KR101902833B1 - Method for eliminating multiple-time-around targets due to ducting propagation - Google Patents

Abstract

The present invention relates to a method for removing multiple-time-around targets which may be generated in a ducting phenomenon in a coherent pulse radar having a fixed pulse repetition frequency (PRF). The method comprises: a step of restoring coherence of a radar signal received from targets existing within a maximum detection distance through phase modulation and demodulation of a transmission pulse radiated in each PRI of a coherent pulse radar; a step of obtaining a power spectrum represented by a range/Doppler region by performing coherent Doppler processing on all reception signals within a given CPI frame; a step of detecting a target by performing range CFAR in a range direction in the range/Doppler region; and a step of removing multiple-time-around targets by performing Doppler CFAR on the target detected in the range CFAR in a Doppler direction.

Description

METHOD FOR ELIMINATING MULTIPLE-TIME-AROUND TARGETS DUE TO DUCTING PROPAGATION BACKGROUND OF THE INVENTION [0001]

The present invention relates to a method for eliminating multiple out-of-period targets that can occur during ducting of a coherent pulse radar having a fixed pulse repetition frequency (PRF).

Coherent pulse radar or pulsed Doppler radar is a radar system capable of target detection and distance / velocity measurements in a cluttered situation.

One of the important scattering characteristics of radar electromagnetic waves is atmospheric refraction that induces the bending phenomenon of electromagnetic waves when radar is radiated. Ducting, a type of atmospheric refraction, is an extreme form of superrefraction that occurs when the refraction gradient of the electromagnetic wave is less than or equal to the radius of the Earth's curvature. Due to the bending of the electromagnetic wave, the electromagnetic waves radiated from the radar are trapped in a parallel-plate waveguide near the surface of the earth.

Spatially, ducts are divided into surface ducts, which are generated from the surface of the earth, and elevated ducts, which occur at high altitudes. When an evaporation duct (evaporation duct) or an upper duct occurs, the radar waveform may reach the horizon too far. This is because the one-way power density attenuation along the distance R is proportional to R ^-2 , but is proportional to R ^-1 in the duct. The radar detection distance can be significantly reduced or increased depending on whether the relative positions of the radar and the target or the radar and the receiver are located inside or outside the duct.

Evaporative ducts or upper ducts can increase radar detection distances, but can have a negative impact on radar performance. An increase in the detection distance means that a target located at a distance well beyond the unambiguous range can be detected. In other words, when a ducting event occurs, the radar can detect a target in the ith distance interval (i = 2, 3, ...) that exceeds the first distance interval (within the maximum detection distance). For example, in the case of Singapore Changi Airport due to ducting, the target detection distance increased by more than 10 times from 33km to 367km. This increase in detection distance is common to all radar systems, regardless of the PRF, because the propagation losses are very small when the radar and the target are located inside the duct.

Figure 1 (a) shows three targets at different distances located within the antenna beam width. Target 1 is located at the actual distance R1 and within the maximum detection distance R _ua , and targets 2 and 3 are located at the actual distance R2 and R3, respectively, in the second and third distance sections. Fig. 1 (b) shows the distance detected by the radar when all the targets and radars in Fig. 1 (a) are located in the duct. Since target 1 is within the maximum detection distance, it is detected at the actual distance R1. Since targets 2 and 3 are located in the second and third distance _regions , they are detected by radar at R _2a = R ₂ - R _ua and R _3a = R ₃ - 2 R _ua distances.

(I-th target, i = 2, 3, ...), which are detected by the radar due to the ducting phenomenon, the actual distance is located in the i-th distance interval (i = 2,3, ...) It is displayed as a false target in the first distance section. Such false targets cause confusion of the radar operator and waste of resources due to unnecessary tracking of the target. The occurrence of a false target is an undesirable phenomenon because it interferes with the actual mission of the radar and may cause danger to the navigation function.

In addition, when ducting occurs, reflection signals from various clusters outside the maximum detection distance are superimposed in the range-Doppler region within the maximum detection distance. Detection performance may be degraded due to the overlapping clutter. Constant False Alarm Rate , The probability of false positives increases as well.

The removal of fake targets detected by ducting is directly related to solving the range ambiguity problem of multiple out-of-cycle targets. That is, if the distance ambiguity problem for the target detected by the radar is solved, the target with the actual distance outside the maximum detection distance can also be eliminated.

Various solutions have been proposed to solve the problem of distance ambiguity of coherent pulse radar. The first approach is to divide the total CPI (Coherent Processing Interval) by several partial CPIs and emit pulses at different fixed PRFs. Generally, this approach consecutively emits two pulses with two different fixed PRFs. The drawbacks of this approach are as follows.

- More PRFs than the number of predicted targets in a given CPI frame is needed to avoid ambiguity.

The increase in the number of PRFs means an increase in dwell time, which means an increase in the total seek time or a decrease in the number of pulses in the CPI. As a result, the signal-to-noise ratio (SNR) of each partial CPI is reduced from a single PRF to 1 / n (n is the number of PRFs).

