Extended target detection method for massive MIMO radar based on antenna grouping

Abstract

The present invention discloses a method for detecting extended targets using a large-scale MIMO radar based on antenna grouping, which relates to the field of signal processing and solves the problem of detecting extended targets using a large-scale MIMO radar. The method includes grouping antennas that receive the transmitted beams of the extended target to be detected according to the receiving object, performing statistical equivalent calculations on the outputs of each group of receiving antennas based on the central limit theorem, and using a detector under the Neyman-Pearson criterion to set a false alarm threshold to derive the statistical equivalent of each group as a detection statistic. The detection probability of the extended target to be detected is calculated based on the statistical characteristics. The method reduces the analysis complexity of the system, obtains the target detection probability of the MIMO radar system, and is beneficial to the design of large-scale MIMO radar systems.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to the problem of detecting extended targets in a massive MIMO radar system. The present invention is applicable to antenna design for a massive MIMO radar system, and specifically to a massive MIMO radar extended target detection method based on antenna grouping. Background Art

[0002] Massive Multiple Input Multiple Output (MIMO) systems are a new and emerging technology that has garnered widespread attention in recent years. (See T.L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp. 3590–3600, November 2010.) Because massive MIMO systems use a very large number of antennas, their application in wireless communications and radar systems can significantly improve performance.

[0003] In massive MIMO radar systems, using a large number of antennas can improve target detection performance. Recently, there has been some research on target detection in massive MIMO radars. For example, in 2020, S. Fortunati et al. utilized the large number of virtual antennas in massive MIMO radar systems to achieve progressive results in target detection with only a single snapshot. (See: S. Fortunati, L. Sanguinetti, F. Gini, M. S. Greco, and B. Himed, “Massive MIMO radar for target detection,” IEEE Transactions on Signal Processing, vol. 68, pp. 859–871, Jan. 2020.) In 2021, A. M. Ahmed et al. proposed a reinforcement learning-based approach to detect multiple targets in massive MIMO radar systems. (See literature: AMAhmed, AAAhmad, S.Fortunati, A.Sezgin, MSGreco, and F.Gini, "A reinforcement learning based approach for multi-target detection in massive MIMO radar," IEEE Transactions on Aerospace and Electronic Systems, pp. 1–1, Feb. 2021.)

[0004] Current research on massive MIMO radar target detection typically considers far-field point targets, with each antenna observing the same target from the same angle. However, in practice, targets often have multiple reflection centers that reflect the transmitted signal, and the reflected echoes may contain information such as different angles and time delays. Therefore, it is more accurate to consider extended targets in practical applications. Furthermore, systems using massive antennas often have large array apertures. In this case, the assumption that the target is far-field may not hold. Consequently, even when observing the same target, antennas separated by large distances will have different observation angles and receive different information about the target, such as the target reflection coefficient. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: the problem of detecting extended targets by massive MIMO radar when the system array aperture is very large. The present invention provides a massive MIMO radar extended target detection method based on antenna grouping to solve the above problem.

[0006] The present invention is achieved through the following technical solutions:

[0007] In a massive antenna MIMO radar system, the antennas receiving the transmitted beams of the extended target to be measured are grouped according to the receiving object. The output of each group of receiving antennas is statistically equivalently calculated based on the central limit theorem. The false alarm threshold of the detector under the Neyman-Pearson criterion is used to derive the statistical equivalent of each group as the detection statistic. The detection probability of the extended target to be measured is calculated based on the statistical characteristics.

[0008] The detailed steps are as follows:

[0009] Step 1: Consider the extended target at (x0, y0) as an array that can emit beams into space, and the aperture of the array on the x-axis is ∈ x , the aperture on the y-axis is ∈ y , define the beam width of the target beam on the x-axis as λ c / ∈ x , the beam width on the y-axis is λ c / ∈ y ;

[0010] Step 2: Analyze the correlation between the target reflection coefficients corresponding to each antenna and propose an antenna grouping method. For simplicity and without loss of generality, assume that the transmitting antennas are placed far enough apart so that the target reflection coefficients associated with different transmitting antennas are independent of each other. Then, for the nth and n'th receiving antennas, if their coordinates meet at least one of the following conditions,

[0011] x r,n -x r,n′ >d(x r,n ,y r,n ,x0,y0)λ c / ∈ x ,y r,n -y r,n′ >d(x r,n ,y r,n ,x0,y0)λ c / ∈ y ,

[0012] Then they belong to different target beams, otherwise they belong to the same target beam. The receiving antennas belonging to different target beams are divided into different groups, and the receiving antennas belonging to the same target beam are divided into one group, where the subscript r represents the receiving antenna;

[0013] Step 3: Write the signals received by N receiving antennas into a vector in the form of groups.

