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摘要: 1比特量化技术在大规模MIMO雷达系统中的应用使得系统成本、功耗及传输带宽显著降低。但这同时也对如何从1比特量化后的数据中提取目标高精度信息提出了严峻挑战。针对基于1比特量化的二次定位算法在低信噪比下定位精度低、鲁棒性差的问题，该文提出了一种基于1比特量化的大规模MIMO雷达系统目标直接定位算法。首先，通过将接收信号进行1比特量化，并推导基于1比特信号的概率分布，建立了关于目标位置的代价函数；其次，通过证明代价函数的凸性，利用梯度下降算法求解了回波中未知的信号参数；最后，根据最大似然估计实现了目标直接定位。仿真实验分析了所提算法的定位性能，结果表明，所提算法仅需传输相较于高精度采样(16比特为例)直接定位算法6.25%的通信带宽，同时其功耗仅为前者的0.1%。此外，与基于1比特量化的二次定位算法相比，所提算法在低信噪比下便可实现对目标位置的有效估计，并且其定位性能在低信噪比和低MIMO天线数量下均明显优于前者。同时，其性能会随着过采样技术的应用进一步提升。Abstract: The application of one-bit quantization technology in a massive MIMO radar system significantly reduced the system cost, power consumption, and transmission bandwidth. However, it also poses a severe challenge to extract high-precision target information from one-bit quantized data. To address the problem of low positioning accuracy and poor robustness of secondary positioning based on one-bit quantization under low Signal-to-Noise Ratio (SNR), this paper proposes a multi-station radar target direct position determination algorithm based on one-bit quantization. First, by quantizing the received signal with one bit, and deriving the probability distribution based on the one-bit signal, the cost function about the target position is established. Second, by proving the convexity of the cost function, the maximum likelihood estimation and gradient descent algorithm are used to solve the unknown signal parameters in the echo. Finally, the direct positioning of the target is achieved according to the maximum likelihood estimation. Simulation experiments were performed to analyze the positioning performance of the proposed algorithm, and the results showed that the proposed algorithm only needed to transmit 6.25% of the communication bandwidth compared with the high-bit sampling (e.g., 16 bits) direct position determination algorithm, and its power consumption is only 0.1% of the former. In addition, compared with the secondary positioning algorithm based on one-bit quantization, the proposed algorithm can achieve an effective estimation of the target position under a low SNR. In addition, its localization performance is significantly better than the former under low SNR and a low number of MIMO antennas. Simultaneously, its performance will be further improved with the application of oversampling technology.
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图 1 基于广域节点分布的大规模MIMO雷达系统定位场景
Figure 1. Location diagram of massive MIMO radar system based on wide-area node distribution
图 5 不同信噪比下1bit-DPD与1bit-IDP有效估计率曲线
Figure 5. Effective estimation rate curves of 1bit-DPD and 1bit-IDP under different SNR
图 6 不同信噪比下1bit-DPD与1bit-IDP以及16bit-DPD的定位性能对比图
Figure 6. Comparison of localization performance of 1bit-DPD, 1bit-IDP and 16bit-DPD under different SNR
图 7 不同过采样因子v下1bit-DPD和1bit-IDP的定位性能对比图
Figure 7. Localization performance of 1bit-DPD and 1bit-IDP under different over-sampling factors v
图 8 不同天线数量下1bit-DPD和1bit-IDP的定位性能
Figure 8. Localization performance of 1bit-DPD and 1bit-IDP under different number of base stations
表 1 式(25)的梯度下降求解步骤
Table 1. The gradient descent solution for Eq. (25)
初始化：$\tilde \alpha _{ {\rm{mn} } }^0$, $0 < \xi \le 1$, $0 < \zeta \le 1$ 迭代：对于$l = 0 \to {l_{\max }}$ 1：计算代价函数$\Xi \left( {\tilde \alpha _{{\rm{mn}}}^l} \right)$和$\nabla \left( {\Xi \left( {\tilde \alpha _{{\rm{mn}}}^l} \right)} \right)$； 2：初始化步长${u^l} = {u_{{\rm{init}}} }$，更新
$\tilde \alpha _{{\rm{mn}}}^{l + 1} = \tilde \alpha _{{\rm{mn}}}^l - {u^l}\nabla \left( {\Xi \left( {{{\tilde \alpha }_{{\rm{mn}}}}} \right)} \right)$；3：当$\Xi \left( {\tilde \alpha _{{\rm{mn}}}^{l + 1}} \right) > \Xi \left( {\tilde \alpha _{{\rm{mn}}}^l} \right) - \xi {u^l}\left\| {\nabla \left( {\Xi \left( {\tilde \alpha _{{\rm{mn}}}^l} \right)} \right)} \right\|_2^2$，令
${u^l} = \zeta {u_{{\rm{init}}} }$更新$\tilde \alpha _{{\rm{mn}}}^{l + 1} = \tilde \alpha _{{\rm{mn}}}^l - {u^l}\nabla \left( {\Xi \left( {{{\tilde \alpha }_{{\rm{mn}}}}} \right)} \right)$； 4：满足停止条件，退出 
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表 2 数据量及功耗对比
Table 2. Comparison of data volume and power consumption
算法 单个采样点数据量 功耗 16bit-DPD 2 Byte(实部/虚部) 约为几瓦 1bit-DPD 1 bit(实部/虚部) 约几毫瓦
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