An analytical evaluation method of coherent MIMO radar signal accumulation performance under random amplitude errors

Abstract

This invention discloses an analytical evaluation method for the signal accumulation performance of coherent MIMO radar under random amplitude errors. Applied to the field of radar technology, it addresses the difficulty in evaluating the signal accumulation performance of coherent MIMO radar under random amplitude errors. This invention constructs a coherent MIMO radar signal model under random amplitude errors, then provides an expression for multi-channel signal accumulation under random amplitude errors, derives the analytical solution for the average echo power of multi-channel signal accumulation in the presence of random amplitude errors, and provides an expression for the accumulation efficiency. For coherent MIMO radar systems, this invention is applicable to evaluating signal accumulation performance under independent and identically distributed (i.i.d.) and independent and non-identically distributed (i.i.d.) random amplitude errors.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a signal accumulation performance evaluation technology for multi-input multi-output radar. Background Technology

[0002] Coherent MIMO (Multiple Input Multiple Output) radar transmits orthogonal signals from multiple radar nodes, simultaneously observes the target, and performs multi-channel signal accumulation, which can significantly improve the echo signal-to-noise ratio and enhance target detection performance. However, amplitude, time, phase, and frequency synchronization among different radar nodes is a prerequisite for achieving coherent accumulation. Therefore, performance evaluation of synchronization errors is of great significance for the system design and performance evaluation of coherent MIMO radar.

[0003] Current research on synchronization error assessment for coherent MIMO radar mainly focuses on time, phase, and frequency synchronization. Q. He et al. discussed the target localization problem of coherent MIMO radar under phase error. Y. Yang et al. presented a phase synchronization method between coherent MIMO radar nodes. Y. Liang et al. presented a method for estimating time and frequency errors between MIMO radar nodes. Furthermore, M. Wang et al. proposed a multi-channel signal accumulation method for coherent MIMO radar based on target parameter estimation and information entropy. However, none of the above works considered the amplitude error problem between different channels of coherent MIMO radar.

[0004] While amplitude error analysis and correction is a classic problem in typical monostatic multichannel radar systems, such as phased array radars, applying existing technologies to coherent MIMO radar systems still faces challenges. First, amplitude error models based on monostatic multichannel systems are difficult to extend to coherent MIMO radar systems, and most existing work assumes that amplitude errors follow a Gaussian random distribution. Second, existing amplitude errors are generally assumed to be independent and identically distributed across different channels, but due to factors such as hardware manufacturing processes and temperature variations, the amplitude errors between channels may be independent and non-identically distributed. Furthermore, existing evaluation methods primarily rely on Monte Carlo methods for numerical calculations, making it difficult to obtain accurate evaluation results. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes an analytical evaluation method applicable to independent identically distributed and independent non-identically distributed amplitude errors, thereby enabling the evaluation of coherent MIMO radar signal accumulation performance under random amplitude errors.

[0006] The technical solution adopted in this invention is: an analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors, comprising:

[0007] S1. In a coherent MIMO radar system, different transmitting nodes transmit orthogonal signals to observe the same target. Different receiving nodes will receive the reflected echo signals from all transmitting nodes at the target.

[0008] S2. Down-convert the received signal and perform matched filtering to obtain echo separation of signals from different transmitting nodes;

[0009] S3. Perform time delay and phase compensation on the separated echo signal to obtain a single-channel compensated signal with random amplitude error;

[0010] S4. Perform multi-channel coherent accumulation based on the echo signal of a single channel;

[0011] S5. Based on the results of multi-channel coherent accumulation, derive the analytical expression for the average power of the echo signal under random amplitude error;

[0012] S6. Based on the analytical expression of echo signal power, obtain the expression for the accumulation efficiency of multi-channel echo;

[0013] S7. Based on the analytical expression for average power obtained in step S5 and the expression for accumulation efficiency obtained in step S6, calculate the results of average power and accumulation efficiency, thereby realizing the evaluation of the accumulation performance of multi-channel signals under random amplitude error.

[0014] The beneficial effects of this invention are as follows: By establishing a coherent MIMO radar echo signal model containing random amplitude errors, this invention derives an analytical expression for the average power of the echo after multi-channel signal accumulation and provides an expression for the accumulation efficiency of multi-channel echoes, thus realizing the performance evaluation of coherent MIMO radar multi-channel signal accumulation under random amplitude errors. This invention can be applied to evaluate signal accumulation performance under independent and identically distributed (i.i.d.) and independent and non-identically distributed (i.i.d.) random amplitude errors, and has the advantages of high computational efficiency and accurate and reliable evaluation results. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention.

