﻿ 改进相关干涉仪算法在DOA估计中的应用
 计算机系统应用  2018, Vol. 27 Issue (12): 129-135 PDF

Application of Improved Correlation Interferometer Algorithm in DOA Estimation
CAI Li-Ping, HU Jia-Liang, CHEN Hai-Hua, TIAN Hui
College of Computer & Communication Engineering, China University of Petroleum, Qingdao 266580, China
Foundation item: Young Scientists Fund of National Natural Science Foundation of China (61601519); Fund of Science and Technology on Electronic Test and Measurement Laboratory (614200105011702)
Abstract: The Correlation Interferometer Algorithm (CIA) is commonly used in the Direction Of Arrival (DOA) estimation. But when it realizes the direction finding, the long and short baselines in the array lead to the problems of baseline symmetry and phase ambiguity. An improved correlation interferometer algorithm based on quadrant classification is proposed. First, the time difference of signals arriving at each element is converted into phase difference, as well as the obtained phase difference is compared with 360°, and the obtained integer and remainder are recorded. Then the remainder is quadrant classified, after which the initial estimated value of the signal is obtained by using a traditional correlation interferometer algorithm. Finally, the final estimate value of the signal is calculated based on the inverse operation. Experimental simulations show that the improved algorithm successfully solves the problems of baseline mirror symmetry and phase ambiguity. Moreover, the accuracy of signal estimation is improved, the computational complexity is reduced, and the real-time performance of direction finding is improved. Therefore, it has significant value in the DOA estimation.
Key words: Direction Of Arrival (DOA) estimation     Correlative Interferometer Algorithm (CIA)     phase difference     computational complexity     quadrant classification     real-time

1 空间谱估计数学模型和相关干涉仪算法 1.1 空间谱估计数学模型

 ${\tau _i} = \frac{R}{c}\cos \left( {\frac{{360 * (i - 1)}}{M} - \theta } \right)$ (1)

 ${\varphi _i} = 360 * \frac{R}{c}\cos \left( {\frac{{360 * (i - 1)}}{M} - \theta } \right)$ (2)

 图 1 空间谱估计数学模型

 $\left\{\begin{gathered} {X_i}(t) = {A_i}\cos ({w_0}t - {\varphi _i}{\text{/2}}) + {N_i}(t) \\ {Y_i}(t) = {B_i}\cos ({w_0}t + {\varphi _i}{\text{/2}}) + {N_i}(t) \\ \end{gathered} \right.$ (3)

1.2 相关干涉仪算法

 ${x_{ij}} = {A_{ij}}\cos ({w_0}t - {\varphi _{ij}}/2)$ (4)

 ${y_{ij}} = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{ij}}/2)$ (5)

 图 2 均匀5阵元天线阵列

 $\left\{\begin{gathered} y1 = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{ij}}/2 + 0^\circ ) \\ y2 = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{ij}}/2 + 90^\circ ) \\ y3 = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{ij}}/2 + 180^\circ ) \\ y4 = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{ij}}/2 + 270^\circ ) \\ \end{gathered} \right.$ (6)

 图 3 相关干涉仪算法原理图

 $\left\{\begin{gathered} A1 = {x_{ij}} + y1 \\ A2 = {x_{ij}} + y2 \\ A3 = {x_{ij}} + y3 \\ A4 = {x_{ij}} + y4 \\ \end{gathered} \right.$ (7)

 ${\varphi _i} = - \arctan \left( {\frac{{|A2{|^2} - |A4{|^2}}}{{|A1{|^2} - |A3{|^2}}}} \right)$ (8)

 ${\theta _i}'{\text{ = }}\frac{{360 * (i - 1)}}{M} \pm {\rm{arc}}\cos \left( {\frac{{{\varphi _i}}}{{360}} \times \frac{\lambda }{R}} \right)$ (9)

2 两类误差模型和改进相关干涉仪算法 2.1 两类误差模型

 ${\rho _i} = \sum {\cos ({\varphi _i} - {\varphi _0})}$ (10)

 ${\rho _i} = \sum {\cos ({\varphi _i} - {\varphi _0}) - } {\text{|sin(}}{\varphi _i} - {\varphi _0}){\text{|}}$ (11)

2.2 改进相关干涉仪算法

1) 将天线阵列分成两个单元, 单元1包含一个阵元作为参考阵元, 单元2包括其他四个阵元作为普通阵元, 如图2.

2) 任意选择一组基线: 选择单元1中的参考阵元和单元2中的第 $i$ 个阵元.

3) 将单元二中接收到的数据通过四步移相(0°/90°/180°/270°), 得到信号数据如公式(6).

4) 将得到的 $\scriptstyle y1,y2,y3,y4$ 中的相位与360°作比取余数 $\scriptstyle {\varphi _{0ij}}$ , 利用象限分类法将 $\scriptstyle {\varphi _{0ij}}$ 分到四个象限中, 这样避免了基线镜像对称和相位模糊问题, 并将 $\scriptstyle {\varphi _{0ij}}$ 带回公式(6)得到 $\scriptstyle y{\text{1}}1,y{\text{2}}2,y3{\text{3}},y4{\text{4}}$ .

 $\scriptstyle \left\{\begin{gathered}\scriptstyle y{\text{1}}1 = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{{\text{0}}ij}}/2 + 0^\circ ) \\\scriptstyle y2{\text{2}} = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{{\text{0}}ij}}/2 + 90^\circ ) \\\scriptstyle y3{\text{3}} = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{{\text{0}}ij}}/2 + 180^\circ ) \\\scriptstyle y4{\text{4}} = {B_{ij}}\cos ({w_0}t{\text{ + }}{\varphi _{{\text{0}}ij}}/2 + 270^\circ ) \\ \end{gathered} \right.$ (12)

5) 将得到的 $\scriptstyle y11, y22, y33, y44$ 与参考阵元接收到的数据 $\scriptstyle {x_{ij}}$ 分别进行图3中的矢量相加得到 $\scriptstyle A1, A2, A3, A4$ , 即:

 $\left\{\begin{gathered}\scriptstyle A1 = {x_{ij}} + y11 \\\scriptstyle A2 = {x_{ij}} + y22 \\\scriptstyle A3 = {x_{ij}} + y33 \\\scriptstyle A4 = {x_{ij}} + y44 \\ \end{gathered}\right.$ (13)

6)将上式得到的 $\scriptstyle A1,A2,A3,A4$ 分别取模平方代入公式(8)、(9)求解 $\scriptstyle\hat \theta$ ;

7)如达到迭代次数 $\scriptstyle NUM$ ( $\scriptstyle NUM$ 的取值只要能排除实验的偶然性即可), 则退出停止, 否则返回步骤2).

3 实验分析

 ${\varphi _i} = 360 * \frac{R}{c}\cos \left( {\frac{{360(i - 1)}}{{\text{5}}} - \theta } \right)$ (14)

 ${\rm{SNR}} = 10{\log _{10}}\frac{{E\left[ {|x(t){|^2}} \right]}}{{{\sigma ^2}}}$ (15)

 ${\rm{RMSE}}= \sqrt {\frac{1}{{NUM}}\sum\limits_{m = 1}^{NUM} {|{{\hat {\hat \theta} }_m} - {\theta _m}{|^2}} }$ (16)

 图 4 短基线测向性能比较

 图 5 长基线测向性能比较

 图 6 不同基线长度与信号波长比条件下的比较

4 结论与展望

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