A low-sidelobe FDA radar communication integrated waveform design method

Abstract

The present invention discloses a low-sidelobe FDA radar communication integrated waveform design method, comprising the following steps: constructing a signal model for the FDA radar communication integration; performing subarray delay design on the FDA radar communication integrated signal to obtain a subarray delay model; selecting a tangent frequency modulation signal as a baseband waveform to obtain a transmission signal model; obtaining an echo signal based on the transmission signal and calculating an ambiguity function; at the radar receiving end, designing an angle-time two-dimensional matched filter with time-varying characteristics based on the ambiguity function, and performing pulse compression and beamforming combined processing on the echo signal; at the communication receiving end, performing corresponding demodulation processing based on the transmission signal and analyzing the bit error rate. The present invention realizes the low-sidelobe design of the FDA radar communication integrated transmission waveform, improves the radar's range and angular resolution, and has a good communication bit error rate. It can also achieve continuous scanning of the range airspace, meeting the requirements of radar communication integrated waveform design.

Description

Technical Field

[0001] The present invention belongs to the interdisciplinary field of radar and communication, relates to waveform design and signal processing technology, and specifically relates to a low-sidelobe FDA radar communication integrated waveform design method. Background Art

[0002] For a long time, radar and communications were designed and developed independently, based on their respective functions and frequency bands. In reality, as typical means of acquiring, processing, transmitting, and exchanging information, radar and communications, while differing in their functions and operating frequencies, share similarities in hardware architecture and operating principles. With the continuous advancement of radar and communications technology, the differences in signal processing and operating frequency bands between radar and communications are gradually narrowing. The operating frequency bands used for communications transmission partially overlap with those used by radar, making radar and communications integration possible. Implementing an integrated radar and communications design not only maximizes resource utilization but also significantly enhances the system's operational capabilities, overcoming limitations such as large footprints, severe electromagnetic interference between devices, and high energy consumption.

[0003] The key to achieving radar and communication integration lies in the design of an integrated transmit waveform. Currently, research on transmit waveform design for radar and communication integration has mostly focused on single antennas, phased arrays, and multiple-input, multiple-output (MIMO) arrays. Early single-antenna radar and communication integration systems suffered from numerous bottlenecks, such as high bit error rates, poor confidentiality, limited waveform design freedom, and a lack of beamforming capabilities. Array radar and communication integration offers high gain, strong directivity, narrow beams, and low sidelobes. It not only focuses transmit power on a specific spatial orientation but also utilizes spatial filtering to suppress signals from other orientations, enhancing transmit and receive signal strength and preventing mutual interference between radar and communication. Furthermore, the use of array antennas allows radar and communication systems to share multiple transmit and receive channels, thereby improving target estimation accuracy and communication reliability. However, the array factor of phased array radar and communication integration lacks temporal coupling. Its beam pointing direction remains constant within the duration of a single pulse, requiring multiple pulses to acquire information from different orientations, thus lacking spatial scanning capabilities.

[0004] A frequency diversity array (FDA) imparts angle-time dependence to the transmit pattern by introducing stepped frequency increments between transmit elements that are much smaller than the carrier frequency and bandwidth. By adjusting the frequency increment size, the transmit beam can automatically scan a specified spatial domain within a single pulse. The paper "WANG Huake, LIAO Guisheng, XU Jingwei, et al. Transmit beampattern design for coherent FDA by piecewise LFM waveform[J]. Signal Processing, 2019, 161:14-24" proposes a pulsed coherent FDA radar model based on linear frequency modulation (LFM). The paper analyzes the relationship between the spatial angle covered by the radar beam and the frequency points of the transmit waveform. By designing the LFM signal in the time domain, the paper achieves flexible control of the FDA transmit pattern. However, when the transmit waveform uses frequency-time modulation, the system's resolution deteriorates rapidly due to the reduced accumulated bandwidth. The literature "WANG Huake, LIAO Guisheng, XU Jingwei, et al. Subarray-based coherent pulsed-LFM frequency diverse array for range resolution enhancement[J]. IET Signal Processing, 2020, 14(4): 251-258." and "WANG Huake, LIAO Guisheng, XU Jingwei, et al. Space-time matched filter design for interference suppression in coherent frequency diverse array[J]. IET Signal Processing, 2020, 14(3): 175-181." respectively proposed to use subarray division and spatial domain coding methods to reduce the main lobe width of the transmit beam, thereby improving the range resolution of the coherent FDA radar. However, since preprocessing in the spatial domain will cause the sidelobe level of the autocorrelation function of the transmit waveform to increase, it is not conducive to high-precision resolution of the target.The document "WANG Zhonghan, SONG Yaoliang. A waveform design method for frequency diverse array systems based on diversity linear chirp waveforms [J]. International Journal of Microwave and Wireless Technologies, 2021: 1-8." proposes an FDA radar waveform design method based on diversity LFM signals. The artificial bee colony algorithm is used to optimize the bandwidth of each LFM signal to reduce the sidelobe level, but the computational complexity and accuracy of the system depend to a great extent on the optimization algorithm used.

