RR, and CO_CRB all decrease, indicating improved estimation performance for heart rate and respiratory rate. Figure 3The results are the heart rate and respiratory rate (ML) estimation results when the LFMCW parameters are set according to the optimization results in Table 2. When the signal-to-noise ratio is high, MSE and CRB can overlap.

[0168] Table 2. Optimization results for MIMO radar with fixed total chirp duration within a frame and different chirp durations.

[0169]

[0170] Table 3 Calculation results of chirp-related parameters

[0171]

[0172] Table 4 Simulation results for MIMO radar with fixed total chirp duration and identical chirp duration within a single frame.

[0173]

[0174] Then, the bandwidth of the chirp signal was fixed, allowing for different chirp signal durations within a frame. Optimization results of the waveform parameters showed that with a fixed chirp signal bandwidth, different chirp signal durations within a frame resulted in a lower CRB. To verify this, a control group was set up, where the chirp signal duration was the same within a frame, and other waveform parameters were set the same as the experimental group.

[0175] The optimization problem was solved using both the GA-based and SQP-based LFMCW waveform parameter optimization algorithms, yielding the same LFMCW parameter optimization results. Table 5 shows the optimization results with different chirp durations when the chirp bandwidth is fixed. The results indicate that the CRB result is smaller when the chirp signal durations within a frame are different. The calculation results of chirp-related parameters when optimizing the chirp duration settings are shown in Table 6.

[0176] Table 5. Optimization results of different chirp time widths within one frame for MIMO radar at B=3.8GHz

[0177]

[0178] Table 6. Calculation results of chirp-related parameters

[0179]

[0180] Table 7. Calculation results of chirp time width being the same within one frame of MIMO radar when B = 3.8 GHz.

[0181]

[0182] To further demonstrate that different chirp signal durations within a frame can yield smaller CRB results, this paper calculates the CRB results for comparison when the chirp bandwidth is fixed and the durations of the chirp signals are the same. Table 7 shows the numerical calculation results of CRB-HR, CRB-RR, and CO-CRB when the chirp durations are the same. Comparing the results in Tables 5 and 7, it can be seen that different chirp signal durations within a frame can yield smaller CRB. Figure 4 The results are the heart rate and respiratory rate (ML) estimation results when the LFMCW parameters are set according to the optimization results in Table 5. When the signal-to-noise ratio is high, MSE and CRB can overlap.