[0014]

[0015] in, The original nth antenna is now the qth antenna of the kth group. k The receiving antennas, the received signal at the lth snapshot, r k is the received signal vector of the kth group.

[0016] If the target does not exist, then

[0017]

[0018] If the target exists, then

[0019]

[0020] in, represents noise that is uncorrelated in time and space, is the target reflection coefficient, For delay, is the signal transmitted by the mth transmitting antenna;

[0021] Step 4: Process the received signal r in groups and get the output of each group.

[0022]

[0023] in for The signal after matched filtering;

[0024] Step 5: Use the central limit theorem to get Statistical equivalence of

[0025] Under the H0 hypothesis,

[0026]

[0027] Under the H1 hypothesis,

[0028]

[0029] in, and They are Mean and variance under H0 and H1;

[0030] Step 6: The detector under the Neyman-Pearson criterion can be derived as

[0031]

[0032] Here, η is a threshold value determined by the required false alarm level.

[0033] Step 7: Based on the statistical characteristics of the detection statistic T, the closed-form expression for the detection probability of the massive MIMO radar system can be obtained as

[0034]

[0035] Among them, the threshold Q(·) is the Q function, and are the mean and standard deviation of the test statistic T under H0 and H1, respectively.

[0036] The theoretical basis of the present invention is as follows:

[0037] For radar systems with large-scale antennas, the array aperture is often large, so the general target far-field assumption may not hold. Then, the angles at which antennas that are far apart observe the target will be different, and the received target reflection coefficient will also be different. nm Based on the correlation between the two, a method of antenna grouping can be proposed. This method regards the extended target as an array that can transmit beams into space, and the beam width of the target beam on the x-axis is λ c / ∈ x , the beam width on the y-axis is λ c / ∈ y If receiving antennas are illuminated by the same target beam, they belong to the same group, and their corresponding received signals are related to the same target reflection coefficient. Otherwise, antennas illuminated by different target beams belong to different groups, and their corresponding received signals are related to different target reflection coefficients. Because large-scale receiving antennas are numerous and some are located far apart, they can be divided into different antenna groups.

[0038] The spatial correlation-based antenna grouping method shows that the reflection coefficients received by antennas in different groups are independent of each other, while the reflection coefficients received by antennas in the same group have the same characteristics. Therefore, it can be assumed that the reflection coefficients received by antennas in the same group are independent and identically distributed.

[0039] For the received signal, each group is processed in the same way. First, the received signal is matched filtered to disperse the signals related to different transmitting antennas, then the matched filtered signal is whitened and normalized, and then the energy of the two filtered signals is calculated. Finally, the divergence between the two energies is calculated to obtain the output signal of each group for different filters. Output signal Contains coefficients related to k and m, which are generalized chi-square distributions. To find the detector, the distribution of the detection statistic will be very complex, and it is impossible to find a closed expression for the detection probability. Considering that the antenna is large-scale, this means that not only the number of antennas for the entire array is sufficient, but also the number of antennas for each group is sufficient. Therefore, the central limit theorem can be used to find Statistical equivalence of It is Gaussian distributed, and its mean and variance under the H0 and H1 assumptions can be obtained.

[0040] Under the Neyman-Pearson criterion, using statistical equivalence Get the target detector, where the detection statistic T is Since the detection statistic is a linear transformation of , the detection statistic is also Gaussian, and its mean and variance can be calculated under the H0 and H1 assumptions. Based on the Gaussian distribution of the detection statistic, a closed-form expression for the detection probability can be derived.

[0041] The present invention has the following advantages and beneficial effects:

[0042] The present invention groups large-scale antennas by analyzing the correlation between target reflection coefficients, and performs statistical equivalence on the output of each group, thereby reducing the analysis complexity of the system.

[0043] The present invention performs target detection based on the statistical equivalence of each group and obtains a closed expression for the target detection probability of a large-scale MIMO radar system, which is beneficial to the design of a large-scale MIMO radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0045] Figure 1 Schematic diagram of a massive MIMO radar system;

[0046] Figure 2 The receiver operating characteristic curves of the detection probability obtained by theory and simulation with different numbers of receiving antennas when the noise variance is set to 4 are as follows;

[0047] Figure 3 The receiver operating characteristic curves of the detection probability obtained from theory and simulation with the false alarm probability changing with different numbers of receiving antennas when the noise variance is set to 10;

[0048] Figure 4 The figure shows the theoretical detection probability changing with the number of receiving antennas under different signal-to-noise ratios when the false alarm probability is set to 0.01. DETAILED DESCRIPTION

[0049] Before describing any embodiment of the present invention in detail, it should be understood that the application of the present invention is not limited to the details of the structure shown in the following description or the accompanying drawings. The present invention may adopt other embodiments and may be implemented or carried out in various ways. Based on the embodiments of the present invention, all other embodiments obtained by ordinary skill in the art without making creative improvements are within the scope of protection of the present invention.