[0005] Currently, most waveform design efforts for FDA are focused on radar or communication systems. Integrating radar and communication using FDA allows beam pointing to change over time within a single snapshot, eliminating the need for specific transmit beamforming to transmit signals to the target and receiver. This not only improves radar detection, positioning, and identification accuracy, but also enhances anti-detection, anti-interference, and anti-interception capabilities during signal transmission, enhancing system flexibility and coordination. Summary of the Invention

[0006] Purpose of the Invention: In integrated FDA radar communication, the randomness of communication information disrupts the coherence between array transmit elements, thereby destroying the array's transmit-receive pattern, resulting in increased range-angle sidelobes and reduced resolution. To embed communication information while preserving the FDA's excellent radar detection capabilities, a low-sidelobe waveform design method for integrated FDA radar communication is provided. This method achieves low sidelobes in both the range and angle dimensions, improving resolution.

[0007] Technical Solution: To achieve the above objectives, the present invention provides a low-sidelobe FDA radar communication integrated waveform design method, comprising the following steps:

[0008] S1: Modulate the communication signal into the transmit waveform of each array element using phase shift keying (PSK) modulation to build an integrated signal model for FDA (Frequency Diverse Array) radar communication.

[0009] S2: Design the subarray delay for the integrated FDA radar communication signal. Two design methods are proposed to introduce delay between subarrays and within subarrays, respectively, to obtain the subarray delay model.

[0010] S3: Based on the subarray delay model, the tangent FM signal is selected as the baseband waveform to obtain the transmit signal model;

[0011] S4: Calculate the ambiguity function based on the transmitted signal and perform analysis;

[0012] S5: At the radar receiver, a two-dimensional angle-time matched filter with time-varying characteristics is designed based on the ambiguity function to perform pulse compression and beamforming on the echo signal.

[0013] S6: At the communication receiving end, corresponding demodulation processing is performed according to the transmitted signal, and the bit error rate is analyzed.

[0014] Furthermore, the construction of the FDA radar communication integrated signal model in step S1 is performed as follows:

[0015] A1: Assume that the number of array elements is M, the array configuration is a one-dimensional uniform linear array, the integrated waveform adopts a pulse transmission system, and phase modulation is used to modulate the communication information into the sub-pulse transmitted by each array element. Each pulse can transmit M communication symbols.

[0016] A2: Calculate the transmitted signal of the mth array element as:

[0017]

[0018] Where m = 1, 2, ..., M; 0 ≤ t ≤ T p , T p is the pulse duration; b m is the phase modulated by the mth array element, which is used to represent the communication information carried. If quaternary transmission is used, its value is "π / 4", "3π / 4", "5π / 4" or "7π / 4"; x(t) is the baseband transmission signal; rect(·) represents the duration T p Rectangular window; f m is the carrier frequency of the signal transmitted by the mth array element:

[0019] f m =f c +(m-1)Δf (2)

[0020] Among them, f c is the reference signal frequency; Δf is the frequency increment, which is much smaller than the carrier frequency and bandwidth.

[0021] A3: Calculate the FDA radar communication integration far-field signal emitted at azimuth angle θ as follows:

[0022]

[0023] Where d = λ / 2 is the array element spacing, and λ is the carrier wavelength.

[0024] Furthermore, the subarray delay design method for the FDA radar communication integrated signal in step S2 is performed as follows:

[0025] B1: Assume there are M sub-matrices, each containing K m There are (1≤m≤M) array elements, and the transmission waveform of each array element is exactly the same.

[0026] B2: For frequency-controlled array design of inter-subarray delay, the delay Δt is introduced to be evenly stepped between different subarrays. For frequency-controlled array design of intra-subarray delay, different subarrays correspond to different delay Δt. m ,1≤m≤M, and the delay is evenly stepped between different array elements in each sub-array.

[0027] The transmit signal of the mth element of TBS-FDA is calculated as:

[0028]

[0029] Calculate the kth element of the mth array of TWS-FDA m The transmitted signal of an array element is:

[0030]

[0031] Where 1≤k m ≤K m .

[0032] B3: Calculate the far-field signal emitted by the m sub-arrays of TBS-FDA at azimuth angle θ:

[0033]

[0034] Among them, K0=0.

[0035] The far-field signal emitted by the m sub-arrays of TWS-FDA at the azimuth angle θ is calculated as:

[0036]

[0037] B4: Calculate the far-field signal emitted by TBS-FDA at azimuth angle θ:

[0038]

[0039]

[0040] Furthermore, the tangent frequency modulation signal model used as the baseband waveform in step S3 is:

[0041]

[0042] Wherein, B is the bandwidth of the transmitted signal; β = arctanα, α is the tangent frequency modulation parameter, and its value range is (-∞, +∞).

[0043] Furthermore, the radar ambiguity function is calculated in step S4 according to the following steps:

[0044] C1: The multidimensional ambiguity function of angle-range-Doppler is defined as:

[0045]

[0046] Where M and N are the number of transmitting and receiving array elements respectively; τ is the time delay; f d is the Doppler frequency shift; θ is the target azimuth; θ′ is the azimuth of the receiving beam; s m (t) and s n (t) are the transmitting waveform of the mth array element and the receiving waveform of the nth array element respectively.

