A method for evaluating non-coherent detection performance of a multi-transmit multi-receive radar

Abstract

This invention discloses a noncoherent detection performance evaluation method for multi-transmitter, multi-receiver radar, belonging to the field of radar technology. The method includes constructing a MIMO radar system model, pre-setting and transmitting M orthogonal signals, which are then reflected by a spatial target and received by N receiving antennas and subjected to matched filtering. The echo signal of the detected target exhibits different distribution fluctuations due to varying transmit / receive links, detection angles, and RCS scattering characteristics in different regions. The method selects the distribution patterns of the signals from each path, noncoherently merges the matched-filtered signals from the M N paths, obtains the noncoherent detection statistics under multi-mode combination, and calculates the false alarm probability P. fa Detection threshold η t and the non-coherent detection probability P d This invention solves the technical problem of rapid evaluation of the non-coherent detection performance of MIMO radar. The evaluation calculation time is greatly shortened, efficiency is improved, and the evaluation results are reliable.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and relates to a method for evaluating the noncoherent detection performance of multiple-transmitter, multiple-receiver radar. Background Technology

[0002] MIMO (multiple-input multiple-output) radars can achieve spatial diversity gain by employing a distributed deployment. Since phase synchronization and coherent accumulation between multiple receiver and transmitter units are difficult to achieve in coherent MIMO radars, non-coherent information combining methods are often used. Furthermore, evaluating the non-coherent detection performance of MIMO radars is crucial for analyzing MIMO radar system performance and guiding MIMO radar system design. False alarm probability and detection probability are commonly used as important indicators to evaluate the detection performance of MIMO radars.

[0003] In real-world scenarios, the detected targets are typically undulating targets that follow a certain distribution. Existing MIMO noncoherent detection performance analysis methods are mainly used to analyze MIMO radar echo signals from all paths that follow the same type of distribution, such as Swerling, Weibull, and Rice distributions. When different transmitting and receiving units of a MIMO radar are spatially separated, the echo signals from different paths exhibit undulating characteristics that follow different types of distributions. In this case, Monte Carlo simulation can be used to obtain the false alarm probability and detection probability of the MIMO radar, but Monte Carlo simulation is very time-consuming. Therefore, finding an effective analysis method is crucial for evaluating the detection performance of MIMO radar under targets with generally undulating characteristics. Summary of the Invention

[0004] The purpose of this invention is to provide a method for evaluating the noncoherent detection performance of MIMO radar, which solves the technical problem of rapid evaluation of the noncoherent detection performance of MIMO radar.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for evaluating the noncoherent detection performance of MIMO radar includes the following steps:

[0007] Step 1: Establish a model building module. In the model building module, construct a MIMO radar system model. The MIMO radar system model is a mathematical model of a MIMO radar system with M transmitting units and N receiving units. There are MN transmitting and receiving paths, which can collect the received signals of each receiving unit in the MIMO radar system.

[0008] Step 2: Establish a filtering module. The filtering module performs matched filtering on all received signals in the MIMO radar system model and the transmitted signals one by one to obtain the corresponding sampled signal output.

[0009] Step 3: Establish an evaluation module. The evaluation module performs mode selection and noncoherent merging processing on all sampled signal outputs to obtain the detection statistics of the noncoherent detector under multiple distribution mode combinations of MIMO radar.

[0010] Step 4: Analyze the two possible scenarios: the target does not exist and the target exists.

[0011] When the target does not exist, the false alarm probability is calculated based on the distribution of the detection statistic, and the detection threshold is determined.

[0012] When the target is present, the non-coherent detection probability of the MIMO radar is calculated using the Marcum function and the probability density function.

[0013] Preferably, when performing step 1, the MIMO radar system model is specifically represented by the following formula:

[0014]

[0015] Where, r k (t) represents the signal received by the k-th receiving unit, and P is the total transmit power. For the signal transmitted by the i-th transmitting unit, τ ki s is the propagation delay of the i-th transmitted signal on the ik-th transmit / receive path. i (t) is the normalized transmitted signal that satisfies ∫ T |s i (t)| 2 dt = 1 and different transmitted signals are orthogonal to each other, where T is the duration of the transmitted signal. It is the target reflection coefficient of the ikth transmit / receive path, with an amplitude of α. ki Phase is w k (t) is a zero-mean complex Gaussian noise signal, denoted as phase They are uniformly distributed in [0, 2π], i = 1, ..., M, k = 1, ..., N.