[0016] Figure 2 The amplitude results are for a single-channel echo signal from a MIMO radar with M=5 transmitting nodes and N=10 receiving nodes under uniform amplitude error.

[0017] Figure 3 This is the average power result after the accumulation of multi-channel signals.

[0018] Figure 4 The accumulation efficiency curve for multi-channel signal accumulation;

[0019] in, Figure 4(a) is the accumulation efficiency curve for transmitting nodes M=5 and receiving nodes N=10. Figure 4 (a) is the accumulation efficiency curve for transmitting nodes M=5 and receiving nodes N=20. Figure 4 (a) is the accumulation efficiency curve with M=5 transmitting nodes and N=30 receiving nodes. Detailed Implementation

[0020] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0021] This invention is verified using Matlab simulation experiments. The correctness and effectiveness of this invention are verified on the scientific computing software Matlab R2019a. The technical solution of this invention is further described below with reference to the accompanying drawings.

[0022] like Figure 1 As shown, the high-speed target coherent accumulation detection method for airborne distributed MIMO radar proposed in this invention includes the following steps:

[0023] S1. During target observation, coherent MIMO radar transmits orthogonal signals from different radar transmitting nodes, and different receiving nodes simultaneously receive the reflected echoes from all transmitting nodes at the target. The expression for the echo with amplitude error received by the nth receiving node is:

[0024]

[0025] Where A represents the signal amplitude without amplitude error, A n,m A represents the random amplitude error of n transmit / receive channels and m transmit / receive channels. n,m It is modeled as a real random variable, and the amplitude errors of different channels are assumed to be independent, but it is not required that the amplitude errors of different channels are identically distributed. M is the number of transmitting radar nodes, ξ is the complex reflection coefficient of the target, and u m Let τ represent the transmitted signal at node m, t represent fast time, and τ represent the transmitted signal at node m. n,m f represents the target delay of the n-transmit / m-receive channel. c θ represents the carrier frequency of the signal. n,m This represents the initial phase of the n-receiver / m-transmitter channel.

[0026] The radar parameters used in this invention are set as follows: the number of radar transmitting nodes M = 5, and the number of radar receiving nodes N = 10, N = 20, and N = 30, respectively. The amplitude signal under error-free conditions is set to A = 1. The simulation takes independent and identically distributed errors as an example, and the amplitude errors A of different channels are... n,m Set to follow mutually independent uniform distributions, with uniform distribution parameter set to A. n,m ~U[-0.5, 0.5].

[0027] The nodes mentioned in this step are specifically explained as follows: Coherent MIMO radar includes multiple radar nodes, where the transmitting nodes transmit orthogonal signals and the receiving nodes receive echo signals.

[0028] S2. The received echo is down-converted, and the baseband signal is matched and filtered using the orthogonal characteristics of the transmitted signal to achieve echo separation of signals from different transmitting nodes. The n-receive / m-transmit channel signal can be represented as...

[0029]

[0030] Where u(t) represents the complex envelope signal of the target after matched filtering.

[0031] S3. Perform time delay and phase compensation on the separated echo signal to obtain a single-channel compensated signal with random amplitude error. The time delay and phase compensation can be expressed as follows:

[0032]

[0033] in, This represents the estimated time delay obtained through matched filtering. This represents the phase estimated by the matched filter output.

[0034] Figure 2 The amplitude results of the single-channel echo signal of a MIMO radar with transmitting node M=5 and receiving node N=10 under uniform amplitude error are shown after matched filtering and time delay phase compensation. Due to the influence of random amplitude error, there are obvious differences in the amplitude of the target signal in different channels.

[0035] S4. Perform multi-channel coherent accumulation based on the echo signal from a single channel. The specific implementation method is as follows:

[0036] Based on the compensated single-channel echo signal, the signal is first rearranged.

[0037]

[0038] Among them, A k =A n,m Let s(t) = ξu(t) represent the target complex envelope signal with scattering coefficients after matched filtering, and k = m + (n-1)M represent the index number of the n-transmit / m-receive channel.

[0039] Then, the multi-channel coherent accumulation expression of the compensated echo signal can be obtained.