[0050] For radar systems with large-scale antennas, the array aperture is often very large, so the general target far-field assumption may not hold. Then, the angles at which antennas that are far apart observe the target will be different, and the received target reflection coefficients will also be different.

[0051] Therefore, the target reflection coefficient ξ received by the antenna is analyzed nm Based on the correlation between the two, a method of antenna grouping can be proposed. This method regards the extended target as an array that can transmit beams into space, and the beam width of the target beam on the x-axis is λ c / ∈ x , the beam width on the y-axis is λ c / ∈ y If the receiving antennas can be illuminated by the same target beam, they belong to the same group, and the corresponding received signals are related to the same target reflection coefficient. Otherwise, antennas illuminated by different target beams belong to different groups, and the corresponding received signals are related to different target reflection coefficients. Because there are many large-scale receiving antennas and some are far away, large-scale receiving antennas can be divided into different antenna groups, such as Figure 1 As shown, Figure 1 Schematic diagram of a massive MIMO radar system, including the target beam formed by the extended target in space and the different groups into which the antennas are divided according to the target beam.

[0052] The specific operations are:

[0053] Step 1: Consider the extended target at (x0, y0) as an array that can emit beams into space, and the aperture of the array on the x-axis is ∈ x , the aperture on the y-axis is ∈ y , define the beam width of the target beam on the x-axis as λ c / ∈ x , the beam width on the y-axis is λ c / ε y ;

[0054] Step 2: Analyze the correlation between the target reflection coefficients corresponding to each antenna and propose an antenna grouping method. For simplicity and without loss of generality, assume that the transmitting antennas are placed far enough apart so that the target reflection coefficients associated with different transmitting antennas are independent of each other. Then, for the nth and n'th receiving antennas, if their coordinates meet at least one of the following conditions,

[0055] x r,n -x r,n′ >d(x r,n ,y r,n ,x0,y0)λ c / ε x ,y r,n -y r,n′ >d(x r,n ,y r,n ,x0,y0)λ c / y ,

[0056] Then they belong to different target beams, otherwise they belong to the same target beam. The receiving antennas belonging to different target beams are divided into different groups, and the receiving antennas belonging to the same target beam are divided into one group;

[0057] The spatial correlation-based antenna grouping method shows that the reflection coefficients received by antennas in different groups are independent of each other, while the reflection coefficients received by antennas in the same group have the same characteristics. Therefore, it can be assumed that the reflection coefficients received by antennas in the same group are independent and identically distributed.

[0058] For the received signal, each group is processed in the same way. First, the received signal is matched filtered to disperse the signals related to different transmitting antennas, then the matched filtered signal is whitened and normalized, and then the energy of the two filtered signals is calculated. Finally, the divergence between the two energies is calculated to obtain the output signal of each group for different filters. Output signal Contains coefficients related to k and m, which are generalized chi-square distributions. To find the detector, the distribution of the detection statistic will be very complex, and it is impossible to find a closed expression for the detection probability. Considering that the antenna is large-scale, this means that not only the number of antennas for the entire array is sufficient, but also the number of antennas for each group is sufficient. Therefore, the central limit theorem can be used to find Statistical equivalence of It is Gaussian distributed, and its mean and variance under the H0 and H1 assumptions can be obtained.

[0059] Under the Neyman-Pearson criterion, using statistical equivalence Get the target detector, where the detection statistic T is Since the detection statistic is a linear transformation of , the detection statistic is also Gaussian, and its mean and variance can be calculated under the H0 and H1 assumptions. Based on the Gaussian distribution of the detection statistic, a closed-form expression for the detection probability can be derived.

[0060] The specific operations are:

[0061] Step 3: Write the signals received by N receiving antennas into a vector in the form of groups.

[0062]

[0063] in, The original nth antenna is now the qth antenna of the kth group. k The receiving antennas, the received signal at the lth snapshot, r k is the received signal vector of the kth group.

[0064] If the target does not exist, then

[0065]

[0066] If the target exists, then

[0067]

[0068] in, represents noise that is uncorrelated in time and space, is the target reflection coefficient, For delay, is the signal transmitted by the mth transmitting antenna;

[0069] Step 4: Process the received signal r in groups and get the output of each group.

