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Multicarrier Waveform Optimization Method for an Intelligent Reflecting Surface-assisted Dual-function Radar-communication System
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摘要: 雷达通信一体化是解决频谱资源拥挤问题的有效途径之一，而共享波形设计是同时实现雷达与通信功能的关键技术，该文旨在解决智能反射面(IRS)辅助雷达通信双功能(DRC)系统的多载波波形优化问题。首先，通过最大化传输功率、通信码字错误率(WEP)、旁瓣幅度与IRS反射系数约束下的雷达互信息(RMI)，构建了双功能发射波形、IRS反射单元、雷达与通信接收波束联合优化模型。其次，提出了基于交替方向最大化(ADM)的多载波波形优化算法，通过将原非凸优化问题分解为若干低复杂度子问题并迭代优化，获得了多载波波形功率分配策略的局部最优解。最后，仿真结果表明，ADM算法能同时实现雷达与通信功能；相较于现有方法有效提升了IRS辅助DRC系统的雷达与通信性能。Abstract: Radar-communication integration is an effective way to solve the congestion problem of spectrum resource. Sharing waveform design is the key technology that realizes the radar and communication functions simultaneously. This study solves the multicarrier waveform optimization problem for an Intelligent Reflecting Surface (IRS)-assisted Dual-function Radar-Communication (DRC) system. First, by maximizing Radar Mutual Information (RMI) along with the constraints of transmission power, Word Error Probability (WEP), sidelobe amplitude and IRS reflection coefficient, a joint optimization model with dual-functional transmit waveform, IRS reflecting units, radar and communication receiving beampattern is constructed. Second, a multicarrier waveform optimization algorithm based on Alternating Direction Maximization (ADM) is proposed. The original non-convex optimization problem is decomposed into several low-complexity subproblems and then iteratively optimized to obtain the local power allocation strategy of the multicarrier waveform. Finally, the simulation results show that the radar and communication functions can be simultaneously realized using the ADM algorithm. For the IRS-assisted DRC system, both the radar and communication performances can be effectively improved compared with those of the existing methods.
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图 2 I-DRC多载波波形设计的仿真场景
Figure 2. Simulation scenario of multi-carrier waveform design for I-DRC
图 3 通信方位角旁瓣幅度分别为–10 dB和–20 dB的发射波束
Figure 3. Transmit beampatterns with sidelobe amplitudes of –10 dB and –20 dB, respectively, towards the communication direction
图 6 I-DRC多载波波形功率分配方案(
${{{P}}_{\text{t}}}{\text{ = 12}}\;{\text{kW}}$ )Figure 6. Power allocation scheme of multi-carrier waveform for I-DRC (
${{{P}}_{\text{t}}}{\text{ = 12}}\;{\text{kW}}$ )
图 7 不同WEP要求下RMI随着发射总功率变化曲线图
Figure 7. Curve of relationship between RMI and total transmit power under different WEP requirements
图 8 ADM, ADSRP, ASK-IE和QAM-IE算法RMI性能比较
Figure 8. RMI Performance comparison for ADM, ADSRP, ASK-IE and QAM-IE algorithms
图 9 WEP随着信噪比变化曲线图(
$ L' = 4 $ )Figure 9. Curve of relationship between WEP and SNR (
$ L' = 4 $ )表 1 基于ADM的多载波波形优化算法
Table 1. ADM based multicarrier waveform optimization method
1 输入：发射和接收阵元数$ {N_{\text{T}}} $和$ {N_{\text{R}}} $；IRS阵元数$ M $；方位角$ {\theta _0} $, $ {\theta _1} $, $ {\theta _{{\text{ris}}}} $, $ {\theta _{{\text{rist}}}} $, $ \varphi $, $ \tilde \varphi $, $ {\phi _0} $和$ {\phi _1} $；子载波数$ K $；
传输总功率${ {{P} }_{\text{t} } }$；信道系数方差$ \sigma _{{\text{r}},k}^2 $, $ \sigma _{{\text{c}},k}^2 $, $ \sigma _{0,k}^2 $, $ \sigma _{1,k}^2 $, $ \sigma _{{\text{ris}},k}^2 $, $ \sigma _{{\text{rist}},k}^2 $, $ \sigma _{\beta ,0,k}^2 $, $ \sigma _{\beta ,1,k}^2 $和$ \sigma _{\gamma ,k}^2 $；旁瓣幅度数$ L $；停止准则$ \varepsilon $。2 输出：双功能发射波束形成矢量$ {{\boldsymbol u}_k} $；接收波束形成矢量$ {{\boldsymbol w}_k} $；RMI。 3 初始化：$ {\boldsymbol u}_k^0 $, $ {{\boldsymbol Q}^0} $, $ {\boldsymbol v}_k^0 $和$ {\boldsymbol w}_k^0 $；迭代索引$ j $。 4 求解松弛优化问题(16)获得$ {\boldsymbol u}_k^j $； 5 求解半正定凸问题(25)获得$ {{\boldsymbol Q}^j} $； 6 根据式(29)获得$ {\boldsymbol v}_k^j $； 7 根据式(32)获得$ {\boldsymbol w}_k^j $； 8 判断式(10)的收敛条件是否满足；若满足，停止迭代；反之，$ j = j + 1 $，并转向步骤4。 
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