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Dual Function Radar and Communication Waveform Design Based on Sub-pulse Hybrid Modulation
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摘要: 针对以雷达探测为首要功能的探通一体(DFRC)波形设计中通信速率低的问题，该文提出了一种基于子脉冲混合调制(SHM)的探通一体波形设计方法，利用波形子脉冲内/间时域、频域和极化域资源进行多维调制，实现了通信速率的有效提升。构建了以最小化正交波形簇自/互相关函数的峰值旁瓣电平(PSL)为准则，考虑SHM信息调制约束和波形恒模约束的一体化波形设计优化问题，并提出了频域主分量最小化(SMM)算法快速求解上述非凸优化问题。此外，提出了一种基于单脉冲的探通一体回波处理方法，使模糊函数零延时截线的第1个零点处多普勒频率变为传统波形的L(子脉冲数)倍，保证了一体化波形的高多普勒容忍度，实现了对高速目标的有效探测。Abstract: To address the low data rate issue in the design of Dual-Function Radar and Communication (DFRC) waveforms with radar detection as the primary function, this paper proposes an information modulation method for multiple sub-pulse structure waveforms called Sub-pulse Hybrid Modulation (SHM). The proposed SHM method utilizes time-, spectral-, and polarization-domain features from inter-subpulse and intra-subpulse sources to convey information. The DFRC waveform design problem is formulated based on minimizing cross- and auto-correlation peak sidelobe levels, while considering constant envelope and SHM constraints. To tackle the resulting nonconvex and nondeterministic polynomial-hard optimization problem, the spectral majorization-minimization algorithm is employed to monotonically decrease the objective function value. Furthermore, this paper explores an echo processing method that makes the Doppler frequency at the first zero point of the zero-delay intercept of the fuzzy function $ L - 1 $ times higher than that of the conventional waveform, where L is the number of sub-pulses. This enhancement ensures high Doppler tolerance for the DFRC waveform and enables effective detection of high-speed targets.
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图 2 多子脉冲结构的复基带波形示意图
Figure 2. The complex baseband waveform with multiple sub-pulse structure
图 6 子脉冲间波形位置排列解调示意图
Figure 6. Inter-sub-pulse waveform position permutation demodulation
图 9 不同通信码片数下通信性能分析
Figure 9. Communication performance analysis with different number of communication codes
图 10 不同相位间隔下通信性能分析
Figure 10. Communication performance analysis with different phase intervals
图 11 不同总码片数下通信性能分析
Figure 11. Communication performance analysis with different total number of codes
图 12 不同正交波形数下通信性能分析
Figure 12. Communication performance analysis with different number of orthogonal waveforms
图 16 基于单脉冲的多目标DFRC探测回波处理结果
Figure 16. The results of single pulse DFRC echo processing for multiple targets
图 17 不同子脉冲数和不同带宽的DFRC探测回波处理结果
Figure 17. The results of single pulse DFRC echo processing with different number of sub-pulses and different bandwidths
表 1 信息解调方法步骤总结
Table 1. Summary of information demodulation methods
信息调制方法 解调步骤1 解调步骤2 解调步骤3 解调步骤4 解调步骤5 子脉冲内波形极化调制 子脉冲划分 计算空间方位$\left( {\theta ,\varphi } \right)$极化分量集合 虚拟极化匹配 子脉冲内CS-PIP调制 子脉冲内波形极化解调 下变频 相位差检测 差值计算 选小估计 子脉冲间波形位置排列调制 子脉冲内波形极化解调 下变频 匹配滤波 峰值提取 峰值选大 
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1 SMM算法求解优化问题$ {P_1} $
1. SMM algorithm for solving optimization problems $ {P_1} $
