Unmanned aerial vehicle-mounted investigation and rapid interference method

Abstract

The invention relates to an unmanned aerial vehicle-mounted investigation and rapid interference method. The method comprises the steps of searching a frequency band where a radar target is located; after the radar frequency band is successfully locked, the equipment processes the analysis and interference functions of the radar signal in parallel, and judges and executes a corresponding interference strategy according to an analysis result; interference strategies are selected step by step according to stages: a device scans radar signals at an interval of 200MHz to complete a target search stage; when the center frequency of the radar signal is locked, entering a target tracking stage; after locking, entering a target optimization stage; if the center frequency changes, entering a target re-search stage, and trying to re-lock the signal; in each stage, the equipment adopts different interference modes: a full forwarding interference mode is used in a target search stage, a slice interference mode is used in a target tracking stage, and a random interference mode is switched in a target re-search stage. According to the method, the dependence on an external independent reconnaissance system and resource scheduling is remarkably reduced, and the load requirements of miniaturization and light weight of the unmanned aerial vehicle are met.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to an unmanned aerial vehicle (UAV)-borne reconnaissance and rapid interference method. Background Art

[0002] With the rapid development of drone technology, drone platforms have become the preferred platform for carrying reconnaissance and jamming equipment due to their unique flexibility, high maneuverability and cost-effectiveness. Integrating jamming equipment on drones not only significantly reduces the power requirements of transceiver equipment, but also greatly expands the application scenarios, especially showing great application potential in high-risk missions. However, traditional jamming equipment is difficult to be directly applied to drone platforms due to limitations in size, weight and power consumption. This urgently requires the development of new, lightweight and efficient drone-mounted jamming equipment.

[0003] In order to meet the needs of integrated reconnaissance and jamming payloads in modern warfare, researchers have begun to explore UAV systems that integrate reconnaissance and jamming functions. Through system optimization design, the aim is to reduce the size of the equipment, power consumption and cost. In recent years, the rapid development of digital and RF SoC technology has made it possible to apply radar reconnaissance and jamming technology in UAV scenarios with limited weight and space.

[0004] At present, a number of reconnaissance and jamming architectures have been proposed and studied, such as the multi-carrier frequency diversity array architecture proposed by Harbin Engineering University, the missile-borne jammer guidance method of the University of Electronic Science and Technology of China, and the integrated RF front end based on the AD9361 chip of the Xi'an Institute of Mechanical and Electrical Information Technology. These studies have made significant breakthroughs in technology, but still face problems such as high complexity and lack of versatility, which limits their widespread application on UAV platforms. Summary of the invention

[0005] In order to solve the problems existing in the background technology, the present invention provides an unmanned aerial vehicle reconnaissance and rapid interference method, comprising:

[0006] There are four stages: target search, target tracking, interference optimization and target re-search;

[0007] During the target search phase:

[0008] The integrated detection and jamming equipment adjusts the local oscillator by a preset frequency step, searches for the frequency band where the radar target is located in a wide frequency band, and in the target search phase, the jamming method adopts the full forwarding mode; after searching the frequency band where the radar target is located, the baseband detects the power value of the radar target signal, and generates the target search enable signal and the instantaneous frequency of the radar target signal;

[0009] During the target tracking phase:

[0010] After the instantaneous frequency of the target search enable signal and the radar target signal is obtained, the channel fast frequency sweep algorithm is used to lock the center frequency of the radar target signal. When the center frequency is locked, the target tracking enable signal is generated. After the center frequency is locked, the interference mode is switched to the slice forwarding mode.

[0011] In the target optimization phase:

[0012] When the target tracking enable signal is detected, the optimal jamming method is selected from the three methods of full forwarding jamming mode, slice forwarding jamming mode and random jamming mode according to the PDW information of the radar target signal;

[0013] During the target re-search phase:

[0014] When the external radar target jumps to other frequency bands, the target tracking enable signal will disappear, the target re-search phase will start, and the interference method will continue the interference strategy of the target optimization phase, rescanning the radar target signal frequency band until the signal frequency band is locked; when the frequency band is locked, it will enter the target tracking phase.