[0047] C2: Calculate the fuzzy function of the TBS-FDA integrated waveform:

[0048]

[0049] C3: Calculate the fuzzy function of the TWS-FDA integrated waveform:

[0050]

[0051] C4: Evaluate the performance of the transmitted waveform in different dimensions using different dimensionality reduction expressions of the multidimensional ambiguity function: Range-Doppler ambiguity function |χ(τ,f d )| θ＝0,θ′＝0 The definition of the traditional ambiguity function is the same as that of the traditional ambiguity function, which analyzes the autocorrelation function and Doppler tolerance of the waveform; the angle-angle ambiguity function Analyze the spatial coverage capability of the signal; distance-angle ambiguity function Analyze the ability of the transmitted waveform to distinguish stationary targets at different directions.

[0052] Furthermore, in step S5, the angle-time two-dimensional matched filter is designed to perform pulse compression and beamforming joint processing on the echo signal according to the following steps:

[0053] D1: Assuming the transmitting and receiving antennas are co-located, the number of receiving array elements is The distance of the target relative to the radar is r1, and the azimuth is θ R .

[0054] D2: Calculate the received echo signal matrix as:

[0055] S R (t-τ R ,θR )=a R (θ R )ξ T s T (t-τ R ,θ R )+v(t) (14)

[0056] Among them, ξ T is the target echo coefficient; τ R =2r1 / c is the round-trip delay of the signal from the reference array element to the target, c is the speed of light; a R (θ)=『1,exp(j2πdsinθ / λ),...,exp(j2πd(N-1)sinθ / λ)] T is the steering vector of the receiving array; s T (t,θ) is the transmitted signal; v(t) is the received noise vector.

[0057] D3: Constructing the angle-time two-dimensional matched filter:

[0058]

[0059] Where θ′ represents the azimuth angle of the receiving gain; (·) * represents the conjugate operation; w R (t,θ′) is the array weight vector for receive beamforming:

[0060]

[0061] D4: Calculate the echo signal after matched filtering:

[0062]

[0063] Where v′(t) is the total received noise of N channels; g T (θ R ,t-τ R ) is the emission pattern of the array:

[0064]

[0065] is the matching function of the transmit-receive pattern:

[0066]

[0067] D5: Calculate the pulse compression signal as:

[0068]

[0069] Furthermore, the demodulation processing and bit error rate analysis at the communication receiving end in step S6 are performed as follows:

[0070] E1: Assume that the communication receiving end is a single antenna, the distance relative to the radar is r2, and the azimuth angle is θ C , using QPSK modulation.

[0071] E2: Calculate the communication receiving signal as:

[0072]

[0073] Among them, α T is the channel gain; n(t) is the channel noise; τ C =r2 / c is the time delay of the signal from the transmitter to the communication receiver; b m,I and b m,Q are the communication information of the mth sub-array in I and Q channels respectively; ψ n is the phase difference caused by the emission steering vector, n = mK m +k m .

[0074] E3: Calculate the coherent demodulated signals of the I and Q channels:

[0075]

[0076]

[0077] Among them, n I (t) and n Q (t) represents the noise of I and Q channels.

[0078] E4: Calculate the mth signal of the I and Q channel separation filter as:

[0079]

[0080]

[0081] Among them, A I and A Q is the amplitude constant; μ=B·tan(2β(m-1)Δt / T p ) / 2tanβ is the baseband modulation frequency.

[0082] E5: Calculate the bit error rate:

[0083]

[0084] Among them, L is a base number; D i represents the minimum value of the Euclidean distance from the i-th constellation point to other constellation points; N0 / 2 is the noise power spectrum density; erfc(·) is the standard complementary error function.

[0085] The present invention proposes a low-sidelobe FDA radar communication integrated waveform design method. PSK is used to modulate communication information. Two design methods, inter-subarray delay and intra-subarray delay, are proposed to restore the correlation of array element transmit waveforms and reduce the range-dimensional sidelobes of the integrated waveform. A tangent frequency-modulated signal is selected as the baseband waveform in the time domain to restore the angular resolution of the integrated waveform. A two-dimensional angle-time matched filter with time-varying characteristics is designed at the receiving end to realize the joint processing of spatial domain transmit beamforming and time domain pulse compression.

[0086] This paper provides a low-sidelobe FDA radar communication integrated waveform design method. Kalman filtering is used to predict the FIM determinant of the target state estimate at time k+1. A cooperative game optimization model for the joint allocation of power and bandwidth for networked radars is established and solved using the Shapley value algorithm combined with the CMA algorithm. The power and bandwidth allocation results that maximize system tracking performance at time k+1 are obtained.

[0087] The above solution can be summarized into the following three steps:

[0088] (1) The sub-array delay of the FDA radar communication integrated signal is designed, and the tangent frequency modulation signal is selected as the baseband waveform in the time domain.

[0089] (2) At the radar receiving end, a two-dimensional angle-time matched filter with time-varying characteristics is designed to perform pulse compression and beamforming on the echo signal.