Claims

1. A method for calculating the LFMCW waveform of a MIMO radar for detecting heart rate and respiratory rate, the method comprising: Step 1: In the transmit segment of the MIMO radar system, the m-th transmit antenna transmits a chirp signal s. ch,m (t) is represented as: Among them, E m T represents the energy of the chirp signal transmitted by the m-th transmitting antenna. ch f represents the chirp signal width. c,m μ represents the starting frequency at which the m-th transmitting antenna transmits the chirp signal. m The frequency modulation slope of the chirp signal transmitted by the m-th transmitting antenna is represented by T; the time interval between adjacent chirps is T. rest This indicates that no signal is transmitted during this period to ensure that the initial phase of the next chirp is known; assume that different transmitted signals satisfy the following formula, i.e., condition 1: s ch,m' * (·) represents the conjugate of the signal transmitted by the m'-th transmitting antenna, τ m'n (t) represents the time delay under the m'n path, c m represents a constant, m and m' represent the transmitting antenna number, represents two different transmitting antennas, and n represents the receiving antenna number; And the transmitted signals from different antennas are orthogonal to each other, i.e., condition 2: τ represents a constant. mn (t) represents the echo delay on the mn path, which contains heartbeat and breathing information; Step 2: At the receiver of the MIMO radar system, the received signal r of the nth radar receiving antenna ch,n (t) is represented as: Where, α mn The complex reflection coefficient on the mn path is represented by μ, the frequency modulation slope of the LFM signal is represented by μ, and the number of transmit antennas in the MIMO system is represented by M. Let σ be the clutter noise of the nth receiver at time t, with a mean of zero and a variance of σ. 2 Both n and time t are independent and identically distributed complex Gaussian white noise; Step 3: The intermediate frequency signal y after mixing and filtering ch,mn (t) is represented as: r * ch,n (t) represents the conjugate of the signal received by the nth receiving antenna, E m' α represents the energy of the signal transmitted by the m'-th transmitting antenna. m'n Let s represent the reflection coefficient at the m'n path. ch,m' The conjugate of the signal transmitted by the m'-th transmitting antenna; Since the transmitted signal satisfies conditions 1 and 2 above, the above equation can be expanded as follows: in, because s ch,m (t) is a known signal, so w mn (t) also follows a Gaussian distribution with a mean of zero and a variance of σ. mn 2 =|s ch,m (t)| 2 σ 2 =E m σ 2 , represented as CN~(0,σ 2 ) Step 4: Considering that the LFMCW signal has Q frames and each frame has P chirps, treat these chirp signals as a time-domain shift of a single chirp signal, and calculate the intermediate frequency signal y after the LFMCW signal has been mixed and filtered. mn,pq (t); Step 5: At the receiver of the MIMO radar system, the LFMCW radar transmits a series of chirp signals and calculates the radar observation vector. Step 6: Likelihood function of LFMCW radar observation vector for: in, Let θ represent the intermediate frequency signal vector, exp{·} represent the exponential operation, M represent the number of transmit antennas, and N represent the number of receive antennas. k pq p represents the k-th sample point of the p-th chirp in the q-th frame. q This represents the p-th chirp of a q-frame, indicated by the superscript. Indicates conjugate transpose, α MN,R α represents the real part of the reflection coefficient along the MN path. MN,I T represents the imaginary part of the reflection coefficient along the MN path. s Indicates the sampling interval; Step 7: Log-likelihood function of LFMCW radar observation vector for: K qp k represents the number of sampling points for the p-th chirp in the q-th frame. qp This represents the k-th sample point of the p-th chirp in the q-th frame; Step 8: Calculate the ML estimate of the unknown parameter vector θ Step 9: Since p(y; θ) is related to the time delay τ mn [k pq The function p(y; θ) represents the likelihood function of the LFMCW radar observation vector, y represents the intermediate frequency signal vector, and τ represents the IF signal vector. mn [] represents the echo delay on the mn path; therefore, an intermediate variable Θ is introduced: Θ=[τ 11 [1,1,1],...,t 11 [K 11 ,1,1],...,t 11 [K p1 ,P1,1],...,t 11 [K PQ ,P Q ,Q],...,τ 1N [K PQ ,P Q ,Q] ... t 11 [1,1,1],...,t 11 [K 11 ,1,1],...,t 11 [K p1 ,P1,1],...,t MN [K PQ ,P Q ,Q],...,τ 1N [K PQ ,P Q ,Q] α 11Re ,α 12Re ,...,α MNRe ,α 11Im ,α 12Im ,...,α MNIm ] T Re denotes taking the real part, and Im denotes taking the imaginary part; Step 10: Define the Fisher information matrix J(θ): Step 11: Calculate the gradient of Θ with respect to θ in, This indicates the initial phase of the chest cavity displacement caused by the heartbeat. The initial phase of the chest cavity displacement caused by respiration is represented by c, where c represents the speed of light. Step 12: Calculate the Fischer information matrix J(θ), and obtain the CRB as follows: CRB is represented as... The final estimated heart rate CRB is: Respiratory rate is estimated as CRB is Step 13: Establish a mathematical model for LFMCW radar waveform design: s.t.f c,pq,lb ≤f c,pq ≤f c,pq,ub m pq,lb ≤μ pq ≤μ pq,ub T ch,pq,lb ≤T ch,pq ≤T ch,pq,ub μ pq T ch,pq <f c,pq,ub -f c,pq,lb Where v1 is the CRB weight for heart rate estimation, v2 is the CRB weight for respiratory rate estimation, and μ pq The frequency modulation slope of the p-th chirp signal in the q-th frame is represented by f, CO_CRB represents the weighted sum of the heart rate and respiratory rate estimates CRB, and f c,pq f represents the starting frequency of the p-th chirp signal in the q-th frame. c,pq,lb f represents the lower bound of the starting frequency of the p-th chirp signal in the q-th frame. c,pq,ub This represents the upper bound of the starting frequency of the p-th chirp signal in the q-th frame, μ. pq,lb μ represents the lower bound of the frequency modulation slope of the p-th chirp signal in the q-th frame. pq,ub T represents the upper bound of the frequency modulation slope of the p-th chirp signal in the q-th frame. ch,pq,lb T represents the lower bound of the time width of the p-th chirp signal in the q-th frame. ch,pq T represents the time width of the p-th chirp signal in the q-th frame. ch,pq,ub This represents the upper bound of the time width of the p-th chirp signal in the q-th frame, [·]. 1,1 express The first row and first column of the matrix, [·] 2,2 express In the second row and second column of the matrix, according to the radar speed measurement principle, when the radar measures speed, the target motion needs to satisfy uniform acceleration motion within one frame of the signal; the chest cavity motion caused by heartbeat and breathing is regarded as uniformly accelerated linear motion, where a is the acceleration of uniformly accelerated linear motion; Step 14: Calculate the LFMCW waveform parameter vector Ψ, represented as: in, f represents the waveform parameter vector of the LFMCW signal transmitted by the m-th transmitting antenna. c,m =[f c,m,11 ,f c,m,21 ,...,f c,m,PQ ] represents the initial frequency vector, which is a 1×PQ dimensional vector, μ m =[μ m,11 ,μ m,21 ,...,μ m,PQ ] represents the frequency modulation slope vector, which is a 1×PQ dimensional vector, T ch,m =[T ch,m,11 ,T ch,m,21 ,...,T ch,m,PQ The chirp time-width vector is represented by ], which is a 1×PQ dimensional vector. The time-width of each frame is represented as a 1×Q dimensional vector T. fr,m =[T fr,m,1 ,T fr,m,2 ,...,T fr,m,Q ]; Step 15: Apply genetic algorithm and quadratic sequence optimization to solve the optimization problem and obtain the LFMCW parameter vector Ψ when the optimal CO_CRB is obtained.