[0070]

[0071] in for The signal after matched filtering;

[0072] Step 5: Use the central limit theorem to get Statistical equivalence of

[0073] Under the H0 hypothesis,

[0074]

[0075] Under the H1 hypothesis,

[0076]

[0077] in, and They are Mean and variance under H0 and H1;

[0078] Step 6: The detector under the Neyman-Pearson criterion can be derived as

[0079]

[0080] Here, η is a threshold value determined by the required false alarm level.

[0081] Step 7: Based on the statistical characteristics of the detection statistic T, the closed-form expression for the detection probability of the massive MIMO radar system can be obtained as

[0082]

[0083] Among them, the threshold Q(·) is the Q function, and are the mean and standard deviation of the test statistic T under H0 and H1, respectively.

[0084] For the convenience of description, we first define the following: where bold capital letters represent matrices, bold lowercase letters represent vectors, (·) * represents conjugation, (·) T represents transpose, (·) H represents the conjugate transpose, Diag(·) represents the block diagonal matrix, diag(·) represents the diagonal matrix, ||·|| represents the l2 norm, I L Represents the L-dimensional identity matrix.

[0085] Consider a massive MIMO radar system where the number of receiving antennas is large. For simplicity, the number of transmitting antennas is assumed to be the same as that of a conventional MIMO radar system. Assume that the positions of the M transmitting antennas and the N receiving antennas are (x t,m ,y t,m ), m=1,…,M, and (x r,n ,y r,n ), n=1,…,N. Assume that there is an extended target composed of a large number of random isotropic and independent scattering points, which are uniformly distributed in [x0-(∈ x / 2), x0+(∈ x / 2)]×[y0-(∈ y / 2),y0+(∈ y / 2)]inside.

[0086] According to the scattering point characteristics of the extended target, the received signal of the nth receiving antenna when the target exists can be expressed as

[0087]

[0088] in, is the equivalent target reflection coefficient of the extended target containing multiple scattering points, τ nm For delay, represents the noise that is uncorrelated in time and space. Assuming that the transmitted signal are narrowband and mutually orthogonal, where E m represents the emission energy, T s represents the sampling interval, and l represents the snapshot number.

[0089] According to the relationship between the target beam and the antenna position, an antenna grouping method based on spatial correlation is proposed. Assume that the transmitting antennas are placed far enough apart so that they belong to different target beams. According to the antenna grouping method, the receiving antennas are divided into different groups. Assume that the receiving antennas are divided into K groups, each group contains Z k antennas, i.e. Collecting the L snapshots received by K groups, the received signal can be written as

[0090]

[0091] in,

[0092]

[0093] represents the signal vector received by the kth group,

[0094]

[0095] is the noise vector, The covariance matrix of the noise can be calculated as

[0096]

[0097] in

[0098]

[0099] From the antenna grouping method, we can know that the reflection coefficients received by different groups are unrelated, that is,

[0100] When n∈k group, n'∈k' group. (7)

[0101] Assuming that the reflection coefficients received by antennas in the same group are independent and identically distributed,

[0102] and When n∈k groups. (8)

[0103] Therefore, the received signal r of group k is k The covariance matrix of can be expressed as

[0104]

[0105] in, It's a Z k ×Z k -dimensional diagonal matrix.

[0106] Process the received signal of each group. Take the received signal of group k as an example, use M groups of matched filters S MP r k The signals associated with different transmitting antennas are separated

[0107]

[0108] in

[0109]

[0110] is the output signal of the mth filter, S MP =[S MP ,1,......,S MP,M ], s MP,m =[s m (T s -τ),...,s m (LT s -τ)] T ,

[0111] In the kth group, the output signal y of the mth filter is km Through whitening filter and normalization filter respectively, and get

[0112]

[0113] and

[0114]

[0115] in,

[0116]

[0117]

[0118] Next, calculate y km,0 and y km,1 Energy

[0119]

[0120] and

[0121]

[0122] Finally, we get x km,0 and x km,1 The divergence between

[0123]

[0124] For each group, the number of antennas is still sufficient. Therefore, the central limit theorem gives Statistical equivalence of Under the H0 hypothesis, in

[0125]

[0126]

[0127] Under the H1 hypothesis, in

[0128]

[0129]

[0130] Collect from K groups and M matched filters Get the signal vector used to detect the target

[0131]

[0132] Then the detector under the Neyman-Pearson criterion can be derived as

[0133]

[0134] Based on the statistical characteristics of the detection statistic T, the closed-form expression of the detection probability of the massive MIMO radar system can be obtained as

[0135]

[0136] Among them, the threshold The mean and standard deviation of the test statistic T under H0 and H1 are

[0137]

[0138]

[0139] and

[0140]

[0141]

[0142] Regarding the extended target detection of massive MIMO radar based on antenna grouping, two examples are given to verify the derived theoretical results and illustrate the benefits brought by massive receiving antennas.