[0090] (3) At the communication receiving end, a corresponding demodulation processing method is established based on the established transmission signal model and its modulation method.

[0091] Beneficial effects: Compared with the prior art, the present invention provides a low-sidelobe FDA radar communication integrated waveform design method, and constructs an FDA radar communication integrated signal model by adopting PSK modulation communication information; two design methods of inter-subarray delay and intra-subarray delay are proposed to restore the time domain correlation of the array element transmission waveform and reduce the distance-dimensional sidelobe of the integrated waveform; and, in the time domain, a tangent frequency modulation signal is selected as the baseband waveform to restore the angular resolution of the integrated waveform; at the radar receiving end, by designing an angle-time two-dimensional matched filter with time-varying characteristics, the spatial domain scanning capability of the integrated waveform is restored, and the joint processing of spatial domain transmission beamforming and time domain pulse compression is realized; at the communication receiving end, the coherent demodulated signal is secondary separated by a channel separation filter to complete information acquisition. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1It is a schematic flow diagram of the present invention;

[0093] Figure 2 The schematic diagrams of two sub-array delay design methods are: Figure 2 (a) and Figure 2 (b);

[0094] Figure 3 It is the simulation diagram of range-Doppler ambiguity function;

[0095] Figure 4 It is the simulation diagram of angle-angle ambiguity function;

[0096] Figure 5 It is a simulation diagram of the distance-angle ambiguity function;

[0097] Figure 6 It is a simulation diagram of the directional pattern;

[0098] Figure 7 This is a bit error rate simulation diagram using BPSK modulation;

[0099] Figure 8 This is a bit error rate simulation diagram using QPSK modulation; DETAILED DESCRIPTION

[0100] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0101] The present invention provides a low sidelobe FDA radar communication integrated waveform design method, such as Figure 1 As shown, it includes the following steps:

[0102] S1: Modulate the communication signal into the transmit waveform of each array element through phase shift keying modulation to build an integrated signal model for FDA radar communication;

[0103] S2: Design the subarray delay for the integrated FDA radar communication signal. Two design methods are proposed to introduce delay between subarrays and within subarrays, respectively, to obtain the subarray delay model.

[0104] S3: Based on the subarray delay model, the tangent FM signal is selected as the baseband waveform to obtain the transmit signal model;

[0105] S4: Calculate the ambiguity function based on the transmitted signal and perform analysis;

[0106] S5: At the radar receiver, a two-dimensional angle-time matched filter with time-varying characteristics is designed based on the ambiguity function to perform pulse compression and beamforming on the echo signal.

[0107] S6: At the communication receiving end, corresponding demodulation processing is performed according to the transmitted signal, and the bit error rate is analyzed.

[0108] The construction of the FDA radar communication integrated signal model in step S1 is carried out as follows:

[0109] A1: Assume that the number of array elements is M, the array configuration is a one-dimensional uniform linear array, the integrated waveform adopts a pulse transmission system, and phase modulation is used to modulate the communication information into the sub-pulse transmitted by each array element. Each pulse can transmit M communication symbols.

[0110] A2: Calculate the transmitted signal of the mth array element as:

[0111]

[0112] Where m = 1, 2, ..., M; 0 ≤ t ≤ T p , T p is the pulse duration; b m is the phase modulated by the mth array element, which is used to represent the communication information carried. If quaternary transmission is used, its value is "π / 4", "3π / 4", "5π / 4" or "7π / 4"; x(t) is the baseband transmission signal; rect(·) represents the duration T p Rectangular window; f m is the carrier frequency of the signal transmitted by the mth array element:

[0113] f m =f c +(m-1)Δf (2)

[0114] Among them, f c is the reference signal frequency; Δf is the frequency increment, which is much smaller than the carrier frequency and bandwidth.

[0115] A3: Calculate the FDA radar communication integration far-field signal emitted at azimuth angle θ as follows:

[0116]

[0117] Where d = λ / 2 is the array element spacing, and λ is the carrier wavelength.

[0118] Reference Figure 2 The subarray delay design method for the FDA radar communication integrated signal in step S2 is performed as follows:

[0119] B1: Assume there are M sub-matrices, each containing Km There are (1≤m≤M) array elements, and the transmission waveform of each array element is exactly the same.

[0120] B2: For frequency-controlled array design of inter-subarray delay, the delay Δt is introduced to be evenly stepped between different subarrays. For frequency-controlled array design of intra-subarray delay, different subarrays correspond to different delay Δt. m ,1≤m≤M, and the delay is evenly stepped between different array elements in each sub-array.

[0121] The transmit signal of the mth element of TBS-FDA is calculated as:

[0122]

[0123] Calculate the kth element of the mth array of TWS-FDA m The transmitted signal of an array element is:

[0124]

[0125] Where 1≤k m ≤K m .

[0126] B3: Calculate the far-field signal emitted by the m sub-arrays of TBS-FDA at azimuth angle θ:

[0127]

[0128] Among them, K0=0.

