Method for weak signal detection using radar signal phase information

Abstract

The present invention provides a method for weak signal detection using radar signal phase information. A phase detection model is established and used to detect radar echo signals, thereby distinguishing target signals from noise signals therein, thereby improving the detection rate. Unlike conventional methods, the method utilizes the phase information of radar signals for detection and adopts second-order moments or sample variances for hypothesis testing, thereby effectively improving the detection rate of echo signals. Through detection and analysis of simulated data, it can be seen that when the signal magnitude s of the target signal is at least close to 1, both the second-order moment and the sample variance statistical test methods can be effectively used for testing, and the detection effect is relatively obvious. Therefore, phase detection can further distinguish target signals from noise signals in false alarm echo signals, thereby reducing the false alarm rate and improving the detection rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal detection, and in particular relates to a method for detecting weak signals by utilizing radar signal phase information. Background Art

[0002] The working process of traditional pulse Doppler radar is generally as follows: the radar transmitter sends a specifically modulated pulse signal through the antenna. The signal propagates in the air and returns to the radar after encountering a target, and is received by the receiver antenna. Among them, the pulse signal emitted by the radar is mainly divided into two parts: one is the baseband signal, also known as the modulation signal, which is a sinusoidal wave signal with a specific waveform formed by modulation such as amplitude modulation, phase modulation or frequency modulation; the other is the carrier signal, which has the function of carrying the modulation signal. Since the frequency of the modulation signal is very low (usually within 1GHz) and the bandwidth is very wide, interference between signals is easy to occur, which is not conducive to long-distance transmission. However, the above-mentioned shortcomings of the modulation signal can be effectively solved by transporting it with a higher frequency (usually around 10GHz) carrier signal.

[0003] Due to energy losses from signal propagation and target reflection, the signals received by the receiver are often very weak. Therefore, they must be amplified by a low-noise amplifier before subsequent demodulation, detection, and display can be performed. However, due to the presence of resistor thermal noise in the amplifier circuit, noise is inevitably added to the signal during the amplification process, affecting the detection of weak signals.

[0004] The basis for radar to measure the distance, speed and other aspects of a target is whether the radar can correctly judge whether it has received a signal, that is, whether the signal can be detected correctly. Usually, the Neyman-Pearson criterion is used, that is, at a given false alarm rate, Under the conditions of SNR and signal-to-noise ratio, the detection rate Reach the maximum.

[0005] False alarm rate It refers to the ratio of noise to signal during signal detection. Since noise is generated continuously, even if the false alarm rate reaches 10 -6 , that is, if there is only one false alarm among 1 million detection points, then the alarm will also give a false alarm once every ten seconds. Therefore, in engineering applications, the false alarm rate should be as low as possible. It refers to the proportion of correctly detected signals to all signals. It is the guarantee for whether all signals can be recognized, and it is also the key to whether the target can be detected correctly and timely.

[0006] Among the existing radar signal detection methods, the most commonly used method is the modulus detection method, which can achieve a false alarm rate of 10 -6, the detection rate can reach 83%. However, due to the limitations of this method itself, the detection rate is difficult to be further improved. Summary of the Invention

[0007] The present invention is made to solve the above-mentioned problems and aims to provide a method for signal detection that uses the phase information of radar signals to establish a reliable detection model, thereby achieving a higher detection rate. The present invention adopts the following technical solutions:

[0008] The present invention provides a method for weak signal detection using radar signal phase information, which is characterized by comprising:

[0009] Step S1, obtaining an echo signal to be detected;

[0010] Step S2, establishing a phase detection model;

[0011] Step S3: Detect the echo signal using the phase detection model to distinguish the target signal and the noise signal in the echo signal.

