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Filter Bank Multi-carrier Waveform Design for Low Probability of Intercepting Joint Radar and Communication System
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摘要: 针对正交频分复用(OFDM)雷达通信一体化波形方案中循环前缀引起的弱回波掩盖问题和敌方战场低截获概率问题，该文提出了基于滤波器组的多载波偏移正交幅度调制(FBMC-OQAM)的低截获雷达通信一体化波形设计方案。分别构建FBMC雷达通信一体化波形与目标检测概率、通信信道容量之间的数学模型，在保证一定系统雷达与通信性能的条件约束下，设计最小化系统总发射功率联合优化问题，优化各个子载波发射功率分配方案。该算法利用测量值和信道状态信息，对下一个脉冲的发射波形参数进行优化设计，实现自适应传输。此外，从平均模糊函数角度分析了FBMC作为雷达信号的可行性和优势。仿真结果表明，与等功率分配方案相比，该文提出的功率分配方案可有效降低一体化系统总发射功率，从而实现低截获性能，并且FBMC波形可有效降低循环前缀引起的距离旁瓣，提高雷达分辨率与信息速率。Abstract: Cyclic prefixes in joint radar and communication systems based on Orthogonal Frequency Division Multiplexing (OFDM) and low probability of interception lead to weak radar echo masking on the battlefield. To address this problem, a low probability of interception waveform design scheme based on Filter Bank Multi-Carrier (FBMC) with Offset Quadrature Amplitude Modulation (FBMC-OQAM) is proposed in this paper. Mathematical models for the FBMC joint radar and communication waveform, target detection probability, and communication channel capacity are established. Under the radar and communication performance constraints required by the system, a joint optimization problem of minimizing the total transmitted power of the system is designed, and the subcarrier and power allocation scheme are optimized. Furthermore, the proposed algorithm can realize adaptive transmission where the parameters of the transmitting waveform can be optimally designed for the next pulse by utilizing the measured values of the current signal and the channel state information. Moreover, the feasibility and advantages of FBMC as the radar signal are analyzed based on the average ambiguity function. Theoretical analysis and simulation experiments show that the power allocation scheme proposed in this paper can effectively reduce the total transmitted power of the system, to achieve low interception performance compared with the equal power allocation. The FBMC waveform can effectively reduce the sidelobes caused by cyclic prefixes, which improves the radar resolution and information rate.
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图 3 OFDM模糊函数、零多普勒图及其零时延图
Figure 3. AAF of OFDM waveform and its zero-Doppler and zero-delay cut
图 4 CP-OFDM模糊函数、零多普勒图及其零时延图
Figure 4. AAF of CP-OFDM waveform and its zero-Doppler and zero-delay cut
图 5 FBMC-OQAM模糊函数、零多普勒图及其零时延图
Figure 5. AAF of FBMC-OQAM waveform and its zero-Doppler and zero-delay cut
图 6 场景1中发射总功率随检测概率变化情况
Figure 6. Total power versus probability of detection in scenario I
图 7 场景2中发射总功率随检测概率变化情况
Figure 7. Total power versus probability of detection in scenario II
图 8 不同方案发射总功率随检测概率变化情况
Figure 8. Total power versus probability of detection in different scheme
图 9 不同方案发射总功率随信道容量变化情况
Figure 9. Total power versus channel capacity in different scheme
表 1 多载波波形仿真参数设置
Table 1. Multi-Carrier waveform parameters setting
波形 符号
周期子载
波数CP长度 符号
数调制方式 滤波器 OFDM 1.65 μs 64 0 4 16QAM 矩形窗 CP-OFDM 2.07 μs 80 0.42 μs 4 16QAM 矩形窗 FBMC-OQAM 0.83 μs 64 0 4 16QAM PHDYAS K=4 
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表 2 PHDYAS滤波器系数
Table 2. PHDYAS filter coefficients
参数 数值 参数 数值 K 4 ${H_1}$ 0.971960 ${H_0}$ 1 ${H_2}$ $\sqrt 2 /2$ ${H_3}$ 0.235147
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表 3 参数
${\boldsymbol{\lambda }}$ 与${\boldsymbol{\eta }}$ 仿真参数设置Table 3.
${\boldsymbol{\lambda }}$ and${\boldsymbol{\eta }}$ parameters setting参数 子信道1 子信道2 子信道3 子信道4 场景1$ {\boldsymbol{\lambda }} $ –0.1369–0.0619i 0.3611+0.2125i 0.0075–0.0921i 0.2667–0.2076i 场景1${\boldsymbol{\eta }}$ –0.046+0.1705i 0.0304+0.1136i 0.0609+0.2273i 0.1218–0.4546i 场景2$ {\boldsymbol{\lambda }} $ 0.6288–0.1170i 0.1064+0.0408i 0.0617+0.0590i 0.0449+0.1549i 场景2${\boldsymbol{\eta }}$ 0.5520+0.1479i 0.0370–0.1380i 0.2070+0.0055i 0.0018–0.0690i
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