[0129] The far-field signal emitted by the m sub-arrays of TWS-FDA at the azimuth angle θ is calculated as:

[0130]

[0131] B4: Calculate the far-field signal emitted by TBS-FDA at azimuth angle θ:

[0132]

[0133]

[0134] The tangent frequency modulation signal model as the baseband waveform in step S3 is:

[0135]

[0136] Wherein, B is the bandwidth of the transmitted signal; β = arctanα, α is the tangent frequency modulation parameter, and its value range is (-∞, +∞).

[0137] The calculation of the radar ambiguity function in step S4 is performed as follows:

[0138] C1: The multidimensional ambiguity function of angle-range-Doppler is defined as:

[0139]

[0140] Where M and N are the number of transmitting and receiving array elements respectively; τ is the time delay; f d is the Doppler frequency shift; θ is the target azimuth; θ′ is the azimuth of the receiving beam; s m (t) and s n (t) are the transmitting waveform of the mth array element and the receiving waveform of the nth array element respectively.

[0141] C2: Calculate the fuzzy function of the TBS-FDA integrated waveform:

[0142]

[0143] C3: Calculate the fuzzy function of the TWS-FDA integrated waveform:

[0144]

[0145] C4: Evaluate the performance of the transmitted waveform in different dimensions using different dimensionality reduction expressions of the multidimensional ambiguity function: Range-Doppler ambiguity function |χ(τ,f d )| θ＝0,θ′＝0 The definition of the traditional ambiguity function is the same as that of the traditional ambiguity function, which analyzes the autocorrelation function and Doppler tolerance of the waveform; the angle-angle ambiguity function Analyze the spatial coverage capability of the signal; distance-angle ambiguity function Analyze the ability of the transmitted waveform to distinguish stationary targets at different directions.

[0146] In step S5, the angle-time two-dimensional matched filter is designed to perform pulse compression and beamforming on the echo signal in combination according to the following steps:

[0147] D1: Assuming the transmitting and receiving antennas are co-located, the number of receiving array elements is The distance of the target relative to the radar is r1, and the azimuth is θ R .

[0148] D2: Calculate the received echo signal matrix as:

[0149] S R (t-τ R ,θ R )=a R (θ R )ξ T s T (t-τ R ,θ R )+v(t) (14)

[0150] Among them, ξ T is the target echo coefficient; τ R =2r1 / c is the round-trip delay of the signal from the reference array element to the target, c is the speed of light; a R (θ)=[1,exp(j2πdsinθ / λ),...,exp(j2πd(N-1)sinθ / λ)] T is the steering vector of the receiving array; s T (t,θ) is the transmitted signal; v(t) is the received noise vector.

[0151] D3: Constructing the angle-time two-dimensional matched filter:

[0152]

[0153] Where θ′ represents the azimuth angle of the receiving gain; (·) * represents the conjugate operation; w R (t,θ′) is the array weight vector for receive beamforming:

[0154]

[0155] D4: Calculate the echo signal after matched filtering:

[0156]

[0157] Where v′(t) is the total received noise of N channels; g T (θ R ,t-τ R ) is the emission pattern of the array:

[0158]

[0159] is the matching function of the transmit-receive pattern:

[0160]

[0161] D5: Calculate the pulse compression signal as:

[0162]

[0163]

[0164] The demodulation processing and bit error rate analysis at the communication receiving end in step S6 are performed as follows:

[0165] E1: Assume that the communication receiving end is a single antenna, the distance relative to the radar is r2, and the azimuth angle is θ C , using QPSK modulation.

[0166] E2: Calculate the communication receiving signal as:

[0167]

[0168] Among them, α T is the channel gain; n(t) is the channel noise; τ C =r2 / c is the time delay of the signal from the transmitter to the communication receiver; b m,I and b m,Q are the communication information of the mth sub-array in I and Q channels respectively; ψ n is the phase difference caused by the emission steering vector, n = mK m +k m .

[0169] E3: Calculate the coherent demodulated signals of the I and Q channels:

[0170]

[0171]

[0172] Among them, n I (t) and n Q (t) represents the noise of I and Q channels.

[0173] E4: Calculate the mth signal of the I and Q channel separation filter as:

[0174]

[0175]

[0176] Among them, A I and A Q is the amplitude constant; μ=B·tan(2β(m-1)Δt / T p ) / 2tanβ is the baseband modulation frequency.

[0177] E5: Calculate the bit error rate:

[0178]

[0179] Among them, L is a base number; D i represents the minimum value of the Euclidean distance from the i-th constellation point to other constellation points; N0 / 2 is the noise power spectrum density; erfc(·) is the standard complementary error function.

[0180] Based on the above, this embodiment provides a simulation example to verify the effectiveness of the present invention. This example uses a 13-transmitter-13-receiver co-located FDA radar communication integrated system, and the simulation environment is MATLAB R2019b.