[0012] Wherein, step S2 includes the following sub-steps:

[0013] Step S2-1: Model the echo signal as a complex signal containing the target signal and the noise signal:

[0014] ,

[0015] Where, is a constant, and Independent and identically distributed in the standard normal distribution , j is the imaginary unit, is the carrier frequency;

[0016] Step S2-2, solving to obtain the phase distribution density function of the echo signal:

[0017] ,

[0018] Where, is the phase of the echo signal, is the cumulative distribution function of the standard normal distribution;

[0019] Step S2-3, taking the signal size s = 0 of the target signal as the original hypothesis, taking N phases from the phase distribution density function as an independent sample;

[0020] Step S2-4, calculating the second-order moments of the N independent samples according to the following formula:

[0021] ,

[0022] Or calculate the sample variance of N independent samples according to the following formula:

[0023] ;

[0024] Step S2-5, using the Monte Carlo method to approximate the probability distribution function of the second-order moment Or the probability distribution function of the sample variance ;

[0025] Step S2-6, perform a null hypothesis test based on the probability distribution function of the second-order moment or the probability distribution function of the sample variance, and calculate or ,like or , then reject the null hypothesis s = 0.

[0026] The method for weak signal detection using radar signal phase information provided by the present invention may also have the following technical features: in step S2-1, the target signal is modeled as a linear frequency modulation signal:

[0027] ,

[0028] Where, is the signal size of the target signal, the initial phase of the target signal is 0,

[0029] The noise signal is modeled as a Gaussian white noise signal:

[0030] .

[0031] The method for weak signal detection using radar signal phase information provided by the present invention may also have such a technical feature, wherein step S2-2 includes the following sub-steps:

[0032] Step S2-2-1, calculate the probability density function of the echo signal:

[0033] ;

[0034] Step S2-2-2, transforming the probability density function of the echo signal to obtain:

[0035] ,

[0036] Where, is the modulus length of the echo signal, is the phase of the echo signal;

[0037] Step S2-2-3, based on the transformed probability density function of the echo signal, calculate the edge density function of the echo signal, that is, the phase distribution density function.

[0038] Functions and effects of the invention

[0039] According to the method for weak signal detection using radar signal phase information of the present invention, a phase detection model is established, and the phase detection model is used to detect radar echo signals, distinguishing target signals and noise signals therein, thereby improving the detection rate. That is, unlike traditional methods, the phase information of the radar signal is used for detection, and the second-order moment or sample variance is used for hypothesis testing, which can effectively improve the detection rate of the echo signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of a method for weak signal detection using radar signal phase information in an embodiment of the present invention.

[0041] Figure 2 4 is a flow chart of step S2 in an embodiment of the present invention.

[0042] Figure 3 is a density function diagram of the phase in an embodiment of the present invention.

[0043] Figure 4 is a density function diagram of the second-order moment in an embodiment of the present invention.

[0044] Figure 5 1 is a schematic diagram of a sequence of real and imaginary parts of an echo signal in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the method of using radar signal phase information to detect weak signals of the present invention is described in detail below with reference to the embodiments and drawings.

[0046] <Example>

[0047] Figure 1 4 is a flow chart of a method for performing weak signal detection using radar signal phase information in this embodiment.

[0048] like Figure 1 As shown, the method for weak signal detection using radar signal phase information specifically includes the following steps:

[0049] Step S1: Acquire the echo signal to be detected.

[0050] Due to the confidential nature of military radar detection data and the extremely small number of target signals in practice, it is difficult to directly obtain a large amount of real data. However, after studying the distribution of radar signals, it was found that the noise in radar signals is mostly Gaussian white noise, while the target signals are mostly linear frequency modulation signals. Therefore, in this embodiment, based on this research result, a large amount of simulated data for testing was generated.

[0051] Figure 5 is a sequence diagram of the real and imaginary parts of the echo signal in this embodiment.

[0052] like Figure 5 As shown in the figure, the real and imaginary parts of the noise are both normally distributed with a mean of 0 and a variance of 0.5, while the target signal is a variable with an initial phase that only changes with time. For the sake of generality, the initial phase of the target signal is set to 0. At this time, the echo signal with the target signal passing through the matched filter is equivalent to a complex signal with a normal distribution with a non-zero mean as the real part and a normal distribution with a zero mean as the imaginary part.

[0053] Step S2: Establish a phase detection model.

[0054] Figure 2 This is a flow chart of step S2 in this embodiment.

[0055] like Figure 2 As shown, step S2 specifically includes the following sub-steps:

[0056] Step S2-1: Model the echo signal as a complex signal containing a target signal and a noise signal.

[0057] According to the above analysis, the target signal is modeled as a constant signal with an initial phase of 0 and a signal size of s, that is, a linear frequency modulation signal:

[0058]

[0059] Where, is the effective value of the signal level (signal size), is the carrier frequency, j is the imaginary unit, and k is the frequency modulation slope.

