MIMO radar sparse array optimization method based on sleep monitoring scenario

Abstract

The present invention discloses a MIMO radar sparse array optimization method based on a sleep monitoring scenario. The sparsity of the array elements is determined in combination with the actual sleep scenario, and the two-dimensional beam angle is constrained. The full angle scan is achieved by changing the beam pointing within the constrained angle, and the highest sidelobe level value of the directional pattern under all angle pointing is obtained. The multi-objective particle swarm iterative model is used to solve the optimal array element spacing, and the excitation coefficient is solved in combination with the convex optimization algorithm, and finally the array element position and excitation coefficient matrix are obtained. Compared with the uniform array, this method reduces the number of array elements, reduces the hardware implementation cost, weight and pressure, and improves the angular resolution; compared with the traditional sparse array algorithm, this method can determine the sparsity of the array elements in combination with the actual sleep scenario, and solves the problem that when the beam pointing changes in the traditional sparse array, the directional pattern will have high sidelobes and large grating lobes, ensuring that the directional pattern under all angle pointing within the constraint range has a low sidelobe level.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular to a MIMO radar sparse array optimization method based on a sleep monitoring scenario. Background Art

[0002] Respiration and heartbeat, as fundamental signals of the human body, are important indicators of health. Traditional contact-based vital sign monitoring devices are inadequate for many specific patients and populations. Therefore, non-contact vital sign monitoring devices, particularly Doppler radar, have become a hot research area. With the continuous expansion of monitoring scenarios, sleep monitoring has become a key research area. Therefore, multi-person sleep vital sign monitoring based on Doppler radar has broad application prospects.

[0003] Since multiple vital sign signals need to be separated during sleep monitoring, angular resolution needs to be improved for close-range situations. For a half-wavelength uniform array, improving angular resolution requires increasing the number of array elements, which greatly increases hardware cost and complexity, making it difficult to implement. In contrast, a sparse array requires fewer elements through sparse element spacing to meet the required resolution, making it an excellent choice. Reducing the Number of Elements in a Linear Antenna Array by the Matrix Pencil Method proposes a sparse array algorithm based on matrix beams, and Optimizing Unequally Spaced Linear Antenna Array by Employing PSO Technique proposes a sparse array algorithm based on particle swarms. However, current sparse array algorithms design arrays based on a single beam direction. When the beam direction changes, the sidelobes of the directional pattern deteriorate dramatically, resulting in the effects of grating lobes. Summary of the Invention

[0004] The purpose of the present invention is to address the problems existing in the above-mentioned prior art and provide a MIMO radar sparse array optimization method based on a sleep monitoring scenario.

[0005] The technical solution to achieve the purpose of the present invention is: a MIMO radar sparse array optimization method based on a sleep monitoring scenario, the method comprising the following steps:

[0006] Step 1: Based on the distance h between the human body and the radar and the shoulder width l of the human body in the actual sleeping scene, calculate the minimum angle θ required to distinguish when two people lie side by side. min , find the minimum antenna synthetic aperture D required R , determine the sparsity μ, initialize the transmitting array element position and receiving element position

[0007] Step 2: Based on the distance h between the human body and the radar and the length d of the bed t and width d r , calculate the azimuth angle θ respectively r and pitch angle θ t The two-dimensional angle range of

[0008] Step 3: According to the two-dimensional angle range, let the receiving array represent the azimuth dimension and the transmitting array represent the elevation dimension; according to the initial receiving array element position Recorded in the azimuth constraint range θ r The maximum level value P of the directional pattern pointing downward at all angles within r ; According to the initial transmitting array element position Recorded in the pitch angle constraint range θ t The maximum level value P of the directional pattern pointing downward at all angles within t ;

[0009] Step 4: Take the maximum level value P obtained at the initial array element position as the result of the fitness function, and perform convex optimization calculation based on the spacing obtained in each iteration to obtain the excitation coefficient w, which replaces the original steering vector R i , repeat step 3 and use the multi-objective particle swarm algorithm to iteratively solve;

[0010] Step 5: When the number of iterations t≤Q and the change between two adjacent iterations is less than δ, exit the iteration and obtain the optimal sparse array element position under the two-dimensional angle constraint. and the complex excitation coefficient matrix W r 、W t .