[0015] The present invention has at least the following beneficial effects

[0016] The present invention designs a UAV-mounted reconnaissance and rapid interference method, which can forward radar signals in the 75MHz to 6GHz frequency band with an instantaneous bandwidth of 200MHz. Compared with the traditional guided receiving system, this method effectively solves the delay problem of signal analysis and interference process, realizes the independent interference task of UAV nodes, and reduces the resource overhead of external reconnaissance guidance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the detection architecture of the present invention;

[0018] Figure 2 It is a system architecture diagram of the present invention. DETAILED DESCRIPTION

[0019] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0020] Example 1, please refer to Figure 1,The present invention provides a UAV-borne reconnaissance and rapid interference method, including: target search, target tracking, interference optimization and target re-search four stages;

[0021] During the target search phase:

[0022] The integrated detection and jamming equipment adjusts the local oscillator by a preset frequency step, searches for the frequency band where the radar target is located in a wide frequency band, and in the target search phase, the jamming method adopts the full forwarding mode; after searching the frequency band where the radar target is located, the baseband detects the power value of the radar target signal, and generates the target search enable signal and the instantaneous frequency of the radar target signal;

[0023] During the target tracking phase:

[0024] After the instantaneous frequency of the target search enable signal and the radar target signal is obtained, the channel fast frequency sweep algorithm is used to lock the center frequency of the radar target signal. When the center frequency is locked, the target tracking enable signal is generated. After the center frequency is locked, the interference mode is switched to the slice forwarding mode.

[0025] In the target optimization phase:

[0026] When the target tracking enable signal is detected, the optimal jamming method is selected from the three methods of full forwarding jamming mode, slice forwarding jamming mode and random jamming mode according to the PDW information of the radar target signal;

[0027] During the target re-search phase:

[0028] When the external radar target jumps to other frequency bands, the target tracking enable signal will disappear, the target re-search phase will start, and the interference method will continue the interference strategy of the target optimization phase, rescanning the radar target signal frequency band until the signal frequency band is locked; when the frequency band is locked, it will enter the target tracking phase.

[0029] Furthermore, the implementation process of the forwarding interference mode includes:

[0030] The forwarding interference mode includes three interference modes: full forwarding mode, slice forwarding mode and random interference mode;

[0031] The workflow of forwarding interference is as follows:

[0032] Step 1: When the detection signal arrives, determine the starting frequency of the signal and whether to update the waveform data in DDR or ROM;

[0033] Step 2: The state machine combines with the control BRAM to select the interference mode and control the modulation in the time domain, frequency domain and power domain;

[0034] Step 3: The modulated waveform enters the transmitting channel and is sent to form a false interference target.

[0035] Furthermore, the implementation of the forwarding interference mode includes:

[0036] Full forwarding interference: After receiving the radar target signal, it is stored in the multi-channel FIFO for caching, and the number, power and delay value of the interference false target waveform in the BRAM are read and controlled. The number controls the number of multi-channel FIFO outputs, the delay controls the output time of different FIFOs, and the power controls the coefficient value of the complex multiplication after the FIFO output. The accumulated value is the combined radar waveform of full forwarding interference. The final waveform is output to realize the full forwarding interference of radar interference false targets;

[0037] Slice forwarding interference: After receiving the radar target signal, it is stored in ROM. The storage capacity of ROM is fixed. When the storage refresh signal is enabled, the radar waveform begins to be stored in ROM. If the next storage refresh signal is not enabled, but the storage capacity of ROM reaches the upper limit, DDR is used for storage; the pulse width is obtained from the PDW information. The length of the slice is 1 / M, where M is the ratio of the power of the false interference target signal to the power of the radar target signal; the slice segment of the storage signal is selected, and the signal is circulated M times as the pulse of the radar target signal. After transmission, M false interference target signals are formed to interfere with the radar target;

[0038] Random forwarding interference: After receiving the radar target signal, it is stored in the DDR, and a random number is generated through the m-sequence (Maximum Length Sequence, i.e., the longest linear feedback shift register sequence). The random number is weightedly calculated to generate the random pulse width length, random delay and random power value of the radar interference false signal; the FSM controls the DDR to read and write data according to the random pulse width length, random delay and random power value of the radar interference false signal to form a radar interference false signal that enters the transmission channel to form a radar interference false target.