- In order to detect a target, m detection (m-of-n rule) of n multiple PRFs within a given CPI frame shall be used and generally 3-of-3, 2-of-4, 5-of- 7 Rules apply. In situations where SNR is reduced, multiple PRFs can be detected as targets, and if only some PRFs are detected, complex algorithms for target detection are needed.

The second scheme is to phase-encode the transmission pulses, and there is a systematic phase coding scheme in which a random phase coding scheme and a predetermined pattern are coded in a predetermined pattern. This scheme is free from the drawbacks of using multiple PRFs because it uses one fixed PRF.

Zrnic and Sachidananda [US Pat. No. 6,081,221, hereinafter referred to as "Prior Art 1"] have proposed a solution for resolving the distance ambiguity in a Doppler weather radar. In the case of a single PRF transmission scheme, the scheme consists of a systematic phase code for transmission pulses and related decoding and signal processing. The coherence of the selected i-th distance interval (i = 1 or 2 in the prior art 1 is described) is restored and the coherence of the other distance sections is not restored. In the signal processing step, the step of separating the signals of the overlapped first and second distance sections and the step of measuring the spectral moment of the separated signals are included, and the processing related to the CFAR is not included.

Shin-Ichi Itoh [8, US Pat. No. 5,079,556, hereinafter referred to as the prior art 2] discloses a method of eliminating multiple cyclic targets and solving the distance ambiguity in a coherent pulse radar having a single fixed PRF. The upper radar employs a phase encoding scheme that includes a device for changing the phase of the transmitted pulse and a device for maintaining and integrating the phase of the received pulse and the coherence of the detected signal. However, since the proposed radar system can not apply the CFAR technique, it can not maintain a constant false alarm rate.

In this way, a coherent pulse radar having a single fixed PRF capable of detecting a target within a maximum detection distance at a high probability and maintaining a constant false alarm rate while eliminating a multiplicity of out-of-period targets caused by a ducting phenomenon with high probability, It is necessary to develop it.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and it is an object of the present invention to provide a method and apparatus for combating CFAR processing for systematic phase encoding and radar received signals under a single fixed PRF condition, The purpose of this paper is to propose a new method for eliminating out-of-cycle targets.

Another object of the present invention is to provide a novel method for effectively eliminating multiple out-of-period targets without significantly degrading the target detection probability within the maximum detection distance.

It is another object of the present invention to provide a novel method having CFAR characteristics for eliminating multiple out-of-period targets.

It is a further object of the present invention to provide a new and improved method for solving the problem of distance ambiguity of multiple out-of-cycle targets in a coherent pulse radar employing a single fixed PRF.

According to an aspect of the present invention, there is provided a method of detecting a pulse in a coherent pulse radar, the method comprising: (S1) modulating a phase of a transmission pulse radiated in each PRI (pulse repetition interval) in a coherent pulse radar; (S2) restoring the coherence of the received radar signal and generating a complex data matrix for all received signals in a given CPI (Coherent Processing Interval) frame, and performing coherent Doppler processing on the data matrix, (Step S3) of obtaining a power spectrum for all the received signals represented by the R / D (Range / Doppler) region through a squared magnitude calculation, and performing Range CFAR processing on the power spectrum of the R / (Step S4), and Doppler CFAR processing is performed on all cells detected as targets by the Range CFAR process, Others include a target step (S5) of removing the signal.

SUMMARY OF THE INVENTION The present invention having the above object is to provide a coherent pulse radar capable of drastically removing a plurality of out-of-period targets that may occur during a ducting phenomenon, It provides a new and improved method to resolve multiple ambiguities of the out-of-period target in a coherent pulse radar that can be efficiently removed, have CFAR characteristics for eliminating multiple out-of-period targets, and further apply a single fixed PRF. .

Brief Description of the Drawings Figure 1 is a graph illustrating the concept of an out-of-period target.
2 is a functional block diagram of a coherent pulse radar system for eliminating multi-periodic targets of a target caused by ducting phenomena.
3 is a functional block diagram of a radar signal processor.
Figure 4 is a flow chart illustrating Range / Doppler CFAR detection.
5 is an exemplary diagram illustrating an array of reference cells for a Range / Doppler CFAR;
6 is an exemplary view showing an arrangement of Doppler CFAR reference cells.
7 is a functional block diagram of a coherent pulse radar system using a two-phase modulation method.
8 is a graph comparing the power spectrum of the primary target and the secondary target after DFT processing in two-phase modulation using OP and MPS codes.
FIG. 9A is a graph comparing the second-order target removal performance of the two-phase modulation using the random phase modulation and the MPS and OP codes. FIG.
FIG. 9B is a graph comparing primary target detection performance before and after application of Doppler CFAR.
FIG. 9C is a graph showing the primary target detection performance loss when Doppler CFAR is applied. FIG.
10 is a graph comparing the removal performance of the secondary target of the OP code of Table 1 with the optimization code of Table 6;
11 is a graph comparing the third target removal performance of the OP code of Table 1 with the optimization code of Table 6;
12 is a graph comparing the second, third and fourth target removal performance of the optimization code of Table 7 with the OP code of Table 1;
13 is a graph showing secondary target removal performance according to the SNR of the optimization code of Table 7. FIG.
14 is a graph showing a scenario in which N _cpi is equal to or smaller than N;
15 is a _graph showing the relationship between the N _cpi value Fig. 2 is a graph showing the secondary target removal performance according to the present invention.
16 is a graph comparing the secondary target removal performance with N _cpi = 16 and N _cpi = 8 for the optimization code in Table 7. [