[0011] Furthermore, in step 1, the minimum angle θ required to be distinguished when two people lie side by side is calculated based on the distance h between the human body and the radar and the shoulder width l of the human body in the actual sleeping scene. min , find the minimum antenna synthetic aperture D required R , determine the sparsity μ, initialize the transmitting array element position and receiving element position Specifically include:

[0012] Step 1-1: Assume that in a real scene, the radar is placed directly above the human body at a height of h, and the shoulder widths of the two subjects are l1 and l2 respectively;

[0013] In steps 1-2, when two people lie side by side, the maximum distance l between the chest rise and fall caused by breathing is approximately:

[0014]

[0015] Combined with the height h, the minimum angle θ that needs to be resolved can be calculated min Approximately:

[0016]

[0017] Steps 1-3, according to the formula:

[0018]

[0019] The minimum antenna aperture required in the horizontal direction, that is, in the azimuth dimension, can be obtained, where θ d is the steering angle of the beam, D R is the equivalent antenna aperture, and λ is the signal wavelength. Let the number of array elements be N, then the sparsity μ is:

[0020]

[0021] Step 1-4, the initial position of each receiving array element is given as In order to achieve angular resolution, the array element spacing must satisfy:

[0022]

[0023] Where, is the last array element position, is the first array element position, D R is the equivalent antenna aperture; similarly, the initial position of the transmitting array element can be obtained as

[0024] Furthermore, in step 2, the distance h between the human body and the radar and the length d of the bed are determined. t and width d r , calculate the azimuth angle θ respectively r and pitch angle θ t The two-dimensional angle range includes:

[0025] Assume that in a real-world scenario, the radar is placed more than one meter above the human body, pointing vertically downward. The transmitting and receiving array elements are both linear arrays and arranged vertically, forming an L shape. The height of the radar from the human body is h, and the width of the bed is d. r , with a length of d t .

[0026] Calculate the azimuth angle θ r and pitch angle θ t The ranges are:

[0027]

[0028]

[0029] Furthermore, in step 3, according to the two-dimensional angle range, the receiving array represents the azimuth dimension and the transmitting array represents the elevation dimension; according to the initial receiving array element position Recorded in the azimuth constraint range θ r The maximum level value P of the directional pattern pointing downward at all angles within r ; According to the initial transmitting array element position Recorded in the pitch angle constraint range θ t The maximum level value P of the directional pattern pointing downward at all angles within t , specifically including:

[0030] Step 3-1: Based on the two-dimensional angle range obtained in step 2, let the maximum azimuth angle be θ rM , then in the azimuth dimension, the one-dimensional pattern function pointing to θ0 is expressed as:

[0031]

[0032] Where θ is the pattern angle, θ0 is the beam pointing direction, and R i is the complex excitation coefficient corresponding to each array element, is the spatial wave number, d ri is the position of each receiving element, N is the number of elements; for the initial element position, R i is the steering vector of each array element, that is

[0033]

[0034] Step 3-2, in [-θ rM ,θ rM ] range, the beam is scanned in steps of Δθ, and the pattern function F is calculated for each angle. ri (θ i ),1≤i≤M, where M is [-θ rM ,θ rM The total number of discrete angle values ​​in the range of Δθ;

[0035] Step 3-3, for any pointing pattern function F ri (θ i ), discard the part corresponding to the main lobe width, and get F ri (θ s ), {θ s} is the discrete angle pointing of the side lobe area. ri (θ s ) Two-step extremum calculation: First, F ri (θ s ) Derivative:

[0036]

[0037] make Record the amplitude of each extreme point n is the number of extreme values; find the maximum value p of each extreme point θi :

[0038]

[0039] p θi That is θ i Peak sidelobe level pointing downwards.

[0040] Step 3-4, record in [-θ rM ,θ rM ] range, with Δθ as the step, the peak sidelobe level of the directional pattern pointing down at M discrete angles:

[0041] PSLL=[p θ1 ,p θ2 ,...,p θM ]

[0042] Where p θi is θ i The maximum sidelobe level pointing downward, find the maximum level value, record it as P r ,Right now:

[0043] P r =max(PSLL)

[0044] Step 3-5: Similarly, in the pitch angle dimension, the transmitting array element repeats steps 3-1 to 3-4 to obtain the maximum level value P t .