输入：$N,L,{{\boldsymbol{q}}^{\left( 0 \right)}},p,{\mathrm{tol}},{N_{\rm c}},{l_{\rm c}},{U_1},\varepsilon ,{U_2}$； 输出：优化问题$ {P_1} $的次优解$ {{\boldsymbol{q}}^ \star } $； 1：$t = 0$，初始化${{\boldsymbol{q}}^{\left( t \right)}} = {{\boldsymbol{q}}^{\left( 0 \right)}}$； 2：$t = t + 1$； 3：计算$ {\boldsymbol{d}}_{l,\hat l}^{\left( {t - 1} \right)},\tilde {\boldsymbol{d}}_{l,\hat l}^{\left( {t - 1} \right)},\tilde {\tilde {\boldsymbol{d}}}_{l,\hat l}^{\left( {t - 1} \right)},\bar {\boldsymbol{d}} _{l,\hat l}^{\left( {t - 1} \right)},\bar {\bar {\boldsymbol{d}} } _{l,\hat l}^{\left( {t - 1} \right)} $； 4：根据式(35)顺序求解$\phi _l^{\left( t \right)}\left( {{h_e}} \right),l = 1,2, \cdots ,L$； 5：若$ \left\| {{{\boldsymbol{q}}^{\left( {t - 1} \right)}} - {{\boldsymbol{q}}^{\left( t \right)}}} \right\| \le {\mathrm{tol}} $, $ {{\boldsymbol{q}}^ \star } = {{\boldsymbol{q}}^{\left( t \right)}} $并退出，否则返回步
骤2。
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表 2 仿真分析信息调制主要参数设置
Table 2. Parameters setting for information modulation simulation
变量类型 变量名 变量取值 变量名 变量取值 子脉冲内CS-PIP调制 子脉冲波形码片数 $N = 512$ 子脉冲内通信码片数 ${N_{\rm c}} = 256$ 相位保护间隔 $\varepsilon = 0.4$ 子脉冲内通信码片相位差集合 $ {U_1}: = \left\{ {0,\pi } \right\} $ 子脉冲间波形排列调制 子脉冲个数 $L = 8$ 子脉冲内波形极化调制 发射极化分量集合
($P = 4$)$ \mathcal{K} : = \left\{ \begin{gathered} [\cos0.0157;\cos0.0157{\text{ }}{{\rm e}^{{\text{j}}0.0628}}] \\ [\cos0.8796;\cos0.8796{\text{ }}{{\rm e}^{{\text{j}}0.0628}}] \\ [\cos0.8796;\cos0.8796{\text{ }}{{\rm e}^{{\text{j}}2.1363}}] \\ [\cos0.8796;\cos0.8796{\text{ }}{{\rm e}^{{\text{j}}4.2097}}] \\ \end{gathered} \right\} $ 发射极化分量集合
($P = 8$)$ \left\{ \begin{gathered} [\cos0.1885;\cos0.1885{\text{ }}{{\rm e}^{{\text{j}}1.4451{\text{ }}}}],[\cos0.5341;\cos0.5341{\text{ }}{{\rm e}^{{\text{j}}4.2097}}] \\ [\cos0.5341;\cos0.5341{\text{ }}{{\rm e}^{{\text{j}}5.5920}}],[\cos0.7069;\cos0.7069{\text{ }}{{\rm e}^{{\text{j}}2.8274}}] \\ [\cos0.8796;\cos0.8796{\text{ }}{{\rm e}^{{\text{j}}1.4451}}],[\cos1.0524;\cos1.0524{\text{ }}{{\rm e}^{{\text{j}}0.0628}}] \\ [\cos1.0524;\cos1.0524{\text{ }}{{\rm e}^{{\text{j}}4.9009}}],[\cos1.3980;\cos1.3980{\text{ }}{{\rm e}^{{\text{j}}2.8274}}] \\ \end{gathered} \right\} $
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表 3 仿真分析基础参数设置
Table 3. Basic parameters setting for simulation
变量 取值 变量名 取值 带宽 B = 5 MHz 子脉冲宽度 $ {T_0} $= 102.4 μs 脉冲宽度 T = 819.2 μs 基带信号采样率 ${f_{\mathrm{s}}} $= 5 MHz 子码片宽度 ${t_b}$ = 0.2 μs 目标回波SNR 0 dB 载频 ${f_0} $= 2 GHz 目标距离 ${R_0} $ = 100 km 目标速度 v = 150 m/s 通信用户方位 $\left( {\theta ,\varphi } \right) = \left( {{{30}^ \circ },{{10}^ \circ }} \right)$
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表 4 一些典型参数下的通信比特数(1个PRT时间)
Table 4. Communication bits for some typical parameters (1 PRT time)
序号 参数设置 SHM LFM-DPSK[16] FNM103[17] FNM311[17] ① $N = 512,{N_{\text{c}}} = 256,L = 8,P = 4$ 6119 4088 103 311 ② $N = 512,{N_{\text{c}}} = 117,L = 8,P = 4$ 4079 4088 103 311 ③ $N = 512,{N_{\text{c}}} = 2,L = 8,P = 4$ 103 4088 103 311 ④ $N = 512,{N_{\text{c}}} = 5,L = 8,P = 4$ 311 4088 103 311 ⑤ $N = 512,{N_{\text{c}}} = 256,L = 16,P = 4$ 12252 4088 103 311 ⑥ $N = 512,{N_{\text{c}}} = 256,L = 8,P = 8$ 6127 4088 103 311
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