While the present invention has been described in connection with certain embodiments, it is obvious that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the invention. It is to be understood, however, that the invention is not intended to be limited to the particular forms disclosed, but on the contrary, is intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the term " comprising " or " consisting of ", or the like, refers to the presence of a feature, a number, a step, an operation, an element, a component, But do not preclude the presence or addition of one or more other features, integers, steps, operations, components, parts, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the contextual meaning of the related art and are to be interpreted as either ideal or overly formal in the sense of the present application Do not.

It is to be understood that the first to second aspects described in the present specification are merely referred to in order to distinguish between different components and are not limited to the order in which they are manufactured, It may not match.

The present invention relates to a method for eliminating multiple out-of-period target targets that can occur during ducting of a coherent pulse radar with a fixed PRF.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a method for removing a plurality of out-of-period targets due to a ducting phenomenon according to the present invention will be described in detail with reference to the accompanying drawings.

Before describing the present invention in detail, the present invention is embodied by a program executed in a computer apparatus, and may be stored in a recording medium executed by a computer apparatus, wherein the recording medium is not necessarily a thing Or a storage medium that is not real-world such as a cloud.

The method largely includes the first to fifth steps, and each step is performed in principle, but it may be carried out by substituting the order if necessary.

For each step, the first step S1 is a step of modulating the phase of the transmission pulse radiated in each PRI in the coherent pulse radar.

The second step S2 is a step of recovering the coherence of the radar signal received from the targets within the maximum detection distance through phase demodulation and generating a complex data matrix for all received signals in a given CPI frame.

In a third step S3, a coherent Doppler process is performed on the data matrix, and a power spectrum is obtained for all received signals represented by R / D (Range / Doppler) .

The fourth step S4 is a step of detecting a target by performing Range CFAR processing on the power spectrum of the R / D region.

The fifth step S5 is a step of performing Doppler CFAR processing on all cells detected as targets by the range CFAR process to remove the multi-periodic target signals.

The above-described method relates to a solution to the problem of the distance ambiguity of a coherent pulse radar. In the coherent pulse radar using only one fixed PRF, the phase Coding and CFAR processing.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

FIG. 2 is a functional block diagram of a coherent pulse radar system for eliminating multi-periodic external targets caused by ducting, FIG. 3 is a functional block diagram of a radar signal processor, and FIG. 4 is a block diagram illustrating a Range / Doppler CFAR detection It is a flowchart.

로 계산할 수 있다. 각 함수 f_r(x)과 f_d(x)는 적용된 CFAR 알고리즘에 의하여 정의된다.The average disturbance power around the CUT (Cell Under Test)

. Each function f _r (x) and f _d (x) is defined by the applied CFAR algorithm.

5 is an exemplary diagram illustrating an arrangement of reference cells for a Range / Doppler CFAR, and FIG. 6 is an exemplary view illustrating an arrangement of reference cells for a Doppler CFAR.

FIGS. 5 and 6 show the principle of selection of a reference cell in the Range / Doppler CFAR, and the functional block diagram of FIG. 2 is configured to be applicable to all phase encoding schemes.

In phase coding, applying a systematic two-phase biphase code can be applied as a reasonable alternative to multi-phase Chu codes, SZ (n / M) and random codes. 2-phase encoding means to set the phase of the transmission pulse to either 0 (0 °) or π (180 °). It should apply a two-phase coding may simplify the implementation of radar to avoid the complex multiplication, such as _{exp (jφ k), exp (} -jφ k) required. Modulation and demodulation of the signal when applying 2-phase coding changes the sign of the I and Q samples of the signal received in the PRI of the I and Q samples of the k-th transmission pulse and the PRI of the k-th transmission pulse with φ _k = It can be implemented easily. In the case of the k-th transmission pulse whose phase is? _K = 0, it is not necessary to change the sign.

FIG. 7 is a functional block diagram of a coherent pulse radar system in which transmission pulses are two-phase modulated. In FIG. 7, the functions of a typical coherent pulse radar in a case where the technique proposed in the present invention is implemented by two- In FIG. 7, the transmission waveform is represented by intermediate frequency (IF) samples stored in a memory in a waveform generator.

The inventive simulation employs systematic two-phase codes. Binary codes such as Barker code, OP (Optimal Periodic) code, MPS (Minimum Peak Sidelobe) code and MLS (Maximum Length Sequence) code are used.

Next, it is assumed that the length L of the code is equal to the maximum number N of pulses that can be processed in the signal processor in the CPI frame consisting of N consecutive pulse repetition periods.