[0045] Furthermore, the maximum level value P obtained at the initial array element position in step 4 is used as the result of the fitness function, and the excitation coefficient w is obtained by convex optimization calculation based on the spacing obtained in each iteration, replacing the original steering vector R i , repeat step 3 and use the multi-objective particle swarm algorithm to iteratively solve, specifically including:

[0046] Taking the receiving array as an example,

[0047] Step 4-1: First, determine the particle swarm size K, the number of particles in the swarm D, which is equal to the number of array element spacings, the maximum number of iterations Q, and the speed v of position updates per iteration.

[0048] In step 4-2, the speed and position of each particle after iteration can be expressed as:

[0049] v ij (t+1)=w·vij (t)+c1r1(t)(p ij (t)-x ij (t))+c2r2(t)(p gj (t)-x ij (t)),t∈{1,Q-1}

[0050] x ij (t+1)=x ij (t)+v ij (t+1),t∈{1,Q-1}

[0051] Where 1≤j≤K, 1≤i≤D, t is the number of iterations, c1, c2 are two speed learning factors, used to control the speed of particle position change; r1, r2 are two random numbers between [0, 1], used to enhance the randomness of the change and prevent the occurrence of local optimal conditions, w is the inertia weight, which remembers the speed information of the previous iteration, p ij (t) is the optimal position of the jth particle swarm, p gj (t) is the global optimal position.

[0052] In step 4-3, in order to prevent the speed of each iteration from being too high, it is necessary to set the upper and lower limits of the speed, that is,

[0053]

[0054] Where, v max and v min are the maximum and minimum change speeds respectively; in order to enhance the sparsity and reduce the coupling degree of the antenna, the spacing d of all array elements is set to meet 0.5λ≤d≤1.5λ.

[0055] In step 4-4, in order to prevent falling into the local minimum, the unique global minimum of convex optimization can be used to obtain the complex excitation coefficient w instead of the steering vector using the convex optimization (CVX) algorithm to further reduce the peak sidelobe level.

[0056] Therefore, a convex optimization model can be established, namely

[0057] min max(|ω H b(θ s )|),s∈{1,...,S}

[0058] st|ω H R i |=1,i∈{1,...,M}

[0059] In the formula, {θ s} is the discrete angle pointing of the side lobe area, S is the number of discrete angle values ​​in the side lobe area, R i is θi The downward steering vector, M is the number of discrete angles in the azimuth dimension with Δθ as the step, b(θ s ) is the complex weight coefficient of the sidelobe area, expressed as:

[0060]

[0061] Step 4-5: Calculate the complex excitation coefficient ω and use it to replace the steering vector to obtain the directional pattern:

[0062]

[0063] Repeat step 3 to obtain the maximum level P after convex optimization of the azimuth dimension r_CVX .

[0064] Similarly, the transmitting array element repeats steps 4-1 to 4-5 in the pitch angle dimension to obtain the maximum level P after convex optimization of the pitch angle dimension. t_CVX .

[0065] Furthermore, in step 5, when the number of iterations t≤Q and the change between two adjacent iterations is less than δ, the iteration is exited to obtain the optimal sparse array element position under the two-dimensional angle constraint. and the complex excitation coefficient matrix W r 、W t , specifically including:

[0066] Step 5-1, taking the receiving array element as an example, repeat step 3, when the maximum level value P r_CVX Exit the iteration when the following conditions are met:

[0067]

[0068] Where t is the number of iterations, satisfying t≤Q, Q is the maximum number of iterations, and δ is a very small positive number;

[0069] Step 5-2: Record the final receiving element position The complex excitation coefficient matrix W for all discrete angles within the angle constraint r :

[0070]

[0071] Where θ i For the azimuth angle [-θ rM ,θ rM ] range, with Δθ as the step, there are M discrete angles, N is the number of receiving array elements, 1≤i≤M.

[0072] Similarly, the transmitting array element repeats step 5, and finally obtains the two-dimensional optimal sparse array element position and the complex excitation coefficient matrix W r 、W t , draw a directional diagram.