[0039] Further, the calculation of the random pulse width length, random delay and random power value of the radar interference false signal includes:

[0040] T=[2,1,1]*W,

[0041] Wherein, W represents the random number generated by the m-sequence, T represents the random pulse width length, random delay and random power set of the radar interference false signal, and the units are: microseconds (us), microseconds (us) and decibel milliwatts (dbm) respectively.

[0042] Furthermore, the PDW information of the radar target signal includes: after successfully locking the frequency band where the radar target signal is located, the orthogonal signal received by the baseband part will accurately calculate its phase information through the CORDIC algorithm; then, the instantaneous phase is used to perform differential operations to resolve the phase ambiguity problem and accurately obtain the instantaneous frequency of the radar target signal; the frequency of the radar target signal is determined by combining the instantaneous frequency data of the baseband part with the local oscillator frequency provided by the RF front end; when the frequency of the radar target signal is locked, the arrival time of the radar target signal is extracted, and a threshold signal is generated based on this; the PDW information of the radar target signal is calculated through the threshold signal.

[0043] Furthermore, the instantaneous frequency of the radar target signal includes:

[0044] The instantaneous phase of the radar target signal is calculated using the CORDIC algorithm. The calculation formula is as follows:

[0045] θ(t)=arctan(y(t),x(t))

[0046]

[0047] Wherein: θ(t) is the instantaneous phase of the radar target signal at time t, f(t) is the instantaneous frequency of the radar target signal at time t; π represents pi; arctan represents the inverse trigonometric function; y(t) represents the real part of the radar target signal collected by the RF front end at time t; x(t) represents the radar target signal collected by the RF front end at time t.

[0048] See also Figure 1 and Figure 2 ,Example 2,This paper proposes a method for unmanned aerial vehicle reconnaissance and rapid interference, such as Figure 1 As shown in the figure. In the traditional workflow of reconnaissance-guided jamming, all work is done serially, and each process is highly correlated. It takes a long time (5-10ms) from signal acquisition, feature extraction, strategy analysis to the final jamming generation. In the architecture of this paper, each process is executed in parallel by hardware, and the processes are independent. Signal acquisition, feature analysis, strategy selection and jamming emission can be carried out in parallel, reducing the delay in the reconnaissance and jamming process, and the reconnaissance process can be jammed synchronously.

[0049] The detailed system architecture of this article is as follows Figure 2As shown. Considering the requirements of hardware resources, algorithm complexity, real-time performance, etc., this paper implements signal acquisition, parameter extraction, strategy analysis, and interference signal generation on the PL side (FPGA) of the digital SoC, and cooperates with the PS side (ARM) to complete the scanning of the local oscillator and the optimization of the interference strategy. During signal acquisition, the detection module uses serial CORDIC and false alarm threshold algorithm to extract the PDW information such as the arrival time, pulse period, pulse width, signal bandwidth, etc. of the pulse signal, and cooperates with FSM to collect and store signals, transmit interference signals, adjust the local oscillator frequency, and determine the interference strategy.

[0050] This paper constructs the following workflow, which includes four stages: target search, target tracking, interference optimization and target re-search. Among them, the target search stage is to scan and search for radar signals with a local oscillator interval of 200MHz. The target tracking stage is to search for radar signals and lock the center frequency of the signal. After locking the center frequency of the signal, it is the interference optimization stage. When the center frequency of the signal changes, try to re-lock the center frequency of the signal, which is the target re-search stage. In the target search stage, the full forwarding interference mode is used, in the target tracking stage, the slice interference mode is used, and in the target re-search stage, the random mode is switched for random interference.

[0051] The interference strategy control is sent down through messages, and the interference strategy message is stored in the control BRAM. The message generated by the hardware uses the PDW local information, including the arrival time, the current pulse width, the instantaneous frequency and the signal amplitude, to determine the stage of the reconnaissance. After the complete PDW information is uploaded to the ARM side, the ARM side will optimize the interference strategy and select the interference strategy according to the pulse width, repetition frequency and signal amplitude. The result is sent down to the BRAM through AXI to update the interference strategy.