[0060] According to the above analysis, the noise signal is modeled as having a mean of 0 and a variance of A stationary normal process, that is, a Gaussian white noise signal:

[0061]

[0062] Therefore, the echo signal containing the target signal and the noise signal can be expressed as the following complex signal:

[0063]

[0064] Where, is a constant, and Independent and identically distributed in the standard normal distribution , j is an imaginary unit. In addition, for the sake of convenience, t is omitted in this formula and the following formulas.

[0065] Step S2-2: Obtain the phase distribution density function of the echo signal.

[0066] Step S2-2 specifically includes the following sub-steps:

[0067] Step S2-2-1, calculate the probability density function of the echo signal.

[0068] In this embodiment, according to the above complex signal, it can be obtained:

[0069]

[0070] Step S2-2-2, perform a simple transformation on the probability density function of the echo signal.

[0071] Let the modulus length of the echo signal be , the phase is , then after a simple transformation we can get:

[0072]

[0073] Step S2-2-3, based on the transformed probability density function, calculate the edge density function of the echo signal, that is, the phase distribution density function:

[0074]

[0075] Where, is the cumulative distribution function of the standard normal distribution, that is:

[0076]

[0077] Step S2-3, taking the signal size s = 0 of the target signal as the original hypothesis, taking N phases from the phase distribution density function as independent samples.

[0078] Among them, under this assumption, obey Uniform distribution on .

[0079] In step S2-4, the second-order moment of N independent samples is calculated according to the following formula:

[0080] ,

[0081] Or calculate the sample variance of N independent samples according to the following formula:

[0082] .

[0083] Step S2-5, use the Monte Carlo method to approximate the probability distribution function of the second-order moment Or the probability distribution function of the sample variance .

[0084] Step S2-6, perform a null hypothesis test based on the probability distribution function of the second-order moment or the probability distribution function of the sample variance, and calculate or ,like or , then reject the null hypothesis s = 0, where is the sample second-order moment, is the sample variance, and both are calculated based on the data to be tested.

[0085] Through the above steps, a phase detection model is established.

[0086] Step S3: Detect the echo signal using a phase detection model to distinguish the target signal from the noise signal in the echo signal, thereby improving the detection rate.

[0087] The effectiveness of the method of this embodiment will be analyzed and tested below.

[0088] Figure 3 It is the density function diagram of the phase in this embodiment.

[0089] like Figure 3 As shown, when the above assumption holds true, that is, when s = 0, the phase of the echo signal is Obey the uniform distribution; when the original hypothesis is not true, the phase The density function of The image will be based on The value of varies.

[0090] Figure 4 It is a function graph of the second-order moment in this embodiment.

[0091] like Figure 4 As shown in the above steps, the Monte Carlo method is used to calculate the second-order moment. Since the distribution of the second-order moment is related to the size of the sample number N, N = 100, 500, 1200, 2000, and 10 simulations are performed on each. 3 The above simulation data are combined to calculate the density function image of the simulated second-order moment, that is, Figure 4 .

[0092] Table 1 is a table of p-values ​​calculated from simulated data in this embodiment.

[0093] Table 1 p-value table

[0094]

[0095] As shown in Table 1, in this embodiment, s = 0.1 and 0.5, and N = 100, 500, 1200, 200, are respectively taken, and the simulation data are simulated 10 times each time, and the p-value results obtained each time are shown in Table 1.

[0096] It can be seen from the p value in Table 1 that when the signal size of the target signal is very small (such as when s = 0.1 in Table 1), the phase detection effect is not good. This is because when s is very small, its distribution is originally very close to the uniform distribution, such as Figure 5 However, in the original threshold detection, the value of s is very large. When s is large and the number of samples is large (such as when s = 0.5 and N = 2000 in Table 1), the phase detection effect is more significant. Therefore, adding phase detection to the existing radar signal detection method can significantly improve the detection rate.

[0097] Table 2 is a statistical power table of the second-order moments calculated from the simulation data in this embodiment.

[0098] Table 2 Statistical power table of second-order moments

[0099]

[0100] Table 3 is a statistical power table of sample variances calculated from simulated data in this embodiment.