[0073] Compared with the prior art, the present invention has the following significant advantages: (1) It is combined with the actual sleeping scene, determines the array sparsity according to actual needs, and only considers the actual required angle range, so the directional pattern sidelobes within the angle constraint are lower and more robust; (2) The peak sidelobe levels of the directional pattern of all-angle beam pointing are compared within the angle range, ensuring that the directional pattern of any beam pointing within the angle constraint has low sidelobes and will not be affected by grating lobes; (3) It has a wide range of applications and is also applicable to different working scenarios. The sparsity setting and angle constraints can be performed according to the needs of each scenario, and the sparse array can be further optimized to better meet the index requirements of the radar system; (4) The proposed sparse array algorithm can solve the problem that the traditional array algorithm only meets the single beam pointing. Within the angle range required by the actual scenario, high sidelobes and grating lobes will not appear when the beam is pointed at any angle.

[0074] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is a flowchart of the MIMO radar sparse array optimization method based on the sleep monitoring scenario of the present invention.

[0076] Figure 2 Schematic diagram of the sleeping scene of the present invention.

[0077] Figure 3 This is a flow chart of the algorithm combining particle swarm optimization and convex optimization in the present invention.

[0078] Figure 4 Schematic diagram of array element positions in the present invention.

[0079] Figure 5 This is the simulation result diagram of the two-dimensional directional pattern in the present invention. Figure 5 (a) is the beam pointing to the center angle (0°, 0°), Figure 5 (b) The beam is pointed at the edge angle (32°, 29°). DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0081] Combine Figure 1This paper proposes a MIMO radar sparse array optimization method for sleep monitoring scenarios. Based on non-contact vital sign theory, the method determines the element spacing sparsity according to the actual scenario, sets angle constraints, and compares the peak sidelobe levels of the beam pattern within the angle constraints. The method then uses a multi-objective particle swarm algorithm to calculate element spacing and a convex optimization algorithm to calculate the complex excitation coefficients. This optimization method is equally applicable to different operating scenarios, and the sparse array can be further optimized by adjusting the sparsity setting and angle constraints based on the needs of each scenario. The specific steps are as follows:

[0082] Step 1: Based on the distance h between the human body and the radar and the shoulder width l of the human body in the actual sleeping scene, calculate the minimum angle θ required to distinguish when two people lie side by side. min , find the minimum antenna synthetic aperture D required R , determine the sparsity μ, initialize the transmitting array element position and receiving element position Specifically:

[0083] In step 1-1, assume that in a real-world scenario, the radar is placed directly above a person at a height h of 1.6 meters. The shoulder widths of the two subjects are l1 and l2, respectively. The shoulder width of an adult lying flat is generally around 0.3 to 0.4 meters. Therefore, l1 = 0.3 meters and l2 = 0.4 meters, respectively.

[0084] In steps 1-2, when two people lie side by side, the maximum distance l between the chest rise and fall caused by breathing is approximately:

[0085]

[0086] Combined with the height h, the minimum angle θ that needs to be resolved can be calculated min Approximately:

[0087]

[0088] Steps 1-3, according to the formula:

[0089]

[0090] It can be found that the minimum number of equivalent array elements required in the horizontal direction, that is, in the azimuth dimension, is ten. d is the steering angle of the beam, D R is the equivalent antenna aperture, and λ is the signal wavelength. If the number of array elements is N, then the sparsity μ is:

[0091]

[0092] Step 1-4, the initial position of each receiving array element is given as In order to achieve angular resolution, the array element spacing must satisfy:

[0093]

[0094] Where, is the last array element position, is the first array element position, D R is the equivalent antenna aperture. Similarly, the initial position of the transmitting array element can be obtained as

[0095] Step 2: Based on the distance h between the human body and the radar and the length d of the bed t and width d r , calculate the azimuth angle θ respectively r and pitch angle θ t The two-dimensional angle range is:

[0096] Step 2-1, such as Figure 2 As shown, the radar is placed more than one meter above the human body, pointing vertically downward. The transmitting and receiving array elements are both linear arrays and arranged vertically, forming an L shape. The height of the radar from the human body is h, and the width of the bed is d. r , with a length of d t Assume h is 1.6 meters and width d r is 1.8 meters, length d t 2 meters.

[0097] Step 2-2, calculate the azimuth angle θ r and pitch angle θ t The ranges are:

[0098]

[0099]

[0100] The calculated azimuth angle range is [-29°, 29°], and the elevation angle range is [-32°, 32°].