변환함으로써 획득할 수 있다. 위상이 π인 송신 펄스의 부호 변경을 고려하면, 2상 코드를 복소 지수(complex exponential) exp(jφ_k)로 표시하는 것이 편리하다. 따라서 위상의 상태가 {0, π}로 구성된 2상 코드는 {1, -1}인 이진 배열로 표시할 수 있으며, 이를 편의상 {+, -}로 표시할 수 있다.The two-phase code array is binary code

. Considering the sign change of the transmission pulse with phase π, it is convenient to express the two-phase code as a complex exponential exp (jφ _k ). Thus, a two-phase code whose phase state is {0, π} can be represented as a binary array of {1, -1}, which can be expressed as {+, -} for convenience.

Table 1 below is an example of MPS, OP code with length N = 16.

값을 곱함으로써 위상이 복조된다. 이후로 와 그에 상응하는 a_k를 각각 위상 변조 코드와 곱셈 코드로 표기한다. 2상 부호화 기법을 적용할 경우 곱셈 코드 배열의 각 원소는 1 또는 -1 로만 구성된다. 따라서 2상 부호화를 사용하면, 복잡한 복소수 곱셈을 적용하지 않고 연산적 측면에서 더 단순한 부호 변환을 적용할 수 있다. 결론적으로 위상 복조 이후 1차 표적 신호에 대한 위상 변조는 완전히 복원되지만, 2차 표적 신호는 위상 차(

) 또는

만큼 변조된 상태로 남아 있게 된다.In Fig. 2, the transmission pulses are a _k = exp ( _j ? _K ), k = 1,2, ... , N, and the received signal is subjected to a corresponding complex conjugate,

And the phase is demodulated. Then, a _k corresponding to a phase modulation code and a multiplication code are written respectively. When two-phase coding is applied, each element of the multiplication code array consists of only 1 or -1. Therefore, by using two-phase encoding, a simpler code conversion can be applied in terms of an arithmetic operation without applying complicated complex multiplication. As a result, the phase modulation for the primary target signal after the phase demodulation is completely reconstructed, but the secondary target signal has the phase difference

) or

As shown in FIG.

Generally, the phase Ψ _{i, k} of the i-th echo signal (i = 1, 2, ...) after phase decoding is as follows.

만큼 위상이 변조된 상태로 남아있게 된다.Therefore, the first echo signal maintains coherence, however, i order (i = 2,3, ...) echo signal is decoded after the phase Ψ _{i, k,} or

As shown in FIG.

로 쉽게 표기 가능하다. i차 위상 변조 수열 c_i,k(k = 1, 2, …, N)를 결정하기 위하여 곱셈 코드를 나타내는 행벡터 A를 순환자리이동(cyclic shift)한 N×N 크기의 행렬 를 도입하는 것이 편리하다. 다음의 표 2는 표 1의 OP 코드를 주기적인 위상 변조 코드로 적용한 경우의 16×16 크기의 행렬 A를 나타낸다. 행렬 A에서 i차 에코 신호의 변조 수열 c_i,k(k = 1, 2, …, N)는 첫 번째 행의 원소와 이에 상응하는 i번째 행의 원소 간 곱셈(element-wise multiplication)으로 계산할 수 있다. 표 3은 행렬 C를 나타내는데, 행렬 C의 i번째 행은 위상 변조 수열 c_i,k를 나타내며 이는 행렬 A를 통해 계산할 수 있다. 표 2, 3 에서 '-'는 -1을, '+'는 1을 나타낸다.When systematic two-phase encoding is used, the phase modulation for the i-th echo signal is performed using a series of elements,

. it is convenient to introduce an N × N matrix obtained by cyclic shifting a row vector A representing a multiplication code to determine an i-th order phase modulation sequence c _{i, k} (k = 1, 2, Do. The following Table 2 shows a 16 × 16 matrix A when the OP code of Table 1 is applied as a periodic phase-modulated code. The modulation sequence c _{i, k} (k = 1, 2, ..., N) of the i-th order echo signal in the matrix A is calculated as an element-wise multiplication of the elements of the first row and the corresponding i- . Table 3 shows the matrix C, where the i-th row of the matrix C represents the phase modulation sequence c _{i, k} , which can be calculated through matrix A. In Table 2 and 3, '-' indicates -1 and '+' indicates 1.

Table 4 shows the input values used for power spectral calculation.

FIG. 8 is a graph comparing the power spectrum after the DFT (Discrete Fourier Transform) of the primary target and the secondary target during two-phase modulation using OP and MPS codes.

After the phase demodulation, the phase of the primary echo signal is completely restored, but the phase of the echo signal after the secondary is not restored and a change occurs in the spectrum. Figure 8 compares the DFT power spectrum of the primary and secondary targets for the phase modulation code (length N = 16) in Table 1.

의 DFT 파워 스펙트럼인 벡터

는 다음과 같이 계산할 수 있다.Vector representing the echo signal

Of the DFT power spectrum of

Can be calculated as follows.

