Research on Radar Clutter Suppression Method Based on Stagger MTI

A large number of clutter interference signals were involved in radar echoes. Radar detection and tracking performance degrade when the signal-to-noise ratio of the echo signal is too low. Therefore, how to suppress clutter interference is a problem that is worth studying in designing. In this paper, the statistical characteristics of radar clutter were analyzed, and a clutter suppression method based on staggered MTI was proposed for the blind speed problem of traditional MTI filters. Simulation experiments verified the model and processing method of staggered filtering. The results indicated that the method improved the blind speed while effectively suppressing the clutter.


Introduction
In the practical detection environment, the radar echoes contain not only the target information of interest but also intermingled with a lot of interference information, which is collectively referred to as clutter [1].Mountains on the ground, buildings, and clutter in the air can generate clutter in the echoes.This clutter is close to the target and moves slowly, but this clutter may be connected near the transmit pulse, which seriously affects target detection and tracking.Therefore, for the radar that can perform adaptive scanning detection in various complex environments, clutter suppression must be added to the signal processing process [2].The recognition statistics for clutter suppression are mainly performed by clutter Doppler characteristics.The principle is to use the difference between clutter and the movement speed of the target relative to the radar to filter the process in the frequency domain.In engineering practice, the composition of clutter is more complex and random, mainly because the clutter model contains a large number of free factors, which are not easy to analyze and study.
The statistical model of clutter is established through the analysis of radar clutter signal time domain and frequency domain characteristics [3].The amplitude probability density and frequency domain power density distribution characteristics of clutter are derived.It is found that the simple moving target indication (MTI) filter cannot effectively suppress clutter.In particular, there are some non-stationary clutters whose Doppler frequencies deviate from zero frequency.Therefore, when designing the MTI filter, the notch width and depth should be in accordance with the clutter distribution characteristics to produce a better clutter suppression effect [4].
For the blind speed phenomenon of traditional MTI filters, a radar clutter suppression method based on staggered MTI is proposed in this paper.The method analyses the method and performance of this stagger MTI filter in clutter rejection performance, eliminating blind speed of moving targets.The algorithm is simulated and analyzed under different conditions, and the results are used to prove the feasibility of the method.

Clutter statistical model
The clutter is present in the normal echoes of radar and can interfere with target detection and tracking.As an undesired signal, clutter has a certain randomness in distribution and will vary with the change of operating environment.By constructing clutter statistical models to study clutter characteristics, it is possible to better optimize signal processing algorithms and simulate the performance of radar systems [5].
Clutter may be stationary or in motion from a Doppler frequency perspective, including echoes from the ground and ground-based construction objects, clouds, rain, flocks of birds, etc.The clutter signal is random with individual clutter components having random phases and random amplitudes.Since the clutter within the sampling unit is a whole clutter composed of a large number of individual clutter, the statistical properties of the clutter are usually described by the probability density function.With the development of radar toward high resolution, the trailing phenomenon also comes along, and the Gamma distribution model can describe this phenomenon more accurately [6].
The probability density function of the Gamma distribution is shown below: where x is the echo amplitude, α and β are the shape and scale parameters respectively, and Γ (α) is the Gamma function.The probability density function and the lapse rate function of the Gamma distribution depend on the shape parameters.As a two-parameter probability density function, the shape of the Gamma distribution family can be flexibly adjusted by changing one of the parameters.As shown in Figure 1, when the parameter α is a fixed value, the peak of the Gamma distribution gradually increases in the process of gradually increasing β, the center of the peak shifts left, and the trailing tail becomes shorter.When the parameter β is fixed, the α gradually increases, the peak of the gamma distribution gradually decreases, the center of the peak moves to the right, and the trailing tail becomes longer.Thus, the Gamma distribution can be used to describe the statistical properties of clutter in different environments.

MTI clutter suppression method
Usually, the clutter signal is mainly located near the zero frequency.MTI suppresses the clutter signal in the echo according to the difference in spectrum between the moving target signal and the clutter signal and completes the detection with less impact on the moving target [7].
The MTI clutter suppression filter has a deep filter notch at zero frequency, and an integer multiple of the PRF (pulse repetition frequency), and the notch has a certain bandwidth to suppress the clutter signal of a certain spectral width.Filter notch width and filter depth can be designed according to the actual situation.MTI filter is divided into the single delay line filter and the double delay line filter, according to the number of delay lines [8]. Figure 2 shows the normalized gain of different cancellers.

Blind speed and its characteristics
When the radar uses a single pulse repetition period of the transmit waveform, its PRF also determines the unblurred frequency of the radar, which is the unblurred speed of the detected target.As the target speed lies at an integer multiple of the PRF, the MTI filter suppresses the target along with the clutter suppression, resulting in a loss of the target, which is the blind speed.As shown below, for a pulsed radar where the transmit signal is pulsed, the PRF of the transmit pulse is denoted by f r .The radial velocity of the moving target with respect to the radar is denoted by v r , then the phase difference of the generated echoes between two adjacent cycles △φ = 2πf d T r where f d = 2v/λ.f d denotes the Doppler frequency generated by the radial velocity v r where T r =1/ f r is the radar pulse repetition period.When △φ is an integer multiple of 2π, the output of the phase detector is the equal-amplitude pulse, which is completely coincident with the fixed target.Hence, the output of the moving target display is zero, and the target velocity at this time is called blind velocity [9].
where f bn is the target Doppler frequency at which the blind velocity is generated.It can be obtained from the equation: Because of the relationship between the blind velocity f bn and its Doppler frequency f bn = 2v bn /λ, the blind velocity v bn can be derived: It is clear from the above equation that when the target signal slides over a distance of half the wavelength or an integer multiple of the wavelength in a repetition cycle, the speed becomes the blind speed.Due to the blind speed generation and its effect, the pulse amplitudes obtained from the filter are equal at adjacent repetition periods when △φ is an integer multiple of 2π, so the result is zero after pair cancellation.From the blind speed formula, when n = 1, the resulting v b0 is considered as the first blind speed point.When n = 2, the resulting v b1 is considered as the second blind speed point, and so on.