[0016] Preferably, when performing step 2, the specific formula for matched filtering is as follows:

[0017]

[0018] Among them, w′ ki It is a complex Gaussian distribution with zero mean. y kiThis is the output of the matched filter.

[0019] Preferably, when performing step 3, the calculation formula for the detection statistic under multiple distribution pattern combinations is as follows:

[0020]

[0021] Here, hypothesis H0 and hypothesis H1 represent the absence of the target and the presence of the target, respectively, and S represents the detection statistic.

[0022] Preferably, step 4 includes the following steps:

[0023] Step 4-1: When the target does not exist, the detection statistic S follows a distribution. False alarm probability P fa Represented as:

[0024]

[0025] Wherein, the threshold value η t Represented as Defined as χ with 2MN degrees of freedom 2 The inverse cumulative distribution function of the distribution, χ represents the degree of freedom u 2 distributed;

[0026] Step 4-2: When the target exists, the detection probability P d It can be represented as:

[0027]

[0028] Where η=ηt / σ 2 Q v (·,·) denotes the v-order Marcum Q-function, f ξ (ξ) is a variable The probability density function;

[0029] Non-coherent detection probability P d The fast version is:

[0030]

[0031] in, m1 is a sufficiently large positive real number, and Δ is the width of each subinterval [hΔ, (h+1)Δ] on the integration region [0, +∞), where h = 1, 2, 3, ...;

[0032] coefficient δ h [L] can be calculated recursively using the following formula:

[0033]

[0034] in, For variable x q The probability density function of q = 1, 2, ..., L Let x be the q-th element of an NM×1 dimensional vector, i = 1, ..., M, k = 1, ..., N.

[0035] The present invention provides a method for evaluating the noncoherent detection performance of MIMO radar, which solves the technical problem of rapid evaluation of the noncoherent detection performance of MIMO radar. The present invention significantly reduces the evaluation calculation time, improves efficiency, and provides reliable evaluation results. Attached Figure Description

[0036] Figure 1 This is the main flowchart of the present invention;

[0037] Figure 2 The distributed MIMO radar noncoherent detection performance curve of this invention;

[0038] Figure 3 This is a flowchart illustrating the processing of MIMO radar received data according to the present invention. Detailed Implementation

[0039] like Figures 1-3 The aforementioned method for evaluating the noncoherent detection performance of MIMO radar includes the following steps:

[0040] Step 1: Establish a model building module. Within this module, construct a MIMO radar system model. This model is a mathematical model of a MIMO radar system with M transmitting units and N receiving units, and has MN transmitting and receiving paths. It can acquire the received signals from each receiving unit in the MIMO radar system. The data processing flow after signal acquisition is as follows: Figure 3 As shown, where:

[0041] r k (t) represents the signal received by the k-th receiving unit;

[0042] P is the total transmit power. The signal transmitted by the i-th transmitting unit;

[0043] τ ki The propagation delay of the i-th transmitted signal in the ik-th transmit / receive path;

[0044] s i (t) is the normalized transmitted signal that satisfies ∫ T |s i (t)| 2 dt = 1 and different transmitted signals are orthogonal to each other, where T is the duration of the transmitted signal;

[0045] It is the target reflection coefficient of the ikth transmit / receive path, with an amplitude of α. ki Phase is phase They satisfy the condition of being uniformly distributed in [0, 2π], i = 1, ..., M, k = 1, ..., N;

[0046] w′ ki It is a zero-mean complex Gaussian noise signal, denoted as

[0047] When performing step 1, the MIMO radar system model is specifically represented by the following formula:

[0048]

[0049] Where, r k (t) represents the signal received by the k-th receiving unit, and P is the total transmit power. For the signal transmitted by the i-th transmitting unit, τ ki s is the propagation delay of the i-th transmitted signal on the ik-th transmit / receive path. i (t) is the normalized transmitted signal that satisfies ∫ T |s i (t)| 2 dt = 1 and different transmitted signals are orthogonal to each other, where T is the duration of the transmitted signal. It is the target reflection coefficient of the ikth transmit / receive path, with an amplitude of α. ki Phase is w k (t) is a zero-mean complex Gaussian noise signal, denoted as phase They are uniformly distributed in [0, 2π], i = 1, ..., M, k = 1, ..., N.