[0052] This architecture has a small delay between the reconnaissance and interference processes. During the reconnaissance process, highly coherent interference signals are continuously emitted, and interference can be performed independently during reconnaissance. Data analysis during the reconnaissance process is performed in the FPGA baseband, the processing process is fast, and the feedback of PDW parameters is faster, which can effectively reduce the risk of being detected. The architecture adopted by the system is suitable for multi-octave signals, which can effectively reduce the cost of the system and the demand for ADC sampling rate. It has the characteristics of low cost and lightweight.

[0053] The basic principle of the channel fast frequency scanning algorithm:

[0054] In order to determine the band range of the radar waveform, the local oscillator (LO) signal frequency of the RF front-end chip must be synchronized first, so that the hardware detection module can detect the radar waveform and output a single-bit pulse signal. When the difference between the received radar signal and the local oscillator frequency is greater than 200MHz, the detection module cannot output a single-bit pulse signal, and the frequency sweep algorithm can complete the signal frequency band lock.

[0055] Assume that the RF sampling signal can be expressed as (1):

[0056]

[0057] Where l(n) represents the intermediate frequency carrier sequence, S(n) represents the radar waveform sequence, and n0(n) represents Gaussian white noise. The correlation function between the received signal P(n) and the intermediate frequency M(n) can be expressed as (2):

[0058]

[0059] Where N represents the sequence length. The intermediate frequency signal l(n) is highly correlated with M(n) and is poorly correlated with n0(n). At the moment n=n+τ, the correlation function value is the largest, and the above formula is simplified to obtain the following formula (3):

[0060]

[0061] Fast frequency sweep algorithm and hardware implementation

[0062] In the scanning process, in addition to detecting and receiving RF radar signals, it is also necessary to extract the PDW of the radar signal. PDW needs to include frequency, amplitude, bandwidth, pulse width, and pulse repetition period. The frequency of the radar signal can be directly extracted by using the first-order differential frequency measurement method based on the coordinate rotation digital computer (CORDIC) method. The amplitude of the received signal is obtained by the CORDIC algorithm, and a differential operation is performed on it, which is formula (4):

[0063]

[0064] Where: w(n) has a mean of 0 and a variance of σ 2 Additive Gaussian complex noise; n(n) is Gaussian noise obeying N(0, σ 2 );;φ s represents a pulse signal; i and j represent adjacent points.

[0065] Assume that the duty cycle of the pulse signal is Δ, and the comprehensive n∈φ s , In two cases, we get formula (5):

[0066]

[0067] The I / Q baseband digital signal collected by the RF front end is passed through the CORDIC IP core to obtain the instantaneous amplitude and instantaneous phase of the signal. The instantaneous phase after detangling is calculated by first-order difference to obtain the instantaneous frequency. The relationship between instantaneous frequency and phase is shown in formula (6):

[0068]

[0069] Where: represents the phase value of the i-th sample point, and T s It represents the sampling period.

[0070] The receiving processing bandwidth of the RF front end is 200MHz. When the signal crosses the intersection range of two channels, the frequency of the local oscillator needs to be adjusted so that it can be within the receiving range of the RF front end. Based on this, the Fibonacci Scanning Algorithm (FSA) is designed to lock the receiving frequency band of the radar signal. Compared with other algorithms, FSA has the characteristics of simple operation, high performance and efficiency. The steps of the FSA algorithm in this article are as follows:

[0071] Step 1: Construct the Fibonacci sequence;

[0072] Step 2: Find the element F(k) in the Fibonacci sequence with a high detection level;

[0073] Step 3: If the maximum frequency exceeds the boundary corresponding to the element F(k), the lookup table is partitioned into intervals F(k+1);

[0074] Step 4: Find the maximum and minimum frequencies at which the detection level is high, and set the mean frequency to the LO frequency.

[0075] Step 5: Repeat step 4 until the LO frequency is locked.