2. The LFMCW waveform calculation method for MIMO radar for detecting heart rate and respiratory rate as described in claim 1, characterized in that, In step 4, the intermediate frequency signal y after the LFMCW signal mixing and filtering is calculated. mn,pq The method for (t) is: Among them, T fr T represents the frame width. chr Indicates the width of chirp, y ch,mn (·) represents the intermediate frequency signal obtained after mixing and filtering the m-th transmitted signal and the n-th received signal; x mn (t)=x r,mn (t)+x h,mn (t), A r,mn A represents the amplitude of thoracic cavity displacement caused by respiration along the mn pathway. h,mn f represents the amplitude of chest cavity displacement caused by heartbeat along the mn path. c,m,pq The starting frequency of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna is μ. m,pq d represents the frequency modulation slope of the q-th chirp in the p-th frame transmitted by the m-th transmitting antenna; 0,mn Let x be the distance between the human body and the radar along path mn. mn (t) Thoracic displacement as a function of time, x r,mn (t) represents the displacement of the thoracic cavity caused by human respiration, x h,mn (t) represents the displacement of the chest cavity caused by the human heartbeat, f r f represents respiratory rate. h The heart rate is represented by the initial phase, which is represented by the following: and 3. The LFMCW waveform calculation method for MIMO radar for detecting heart rate and respiratory rate as described in claim 1, characterized in that, Step 5 involves calculating the radar observation vector. The method is as follows: Let y be one of the elements. mn,pq ; y mn,pq =[y mn,pq [1,1,1],...,y mn,pq [K 11 ,1,1],...,y mn,pq [K p1 ,P1,1],...,y mn,pq [K PQ ,P Q ,Q]], K PQ P represents the number of sampling points for the P-th chirp in the Q-th frame. Q This represents the number of chirps in the Q-th frame.

4. The LFMCW waveform calculation method for MIMO radar for detecting heart rate and respiratory rate as described in claim 1, characterized in that, In step 8, the ML estimate of the unknown parameter vector θ is calculated. The method is as follows:

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