Equation 1

는 DFT된 복소수 샘플로 이루어진 벡터이고, u는 정규화 벡터로

이다. 도 8 은 표 4의 입력 데이터를 이용하여 Matlab에서 FFT(Fast Fourier Transform, 고속 푸리에 변환)를 수행한 것이다.From here

Is a vector of complex samples of DFT and u is a normalized vector

to be. FIG. 8 shows an FFT (Fast Fourier Transform) performed in Matlab using the input data in Table 4.

The unit-norm vector u corresponding to the I-order echo signal can be calculated as follows.

Equation 2

Here, c _i corresponds to the i-th row of the matrix C obtained by cyclically shifting the phase modulation code, and the vector g _ant represents the amplitude modulation of the received signal by the antenna pattern. where y is the Doppler frequency normalized by the Doppler frequency f _d and the pulse repetition frequency F _r (y = f _d / F _r ), and the symbol ° is the vector between the elements of the vector It means multiplication.

As can be seen from FIG. 8, the power spectrum of the first echo signal is concentrated around the zero Doppler frequency, while the power spectrum of the second echo signal of the OP and MPS codes is spread over the entire Doppler domain. The power spectrum of the echo signal above the third order also shows a similar pattern.

It is proposed to perform the CFAR (Doppler CFAR) in the Doppler domain after performing the range CFAR (Range CFAR) in the previously performed range using the difference of the spectrum shapes of the first echo signal and the second-order echo signal do. In this case, it is possible to obtain an effect of preventing the echo signal of the second or higher order from being detected without significantly affecting the detection performance of the first echo signal.

Range CFAR and Doppler CFAR differ in the way they take reference samples. Range CFAR selects samples around the CUT as reference samples on the distance axis, while Doppler CFAR selects samples around the CUT as reference samples on the Doppler axis. Figures 5, 6 (a), 6 (b), and 6 (c) show how the reference samples are selected in Range CFAR and Doppler CFAR, respectively. The reasons for combining Range CFAR and Doppler CFAR are as follows.

First, because the power spectrum is widely distributed in the Doppler domain, the probability of the target to be detected by Range CFAR is relatively low compared to the primary target signal.

Second, even if one or more samples in a widely distributed spectrum are detected as Target in Range CFAR due to high SNR etc., then the probability of being detected as a target through Doppler CFAR is much lower than that of the primary target signal. This is because the reference samples used in Doppler CFAR to calculate the detection reference value are selected from the widely distributed spectra. In the case of the primary target signal, the energy is concentrated at a specific location in the Doppler domain, while the target signal in the second or higher order is distributed over the entire Doppler domain. Therefore, the detection reference value calculated from the dispersed spectrum of the second-order or higher-order target signal becomes much higher than the detection reference value calculated from the concentrated spectrum having the low side-lobe level of the primary target signal. The spectrum of the primary target signal having a low sidelobe level hardly causes degradation in detection performance.

If the detection criterion value increases significantly under the same conditions, the detection probability is greatly reduced. Therefore, when the phase is modulated / demodulated based on the first echo signal and the combination of Range / Doppler CFAR is used, it is possible to effectively remove the second or higher target with almost no drop in detection probability for the primary target.

중 적어도 한 샘플 S_k가 Range/Doppler CFAR 이후 표적으로 탐지될 확률을 의미하는 '종합 탐지 확률' 개념을 사용하도록 하겠다. 제거해야 할 필요가 있는 2차 이상의 표적의 대해서는, 탐지 확률이 낮을수록 제거 성능이 우수함을 의미하므로 '표적 제거 성능'이라는 개념을 사용하도록 하겠다. i번째 표적의 종합 탐지 확률이 Pⁱ _OD일 경우, 이에 상응하는 표적 제거 확률(Pⁱ _E)은

로 나타낼 수 있다.To determine the overall detection performance for the i-th target (i = 1,2, ...), the Doppler spectrum of the target

We will use the concept of 'total detection probability', which means the probability that at least one sample S _k will be detected as a target after Range / Doppler CFAR. For targets with a second or higher order that need to be removed, the lower the detection probability, the better the removal performance. Therefore, the concept of 'target removal performance' will be used. If the total detection probability of the i-th target is P ⁱ _OD , the corresponding target removal probability (P ⁱ _E )

.

To demonstrate the effectiveness of the present invention, the total detection probabilities for the primary and secondary ideal targets were calculated by performing independent Monte-Carlo simulations ¹⁰⁶ times. This calculation assumes that the noise of the radar receiver is in accordance with the standard normal distribution (Gaussian distribution with zero mean and standard deviation of 1) and that the RCS variation of the target is according to the Swerling 1 model. The I and Q samples for noise are simulated assuming that they are independent random variables according to the Gaussian distribution.

First, the primary target signal is simulated by the following equation.

Equation 3

Here, the primary target signal strength P _1t is an exponential random variable with an average SNR _1t P _n . SNR _1t is the SNR of the primary target, P _n is the receiver noise signal strength, and P _{n =} σ ² .

Next, the i-th target (i = 1, 2, 3, ...) signal is simulated by the following equation.

Equation 4

Here, the signal intensity P _it of the i-th target is an exponential random variable whose average is SNR _it P _n . SNR _it is the SNR of the i-th target, g _ant , ω and other parameters are given in Table 4.