[0143] In these two examples, based on the above embodiments, it is assumed that the extended target is located at (3,3) km, and the apertures on the x-axis and y-axis are ∈ x =50m and∈ y =50m. Assume there are M=3 transmitting antennas, located at (0,3)km, (-1,1)km and (-5,0)km respectively. The transmitted waveform is Where T0 = 1ms, T s =1 / 2000s, f Δ =20 / T0. Assume that the number of large-scale receiving antennas is N, and their positions are ((n-1)d, 0)m, where the antenna spacing d = λ / 2, and the carrier λ = c / f c , carrier frequency f c =10 9 Hz, c is the speed of light. The signal-to-noise ratio is defined as For simplicity, assume that E m =1,

[0144] In Example 1, Figure 2 and Figure 3 Simulates different The receiver operating characteristic curve, showing the detection probability changing with the false alarm probability under different receiving antenna numbers, verifies the correctness of the theoretical derivation results when the number of antennas is large enough, that is, they can overlap well with the simulation results, which is consistent with the central limit theorem used.

[0145] In Example 2, Figure 4 Simulations show how detection probability varies with the number of antennas at different signal-to-noise ratios. This demonstrates the advantages of large-scale antennas: when a large number of antennas is used, detection probability can be very high even at low signal-to-noise ratios. It also shows that after a certain number of antennas is reached, the detection probability reaches 1, and adding more antennas at this point does not significantly improve detection performance.

[0146] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for extended target detection in a massive MIMO radar based on antenna grouping, characterized by: In a massive MIMO radar system, the antennas receiving the transmitted beams of the extended target to be detected are grouped according to the receiving object. The outputs of each group of receiving antennas are statistically equivalently calculated based on the central limit theorem. The false alarm threshold of the detector under the Neyman-Pearson criterion is used to derive the statistical equivalent of each group as a detection statistic. The detection probability of the extended target to be detected is calculated based on the statistical characteristics. Among them, n and n ' receiving antennas, determine whether it is the same extended target beam, the target beam coordinates received by the receiving antenna ( x r,n , y r,n )and( x r,n’ , y r,n’ ), if at least one of the following conditions is met, they are different target beams; otherwise, they belong to the same target beam. The receiving antennas belonging to different target beams are divided into different groups, and the receiving antennas belonging to the same target beam are divided into one group. The conditions are: , where the extended target position to be measured is ( x 0, y 0), the expansion target is x The diameter of the hole on the shaft is ,exist y The diameter of the hole on the shaft is , the target beam is x The beam width on axis is ,exist y The beam width on axis is , corner mark r represents the receiving antenna, It also includes the following processing, N The vector obtained by grouping the signals received by the receiving antennas is: ,in, For the original n antenna, now for the k The first The receiving antenna, l A quick shot of the received signal, For the k The received signal vector of each group; For the signal received by the receiving antenna, if the target does not exist, then , if the target exists, then ,in, represents noise that is uncorrelated in time and space, is the target reflection coefficient, For delay, For the m The signal transmitted by the transmitting antenna; The detailed process of processing the received signal after grouping is as follows: Packet pair receiving signal r Process and get the output of each group. ,in, , for The signal after matched filtering; Then use the central limit theorem to get Statistical equivalence of , exist H 0 assumption, ， exist H 1Assume that ， in, and They are exist H 0 and H Mean and variance under 1; Then the detector under the Neyman-Pearson criterion can be derived as ， in, is the threshold value determined by the required false alarm level; The closed-form expression of the detection probability of the massive MIMO radar system is obtained as follows: ， Among them, the threshold , for Q function.

2. The method for extended target detection using massive MIMO radar based on antenna grouping according to claim 1, wherein: Antennas are grouped according to the receiving beams to which they belong. Receiving antennas that receive the same transmitting beam are grouped together, and the reflection coefficients of transmitting beams received by antennas in different groups are unrelated.

3. The method for extended target detection in a massive MIMO radar based on antenna grouping according to claim 2, wherein: For the grouped received signal processing, a matched filter is used to separate the related signals of different transmitting antennas, and the output signal of the matched filter is then processed and output through a whitening filter and a normalization filter.

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