Analytic evaluation method for coherent MIMO radar signal accumulation performance under random amplitude error

Abstract

The invention discloses an analysis and evaluation method for coherent MIMO radar signal accumulation performance under a random amplitude error, is applied to the technical field of radars, and constructs a coherent MIMO radar signal model under the random amplitude error in order to solve the problem that the coherent MIMO radar signal accumulation performance under the random amplitude error is difficult to evaluate. Then a multi-channel signal accumulation expression under the random amplitude error is given, an echo average power analytic solution of multi-channel signal accumulation under the existence of the random amplitude error is obtained through derivation, and an accumulation efficiency expression is given. For a coherent MIMO radar system, the method can be suitable for evaluating the signal accumulation performance under independent identically distributed and independent non-identically distributed random amplitude errors.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to a signal accumulation performance evaluation technology for a multi-input multi-output radar. Background Art

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

[0003] At present, the research on synchronization error evaluation of coherent MIMO radar mainly focuses on time, phase and frequency synchronization. Q. He et al. discussed the target positioning problem of coherent MIMO radar in the presence of phase error. Y. Yang et al. proposed a phase synchronization method between coherent MIMO radar nodes. Y. Liang et al. proposed an estimation method for time and frequency errors between MIMO radar nodes. In addition, M. Wang et al. proposed a multi-channel signal accumulation method for coherent MIMO radar based on target parameter estimation and information entropy. However, the above works did not consider the amplitude error problem between different channels of coherent MIMO radar.

[0004] Although the analysis and correction of amplitude errors is a classic problem in typical single-base multi-channel radar systems, such as phased array radars, there are still difficulties in applying existing technologies to coherent MIMO radar systems. First, the amplitude error model based on single-base multi-channel is difficult to extend to coherent MIMO radar systems, and most existing works assume that the amplitude error obeys a Gaussian random distribution. Then, the existing amplitude errors are basically assumed to be independent and identically distributed between different channels, but due to factors such as hardware manufacturing process and temperature changes, the amplitude errors between channels may be independent and non-identically distributed. In addition, the existing evaluation methods mainly use the Monte Carlo method for numerical calculations, and it is difficult to obtain accurate evaluation results. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes an analytical evaluation method applicable to independent and identically distributed and independent non-identical distribution amplitude errors, which realizes the evaluation of the accumulation performance of coherent MIMO radar signals under random amplitude errors.

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

[0007] S1. Different transmitting nodes of the coherent MIMO radar system transmit orthogonal signals to observe the same target, and different receiving nodes will receive the reflected echo signals of 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, performing time delay and phase compensation on the separated echo signal to obtain a signal with random amplitude error after single channel compensation;

[0010] S4, performing multi-channel coherent accumulation according to the echo signal of the single channel;

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

[0012] S6. According to the analytical expression of the echo signal power, an expression of the accumulation efficiency of the multi-channel echo is obtained;

[0013] S7. Based on the analytical expression of the average power obtained in step S5 and the expression of the accumulation efficiency obtained in step S6, the results of the average power and the accumulation efficiency are calculated, thereby evaluating the accumulation performance of the multi-channel signal under random amplitude errors.

[0014] Beneficial effects of the invention: The invention establishes a coherent MIMO radar echo signal model containing random amplitude errors, derives an analytical expression for the average power of echoes after multi-channel signal accumulation, and gives an expression for the accumulation efficiency of multi-channel echoes, thereby realizing the performance evaluation of multi-channel signal accumulation of coherent MIMO radar under random amplitude errors. The invention can be applied to the evaluation of signal accumulation performance under the conditions of independent and identically distributed and independent non-identical distributed random amplitude errors, and has the advantages of high computational efficiency and accurate and reliable evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the present invention.

[0016] Figure 2 This is the amplitude result of the single-channel echo signal of the MIMO radar with M transmitting nodes = 5 and N receiving nodes = 10 under uniform amplitude error.

[0017] Figure 3 It is the average power result after accumulating multi-channel signals.

[0018] Figure 4 Cumulative efficiency curves for multi-channel signal accumulation;

[0019] in, Figure 4(a) is the accumulation efficiency curve when the transmitting nodes are M=5 and the receiving nodes are N=10. Figure 4 (a) is the accumulation efficiency curve when the transmitting nodes are M=5 and the receiving nodes are N=20. Figure 4 (a) is the accumulation efficiency curve when M=5 transmitting nodes and N=30 receiving nodes. DETAILED DESCRIPTION

[0020] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.