[0101] Step 3: Based on the calculated two-dimensional angle range, let the receiving array represent the azimuth dimension and the transmitting array represent the elevation dimension. Record the azimuth constraint range θ r The maximum level value P of the directional pattern pointing downward at all angles within r According to the initial transmitting array element position Record the pitch angle constraint range θ t The maximum level value P of the directional pattern pointing downward at all angles within t , the specific steps are as follows:

[0102] In step 3-1, taking the transmitting array element as an example, the pattern function is expressed as:

[0103]

[0104] Where θ is the pattern angle, θ0 is the beam pointing direction, and R i is the complex excitation coefficient corresponding to each array element, is the spatial wave number, d ri is the position of each receiving element, and N is the number of elements. For the initial element spacing, R i is the steering vector of each array element, that is

[0105]

[0106] Where θ is the beam pointing direction.

[0107] Step 3-2: In the range of [-29°, 29°], the beam is scanned with Δθ as the step, usually Δθ = 1°, and the pattern function F is calculated for each angle. ri (θ i ), (1≤i≤M), where M is the total number of discrete angle values ​​in the range [-29°, 29°] with a step of Δθ.

[0108] Step 3-3, for any pointing pattern function F ri (θ i ), discard the part corresponding to the main lobe width, and get F ri (θ s ), {θ s} is the discrete angle pointing of the side lobe area. ri (θ s ) Two-step extremum calculation: First, F ri (θ s ) Derivative:

[0109]

[0110] make Record the amplitude of each extreme point n is the number of extreme values. Find the maximum value p of each extreme point θi :

[0111]

[0112] p θi That is θ i Peak sidelobe level pointing downwards.

[0113] Step 3-4, record in [-θ rM ,θ rM] range, with Δθ as the step, the peak sidelobe level of the directional pattern pointing down at M discrete angles:

[0114] PSLL=[p θ1 ,p θ2 ,...,p θM ]

[0115] Where p θi is θ i The maximum sidelobe level pointing downward, find the maximum level value, record it as P r ,Right now:

[0116] P r =max(PSLL)

[0117] Step 3-5: Similarly, in the pitch angle dimension, the transmitting array element repeats steps 3-1 to 3-4 to obtain the maximum level value P t .

[0118] Step 4: Take the maximum level value P obtained at the initial array element position as the result of the fitness function, and perform convex optimization calculation based on the spacing obtained in each iteration to obtain the excitation coefficient w, which replaces the original steering vector R i , repeat step 3 and use the multi-objective particle swarm algorithm to iteratively solve, specifically including:

[0119] Step 4-1: First, determine the particle swarm size K, the number of particles in the swarm D, the maximum number of iterations Q, and the speed v of position update for each iteration; where D is equal to the number of array element spacings;

[0120] In step 4-2, the velocity and position of each particle after iteration are expressed as:

[0121] v ij (t+1)=w·v ij (t)+c1r1(t)(p ij (t)-x ij (t))+c2r2(t)(p gj (t)-x ij (t)),t∈{1,Q-1}

[0122] x ij (t+1)=x ij (t)+v ij (t+1),t∈{1,Q-1}

[0123] Where, 1≤j≤K, 1≤i≤D, t is the number of iterations, c1, c2 are two speed learning factors, used to control the speed of particle position change; r1, r2 are two random numbers between [0, 1], used to enhance the randomness of the change and prevent the occurrence of local optimal conditions, w is the inertia weight, which remembers the speed information of the previous iteration, p ij (t) is the optimal position of the jth particle swarm, p gj (t) is the global optimal position;

[0124] Step 4-3, set the upper and lower limits of the speed, that is

[0125]

[0126] Where, v max and v min are the maximum and minimum change speeds respectively; in order to enhance the sparsity and reduce the coupling degree of the antenna, the spacing d of all array elements is set to meet 0.5λ≤d≤1.5λ;

[0127] In step 4-4, the complex excitation coefficient w is obtained by using the convex optimization algorithm to replace the steering vector to further reduce the peak sidelobe level. Therefore, a convex optimization model is established, that is,

[0128] min max(|ω H b(θ s )|),s∈{1,...,S}

[0129] st|ω H R i |=1,i∈{1,...,M}

[0130] In the formula, {θ s} is the discrete angle pointing of the side lobe area, S is the number of discrete angle values ​​in the side lobe area, R i is θ i The downward steering vector, M is the number of discrete angles in the azimuth dimension with Δθ as the step, b(θ s ) is the complex weight coefficient of the sidelobe area, expressed as:

[0131]

[0132] Step 4-5: Calculate the complex excitation coefficient ω and use it to replace the steering vector to obtain the directional pattern:

[0133]

[0134] Repeat step 3 to obtain the maximum level P after convex optimization of the azimuth dimension r_CVX ;

[0135] Similarly, the transmitting array element repeats steps 4-1 to 4-5 in the pitch angle dimension to obtain the maximum level P after convex optimization of the pitch angle dimension. t_CVX .