In Equation (4), it is assumed that the number of pulses (N _cpi ) including the i-th target signal in the CPI frame is N _cpi = N (N _cpi <N will be described later). Also, the antenna rotates at a constant angular velocity in the azimuth direction, and the phase modulation sequence of size N related to the i-th target signal is simulated by using randomly using N vectors obtained by cyclically shifting the phase modulation code . Therefore, the probability of occurrence of each vector is 1 / N, and the vector c _i of Equation 4 randomly selects one of N vectors. It was also simulated with the assumption that the position of the target in the azimuth reference is also random. Thereafter, analysis of the target removal performance of the present invention is performed using the above simulation conditions.

In this performance analysis, Range / Doppler CFAR is implemented by applying general CA CFAR algorithm. For the range CFAR, the number of reference samples M = 24, the false alarm rate P _faRng = 10 ^-6 , and the reference value coefficient α = 0.7782794 were used. For the Doppler CFAR, the setpoints in Table 5 were used. In Table 5, P _faDop is the false alarm rate and β is the reference value coefficient. The variables α and β were calculated by the following equation.

Equation 5

9 is a graph showing the performance of the 2-phase modulation using the random phase modulation and the MPS and OP codes. The phase values at random phase modulation were generated as independent random variables evenly distributed at [0, 2π]. The detection performance changes with the change of the false alarm rate P _faDop under the assumption that the SNRs of the first and second targets are the same (SNR _1t = SNR _2t = 10dB).

9A is a graph simulating the total detection probability P ² _DO for a secondary target during random phase modulation and systematic two-phase modulation (MPS / OP code application in Table 1).

FIG. 9B is a graph simulating the probability (overall detection probability) P ¹ _DO that the primary target is detected after performing both the probability P ¹ _DRng and the range / Doppler CFAR where the primary target is detected in the range CFAR. In the case of the primary target, the detection performance of the primary target is not influenced by the phase modulation code because the modulated phase is completely reconstructed through the modulation / demodulation step.

FIG. 9C is a graph showing the detection performance degradation (L ¹ _PD ) for the primary target according to the change in the false alarm rate (P _faDop ). L ¹ _PD can be calculated by the following equation.

Equation 6

9A shows that the two-phase modulation using the OP code is superior to the two-phase modulation using the MPS code. An example synthesis detection probability of the secondary target at the time P = 10 ^-3 _faDop day for OP code _{^{P 2 DO = 1.71 × 10 -3}} , for MPS codes P ² _DO = 19.95 × 10 ^{- 3} to the OP code, Is much lower. This means that the OP code is superior to the MPS code in the secondary target removal performance. In the case of random phase modulation, the secondary target removal performance is considerably lower than that of 2-phase modulation using MPS and OP codes. It is therefore undesirable to apply random phase modulation to implementations of the present invention.

9b and c, it can be seen that the deterioration of the detection performance of the primary target to be managed in order to secure the secondary target removal performance is very small. For example, when P _faDop = 10 ^-4 , the detection probability for the primary target is insignificant as L ¹ _PD = 0.754%, but P ² _DO = 1.23 × 10 ^-4 when the secondary target detection probability is OP code, MPS Code, P ² _DO = 1.41 × 10 ^-4 , which means that the secondary target removal performance is very good.

The following two conclusions are possible through Fig.

First, by adjusting the detection threshold of the Doppler CFAR, the secondary target can be effectively removed without degrading the detection performance of the primary target.

Second, through the performance difference of the OP & MPS code of FIG. 9A, it can be seen that what two-phase modulation code has a great influence on the performance. In general, the phase-modulated code can be optimized to minimize the overall detection prob- ability for targets above the second order. However, to solve this optimization problem, it is difficult to present the solution to this problem mathematically at this point, since we must consider very complex factors.

Therefore, the present invention proposes an approximate solution which is close to the solution as far as the optimization problem is concerned. 9a and b, it can be seen that the overall detection probability for the primary target is very high compared to the secondary target. The reason for this difference is that the power spectra of the primary and secondary target signals show a large difference from each other. In FIG. 8, it can be seen that the primary target signal has energy concentrated in only one sample in the Doppler domain and relatively much lower energy in the other samples. In this case, since the detection reference value of the Range / Doppler CFAR is calculated from the samples around the CUT, the CUT sample with high energy far exceeds the detection reference value of the Range / Doppler CFAR.

For this reason, the overall detection probability for the primary target may vary depending on the SNR _1t , but it can basically remain at a very high level. On the other hand, the energy of the secondary target signal is spread widely over the entire Doppler domain without samples having significantly higher energy. This not only lowers the detection probability of Range CFAR but also seriously reduces the detection probability of Doppler CFAR. In practice, the samples used to determine the detection threshold for the Doppler CFAR for the secondary target are at approximately the same level as the target signal strength. Therefore, the probability that the secondary target signal exceeds the Doppler CFAR detection reference value is much lower than the primary target signal. Thus, the overall detection probability of the secondary target is basically very low compared to the primary target.