[0021] The present invention is verified by the method of Matlab simulation experiment, and the correctness and effectiveness of the present invention are verified on the scientific computing software Matlab R2019a. The technical scheme of the present invention is further described below in conjunction with the accompanying drawings.

[0022] like Figure 1 As shown, the airborne distributed MIMO radar high-speed target coherent accumulation detection method proposed by the present invention comprises the following steps:

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

[0024]

[0025] Where A represents the signal amplitude when there is no amplitude error, A n,m A represents the random amplitude error of n receiving and m transmitting channels. n,m is modeled as a real random variable, and the amplitude errors of different channels are assumed to be independent of each other, 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 represents the transmission signal of the mth node, t represents the fast time, τ n,m represents the target delay of n receiving and m transmitting channels, f c represents the carrier frequency of the signal, θ n,m Indicates the initial phase of the n-receive and m-transmit channels.

[0026] The radar parameters used in the present invention are set as follows: the number of radar transmitting nodes M = 5, the number of radar receiving nodes is set to N = 10, N = 20, and N = 30 respectively. The amplitude signal when there is no error 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 obey independent uniform distribution, and the uniform distribution parameter is set to A n,m ~U[-0.5, 0.5].

[0027] The nodes described in this step are specifically explained as follows: the coherent MIMO radar includes multiple radar nodes, wherein the transmitting node transmits orthogonal signals and the receiving node receives echo signals.

[0028] S2, down-convert the received echoes, and use the orthogonal characteristics of the transmitted signal to perform matched filtering on the baseband signal to achieve echo separation of signals from different transmitting nodes, where the n-receive and m-transmit channel signals can be expressed as

[0029]

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

[0031] S3, delay and phase compensation is performed on the separated echo signal to obtain a signal with random amplitude error after single-channel compensation, where the delay and phase compensation can be expressed as

[0032]

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

[0034] Figure 2 The amplitude results of the single-channel echo signal of the MIMO radar with M=5 transmitting nodes and N=10 receiving nodes 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 amplitudes of target signals in different channels.

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

[0036] According to the compensated single-channel echo signal, the signal is first rearranged

[0037]

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

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

[0040]

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

[0042] S5. Calculate the analytical expression of the average power of the echo signal under random amplitude error based on the coherent accumulation results of multiple channels. The specific implementation method is:

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

[0044]

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

[0046]

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

[0048]

[0049] 2) Assume that the probability density function of the random amplitude error of the kth 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 expected operation.

[0054] 4) In order to derive the average power of the signal under the amplitude error, the present invention defines

[0055] E[P y (NM)]=N 2 M 2 A 2 +E 1 (NM)+E 2 (NM) (11)

[0056] in,

[0057]

[0058] In calculating E 1 (NM) and E 2 Before (NM), first define (Ak ) 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, E 1 (NM) can be expressed as

[0063]

[0064] In order to derive E 2 (NM), first separate q = NM and k = NM from the integral kernel, and we can get

[0065]

[0066] First, perform the innermost integral and define

[0067]

[0068] Using the independence of errors between different channels, we can get

[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 E in formula (21) 2 (NM) can be written in a recursive form, E 2 (NM) can be expressed as

[0078]

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

[0080]

[0081] The average power closed-form solution derived by the present invention is used to calculate the average power under random amplitude error. The results of the analytical solution and the Monte Carlo simulation are as follows: Figure 3 The number of Monte Carlo is 10. 6 The results of the analytical solution are basically consistent with the Monte Carlo results under three sets of simulation parameters: transmitting node M = 5, receiving node N = 10; transmitting node M = 5, receiving node N = 20; transmitting node M = 5, receiving node N = 30, which proves the effectiveness and accuracy of the proposed closed-form solution. S6. According to the analytical expression of the echo signal power, the multi-channel echo accumulation efficiency is calculated. The accumulation efficiency is defined as

[0082]

[0083] Among them, A max Indicates the maximum signal amplitude in the NM channel, which is expressed as

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

[0085] Among them, max{·} represents the maximum value operation.

[0086] The efficiency calculation under random amplitude error is performed using the closed-form solution of cumulative efficiency derived by the present invention. The results of the analytical solution and the Monte Carlo simulation are shown in Figure 4 The number of Monte Carlo is 10. 6 Second-rate, Figure 4 (a) The analytical solution and Monte Carlo simulation results are given for M = 5 transmitting nodes and N = 10 receiving nodes; Figure 4 (b) The analytical solution and Monte Carlo simulation results are given for M = 5 transmitting nodes and N = 20 receiving nodes; Figure 4(c) gives the analytical solution and Monte Carlo simulation results for transmitting nodes M = 5 and receiving nodes N = 30. The analytical solution of the accumulation efficiency is very consistent with the Monte Carlo result, which proves the effectiveness of the average power and accumulation efficiency calculated by the closed-form solution of the accumulation efficiency of the present invention.

