Multi-User and Multi-Target Constant Waveform Design of Dual-Function Radar and Communication System
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摘要: 双功能雷达通信一体化系统可以使硬件和频谱资源得到有效利用，是解决当前无线频谱资源紧张问题的一种有效途径。该文针对同时多目标探测与多用户通信场景，以雷达接收回波的信干噪比(SINR)为指标保障雷达的探测性能，采用通信多用户干扰(MUI)作为通信指标保证通信传输性能。与此同时，为保证发射端功率放大器工作在饱和区域，增加了波形恒模的约束条件。该文通过对波形以及滤波器的联合优化，提出了一种在满足通信MUI功率一定的情况下，最大化雷达多目标探测回波最小信干噪比(SINR)的波形设计优化模型。针对此优化问题，采用了交替迭代优化的方法来求解此问题。仿真结果表明，所设计的波形在多目标探测以及多用户通信场景下，通过调整通信MUI功率门限，可以在保证通信MUI功率性能前提下，实现对多目标回波最小SINR的优化。Abstract: The Dual-Functional Radar-Communication (DFRC) system can effectively utilize hardware and spectrum resources, which is an effective way to solve the shortage of the wireless spectrum resource. In this paper, for the scenario of simultaneous multi-target detection and multi-user communication, the Signal-to-Interference-Noise Ratio (SINR) of the radar received echo is used as an index to guarantee the detection performance, and the Multi-User Interference (MUI) of the communication is used as a communication index to guarantee the transmission performance of communication. Meanwhile, constraints on the constant modulus of the waveform are added to ensure that the power amplifier at the transmitter operates in the saturation region. The paper proposes a mathematical model for waveform design that maximizes the minimum SINR of the radar multi-target echoes while satisfying a certain amount of the communication MUI energy by jointly optimizing the waveforms as well as the filters. For this optimization problem, the method of alternating iterative optimization is adopted to solve the problem. Simulation results show that the designed waveform ensures both radar and communication related performance in simultaneous multi-target detection and multi-user communication scenarios.
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算法1 求解问题(21)算法流程 输入：初始化变量${{\boldsymbol{s}}^{(0)}}$, ${e^{(0)}}$, ${\beta ^{(0)}}$, ${\delta _s}$和$ {\delta _\beta } $。 输出：问题式(38)的解$s$； 第1步：$j = 0$； 第2步：${{\boldsymbol{s}}^{(j - 1)}}{\text{ = }}{{\boldsymbol{s}}^{(0)}},\;{e^{(j - 1)}}{\text{ = }}{e^{(0)}}$； 第3步：求解问题式(38)得到$ ({{\boldsymbol{s}}^{(j)}},{e^{(j)}},{\beta ^{(j)}}) $； 第4步：若${\left\| {{\beta ^{(j)}}} \right\|_1} < \tau $，则输出$ {\boldsymbol{s}} = {{\boldsymbol{s}}^{(j)}} $，否则继续下一步 第5步：${{\boldsymbol{s}}^{(0)}}{\text{ = }}{{\boldsymbol{s}}^{(j)}},\;{e^{(0)}}{\text{ = }}{e^{(j)}},\;j{\text{ = }}j + 1$返回第2步 
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算法2 交替迭代优化算法流程 输入：初始化变量${s^{(0)}}$, ${e^{(0)}}$, ${\beta ^{(0)}}$, ${\delta _s}$, $ {\delta _\beta } $和$\kappa $。 输出：问题式(16)的解${s^{(*)}}$,$\left\{ {{\boldsymbol{w}}_m^*} \right\}_{m = 1}^M$。 第1步：$c = 0$，构$ {{\chi }_m}\left( {{{\boldsymbol{s}}^{(0)}}} \right) $, $ {{\boldsymbol{\varLambda}} _m}\left( {{{\boldsymbol{s}}^{(0)}}} \right) $； 第2步：求解问题式(19)得到$\left\{ {{\boldsymbol{w}}_m^{(0)}} \right\}_{m = 1}^M$； 第3步：$c = c + 1$； 第4步：构造$ {{{\boldsymbol{\varOmega}} }_m}\left( {{\boldsymbol{w}}_m^{(c - 1)}} \right) $, $ {{\boldsymbol{\varGamma}}_m}\left( {{\boldsymbol{w}}_m^{(c - 1)}} \right) $，求解问题式(21)
得到${{\boldsymbol{s}}^{(c)}}$；第5步：构造$ {{\chi }_m}\left( {{{\boldsymbol{s}}^{(c)}}} \right) $, $ {{\boldsymbol{\varLambda}} _m}\left( {{{\boldsymbol{s}}^{(c)}}} \right) $ ，求解问题式(19)，得到
$\left\{ {{\boldsymbol{w}}_m^{(c)}} \right\}_{m = 1}^M$第6步：计算${\min _{\forall m}}{\text{SIN}}{{\text{R}}_m}\left( {{\boldsymbol{s}},{{\boldsymbol{w}}_m}} \right)$ 若$ |\min _{_{\forall m}}^j{{{\mathrm{SINR}}} _m}\left( {{{\boldsymbol{s}}^{(c)}},{\boldsymbol{w}}_m^{(c)}} \right) - \min _{_{\forall m}}^{(c - 1)}{{{\mathrm{SINR}}} _m}$
$\left( {{{\boldsymbol{s}}^{({c} - 1)}},{\boldsymbol{w}}_m^{(c - 1)}} \right)|{\text{ }} < {\text{ }}\kappa $，输出${s^{(*)}}$=${s^{(c)}}$, $\left\{ {{\boldsymbol{w}}_m^*} \right\}_{m = 1}^M = \left\{ {{\boldsymbol{w}}_m^{(c)}} \right\}_{m = 1}^M$，否则返回第3步。
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