On the concept and application of filtering in radar signal processing

During postgraduate study , The teacher said that the essence of radar signal processing is wave filtering , I couldn't fully understand the meaning of this sentence before , Recently, after engineering practice and theoretical study , Also gradually formed their own views .
Filtering in popular terms , It's like a sieve , Filter out the desired part from the signal , Filter out the unwanted parts as much as possible . Or give the desired signal a gain value , Give unwanted signals （ Or noise ） An attenuation value , Increase the signal-to-noise ratio .
In signal processing, filters in a narrow sense usually refer to digital filters , The filtering function is realized by setting different frequency responses in the frequency domain . Filtering in a broad sense refers to an idea of signal processing . Next, combined with different signal processing methods, we briefly talk about filtering in the fast time dimension （ Distance dimension ）、 Slow time dimension （ Doppler velocity dimension ）、 Spatial dimension （ Azimuth dimension ） Application in signal processing , Try not to list formulas , In simple words .

#1、 Fast time dimension （ Take pulse compression as an example ）
In the radar system , Time domain （ Fast time ） After the conversion with the speed of light, it can be understood as the distance dimension . Take pulse compression as an example , Pulse compression is a method to increase the signal-to-noise ratio of the target through the matched filter in the echo range dimension . The filtering criterion of matched filter is “ matching ”, Generate matched filter coefficients based on known transmission signals , By convolution （ relevant ） Find the target signal in the echo , Because the target signal and the transmitted signal have the same modulation law , Can match the matched filter “ matching ” On , After correlation, energy accumulation in time domain can be realized , Other noises do not have the modulation law of the transmitted signal , It is impossible to accumulate energy in the time domain , The signal-to-noise ratio is improved , That is, the target signal is filtered “ wave filtering ” function .

#2、 Slow time dimension
Slow time dimension （ Doppler ） The filter on is most widely used in radar signal processing , Commonly used in Doppler processing FFT,MTI,MTD And so on can be understood as filters or filter banks . The filtering criterion of the slow time dimension filter is to filter the signal of a specific Doppler frequency .
The movement of radar target will produce Doppler frequency , Sampling the slow time dimension of echo is equivalent to sampling the Doppler frequency of echo , Different targets and clutter have different Doppler frequencies , Therefore, the frequency domain filtering of the slow time dimension signal can separate the target from the clutter .
MTI As a good method of filtering clutter , Because the implementation is simple , The effect is good , It is widely used in Engineering , The common implementation method is design FIR filter , Set notch at Doppler frequency of clutter （ For example 0 Frequency setting notch filters out ground clutter ）, Then through the sampling of slow time dimension , Process the same distance unit of multiple pulses , Realize filtering . Its essence is a high pass filter . Realization MTI The simplest way is to subtract two consecutive pulses .
MTD It is also a processing method of slow time dimension ,MTI The main purpose of is to filter out clutter , So the goal will naturally stay . and MTD The main purpose of is to detect targets in clutter ,MTD The essence of is a group of narrow-band filter banks , The simplest way to implement it is FFT.

FFT yes DFT Fast implementation method of ,DFT As a time-frequency domain conversion method , What is the connection with the filter ？
We know , Fourier transform can get the spectrum of time-domain signal , And has limited resolution . With 8 Point FFT For example , Actually from below FFT The frequency response diagram of ,FFT It is composed of multiple filters uniformly distributed in the frequency domain , take -π To +π The normalized frequencies between are divided into uniform 8 paragraph , Each segment is covered by a band-pass filter , Each band-pass filter has a gain for the signal near its central frequency , At other frequencies there are notches , The signal near the current center frequency can pass through the filter , That is, it realizes the filtering and energy accumulation of the current frequency , Get the energy value .8 The results of filters are superimposed , You can get the energy value of each frequency , That is, spectrum .

therefore ,FFT It can be understood as bandpass filter bank （ Or narrowband filter banks ）, utilize FFT To achieve MTD It is relatively simple and fast , In the project, if the calculation speed is required to be high, it can be used , But with FFT Realization MTD There are also some problems , First ,FFT The filter sidelobe of is high , The ratio of main to auxiliary is insufficient , Affect the detection ability of the target ; secondly ,FFT The frequency response of is relatively fixed , Sometimes it cannot meet the special requirements in the project . And use FIR Although the calculation of filter bank is large , But the design is flexible , Low sidelobe , Better performance . Design in the project FIR Filter bank implementation MTD Please refer to teacher chenboxiao's 《 Analysis and design of modern radar system 》 A Book .

#3、 Spatial dimension
Different from fast time and slow time dimension filtering , Spatial domain filtering is to filter the received signals in space , Simply speaking , It is to filter out signals in a certain direction in horizontal or vertical space , Filter out signals from other directions .
The most intuitive embodiment of spatial domain filtering is not in signal processing , In the antenna pattern , In the design stage of antenna , Antenna engineers carefully designed , Let the antenna have a more ideal beam , It has large gain in useful space , And in a space of no interest （ For example, antenna side 、 Back ） Gain as small as possible .
Beyond antenna design , Beamforming is an important means to realize spatial filtering . Take the horizontal angle as an example , In the case of uniform linear array , Want to achieve a certain angle （ for example 30 degree ） Spatial filtering , The simplest method is to align the beam of the antenna by adjusting the phase of each array element through the phase shifter according to the preset guidance vector 30 degree , Then the antenna pattern will be in 30 The direction of degrees has a large gain , At other angles, it has smaller gain , This method is beam forming , And it is beamforming processed at the transmitter .
Another kind of beam forming is done in the process of signal processing , It is called digital beamforming （DBF）.DBF There is no need to modulate the beam at the transmitter , Instead, the received signals of different array elements are weighted and summed in the digital domain . According to the preset beam forming angle , A set of weight vectors can be calculated , The principle is that the target at a certain angle will produce phase difference caused by wave path difference on different array elements , This phase difference can be compensated by this set of weight vectors , Achieve in-phase addition of target echoes at a certain angle , Make the echo signal at this angle have the maximum gain , A pointing beam is simulated at this angle .
Back to the concept of filtering ,DBF The method of realizing spatial domain filtering is very similar to the filter mentioned above , Through a set of weight vectors （ Filter coefficients ） Achieve a certain direction （ frequency ） Filtering of .
Many beginners are learning millimeter wave radar , Would be right TI Of demo Inside use FFT The angle estimation method to achieve the goal is confused , I can't understand why it is carried out in the antenna dimension FFT You can get the angle of the target , Why it works FFT To achieve DBF. Actually , use FFT Realization DBF And the idea and application of target angle estimation FFT Realization MTD The idea is exactly the same ,MTD It is to search the results of multiple frequency domain filters and select the largest , Detect the target and get its Doppler frequency ; While using FFT The target angle estimation is carried out many times in all angle ranges DBF, Form multiple spatial domain filters , Search within the horizontal angle , The output of the spatial filter corresponding to the target angle will have a peak , Perform peak search on all filter outputs in the filter bank , You can detect the target and get its orientation .

# summary
Many seemingly different methods and concepts in radar signal processing are essentially interlinked , For example, a FFT Many signal processing methods can be realized , For example, a “ wave filtering ” You can summarize the essence of most methods . For different signal processing dimensions 、 Different signal processing methods , Mastering its essence is the key .
The above is a little gain from the recent learning process , As a study note , And the limit of the level , There are inevitably shortcomings , Welcome to exchange .