[0136] Step 5: When the number of iterations t≤Q and the change between two adjacent iterations is less than δ, exit the iteration and obtain the optimal sparse array element position under the two-dimensional angle constraint. and the complex excitation coefficient matrix W r 、W t , specifically including:

[0137] Step 5-1, taking the receiving array element as an example, repeat step 3, when the maximum level value P r_CVX Exit the iteration when the following conditions are met:

[0138]

[0139] Wherein, t is the number of iterations, satisfying t≤Q, Q is the maximum number of iterations, δ is a very small positive number, which is set to 1e-8 in this invention;

[0140] Step 5-2: Record the final receiving element position The complex excitation coefficient matrix W for all discrete angles within the angle constraint r :

[0141]

[0142] Where θ i (1≤i≤M) is the direction angle dimension range [-29°, 29°] with Δθ as the step, with a total of M discrete angles. Similarly, the transmitting array element repeats step 5, and finally obtains the two-dimensional optimal sparse array element position and the complex excitation coefficient matrix W r 、W t , draw the directional diagram. The parameters in the process are set as follows:

[0143] Angle constraint range: Azimuth: [-29°, 29°]; Elevation: [-32°, 32°]

[0144] Array element spacing range: [d min ,d max ]=[0.5λ,1.5λ]

[0145] Number of array elements: Both the transmitting and receiving array elements are six-element arrays, sparse to ten-element half-wavelength uniform linear arrays

[0146] Transmitted signal: MIMO radar system uses 2.4GHz continuous wave (CW) signal with wavelength

[0147] Particle swarm parameters: population size K = 50, number of independent variables D = 3, maximum number of iterations is 100

[0148] Iteration parameters: speed learning factor c1=c2=2; randomness parameters r1, r2 are random numbers in [0,1]; inertia weight ω=0.25

[0149] Particle velocity range: [V max ,V min ]=[-0.2,0.2]

[0150] Through the above steps, we can finally obtain the optimal sparse array after optimization by particle swarm and convex optimization algorithm.

[0151] Combine Figure 4 、 Figure 5 : Figure 4 This is a schematic diagram of the position of the two-dimensional transceiver array obtained after optimization by the algorithm of the present invention. Figure 5 is the two-dimensional pattern calculated based on the array position, Figure 5 (a) is the beam pointing to the center angle (0°, 0°), Figure 5 (b) The beam is pointed at the edge angles (32°, 29°). It can be seen from the figure that within the range of angle constraints, the radiation pattern will not be affected by high side lobes and large grating lobes.

[0152] In summary, the sparse array element positions and complex excitation coefficients obtained by the intelligent optimization algorithm of the present invention can achieve the two-dimensional radiation pattern without high sidelobes and large grating lobes when the beam is pointed in any direction within the angular range required by the actual scenario, thereby realizing the sparse array optimization design of MIMO radar based on the sleep monitoring scenario.

Claims

1. A MIMO radar sparse array optimization method based on a sleep monitoring scenario, characterized in that: The method comprises the following steps: Step 1: Based on the distance h between the human body and the radar and the shoulder width l of the human body in the actual sleeping scene, calculate the minimum angle θ required to distinguish when two people lie side by side. min , find the minimum antenna synthetic aperture D required R , determine the sparsity μ, initialize the transmitting array element position and receiving element position Step 2: Based on the distance h between the human body and the radar and the length d of the bed t and width d r , calculate the azimuth angle θ respectively r and pitch angle θ t The two-dimensional angle range of Step 3: According to the two-dimensional angle range, let the receiving array represent the azimuth dimension and the transmitting array represent the elevation dimension; according to the initial receiving array element position Recorded in the azimuth constraint range θ r The maximum level value P of the directional pattern pointing downward at all angles within r ; According to the initial transmitting array element position Recorded in the pitch angle constraint range θ t The maximum level value P of the directional pattern pointing downward at all angles within t ; Step 4: Take the maximum level value P obtained at the initial array element position as the result of the fitness function, and perform convex optimization calculation based on the spacing obtained in each iteration to obtain the excitation coefficient w, which replaces the original steering vector R i , repeat step 3 and use the multi-objective particle swarm algorithm to iteratively solve; Step 5: When the number of iterations t≤Q and the change between two adjacent iterations is less than δ, exit the iteration and obtain the optimal sparse array element position under the two-dimensional angle constraint. and the complex excitation coefficient matrix W r 、W t .