[0050] The echo signals from detected targets on different transmit and receive paths of MIMO radar exhibit various fluctuating distribution characteristics, such as Swerling-Chi distribution, Weibull distribution, and Rice distribution, with corresponding probability density functions of form f. S f W f R Without loss of generality, define the parameters. The probability density function is Where f g ∈{f S f W f R In practical applications, the distribution characteristics of the detected target echo signals in MIMO radars along different transmit and receive paths are not limited to the three distributions mentioned above.

[0051] Step 2: Establish a filtering module. The filtering module performs matched filtering on all received signals in the MIMO radar system model and the transmitted signals one by one to obtain the corresponding sampled signal output.

[0052] When performing step 2, the specific formula for matched filtering is as follows:

[0053]

[0054] Among them, w′ ki It is a complex Gaussian distribution with zero mean. y ki This is the output of the matched filter.

[0055] Step 3: Establish an evaluation module. The evaluation module performs mode selection and noncoherent merging processing on all sampled signal outputs to obtain the detection statistics of the noncoherent detector under multiple distribution mode combinations of MIMO radar. This invention can be used for noncoherent merging of multiple single-mode distributions, and it is also applicable to noncoherent hybrid merging under multiple different distribution modes.

[0056] When performing step 3, the calculation formula for the detection statistic under multiple distribution pattern combinations is as follows:

[0057]

[0058] Here, hypothesis H0 and hypothesis H1 represent the absence of the target and the presence of the target, respectively, and S represents the detection statistic.

[0059] Step 4: Analyze the two possible scenarios: the target does not exist and the target exists.

[0060] When the target does not exist, the false alarm probability is calculated based on the distribution of the detection statistic, and the detection threshold is determined.

[0061] When the target is present, the non-coherent detection probability of the MIMO radar is calculated using the Marcum function and the probability density function.

[0062] Step 4 includes the following steps:

[0063] Step 4-1: When the target does not exist, the detection statistic S follows a distribution. False alarm probability P fa Represented as:

[0064]

[0065] Wherein, the threshold value η t Represented as Defined as χ with 2MN degrees of freedom 2 The inverse cumulative distribution function of the distribution, χ represents the degree of freedom u 2 distributed;

[0066] Step 4-2: When the target exists, the detection probability P d It can be represented as:

[0067]

[0068] Where η=η t / σ 2 Q v (·,·) denotes the v-order Marcum Q-function, f ξ (ξ) is a variable The probability density function;

[0069] Non-coherent detection probability P d The fast version is:

[0070]

[0071] in, m1 is a sufficiently large positive real number, and Δ is the width of each subinterval [hΔ, (h+1)Δ] on the integration region [0, +∞), where h = 1, 2, 3, ...;

[0072] coefficient δ h [L] can be calculated recursively using the following formula:

[0073]

[0074] in, For variable x q The probability density function of q = 1, 2, ..., L Let x be the q-th element of an NM×1 dimensional vector, i = 1, ..., M, k = 1, ..., N.

[0075] In this embodiment, to simplify the symbolic representation during actual calculations, L = MN parameters can be used. Transform into an NM×1 dimensional vector x, such that the (i-1)N+kth element of x is Then ξ can be expressed as:

[0076]

[0077] Furthermore, the fast form of the probability density function of variable ξ can be expressed as:

[0078]

[0079] in, m1 is a sufficiently large positive real number, and Δ is the width of each subinterval [hΔ, (h+1)Δ] on the integration region [0, +∞), where h = 1, 2, 3, ...

[0080] coefficient δ h [L] can be calculated recursively using the following formula:

[0081]

[0082] in, For variable x q The probability density function of q = 1, 2, ..., L.

[0083] Marcum function Substituting the series form of the probability density function of the variable ξ into the fast form of the detection probability P d In the calculation formula, the Marcum function The series form of is expressed by the following formula:

[0084]

[0085] Through mathematical calculations, the noncoherent detection probability P under various distribution mode combinations of MIMO radar can be obtained. d The fast version is:

[0086]

[0087] Since the fast formula for noncoherent detection probability proposed in this invention involves the summation of two infinite series, its finite truncation form is often used in practical applications to quickly evaluate the noncoherent detection probability, namely:

[0088]

[0089] Where, N p and N h This represents the corresponding number of truncated terms.