[0076] Since the information extracted from the received signal is used to adjust the local oscillator frequency, the mean frequency is obtained through the maximum and minimum frequency values, and the local oscillator frequency is adjusted to the mean frequency. If the mean frequency changes after iteration, the local oscillator frequency will continue to be adjusted until the scanning process stops without error and the local oscillator frequency is locked. This method is suitable for RF front-end hardware systems with different bandwidths, reduces the high power consumption and high cost of traditional systems in large instantaneous broadband signal interception, and significantly reduces the consumption of RF front-end resources of drone payloads.

[0077] Interference modulation

[0078] The interference strategy is selected based on the slice PDW information and the full PDW information, and the interference strategy is subdivided into three interference modes: full forwarding, slice forwarding, and random forwarding. The three interference modes are all composite modulation technologies in the time domain, frequency domain, and power domain.

[0079] The workflow of forwarding interference is as follows:

[0080] Step 1: The detection signal reaches the starting frequency of the judgment signal to determine whether to update the waveform data in DDR.

[0081] Step 2: The state machine (FSM) combines with the control BRAM to select the interference mode and control the modulation in the time domain, frequency domain and power domain.

[0082] Step 3: The waveform enters the transmitting channel to form a transmission.

[0083] The state machine FSM cooperates with the control BRAM to combine the time domain, frequency domain and power domain technologies to perform complex modulation on the radar signal samples.

[0084] In the time domain, multiple FIFO queues are used to read out the data in the DDR to realize data caching. The readout control and delay control of multiple FIFOs are performed according to the control information of the control BRAM, so that each FIFO channel can independently delay the forwarding of the waveform to ensure that the interference pulse can accurately enter the range tracking gate of the radar receiver. In the frequency domain, digital Doppler modulation is implemented on the radar signal samples. In the power domain, the controller reads the control BRAM to accurately control the power of each FIFO output signal, where the intensity ratio between the interference signal and the target signal (interference-to-signal ratio) directly depends on the minimum signal-to-noise ratio required for the radar to detect the target echo.

[0085] In summary, the present invention designs a method for UAV-borne reconnaissance and rapid interference, which can forward radar signals in the frequency band of 75MHz to 6GHz, and the instantaneous bandwidth is 200MHz; compared with the traditional guided receiving system, this method effectively solves the delay problem of signal analysis and interference process, realizes the independent interference task of UAV node, and reduces the resource overhead of external reconnaissance guidance. At the same time, in view of the low cost, low power consumption, high efficiency and other problems that UAV interference nodes need to solve in the interception of interference target signals, this paper proposes a new fast frequency scanning algorithm (Fibonacci Scanning Algorithm, referred to as FSA) by adopting a fixed intermediate frequency bandwidth (200MHz) combined with a fast frequency sweeping signal parameter measurement mode. The algorithm can dynamically adjust the frequency sweeping step and frequency sweeping direction in real time through a fast frequency sweeping mechanism, thereby accurately locking the signal frequency, effectively solving the high power consumption and high cost problems caused by the interception of large instantaneous broadband signals in traditional reconnaissance systems, and greatly reducing the resource consumption of UAV payloads.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for unmanned aerial vehicle reconnaissance and rapid interference, characterized in that: include: There are four stages: target search, target tracking, interference optimization and target re-search; During the target search phase: The integrated detection and jamming equipment adjusts the local oscillator by a preset frequency step, searches for the frequency band where the radar target is located in a wide frequency band, and in the target search phase, the jamming method adopts the full forwarding mode; after searching the frequency band where the radar target is located, the baseband detects the power value of the radar target signal, and generates the target search enable signal and the instantaneous frequency of the radar target signal; During the target tracking phase: After the instantaneous frequency of the target search enable signal and the radar target signal is obtained, the channel fast frequency sweep algorithm is used to lock the center frequency of the radar target signal. When the center frequency is locked, the target tracking enable signal is generated. After the center frequency is locked, the interference mode is switched to the slice forwarding mode. In the target optimization phase: When the target tracking enable signal is detected, the optimal jamming method is selected from the three methods of full forwarding jamming mode, slice forwarding jamming mode and random jamming mode according to the PDW information of the radar target signal; During the target re-search phase: When the external radar target jumps to other frequency bands, the target tracking enable signal will disappear, the target re-search phase will start, and the interference method will continue the interference strategy of the target optimization phase, rescanning the radar target signal frequency band until the signal frequency band is locked; when the frequency band is locked, it will enter the target tracking phase.