By appropriately adjusting the phase modulation code so that the power spectrum for the secondary target is close to a uniform spectrum, the overall detection probability for the secondary target can be minimized. In order to quantify the performance of such a phase-modulated code, the Euclidean distance is used in the present invention, and the Euclidean distance D can be calculated as follows.

Equation 7

Where S _k is the k th sample in the power spectrum and S _o is a constant representing the magnitude of the samples in a uniform spectrum.

According to Parseval's theorem, the relationship between the signal vector u and the DFT power spectrum S of this vector can be expressed as:

Equation 8

를 나타낸다. 벡터 u가 정규화 되었다면, 즉,

일 경우, 파워 스펙트럼의 평균값도 1이 된다. 벡터 u가 정규화 되었다면, 파워 스펙트럼의 평균값은 위상 변조 코드에 무관하게 1이 되기 때문에 수식7에서 S_o=1로 설정할 수 있다.The right side of Equation 8 represents the average value of the power spectrum and the left side is the norm of the vector u

. If the vector u is normalized, i. E.

, The average value of the power spectrum is also 1. If the vector u is normalized, the mean value of the power spectrum is 1 regardless of the phase modulation code, so that S _o = 1 in Equation 7 can be set.

Through this, a complex problem of finding a phase-modulated code that minimizes the overall detection probability for the secondary target can be converted into a simple problem of finding a phase-modulated code that minimizes the Euclidean distance D. Although it is not guaranteed that the code that minimizes the Euclidean distance D is the optimal code that minimizes the total detection probability, it is inferable that the code is close to the optimal code.

Since the norm of the signal vector for the i-th target is independent of the i-th phase modulation sequence c _i , the normalized signal vector of Equation 2 is used to optimize the phase modulation code. Where the vector c _i is determined by the phase modulation code that is changed during the optimization process.

Strictly speaking, if the phase modulation sequence for the i-th target signal is randomly designed, the minimum value of the Euclidean distance D can be directly used to optimize the phase modulation code, since a number of N cases occur when a given phase- It can not be applied. As an optimization method applicable to such a design, a minimax (a technique for minimizing the estimated maximum loss) can be used. The min max technique applied to optimize the phase modulation code in the present invention will be described below.

Table 6 shows the optimal codes for minimizing the detection probability of the secondary target among the phase-modulated two-phase codes of length N = 16 using the min-max technique. These codes were calculated by exhaustive search of all possibilities under N _cpi = N. In order to find the optimal code, code of 2 ^N -1 (excluding all 0 codes) which can be combined when the length is N was sequentially analyzed. For the p-th code, the distance D _q (q = 1, 2, ..., N) resulting from the N cyclic shifts is calculated using Equation 7 and the maximum distance D _max (p) = max {D _q } = 1, 2, ..., N) and the corresponding cyclic shift. And Mini Max distance _{D minmax = min {D max (} p)} (p = 1,2, ..., N) to, and through this condition calculated by D _max (p) = D code optimal code satisfying the _minmax .

의 순환자리이동에 대한 파워 스펙트럼은 동일하다. 그러나 본 발명의 최적화 코드 산출 과정에서는 주어진 위상 변조 코드에 대한 모든 순환자리이동에 대하여 거리 D_q (q=1,2,…,N)를 계산한다. 그 이유는 안테나 패턴에 의한 수신 신호의 진폭 변조,도플러 스펙트럼 산출 전 진폭의 가중치로 인해 이러한 순환자리이동에 대한 i차 표적 신호에 대한 파워 스펙트럼이 동일하지 않기 때문이다.According to the cyclic shift principle for DFT,

The power spectra for the cyclic shift of the antenna are the same. However, in the optimization code calculation process of the present invention, the distances D _q (q = 1, 2, ..., N) are calculated for all cyclic shifts of a given phase-modulated code. This is because the power spectrum for the i-th target signal for this cyclic shift is not the same due to the amplitude modulation of the received signal by the antenna pattern and the weight of the amplitude before Doppler spectrum calculation.

Comparing the Min Max distance for the OP code in Table 1 and the Min Max distance for the optimization code in Table 6, it can be seen that D _minmax = 18.085, and in the case of the optimization code in Table 6, D _minmax = 7.116, and the optimization code in Table 6 is superior to the OP code in the secondary target removal performance.

In FIG. 10, the optimization code (first row) of Table 6 and the second target removal performance of the OP code of Table 1 were compared. P _faDop = 10 ^-2 days time, a comprehensive detection probability of better optimized code in Table 6, about 3.62 times (0.04097 / 0.01131), and when one gradually lowered to 2.87 times more P _faDop = 10 ^-4 (0.000115 / 0.00004) great.

11 is a graph comparing the third-order target removal performance of the optimization code of Table 6 with the OP code of Table 1. FIG. The optimization code of Table 6 is superior to the OP code of Table 1 for the secondary target removal performance, but the optimization code of Table 6 is lower than the OP code of Table 1 for the third target removal performance. To overcome these problems, we propose an integrated indicator, D _MC , which can reflect both secondary and tertiary target removal performance.