[0090] This embodiment uses a distributed MIMO radar system with 2 transmitting units and 3 receiving units as an example for illustration. The signal received by the k-th receiving unit is:

[0091]

[0092] Where, r k (t) represents the signal received by the k-th receiving unit, and P is the total transmit power. For the signal transmitted by the i-th transmitting unit, τ ki s is the propagation delay of the i-th transmitted signal on the ik-th transmit / receive path. i (t) is the normalized transmitted signal that satisfies ∫ T |si [t)| 2 dt = 1 and different transmitted signals are orthogonal to each other, where T is the duration of the transmitted signal. It is the target reflection coefficient of the ikth transmit / receive path, with an amplitude of α. ki Phase is w k (t) is a zero-mean complex Gaussian noise signal, denoted as phase They are uniformly distributed in [0, 2π], i = 1, ..., M, k = 1, ..., N.

[0093] MIMO radar detects target echo signals through different transmit and receive paths, exhibiting various fluctuating distributions such as Swerling-Chi, Weibull, and Rice distributions, with corresponding probability density functions of form f. S f W f R Without loss of generality, define the parameters. The probability density function is Where f g ∈{f S f W f R}

[0094] Assuming parameters The probability density distribution function is shown in Table 1.

[0095]

[0096] Table 1

[0097] Received signal r k (t) through s i After applying the matched filter to (t), the sampled output is:

[0098]

[0099] Among them, w′ ki Follows a zero-mean complex Gaussian distribution y ki For the output of the matched filter, i = 1, 2, k = 1, 2, 3.

[0100] By performing distribution mode selection and noncoherent merging processing on the signal sampled after the matched filter, the detection statistics of the noncoherent detector under multiple distribution mode combinations of distributed MIMO radar can be obtained as follows:

[0101]

[0102] Here, H0 and H1 represent whether the target does not exist or the target exists, respectively.

[0103] False alarm probability P fa and threshold value η t It can be represented as:

[0104]

[0105]

[0106] in, Defined as χ with 12 degrees of freedom 2 The inverse cumulative distribution function of the distribution.

[0107] Non-coherent detection probability P d The fast version is:

[0108]

[0109] in, m1 is a sufficiently large positive real number, and Δ is the width of each subinterval [hΔ, (h+1)Δ] on the integration region [0, +∞), where h = 1, 2, 3, ...

[0110] coefficient δ h [L] can be calculated recursively using the following formula:

[0111]

[0112] Here, x is a 6×1 dimensional vector such that the 2(i-1)+kth element of x is For variable x q The probability density function of q = 1, 2, ..., L.

[0113] The simulation experiment in this embodiment:

[0114] The simulation experiment is based on the signal-to-noise ratio (SNR) = P / σ. 2 The noncoherent detection performance of the MIMO radar at 1dB, 2dB, 4dB, and 6dB respectively was simulated. The results of this invention were compared with the Monte Carlo simulation results to form a comparison chart of the noncoherent detection performance curves of a 2-transmit, 3-receive MIMO radar. Figure 3 As shown. In the Monte Carlo simulation experiment, the value used to calculate the false alarm probability P is... fa The Monte Carlo number is 100 / P fa , used to calculate the detection probability P d The Monte Carlo number is 10 4 .

[0115] In the fast calculation method proposed in this invention, parameter Np N h The values ​​of m1 and Δ are set to N respectively. p =25, N h =70, m1=130, Δ=0.32. from Figure 3 It can be seen that the results of the fast calculation method proposed in this invention are in good agreement with the Monte Carlo simulation results, verifying the effectiveness of the proposed fast calculation method. Furthermore, when the false alarm probability is 10... -5 The Monte Carlo simulation method requires 17.6s, 17.4s, 17.3s, and 17.28s to calculate the detection probabilities corresponding to signal-to-noise ratios of 1dB, 2dB, 4dB, and 6dB, respectively, while the fast calculation method proposed in this invention requires only 0.1s. This demonstrates that the computation speed of the method proposed in this invention is significantly faster than that of the Monte Carlo simulation method.