2. The MIMO radar sparse array optimization method based on the sleep monitoring scenario according to claim 1 is characterized in that: As described in step 1, based on the distance h between the human body and the radar and the shoulder width l of the human body in the actual sleeping scene, calculate the minimum angle θ required to distinguish when two people lie side by side. min , find the minimum antenna synthetic aperture D required R , determine the sparsity μ, initialize the transmitting array element position and receiving element position Specifically include: Step 1-1: Assume that in a real scene, the radar is placed directly above the human body at a height of h, and the shoulder widths of the two subjects are l1 and l2 respectively; In steps 1-2, when two people lie side by side, the maximum distance l between the chest cavity rises and falls caused by breathing is approximately: Combined with the height h, the minimum angle θ that needs to be resolved can be calculated min Approximately: Steps 1-3: Calculate the equivalent antenna aperture, i.e. the minimum antenna synthetic aperture D R , the formula is: Where θ d is the steering angle of the beam, λ is the signal wavelength; Let the number of array elements be N, then the sparsity μ is: Step 1-4, the initial position of each receiving array element is given as To achieve angular resolution, the array element spacing should meet the following requirements: Where, is the last array element position, is the first array element position, D R is the equivalent antenna aperture; similarly, the initial position of the transmitting array element can be obtained as 3. The MIMO radar sparse array optimization method based on the sleep monitoring scenario according to claim 2 is characterized in that: As described in step 2, the distance h between the human body and the radar and the length d of the bed t and width d r , calculate the azimuth angle θ respectively r and pitch angle θ t The two-dimensional angle range includes: Assume that in a real-world scenario, the radar is placed more than one meter above the human body, pointing vertically downward. The transmitting and receiving array elements are both linear arrays and arranged vertically, forming an L shape. The height of the radar from the human body is h, and the width of the bed is d. r , with a length of d t ; Calculate the azimuth angle θ r and pitch angle θ t The ranges are:

4. The MIMO radar sparse array optimization method based on the sleep monitoring scenario according to claim 3 is characterized in that: In step 3, according to the two-dimensional angle range, let the receiving array represent the azimuth dimension and the transmitting array represent the elevation dimension; according to the initial receiving array element position Recorded in the azimuth constraint range θ r The maximum level value P of the directional pattern pointing downward at all angles within r ; According to the initial transmitting array element position Recorded in the pitch angle constraint range θ t The maximum level value P of the directional pattern pointing downward at all angles within t , specifically including: Step 3-1: Based on the two-dimensional angle range obtained in step 2, let the maximum azimuth angle be θ rM , then in the azimuth dimension, the one-dimensional pattern function pointing to θ0 is expressed as: Where θ is the pattern angle, θ0 is the beam pointing direction, and R i is the complex excitation coefficient corresponding to each array element, is the spatial wave number, d ri is the position of each receiving element, N is the number of elements; for the initial element position, R i is the steering vector of each array element, that is Step 3-2, in [-θ rM ,θ rM ] range, the beam is scanned in steps of Δθ, and the pattern function F is calculated for each angle. ri (θ i ),1≤i≤M, where M is [-θ rM ,θ rM The total number of discrete angle values ​​in the range of Δθ; Step 3-3, for any pointing pattern function F ri (θ i ), discard the part corresponding to the main lobe width, and get F ri (θ s ), {θ s } is the discrete angle pointing of the side lobe area; ri (θ s ) performs two-step extreme value calculation: First, F ri (θ s ) Derivative: make Record the amplitude of each extreme point n is the number of extreme values; find the maximum value p of each extreme point θi : p θi That is θ i Peak sidelobe level pointing downward; Step 3-4, record in [-θ rM ,θ rM ] range, with Δθ as the step, the peak sidelobe level of the directional pattern pointing down at M discrete angles: PSLL=[p θ1 ,p θ2 ,...,p θM ] Where p θi is θ i The maximum sidelobe level pointing downward, find the maximum level value, record it as P r ,Right now: P r =max(PSLL) Step 3-5: Similarly, in the pitch angle dimension, the transmitting array element repeats steps 3-1 to 3-4 to obtain the maximum level value P t .