Equation 9

Where D ² and D ³ represent the Euclidean distances for the secondary and tertiary targets, respectively.

Table 7 shows the optimal codes for minimizing the detection probabilities of the secondary and tertiary targets among the phase-modulated two-phase codes of length N = 16 using the min-max technique. These codes were calculated using the same optimization method as Table 6 under the condition that N _cpi = N.

12 is a graph showing a comparison of the second, third and fourth target removal performance of the optimization code of Table 7 and the OP code of Table 1; It can be seen that the optimization code of Table 7 is superior to the OP code of Table 1 for the second, third and fourth target removal performance.

13 is a graph showing the secondary target removal performance according to the SNR of the optimization code of Table 7. FIG. In the condition of P _faDop ≤ 10 ^-2.5 , it can be seen that the false target removal performance improves remarkably as the SNR increases.

The target removal performance is analyzed under the condition that N _cpi = N, that is, the number of PRIs (N _cpi ) including the target signal in a given CPI frame is equal to the total number of PRIs (N) constituting the CPI. From now on N _cpi &Lt; N. &Lt; / RTI &gt; In this case, the i-th order (i = 2, 3, ...) target signal can be simulated as follows.

Equation 10

이며, N_cpi=6이고 CPI 프레임의 뒤쪽에 위치한 경우

임을 확인할 수 있다.Here, P _{it is the} exponential random variable, and the vectors g _ant and ω are described in Table 4. A vector h _i of length N can be obtained by transforming a vector c _i representing the ith row of the matrix C corresponding to a given phase modulation code. The operator T defines the deformation pattern of the vector c _i according to the placement pattern of the PRI in which the target signal in the current CPI frame is detected for the i-th target. Figures 14 (a), 14 (b) and 14 (c) show how the operator T operates through three patterns in which a secondary target signal is detected when N = 8. When N _cpi = N, h ₂ = c ₂ , N _cpi = 7 and is located in front of the CPI frame

, And N _cpi = 6 and located behind the CPI frame

.

FIG. 15 shows secondary target removal performance according to the N _cpi value under the conditions of P _faDop = 10 ^-2 and SNR _2t = 10 dB for the optimization code (first row) in Table 7. When N _cpi = 8, . &Lt; / RTI &gt;

FIG. 16 is a graph comparing performance of N _cpi = 16 and N _cpi = 8 for the optimization code (first row) in Table 7. FIG. Although the performance degradation occurs when N _cpi = N, it can be seen that the secondary target detection probability can be maintained at a substantially low level in the condition of P _faDop ≤ 10 ^-3 , which shows sufficient secondary target removal performance.

While the invention has been shown and described with reference to certain embodiments thereof, it will be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (8)

Modulating a phase of a transmission pulse radiated in each PRI (Pulse Repetition Interval) in a coherent pulse radar (S1);
(S2) restoring the coherence of the radar signal received from the targets within the maximum detection distance through phase demodulation and generating a complex data matrix for all received signals in a given CPI (Coherent Processing Interval) frame;
Performing coherent Doppler processing on the data matrix and obtaining a power spectrum for all received signals represented by a range / Doppler (R / D) region through a magnitude squaring operation;
Performing Range CFAR processing on the power spectrum of the R / D region to detect a target (S4); And
Performing a Doppler CFAR process on all cells detected as targets by the Range CFAR process to remove a plurality of out-of-period target signals (S5);
Lt; / RTI &gt;
The phase of the transmission pulse is determined by a systematic code of period N, where N is the number of consecutive PRIs constituting a CPI frame.
The phase modulation and demodulation in the steps (S1) and (S2)

- S _k is the k-th sample in the power spectrum
- S _o is a constant representing the size value of the samples in a uniform spectrum
Wherein the Euclidean distance (D) is minimized by applying an optimization code to minimize the Euclidean distance (D).
The method according to claim 1,
Wherein S _o is 1 according to Parseval's theorem. &Lt; RTI ID = 0.0 &gt; 8. &lt; / RTI &gt;
The method according to claim 1,
The optimization code may be generated by a minimax technique under the following conditions:
D _max (p) = D _minmax
- D _max (p) = max {D _q } (p = 1,2, ..., N)
- D _q (q = 1, 2, ..., N) is the distance
- D _minmax = min {D _max (p)} (p = 1,2, ..., N)
Wherein the plurality of the out-of-period targets are removed by the ducting phenomenon.
The method according to claim 1,
The Euclidean distance (D)

- D ² is the Euclidean distance for the secondary target
- D ³ is the Euclidean distance for the third target
Wherein the Euclidean distance is determined by the Euclidean distance (D _MC) .
The method according to claim 1,
In the step (S3)
Wherein the power spectrum refers to a range / Doppler real data matrix (B) to which a squared magnitude calculation is applied after Doppler processing the data matrix (A).
The method of claim 5,
The step (S4)
And performing Range CFAR on all Range / Doppler cells of the real data matrix (B).
delete 7. The method according to any one of claims 1 to 6,
Wherein the steps (S1) to (S5) are performed sequentially for each CPI frame.

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