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Research on Joint Design of Transceiver for MIMO Radar-communication Integration under Extended Clutter
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摘要: 针对雷达通信一体化(RCI)在扩展杂波环境中目标检测能力弱和通信性能受限制的问题，该文提出一种扩展目标脉冲响应(TIR)不确定性集合下MIMO RCI系统发射信号波形和接收滤波器联合优化算法。首先，考虑到实际中无法预先准确获得扩展TIR，该文建立TIR存在于球面不确定性集合下，以最大化最小信干噪比为目标的优化函数。其次，为了保障MIMO RCI系统服务每个用户的信息传输可靠性，采用每用户干扰约束，并引入相似性和峰均比约束以确保发射波形具备良好的模糊函数特性。针对构建的非凸二次约束分式规划问题，该文提出了一种循环优化算法迭代优化发射信号波形和接收滤波器。该算法先利用广义瑞利熵获得最优接收滤波器；再利用拉格朗日对偶原理，将原NP-Hard问题中的非凸部分转化为凸问题，并通过半正定优化方法求解。此外，该文也给出了收敛性和计算复杂度分析。仿真结果表明，提出的算法能在扩展杂波背景下有效提高雷达信干噪比，同时满足多用户通信需求。Abstract: In light of challenges related to weak target detection and limited communication performance in extended clutter environments, this paper proposes a joint design of a transmit waveform and receive filter within a Multiple-Input Multiple-Output (MIMO) Radar Communication Integration (RCI) system, considering the uncertainty in the extended Target Impulse Response (TIR). Due to difficulties in accurately determining the extended TIR, an objective function was formulated to maximize the minimum Signal-to-Interference-plus-Noise Ratio (SINR) within a set of sphere TIR uncertainties. To ensure reliable information transmission for each user and to achieve desirable properties of the ambiguity function for the transmission waveform, per-user interference constraints were imposed, along with constraints on waveform similarity and peak-to-average ratio. A cyclic optimization algorithm was introduced to address the nonconvex quadratic constrained fractional programming problem. The optimal receive filter was first derived using a generalized Rayleigh quotient, and the nonconvex part of the original NP-Hard problem was then transformed into a convex problem using the Lagrange duality principle and subsequently solved by the semidefinite optimization method. Also, the convergence and computational complexity of the proposed algorithm are thoroughly discussed. Furthermore, the simulation results confirmed that the algorithm effectively enhances SINR in extended clutter environments and fulfills the communication needs of multiple users.
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图 1 MIMO雷达通信一体化系统
Figure 1. Multi-input multi-output radar-communication integration system
图 4 不同凸集参数下输出SINR对比
Figure 4. Comparison of output SINR under different convex set parameters
图 6 一体化系统波束方向图(杂波性能)
Figure 6. Beam pattern of the integrated system (clutter performance)
图 7 不同相似性约束下输出SINR对比
Figure 7. Comparison of output SINR under different similarity constraints
图 8 不同相似性约束下波形模糊函数对比
Figure 8. Comparison of ambiguity functions under different similarity constraints
图 9 不同用户互干扰能量下输出信噪比对比
Figure 9. Comparison of output SINR under different mutual user interference energies
图 10 合成通信信号质量($\varepsilon = \mathop {10}\nolimits^{ - 5} $)
Figure 10. Quality of synthesized communication signals ($\varepsilon = \mathop {10}\nolimits^{ - 5} $)
图 11 用户的数量对互干扰能量影响
Figure 11. Influence of number of users on mutual user interference energies
图 12 雷达性能和通信性能权衡
Figure 12. Trade-off between radar performance and communication performance
1 联合优化算法
1. Joint optimization algorithm
输入：${{\boldsymbol{H}}_{\mathrm{T}}},\left\{ {{{\boldsymbol{H}}_{{\mathrm{c}},p}}} \right\}_1^P,{{\boldsymbol{D}}_{\mathrm{c}}},{{\boldsymbol{R}}_{\mathrm{c}}},{{\boldsymbol{R}}_{\mathrm{n}}},{{\boldsymbol{t}}_0},r,{\varepsilon _{\mathrm{s}}}$ 初始化： 初始化迭代轮数$k = 0$和发射波形${{\boldsymbol{s}}^{(0)}}$，通过式(26)来计算
最优${{\boldsymbol{w}}^{(0)}}$，记录最小化输出的$ {\text{SINR}} $为${\text{SIN}}{{\text{R}}^{(0)}}$。迭代： 步骤1 通过解决式(38)来得到最优波形协方差矩阵${\boldsymbol{R}}_{\rm{s}}^{(n + 1)}$； 步骤2 $n = n + 1$，通过计算式(26)来得到并且记录最小化
输出的$ {\text{SINR}} $为${\text{SIN}}{{\text{R}}^{(n)}}$；步骤3 如果符合迭代停止条件
$\left| {{\text{SIN}}{{\text{R}}^{(n)}} - {\text{SIN}}{{\text{R}}^{(n - 1)}}} \right|/{\text{SIN}}{{\text{R}}^{(n - 1)}} \le {\varepsilon _{\mathrm{s}}}$则停止；否则转
至步骤1。其中，${\varepsilon _{\mathrm{s}}}$为停止的阈值，本文设置为${10^{ - 4}}$。合成波形： 通过随机化方案从${\boldsymbol{R}}_{\text{s}}^{(n)}$合成${{\boldsymbol{s}}^{(n)}}$，合成次数设置为${N_g}$次，
${N_g}$越大其合成波形的质量越高，若无法满足约束，则以
$ {\boldsymbol{R}}_s^{(n + 1)} $最大特征值对应的向量作为次优解。输出：${{\boldsymbol{s}}^*} = {{\boldsymbol{s}}^{(n)}};{{\boldsymbol{w}}^*} = {{\boldsymbol{w}}^{(n)}}$。 
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表 1 不同信杂比下最大迭代轮次
Table 1. Maximum iteration rounds under different SCR
SCR (dB) 最大轮次 –10 53 –5 44 0 39 5 27 10 19 15 13
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