[0181] The specific experimental process is:

[0182] Step 1: Build a signal model for FDA radar communication integration

[0183] Table 1 Basic simulation parameters

[0184] parameter Numerical parameter Numerical <![CDATA[Carrier frequency f c > 3GHz Array element spacing d 0.05m Bandwidth B 100MHz Frequency increment Δf 200kHz <![CDATA[Pulse width T p > 5μs Pulse period PRI 50μs Number of transmitting subarrays M 13 Number of receiving sub-arrays N 13 <![CDATA[Initial azimuth θ0]]> 0° Tangent frequency modulation parameter α 2.1

[0185] Step 2: Subarray Delay Design

[0186] The sub-array delay design is carried out for the integrated signal of FDA radar communication. The array elements in the sub-array adopt a regular configuration, namely K m =2,1≤m≤M; BST-FDA delay Δt=0.01s; WST-FDA delay Δt m =0.01s+m×0.01s.

[0187] Step 3: Select the tangent FM signal as the baseband waveform

[0188] The two subarray delay-based low sidelobe design methods essentially compromise the correlation of the transmitted waveform in the time and spatial domains. Although they can enhance the correlation of the transmitted waveform of each array element in the time domain, the enhanced range resolution comes at the expense of angular resolution. This degradation is particularly severe when the baseband waveform uses an LFM signal, which has high autocorrelation sidelobes.

[0189] To this end, we propose using a tangent frequency-modulated signal as the baseband transmit waveform to restore angular resolution. Thanks to the full spatial range of the tangent trigonometric function, the parameter range of the tangent frequency-modulated signal is (-∞, +∞). When α = 0, the tangent frequency-modulated signal is equivalent to an LFM signal. As the value of α increases, the sidelobes of the tangent frequency-modulated signal decrease, accompanied by a widening of the mainlobe. However, this problem can be resolved through subarray delay design methods. Therefore, by selecting an appropriate value for the parameter α, good range-angle resolution can be achieved.

[0190] The radar communication integrated transmission waveforms of "tangent FM + TBS-FDA" and "tangent FM + TWS-FDA" proposed in this invention are evaluated from multiple dimensions and compared with the integrated waveform of "tangent FM + communication coding".

[0191] Figure 3 The range-Doppler ambiguity functions of the three waveforms |χ(τ,f d )|θ＝0,θ′＝0 Simulation results. Figure 3 Although the "tangential frequency modulation + communication coding" waveform in (a) has a relatively narrow mainlobe width, the randomness of the communication coding causes a sharp increase in the sidelobe level. Using only the NLFM signal as the baseband waveform cannot repair the loss of waveform coherence. Figure 3 (b) “Tangential FM+BST-FDA” and Figure 3 The “tangent FM + WST-FDA” waveform in (c) significantly reduces the sidelobes by introducing time delays between and within subarrays, while also reducing the mainlobe width and enhancing the range resolution. Figure 3 (d) shows the time delay slices of the three waveforms, with maximum sidelobe levels of -6.57dB, -31.89dB, and -30.79dB, respectively.

[0192] Figure 4 The angle-angle ambiguity functions of three waveforms are given Simulation results. Figure 4 The phased array radar in (a) can only generate gain when the target azimuth, receiving azimuth, and starting azimuth are equal. Figure 4 (b) "Tangent FM + communication coding" waveform and Figure 4 The angle-angle ambiguity function of the "tangent FM + TBS-FDA" waveform in (c) forms gains on both the main diagonal and the subdiagonal, indicating that the "grating lobe" phenomenon occurs when beamforming the target azimuth at the receiver. This causes interference signals from undesired directions to be received simultaneously, hindering signal processing. Figure 4 The angle-angle ambiguity function of the "Tangent FM + TWS-FDA" waveform in (d) forms high gain only on the main diagonal, indicating that gain can only be generated when the target azimuth is equal to the receiving azimuth. This is independent of the transmit beamforming and has full spatial coverage capability.

[0193] Figure 5 The range-angle ambiguity functions of the three waveforms are given Simulation results. Figure 5 (a) and Figure 5 (b) shows that when the baseband waveform is an LFM signal, the gains of TBS-FDA and TWS-FDA in multiple angle regions are greater than -10dB, and they have no angle resolution. Figure 5 (c) and Figure 5 (d) shows that when the baseband waveform uses a tangent FM signal, the energy of the integrated waveform is only concentrated at the receiving angle, which can effectively restore the angular resolution. Figure 5 (e) and Figure 5 (f) is the angular resolution diagram of TBS-FDA and TWS-FDA. Using the tangent FM signal as the baseband waveform can reduce the sidelobe level of the angular resolution diagram to below -15dB.

[0194] Step 4: Process the echo signal using an angle-time two-dimensional matched filter

[0195] The angle-time two-dimensional matched filter proposed in this invention achieves a good matching response to the transmission pattern. To demonstrate the effectiveness of this invention, simulations of the transmission pattern and the transmit-receive pattern were performed, and the spatial scanning capability of the system was verified by setting different frequency increments Δf and starting azimuth angles θ0.