[0040]

[0041] Where N represents the number of receiving radar nodes.

[0042] S5. Based on the coherent accumulation results of multiple channels, calculate the analytical expression for the average power of the echo signal under random amplitude error. The specific implementation method is as follows:

[0043] 1) The accumulated echo signal power can be expressed as:

[0044]

[0045] Then, the echo power can be rewritten as

[0046]

[0047] in,(·) * This represents the conjugate operation on complex numbers. Because the result of s(t)s*(t) is a constant, it is independent of amplitude error. Therefore, the echo power can be expressed as...

[0048]

[0049] 2) Assume the probability density function of the random amplitude error of the k-th channel is f k Because the random amplitude errors between different channels are independent of each other, the joint probability density function of NM channels can be expressed as:

[0050]

[0051] 3) The average echo power after multi-channel accumulation can be expressed as:

[0052]

[0053] Where E[·] represents the desired operation.

[0054] 4) To derive the average signal power under amplitude error, this invention defines...

[0055] E[P y (NM)]=N 2 M 2 A 2 +E1(NM)+E2(NM) (11)

[0056] in,

[0057]

[0058] Before calculating E1(NM) and E2(NM), we first define (A k ) 2 The expectation is expressed as

[0059] g k =∫(A k ) 2 f k dA k (12)

[0060] A k The expectation is expressed as

[0061] e k =∫A k f k dA k (13)

[0062] Then, E1(NM) can be expressed as

[0063]

[0064] To derive E2(NM), we first separate q = NM and k = NM from the integral kernel, which gives us...

[0065]

[0066] First, perform the innermost integral, defining...

[0067]

[0068] By utilizing the independence of errors between different channels, we can obtain

[0069]

[0070] Substituting k = NM into formulas (12) and (13), we can obtain...

[0071] g MN =∫(A NM ) 2 f MN dA MN (18)

[0072] e NM =∫A NM f NM dA NM (19)

[0073] Substituting equations (18) and (19) into equation (17), we can obtain...

[0074]

[0075] Substituting equation (20) into equation (15), we can obtain...

[0076]

[0077] Note that E2(NM) in equation (21) can be written in a recursive form, and E2(NM) can be expressed as

[0078]

[0079] Substituting equations (22) and (14) into equation (11), we can obtain...

[0080]

[0081] The average power is calculated under random amplitude error using the closed-form solution of the average power derived in this invention. The results of the analytical solution and the Monte Carlo simulation are as follows: Figure 3 As shown. The number of Monte Carlo is 10. 6 In three sets of simulation parameters—transmitter M=5, receiver N=10; transmitter M=5, receiver N=20; and transmitter M=5, receiver N=30—the analytical solution results are basically consistent with the Monte Carlo results, proving the effectiveness and accuracy of the proposed closed-form solution. S6. Based on the analytical expression of echo signal power, the multi-channel echo accumulation efficiency is calculated. The accumulation efficiency is defined as…

[0082]

[0083] Among them, A max The maximum signal amplitude in the NM channel is represented as...

[0084] A max =A + max{A k}, k=1,2,…,MN (25)

[0085] Here, max{·} represents the operation of taking the maximum value.

[0086] The efficiency calculation under random amplitude error is performed using the closed-form solution of the cumulative efficiency derived in this invention. The results of the analytical solution and the Monte Carlo simulation are as follows: Figure 4 As shown. The number of Monte Carlo is 10. 6 Second-rate, Figure 4 (a) Analytical solutions and Monte Carlo simulation results are given for transmitting node M=5 and receiving node N=10; Figure 4 (b) Analytical solutions and Monte Carlo simulation results are given for transmitting node M=5 and receiving node N=20; Figure 4 (c) Analytical solutions and Monte Carlo simulation results are presented for transmitting node M=5 and receiving node N=30. The analytical solution and Monte Carlo results for the accumulation efficiency are in excellent agreement, proving the effectiveness of the average power and accumulation efficiency calculated by the closed-form solution of the present invention.

[0087] S7. Based on the results of average power and accumulation efficiency, evaluate the accumulation performance of multi-channel signals under random amplitude error.

[0088] Based on average power Figure 3 and cumulative efficiency Figure 4 The results can be used to evaluate the signal accumulation performance of a coherent MIMO radar system under random amplitude errors.