[0116] This invention involves constructing a MIMO radar system model, transmitting M different orthogonal signals through M transmitting antennas, reflecting them off a spatial target, and then receiving them through N receiving antennas via matched filtering of the MN paths formed by the transmit and receive links. When the MIMO radar detects a target from different angles via different transmit and receive links, the echo signal from the target exhibits different distribution fluctuations due to varying RCS (Radar Cross Section) scattering characteristics in different regions. The distribution patterns of the signals from each transmit and receive path after matched filtering are selected, and then the matched-filtered signals from the MN paths are noncoherently combined to obtain noncoherent detection statistics under multi-mode combinations. This patent is applicable to both noncoherent combining of multiple single distribution patterns and noncoherent mixed combining of multiple different distribution patterns. Then, the false alarm probability P is calculated separately. fa Detection threshold η t and the non-coherent detection probability P d .

[0117] The present invention provides a method for evaluating the noncoherent detection performance of MIMO radar, which solves the technical problem of rapid evaluation of the noncoherent detection performance of MIMO radar. The present invention significantly reduces the evaluation calculation time, improves efficiency, and provides reliable evaluation results.

Claims

1. A method for evaluating the noncoherent detection performance of a multi-transmitter, multi-receiver radar, characterized in that: Includes the following steps: Step 1: Establish a model building module. In the model building module, construct a MIMO radar system model. The MIMO radar system model is a mathematical model of a MIMO radar system with M transmitting units and N receiving units. There are MN transmitting and receiving paths, which can collect the received signals of each receiving unit in the MIMO radar system. Step 2: Establish a filtering module. The filtering module performs matched filtering on all received signals in the MIMO radar system model and the transmitted signals one by one to obtain the corresponding sampled signal output. Step 3: Establish an evaluation module. The evaluation module performs mode selection and noncoherent merging processing on all sampled signal outputs to obtain the detection statistics of the noncoherent detector under multiple distribution mode combinations of MIMO radar. The formula for calculating the detection statistic under a combination of multiple distribution patterns is as follows: ； Where, assuming H 0 and hypothesis H 1 represents the absence of the target and the presence of the target, respectively. S This represents the detection statistic; P is the total transmission power. For amplitude; For phase; It is a zero-mean complex Gaussian noise signal; i and k are both variables. ;j is the imaginary unit, j is related to the phase Together they constitute the complex baseband representation of the signal; Step 4: Analyze the two possible scenarios: the target does not exist and the target exists. When the target does not exist, the false alarm probability is calculated based on the distribution of the detection statistic, and the detection threshold is determined. When the target is present, the non-coherent detection probability of the MIMO radar is calculated using the Marcum function and the probability density function.

2. The method for evaluating the noncoherent detection performance of a multi-transmitter, multi-receiver radar as described in claim 1, characterized in that: When performing step 1, the MIMO radar system model is specifically represented by the following formula: ； in, The signal received by the k-th receiving unit, where P is the total transmit power. The signal transmitted by the i-th transmitting unit Let be the propagation delay of the i-th transmitted signal in the ik-th transmit / receive path. To ensure the normalized transmitted signal satisfies Furthermore, the different transmitted signals are orthogonal to each other, where T is the duration of the transmitted signal. It is the target reflection coefficient of the ikth transmit / receive path, and its amplitude is Phase is , It is a zero-mean complex Gaussian noise signal, denoted as phase Satisfying Uniformly distributed inside .

3. The method for evaluating the noncoherent detection performance of a multiple-send, multiple-receiver radar as described in claim 2, characterized in that: When performing step 2, the specific formula for matched filtering is as follows: ； in, It is a complex Gaussian distribution with zero mean. , This is the output of the matched filter.

4. The method for evaluating the noncoherent detection performance of a multiple-send, multiple-receiver radar as described in claim 3, characterized in that: Step 4 includes the following steps: Step 4-1: When the target does not exist, the detection statistic S follows a distribution. False alarm probability P fa Represented as: ； Among them, threshold value η t Represented as Defined as having 2MN degrees of freedom The inverse cumulative distribution function of the distribution, Describing the degrees of freedom as u of distributed; Step 4-2: Detection probability when the target exists P d It can be represented as: ； in, express v Marcum Q function of order, For variables The probability density function; Non-coherent detection probability P d The fast version is: ； in, m1 is a sufficiently large positive real number. It is the integration region each sub-interval Interval width, ; coefficient It can be calculated recursively using the following formula: ； in, For variables The probability density function, for The first dimension of vector x One element, .

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