5. The MIMO radar sparse array optimization method based on the sleep monitoring scenario according to claim 4 is characterized in that: In step 4, the maximum level value P obtained at the initial array element position is used as the result of the fitness function. The excitation coefficient w is obtained by convex optimization calculation based on the spacing obtained in each iteration, replacing the original steering vector R i , repeat step 3 and use the multi-objective particle swarm algorithm to iteratively solve, specifically including: For the receiving array element, Step 4-1: First, determine the particle swarm size K, the number of particles in the swarm D, the maximum number of iterations Q, and the speed v of position update for each iteration; where D is equal to the number of array element spacings; In step 4-2, the velocity and position of each particle after iteration are expressed as: v ij (t+1)=w·v ij (t)+c1r1(t)(p ij (t)-x ij (t))+c2r2(t)(p gj (t)-x ij (t)),t∈{1,Q-1} x ij (t+1)=x ij (t)+v ij (t+1),t∈{1,Q-1} Where, 1≤j≤K, 1≤i≤D, t is the number of iterations, c1, c2 are two speed learning factors, used to control the speed of particle position change; r1, r2 are two random numbers between [0, 1], used to enhance the randomness of the change and prevent the occurrence of local optimal conditions, w is the inertia weight, which remembers the speed information of the previous iteration, p ij (t) is the optimal position of the jth particle swarm, p gj (t) is the global optimal position; Step 4-3, set the upper and lower limits of the speed, that is Where, v max and v min are the maximum and minimum change speeds respectively; in order to enhance the sparsity and reduce the coupling degree of the antenna, the spacing d of all array elements is set to meet 0.5λ≤d≤1.5λ; In step 4-4, the complex excitation coefficient w is obtained by using the convex optimization algorithm to replace the steering vector to further reduce the peak sidelobe level. Therefore, a convex optimization model is established, that is, minmax(|ω H b(θ s )|),s∈{1,...,S} s.t.|ω H R i |=1,i∈{1,...,M} In the formula, {θ s } is the discrete angle pointing of the side lobe area, S is the number of discrete angle values ​​in the side lobe area, R i is θ i The downward steering vector, M is the number of discrete angles in the azimuth dimension with Δθ as the step, b(θ s ) is the complex weight coefficient of the sidelobe area, expressed as: Step 4-5: Calculate the complex excitation coefficient ω and use it to replace the steering vector to obtain the directional pattern: Repeat step 3 to obtain the maximum level P after convex optimization of the azimuth dimension r_CVX ; Similarly, the transmitting array element repeats steps 4-1 to 4-5 in the pitch angle dimension to obtain the maximum level P after convex optimization of the pitch angle dimension. t_CVX .

6. The MIMO radar sparse array optimization method based on the sleep monitoring scenario according to claim 5 is characterized in that: In step 5, when the number of iterations t≤Q and the change between two adjacent iterations is less than δ, the iteration is exited to obtain the optimal sparse array element position under the two-dimensional angle constraint. and the complex excitation coefficient matrix W r 、W t , specifically including: Step 5-1: For the receiving array element, repeat step 3. When the maximum level value P r_CVX Exit the iteration when the following conditions are met: Where t is the number of iterations, satisfying t≤Q, Q is the maximum number of iterations, and δ is a very small positive number; Step 5-2: Record the final receiving element position The complex excitation coefficient matrix W for all discrete angles within the angle constraint r : Where θ i For the azimuth angle [-θ rM ,θ rM ] range, with Δθ as the step, a total of M discrete angles, N is the number of receiving array elements, 1≤i≤M; Similarly, the transmitting array element repeats step 5, and finally obtains the two-dimensional optimal sparse array element position and the complex excitation coefficient matrix W r 、W t , draw a directional diagram.

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