[0196] Figure 6 When Δf=1 / T p , θ0=0° and Δf=1 / 2T p , simulation results of the transmit pattern and transmit-receive pattern when θ0=30°. Figure 6 (a) and Figure 6 The transmission pattern of (c) is disordered, which is due to the modulation of the random communication phase information. Figure 6 (b) and Figure 6 The transmit-receive pattern in (d) is the product of the transmit pattern and the receive matching function. It can be seen that the angle-time two-dimensional matched filter can effectively restore the FDA's uniform "S"-shaped pattern, demonstrating excellent spatial scanning capabilities. In practical applications, the values ​​of Δf and θ0 can be set based on the specific locations of the radar and communication targets to maximize the waveform gain of the integrated system.

[0197] Step 5: Communication demodulation processing and bit error rate simulation

[0198] The simulation parameters of the communication are set as follows: the channel noise is Gaussian white noise, the signal-to-noise ratio is -10 to 30 dB, the system transmits a total of 5000 pulses, and each pulse carries M = 13 bit code elements.

[0199] Figure 7 (a) and Figure 7 (b) is the bit error rate simulation of the "tangent FM + TBS-FDA" and "tangent FM + TWS-FDA" waveforms when using BPSK modulation. Figure 8 (a) and Figure 8 (b) shows the bit error rate simulation of the "Tangent FM + TBS-FDA" and "Tangent FM + TWS-FDA" waveforms using QPSK modulation. As can be seen from the figure, when the inter-subarray delay design is used, the bit error rate curve basically coincides with the theoretical value and is independent of the frequency modulation parameter α. This shows that the design of combining inter-subarray delay with the tangent FM signal does not affect the system's noise immunity. When the intra-subarray delay design is used, the bit error rate curve still coincides with the theoretical value when α is low, but as α increases, the system's noise immunity performance decreases slightly.

[0200] The above examples verify the correctness, effectiveness and reliability of the present invention.

Claims

1. A low-sidelobe FDA radar communication integrated waveform design method, characterized in that: The steps include: S1: Modulate the communication signal into the transmit waveform of each array element through phase shift keying modulation to build an integrated signal model for FDA radar communication; S2: Design the subarray delay for the integrated FDA radar communication signal. Two design methods are proposed to introduce delay between subarrays and within subarrays, respectively, to obtain the subarray delay model. S3: Based on the subarray delay model, the tangent FM signal is selected as the baseband waveform to obtain the transmit signal model; S4: Calculate the ambiguity function based on the transmitted signal and perform analysis; S5: At the radar receiver, a two-dimensional angle-time matched filter with time-varying characteristics is designed based on the ambiguity function to perform pulse compression and beamforming on the echo signal. S6: At the communication receiving end, corresponding demodulation processing is performed according to the transmitted signal, and the bit error rate is analyzed; The demodulation processing and bit error rate analysis at the communication receiving end in step S6 are performed as follows: E1: Assume that the communication receiving end is a single antenna, the distance relative to the radar is r2, and the azimuth angle is θ C , using QPSK modulation; E2: Calculate the communication receiving signal as: Among them, S T () represents the transmitted signal; x[] represents the baseband transmitted waveform; α T is the channel gain; n(t) is the channel noise; τ C =r2 / c is the time delay of the signal from the transmitter to the communication receiver; b m,I and b m,Q are the communication information of the mth sub-array in I and Q channels respectively; ψ n is the phase difference caused by the emission steering vector, n = mK m +k m ; Δt is the time delay of TBS-FDA; f m is the carrier frequency of the signal transmitted by the mth array element: E3: Calculate the coherent demodulated signals of the I and Q channels: Among them, n I (t) and n Q (t) represents the noise of I and Q channels; T p is the pulse duration; Δf is the frequency increment; K m is the number of array elements in the mth sub-matrix; E4: Calculate the mth signal of the I and Q channel separation filter as: Among them, A I and A Q is the amplitude constant; μ=B·tan(2β(m-1)Δt / T p ) / 2tanβ is the baseband frequency modulation rate; B is the transmission signal bandwidth; β=arctanα, α is the tangent frequency modulation parameter, and its value range is (-∞,+∞); E5: Calculate the bit error rate: Among them, L is a base number; D i represents the minimum value of the Euclidean distance from the i-th constellation point to other constellation points; N0 / 2 is the noise power spectrum density; erfc(·) is the standard complementary error function.

2. The method for designing an integrated waveform for FDA radar communication with low side lobes according to claim 1, characterized in that: The construction of the signal model for the integration of FDA radar communication in step S1 includes the following steps: A1: Assume that the number of array elements is M, the array configuration is a one-dimensional uniform linear array, the integrated waveform adopts a pulse transmission system, and the communication information is modulated into the sub-pulse transmitted by each array element using phase modulation. Each pulse can transmit M communication symbols; A2: Calculate the transmitted signal of the mth array element as: Where m = 1, 2, …, M; 0 ≤ t ≤ T p , T p is the pulse duration; b m is the phase modulated by the mth array element, which is used to represent the communication information carried; x(t) is the baseband transmission signal; rect(·) represents the duration T p Rectangular window; f m is the carrier frequency of the signal transmitted by the mth array element: f m =f c +(m-1)Δf (2) Among them, f c is the reference signal frequency; Δf is the frequency increment, which is much smaller than the carrier frequency and bandwidth; A3: Calculate the FDA radar communication integration far-field signal emitted at azimuth angle θ as follows: Where d = λ / 2 is the array element spacing, and λ is the carrier wavelength.