[0089] For example, such as Figure 4 As shown, when the amplitude error parameter A k When the value is 0.1, based on the expression for average power, the average power is 33.9797 dBW for transmitting node M=5 and receiving node N=10; 40.0001 dBW for transmitting node M=5 and receiving node N=20; and 43.5219 dBW for transmitting node M=5 and receiving node N=30. Note the amplitude error A. k When the value is 0, the average power is 33.9794 dBW for transmitting node M=5 and receiving node N=10; 40 dBW for transmitting node M=5 and receiving node N=20; and 43.5218 dBW for transmitting node M=5 and receiving node N=30. Furthermore, according to the calculation results of the accumulation efficiency expression, the accumulation efficiency is greater than 0.8 for all three sets of simulation parameters: transmitting node M=5 and receiving node N=10; transmitting node M=5 and receiving node N=20; and transmitting node M=5 and receiving node N=30. Therefore, for the amplitude error parameter A... k With a value of 0.1, the accumulation performance of the coherent MIMO radar is good, as can be seen from the average power and accumulation efficiency indicators.

[0090] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. An analytical evaluation method for the signal accumulation performance of coherent MIMO radar under random amplitude error, characterized in that, include: S1. In a coherent MIMO radar system, different transmitting nodes transmit orthogonal signals to observe the same target. Different receiving nodes will receive the reflected echo signals from all transmitting nodes at the target. S2. Down-convert the received signal and perform matched filtering to obtain echo separation of signals from different transmitting nodes; S3. Perform time delay and phase compensation on the separated echo signal to obtain a single-channel compensated signal with random amplitude error; S4. Perform multi-channel coherent accumulation based on the echo signal of a single channel; S5. Based on the results of multi-channel coherent accumulation, derive the analytical expression for the average power of the echo signal under random amplitude error; the implementation process of step S5 includes the following sub-steps: S51. Based on the multi-channel coherent accumulation expression in step S4, the accumulated echo signal power is expressed as: （6）； Then, the echo power is rewritten as: （7）； in, This represents the conjugate operation on complex numbers. Indicates the first Random amplitude error of each channel; because The result is a constant, independent of the amplitude error; therefore, it can be ignored. The echo power is further expressed as: （8）； S52. Assume the probability density function of the random amplitude error of the k-th channel is: Because the random amplitude errors between different channels are independent of each other, therefore The joint probability density function of the channels is expressed as: （9）； S53, The average echo power after multi-channel accumulation is expressed as: （10）； definition: （11）； in, This indicates the desired operation. , ； S54, In order to calculate and First, define The expectation is expressed as: （12）； but The expectation is expressed as: （13）； Then, based on equation (13), Represented as: （14）； In order to derive First, separate from the integrator kernel and ,get: （15）； First, perform the innermost integral, defining: （16）； By utilizing the independence of random amplitude errors between different channels, we obtain: （17）； Substitute From equations (12) and (13), we get: （18）； （19）； Will and Substituting into equation (17), we get: （20）； Substituting equation (20) into equation (15), we get: （21）； If equation (21) is written in recursive form, then Represented as: （22）； Substituting equations (22) and (14) into equation (11), we obtain the analytical expression for the echo signal power under random amplitude error: （23）； in, Indicates in The maximum signal amplitude in the channel; The expression for the accumulation efficiency of the multi-channel echo in step S6 is: ； S6. Based on the analytical expression of echo signal power, obtain the expression for the accumulation efficiency of multi-channel echo; S7. Based on the analytical expression for average power obtained in step S5 and the expression for accumulation efficiency obtained in step S6, calculate the results of average power and accumulation efficiency, thereby realizing the evaluation of the accumulation performance of multi-channel signals under random amplitude error.

2. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude error according to claim 1, characterized in that, The multi-channel coherent accumulation expression in step S4 is: ； in, This represents the signal amplitude when there is no amplitude error. Indicates the first Random amplitude error of each channel, This represents the target complex envelope signal with scattering coefficients after matched filtering. Indicates the channel index number. , Indicates the serial number of the transmitting radar node. This represents the receiving radar node number, M represents the number of transmitting radar nodes, and N represents the number of receiving radar nodes.

3. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude error according to claim 2, characterized in that, It represents independent and identically distributed random amplitude errors.

4. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude error according to claim 2, characterized in that, It represents independent, non-uniformly distributed random amplitude errors.

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