[0101] Table 3 Statistical power table of sample variance

[0102]

[0103] As shown in Table 2 and Table 3, when p = 0.05, 10 simulations are performed for N = 200, 500, 1200, and 2000. 5 Set of simulated data, for N = 500 simulations 10 4 The probability of rejecting the null hypothesis s = 0 is calculated by using the group of simulated data. The results are shown in Table 2 for the second-order moment method and in Table 3 for the sample variance method.

[0104] As can be seen from Tables 2 and 3, when s is at least close to 1 (corresponding to s = 0.8 and above in Tables 2 and 3), both statistical tests can be effectively performed. Overall, when the parameters are the same, the accuracy of the test using the second moment is slightly higher than that using the sample variance, but the difference is small. This is because the second moment and the sample variance have the same expectation, but the variance of the sample variance is larger (the sample variance is additionally reduced by the square of the sample expectation).

[0105] Through the above-mentioned phase detection, it is possible to distinguish the target signal from the noise signal in the false alarm echo signal, thereby reducing the false alarm rate, that is, improving the detection rate.

[0106] In summary, according to the method of this embodiment, the detection rate of radar signals is further improved by adding phase detection.

[0107] Example Function and Effect

[0108] According to the method for weak signal detection using radar signal phase information provided in this embodiment, a phase detection model is established, and the phase detection model is used to detect radar echo signals, distinguishing target signals from noise signals therein, thereby improving the detection rate. That is, unlike traditional methods, the phase information of the radar signal is used for detection, and the second-order moment or sample variance is used for hypothesis testing, which can effectively improve the detection rate of the echo signal.

[0109] In the embodiment, through the detection and analysis of the simulation data, it can be seen that when the signal size s of the target signal is at least close to 1, both the second-order moment and the sample variance statistical test methods can be effectively used for testing, and the detection effect is more obvious. Therefore, through phase detection, the target signal and the noise signal can be further distinguished in the false alarm echo signal, thereby reducing the false alarm rate, that is, improving the detection rate.

[0110] The above embodiments are only used to illustrate specific implementations of the present invention, and the present invention is not limited to the description scope of the above embodiments.

Claims

1. A method for weak signal detection using radar signal phase information, characterized in that: include: Step S1, obtaining an echo signal to be detected; Step S2, establishing a phase detection model; Step S3: Detect the echo signal using the phase detection model to distinguish the target signal and the noise signal in the echo signal. Wherein, step S2 includes the following sub-steps: Step S2-1: Model the echo signal as a complex signal containing the target signal and the noise signal: ， Where, is a constant, and Independent and identically distributed in the standard normal distribution , j is the imaginary unit, is the carrier frequency; Step S2-2, solving to obtain the phase distribution density function of the echo signal: ， Where, is the phase of the echo signal, is the cumulative distribution function of the standard normal distribution; Step S2-3, taking the signal size s = 0 of the target signal as the original hypothesis, taking N phases from the phase distribution density function As independent samples, obey Uniform distribution on ; Step S2-4, calculating the second-order moments of the N independent samples according to the following formula: ， Or calculate the sample variance of N independent samples according to the following formula: ； Step S2-5, using the Monte Carlo method to approximate the probability distribution function of the second-order moment Or the probability distribution function of the sample variance ; Step S2-6, perform a null hypothesis test based on the probability distribution function of the second-order moment or the probability distribution function of the sample variance, and calculate or ,like or , then reject the null hypothesis s = 0, where, is the sample second-order moment, is the sample variance.

2. The method for weak signal detection using radar signal phase information according to claim 1, wherein: in, In step S2-1, the target signal is modeled as a linear frequency modulation signal: ， Where, is the signal size of the target signal, the initial phase of the target signal is 0, k is the frequency modulation slope, The noise signal is modeled as a Gaussian white noise signal: 。 3. The method for weak signal detection using radar signal phase information according to claim 1, wherein: in, Step S2-2 includes the following sub-steps: Step S2-2-1, calculate the probability density function of the echo signal: ； Step S2-2-2, transforming the probability density function of the echo signal to obtain: ， Where, is the modulus length of the echo signal, is the phase of the echo signal; Step S2-2-3, based on the transformed probability density function of the echo signal, calculate the edge density function of the echo signal, that is, the phase distribution density function.

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