2. The method for unmanned aerial vehicle detection and rapid interference according to claim 1 is characterized in that: The implementation process of the forward interference mode includes: The forwarding interference mode includes three interference modes: full forwarding mode, slice forwarding mode and random interference mode; The workflow of forwarding interference is as follows: Step 1: When the detection signal arrives, determine the starting frequency of the signal and whether to update the waveform data in DDR or ROM; Step 2: The state machine combines with the control BRAM to select the interference mode and control the modulation in the time domain, frequency domain and power domain; Step 3: The modulated waveform enters the transmitting channel and is sent to form a false interference target.

3. The method for unmanned aerial vehicle detection and rapid interference according to claim 2 is characterized in that: Implementation of forwarding interference mode, including: Full forwarding interference: After receiving the radar target signal, it is stored in the multi-channel FIFO for caching, and the number, power and delay value of the interference false target waveform in the BRAM are read and controlled. The number controls the number of multi-channel FIFO outputs, the delay controls the output time of different FIFOs, and the power controls the coefficient value of the complex multiplication after the FIFO output. The accumulated value is the combined radar waveform of full forwarding interference. The final waveform is output to realize the full forwarding interference of radar interference false targets; Slice forwarding interference: After receiving the radar target signal, it is stored in ROM. The storage capacity of ROM is fixed. When the storage refresh signal is enabled, the radar waveform begins to be stored in ROM. If the next storage refresh signal is not enabled, but the storage capacity of ROM reaches the upper limit, DDR is used for storage; the pulse width is obtained from the PDW information. The length of the slice is 1 / M, where M is the ratio of the power of the false interference target signal to the power of the radar target signal; the slice segment of the storage signal is selected, and the signal is circulated M times as the pulse of the radar target signal. After transmission, M false interference target signals are formed to interfere with the radar target; Random forwarding interference: After receiving the radar target signal, it is stored in the DDR, and a random number is generated through the m sequence. The random number is weighted to generate the random pulse width length, random delay and random power value of the radar interference false signal; FSM controls the DDR to read and write data according to the random pulse width length, random delay and random power value of the radar interference false signal to form a radar interference false signal that enters the transmission channel to form a radar interference false target.

4. The method for unmanned aerial vehicle detection and rapid interference according to claim 3 is characterized in that: The calculation of the random pulse width, random delay and random power value of the radar interference false signal comprises: T=[2,1,1]*W, Wherein, W represents the random number generated by the m-sequence, T represents the random pulse width length, random delay and random power set of the radar interference false signal, and the units are: microseconds (us), microseconds (us) and decibel milliwatts (dbm) respectively.

5. The method for unmanned aerial vehicle detection and rapid interference according to claim 3 is characterized in that: The PDW information of the radar target signal includes: after successfully locking the frequency band where the radar target signal is located, the orthogonal signal received by the baseband part will accurately calculate its phase information through the CORDIC algorithm; then, the instantaneous phase is used to perform differential operations to resolve the phase ambiguity problem and accurately obtain the instantaneous frequency of the radar target signal; the frequency of the radar target signal is determined by combining the instantaneous frequency data of the baseband part with the local oscillator frequency provided by the RF front end; when the frequency of the radar target signal is locked, the arrival time of the radar target signal is extracted, and a threshold signal is generated based on this; the PDW information of the radar target signal is calculated through the threshold signal.

6. The method for unmanned aerial vehicle detection and rapid interference according to claim 5, characterized in that: The instantaneous frequency of the radar target signal includes: The instantaneous phase of the radar target signal is calculated using the CORDIC algorithm. The calculation formula is as follows: θ(t)=arctan(y(t),x(t)) Where: θ(t) is the instantaneous phase of the radar target signal at time t, f(t) is the instantaneous frequency of the radar target signal at time t; π represents pi; arctan represents the inverse trigonometric function; y(t) represents the real part of the radar target signal collected by the RF front end at time t; x(t) represents the imaginary part of the radar target signal collected by the RF front end at time t.

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