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

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

[0089] For example, Figure 4 As shown, when the amplitude error parameter A k When it is 0.1, according to the calculation result of the expression of average power, the transmitting node M = 5, the receiving node N = 10, the average power is 33.9797dBW; the transmitting node M = 5, the receiving node N = 20, the average power is 40.0001dBW; the transmitting node M = 5, the receiving node N = 30, the average power is 43.5219dBW. Note that the amplitude error A k When it is 0, the transmitting node M = 5, the receiving node N = 10, the average power is 33.9794dBW; the transmitting node M = 5, the receiving node N = 20, the average power is 40dBW; the transmitting node M = 5, the receiving node N = 30, the average power is 43.5218dBW. In addition, according to the calculation results of the accumulation efficiency expression, the accumulation efficiency under the three sets of simulation parameters of transmitting node M = 5, receiving node N = 10; transmitting node M = 5, receiving node N = 20; transmitting node M = 5, receiving node N = 30 is greater than 0.8. Therefore, for the amplitude error parameter A k is 0.1. From the indicators of average power and accumulation efficiency, it can be found that the accumulation performance of the coherent MIMO radar is better at this time.

[0090] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. An analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors, characterized in that: include: S1. Different transmitting nodes of the coherent MIMO radar system transmit orthogonal signals to observe the same target, and different receiving nodes will receive the reflected echo signals of 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, performing time delay and phase compensation on the separated echo signal to obtain a signal with random amplitude error after single channel compensation; S4, performing multi-channel coherent accumulation according to the echo signal of the single channel; S5. Based on the results of multi-channel coherent accumulation, an analytical expression for the average power of the echo signal under random amplitude error is derived; S6. According to the analytical expression of the echo signal power, an expression of the accumulation efficiency of the multi-channel echo is obtained; S7. Based on the analytical expression of the average power obtained in step S5 and the expression of the accumulation efficiency obtained in step S6, the results of the average power and the accumulation efficiency are calculated, thereby evaluating the accumulation performance of the multi-channel signal under random amplitude errors.

2. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors according to claim 1 is characterized in that: The multi-channel coherent accumulation expression in step S4 is: Where A represents the signal amplitude when there is no amplitude error, A k represents the random amplitude error of the kth channel, s(t) represents the target complex envelope signal with scattering coefficient after matched filtering, k represents the index number of the channel, k=m+(n-1)M, m represents the transmitting radar node number, n 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 errors according to claim 2 is characterized in that: A k are independent and identically distributed random amplitude errors.

4. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors according to claim 2, characterized in that: A k are independent non-identically distributed random amplitude errors.

5. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors according to claim 3 or 4, characterized in that: 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: Then, the echo power can be rewritten as: in,(·) * represents the conjugate operation of the complex number, Aq represents the random amplitude error of the qth channel; Because s(t)s * The result of s(t) is a constant, independent of the amplitude error; therefore, s(t) is ignored. * (t), the echo power is further expressed as: S52, assuming that the probability density function of the random amplitude error of the kth 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 is expressed as: S53, the average echo power after multi-channel accumulation is expressed as definition E[P y (NM)]=N 2 M 2 A 2 +E1(NM)+E2(NM) (11) Among them, E[·] represents the expected operation, S54. To calculate E1(NM) and E2(NM), first define (A k ) 2 The expectation is expressed as g k =∫(A k ) 2 favorite k and k (12) Then A k The expectation is expressed as yes k =∫A k f k dA k . (13) Then, based on formula (13), E1(NM) is expressed as To derive E2(NM), we first separate q=NM and k=NM from the integral kernel, obtaining First, perform the innermost integral and define Then, using the independence of random amplitude errors between different channels, we get Substituting k = NM into equation (12) and equation (13), we obtain g MN =∫(A NM ) 2 favorite MN and MN (18) yes NM =∫A NM f NM dA NM (19) G MN and e NM Substituting into formula (17), we get Substituting equation (20) into equation (15), we get If equation (21) is written in recursive form, E2(NM) can be expressed as Substituting equation (22) and equation (14) into equation (11), we can obtain the analytical expression of the echo signal power under random amplitude error: Among them, A max Indicates the maximum signal amplitude in the NM channel.

6. The analytical evaluation method for the accumulation performance of coherent MIMO radar signals under random amplitude errors according to claim 5, characterized in that: The expression of the accumulation efficiency of the multi-channel echo in step S6 is:

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