3. The low sidelobe FDA radar communication integrated waveform design method according to claim 1 is characterized in that: The subarray delay design method for the FDA radar communication integrated signal in step S2 is performed as follows: B1: Assume there are M sub-matrices, each containing K m ,1≤m≤M array elements, the transmission waveform of each array element is exactly the same; B2: For frequency-controlled array design of inter-subarray delay, the delay Δt is introduced to be evenly stepped between different subarrays. For frequency-controlled array design of intra-subarray delay, different subarrays correspond to different delay Δt. m ,1≤m≤M, and the delay is evenly stepped between different array elements in each subarray; The transmit signal of the mth subarray of TBS-FDA is calculated as: Calculate the kth sub-matrix of TWS-FDA m The transmitted signal of an array element is: Where 1≤k m ≤K m ; B3: Calculate the far-field signal emitted by the mth subarray of TBS-FDA at azimuth angle θ: The far-field signal emitted by the mth subarray of TWS-FDA at azimuth angle θ is calculated as: B4: Calculate the far-field signal emitted by TBS-FDA at azimuth angle θ: Among them, T p is the pulse duration, b m is the phase of the mth sub-array modulation, f m is the carrier frequency of the mth subarray transmission signal, d = λ / 2 is the array element spacing, λ is the carrier wavelength, and x(t) is the baseband transmission signal.

4. The method for designing a low-sidelobe FDA radar communication integrated waveform according to claim 1, characterized in that: The tangent frequency modulation signal model as the baseband waveform in step S3 is: Among them, T p is the pulse duration; B is the transmission signal bandwidth; β = arctanα, α is the tangent frequency modulation parameter, and its value range is (-∞, +∞).

5. The method for designing a low-sidelobe FDA radar communication integrated waveform according to claim 1, characterized in that: The calculation of the radar ambiguity function in step S4 is performed as follows: C1: The multidimensional ambiguity function of angle-range-Doppler is defined as: Where M and N are the number of transmitting and receiving array elements respectively; τ is the time delay; f d is the Doppler frequency shift; θ is the target azimuth; θ′ is the azimuth of the receiving beam; s m (t) and s n (t) are the transmit waveform of the mth array element and the receive waveform of the nth array element respectively; C2: Calculate the fuzzy function of the TBS-FDA integrated waveform: C3: Calculate the fuzzy function of the TWS-FDA integrated waveform: Where d = λ / 2 is the array element spacing; λ is the carrier wavelength; b m and b n is the phase of the mth and nth sub-array modulation; Δf is the frequency increment; x(t) is the baseband transmission signal; Δt is the TBS-FDA delay; K m is the number of array elements in the mth sub-array; Δt m is the time delay of the mth subarray of TBS-FDA; C4: Evaluate the performance of the transmitted waveform in different dimensions using different dimensionality reduction expressions of the multidimensional ambiguity function: Range-Doppler ambiguity function |χ(τ,f d )| θ＝0,θ′＝0 The definition of the traditional ambiguity function is the same as that of the traditional ambiguity function, which analyzes the autocorrelation function and Doppler tolerance of the waveform; the angle-angle ambiguity function Analyze the spatial coverage capability of the signal; distance-angle ambiguity function Analyze the ability of the transmitted waveform to distinguish stationary targets at different directions.

6. The method for designing a low-sidelobe FDA radar communication integrated waveform according to claim 1, characterized in that: In step S5, the angle-time two-dimensional matched filter is designed to perform pulse compression and beamforming combined processing on the echo signal in the following steps: D1: Assuming the transmitting and receiving antennas are co-located, the number of receiving array elements is The distance of the target relative to the radar is r1, and the azimuth is θ R , M is the number of sub-arrays; D2: Calculate the received echo signal matrix as: S R (t-t R ,i R )=a R (i R )ξ T s T (t-t R ,i R )+v(t) (14) Among them, ξ T is the target echo coefficient; τ R =2r1 / c is the round-trip delay of the signal from the reference array element to the target, c is the speed of light; a R (θ)=[1,exp(j2πdsinθ / λ),...,exp(j2πd(N-1)sinθ / λ)] T is the steering vector of the receiving array; s T (t,θ) is the transmitted signal; v(t) is the received noise vector; D3: Constructing the angle-time two-dimensional matched filter: Where θ′ represents the azimuth angle of the receiving gain; (·) * represents the conjugate operation; w R (t,θ′) is the array weight vector for receive beamforming: Where d = λ / 2 is the array element spacing; λ is the carrier wavelength; Δf is the frequency increment; D4: Calculate the echo signal after matched filtering: Where v′(t) is the total received noise of N channels; g T (θ R ,t-τ R ) is the emission pattern of the array; Δt is the time delay of TBS-FDA; b m is the phase modulated by the mth sub-array; Among them, f c is the reference signal frequency; is the matching function of the transmit-receive pattern: D5: Calculate the pulse compression signal as:

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