Staggered MTI filtering method
Staggered PRF means that multiple pulse repetition cycles are combined to transmit.The combination code of multiple pulse repetition frequencies in the pulse-staggered PRF operation method is the staggered code [10].It is assumed that the radar operates with staggered repetition frequencies f r0 and f r1 , which correspond to pulse repetition periods T r0 and T r1 .When the blind speed occurs for both PRFs, it is the blind speed after the staggered PRF mode is used.Letting the Doppler frequency be f d at this time, we will have: where n 0 and n 1 are integers.So f d can be expressed as: If the same time is used to represent T r0 and T r1 , that is: where a and b are mutually exclusive, the first blind speed of the radar is located at n 1 = a and n 2 = b when this staggered PRF operation mode is used.n 1 : n 2 is called the staggered ratio, and the first blind speed of the radar is f d = 1/△T.The first blind speed is expanded by a factor of where v r is the first blind speed of equal-T mode, and v d is the first blind speed of variable-T mode; where T i is the repetition period, N is the total number of PRTs and △T is the maximum convention of each pulse repetition period.
, 1,2, , K 1 , K 2 , …, K N are called reference codes.The average pulse repetition period of the radar is: where f r is the average pulse PRF and f b is the blind speed of the reference PRF.At this time, the first blind speed of the radar is expanded by K a times.Figure 3 illustrates the comparison of the amplitudefrequency response of the MTI filter for the staggered PRF and the uniform PRF.Comparing the plots of the characteristics of the staggered PRF and uniform PRF filters, it can be seen that the frequency response characteristics of the passband of the staggered PRF filter are flatter.Although the staggered filter has a certain notch in the passband, the depth of the notch is limited and does not cause much loss to the signal.Therefore, the first blind speed can be pushed further when the staggered PRF is used.In engineering practice, not only does the radar require the size of the first blind velocity to meet the system requirements after the stagger, but it also requires a flat filter response curve in the first blind velocity range.The zero depth of the first stage should be as shallow as possible to avoid losing the target, which requires the selection of the appropriate number of pulses for the stagger and the optimal stagger ratio to achieve.The optimal stagger ratio can be obtained by genetic algorithm, particle swarm algorithm, and other methods.

Evaluation method for clutter suppression effect
Improvement factors are usually used to evaluate the performance of the stagger MTI filter.The definition of improvement factor is expressed as: where S i and S o are the average power values of the signal, G is the average gain of the system, and CA is the clutter attenuation.The improvement factor is required to be greater than 50 dB low altitude detection radar, while the traditional MTI clutter improvement factor is about 40 dB.The performance of stagger MTI filters is determined by the depth of the first zero point of the filter.Typically, the depth of the first zero point is required to be less than 20 dB.

Simulation
A radar simulation model is designed by using MATLAB with a PRF of about 15 kHz and a maximum blur-free distance of about 10 km.Two moving targets are defined, the first one is located at 4 km with a speed of half the blind speed and the second one is located near 6 km with a speed equal to the blind speed.The clutter signals are generated according to the Gamma distribution model and processed by using uniform PRF and stagger PRF filters respectively.The results are shown below.
The MTI filter with uniform PRF is used to remove the clutter component from the echo, and the simulation results are shown in Figure 4.In Figure 4, it can be seen that before MTI filtering, both targets are hidden in the clutter.Due to the loss of signal propagation in space, the clutter power decreases as the distance increases.After MTI filtering, most of the clutter will be filtered out, except for some random noise.The echoing noise is no longer correlated with the distance and only reflects the internal noise of the receiver system, which also shows the clutter rejection capability of the MTI filter.However, only the first target located near 4 km is detected in the MTI filter output echo.Since the second target located near 6 km has a dynamic velocity that is equal to the blind speed point of the system, it has been filtered out by the MTI filter.
Using the staggered PRF filtering process, 12 kHz is added as the second PRF to make the MTI filter in staggered PRF mode.The simulation results are shown in Figure 5, and the second target located near 6 km can be detected normally.
In summary, the improvement factor of the staggered MTI filter designed in this article is greater than 55 dB and the depth of the first zero point is less than 20 dB.However, when the external electromagnetic environment is harsh and the clutter changes violently, the clutter suppression performance of the filter designed in this article will deteriorate.In the future, adaptive methods will be used to improve the filter performance based on this article.

Conclusion
On the basis of studying the radar clutter characteristics and common methods of clutter suppression, this paper proposed a method of radar clutter suppression based on staggered MTI for the problems of blind speed in the traditional moving target display filter.Several factors affecting clutter suppression in stagger MTI clutter suppression are given by blind speed and stagger codes and the analysis needed to improve clutter suppression performance.The simulation results showed that the method extended the blind velocity points in the detection process while improving the clutter improvement factor, which verified the effectiveness of the method.

Figure 1 .
Figure 1.Gamma probability density distribution of different parameters.

Figure 2 .
Figure 2. The normalized gain of different cancellers.

Figure 3 .
Figure 3.Comparison of Staggered PRF and Uniform PRF Filters