﻿ 基于带宽优化的载波跟踪算法
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Carrier tracking algorithm based on bandwidth optimization
MU Weiqing, LIU Rongke , SONG Qingping, DUAN Ruifeng
School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract: In the existing high dynamic weak signal carrier tracking algorithm, frequency locked loops (FLL) auxiliary phase locked loops (PLL) carrier tracking algorithm has the problem that the loop adjusted discontinuously, and easily lost lock. More optimal combination FLL with PLL algorithm and transition process of combination loop were given, threshold for state transition was determined. Aiming at the problem that bandwidth adjustment is not accurate, the optimal PLL loop bandwidth and the bandwidth adjustment strategy were confirmed, the loop bandwidth was adjusted in real-time. In the presence of jerk cases and signal-to-noise ration is 3dB, the tracking error is around 3Hz.
Key words: high-dynamic     low signal-to-noise ratio     carrier tracking     frequency locked loops     phase locked loop

1 FLL-PLL载波跟踪算法 1.1 FLL和PLL鉴别器的设计

 图 1 鉴频器和鉴相器的结构Fig. 1 Structure of frequency discriminator and phase discriminator

1.2 环路滤波器的设计

 图 2 二阶FLL辅助三阶PLL环路的滤波器结构Fig. 2 Loop filter structure of second-order FLL auxiliary third-order PLL

2 FLL-PLL组合算法的优化

FLL-PLL的载波跟踪算法,既要保证锁定速度,又要提高环路的跟踪精度,FLL-PLL的载波跟踪方案的优化主要从组合环路的状态确定和状态转变的门限值确定进行.FLL-FPLL-PLL组合算法具有较优性能的环路闭合过程是:以FLL的形式牵引至频率锁定,然后过渡到FLL辅助PLL的方式,至相位锁定,之后再转换为PLL单独工作的精确跟踪模式,直到相位锁定丢失.FLL-FPLL-PLL组合环路状态之间的状态转换门限值是根据蒙特卡罗仿真实验以及借鉴工程实现的经验值确定的,根据门限值进行状态转换可以增加跟踪环路转换连续性和跟踪精确度,减少环路失锁的概率.

2.1 组合环路的状态分析

FLL-PLL的跟踪方案,即为FLL先牵引至锁定状态,然后PLL单独工作的方式.由于FLL是在PLL的前一个积分环节进入环路,从FLL的跟踪直接切换至PLL跟踪状态,显然环路状态的过渡不连续,会影响环路跟踪性能,甚至出现环路失锁的问题.

FLL-FPLL跟踪方案,FLL牵引而后转换为FLL和PLL同时工作的组合方式FPLL.由于二阶FLL的相位跟踪精度低于三阶PLL,并且在环路滤波器的工作过程中,是将FLL输出的频率误差和PLL输出的相位误差进行融合处理,会引入较大的环路误差,因此FLL和PLL同时工作的方式会使环路的误差增大.FLL-FPLL跟踪方案切换至FPLL状态后,在低信噪比的信道环境下融入噪声过大易使环路失锁.FLL-FPLL-PLL的跟踪过程中，当环路处于PLL单独精确跟踪阶段,相比前一阶段的FPLL环路误差会明显减小.

2.2 状态转换门限的确定

3 FLL-FPLL-PLL跟踪环路的优化

1) FLL在牵引跟踪状态,带宽要尽量设置得宽,提高锁定速度.

2) 当转换至FPLL状态,FLL环的环路带宽减少,PLL带宽在调整范围内选择最大值.

PLL的总误差函数关系式为

Minimize:

Subject to:

 迭代次数 函数值 最大约束 方向导数 一阶最优值 0 7.134 86 0 1 6.482 74 -4.844 -0.854 0.505 2 5.136 31 0 -0.687 0.204 3 5.063 08 0 -0.204 0.185 4 4.882 76 0 -0.166 0.054 3 5 4.851 94 0 -0.054 3 0.020 8 6 4.845 46 0 -0.020 8 0.004 3 7 4.845 12 0 -0.004 43 0.000 479 8 4.845 11 0 -0.000 479 1.27×10-5

1) 目标函数的最小误差为4.845 1，远小于PLL的失锁极限值15°,表明信号存在加加速度分量的情况下,二阶FLL辅助三阶PLL的工作方式可以稳定的工作.

2) 带宽为16 Hz、载噪比为35 dB时误差取得最小值,验证了载噪比越高PLL的跟踪精度越高的结论.

3) 在带宽调整优化的过程中,由于相位抖动误差和动态应力误差存在矛盾性,并不是带宽值越小相位误差越少,而是存在最优值.因此在高动态的航天测控通信环境下,可以根据其实际情况计算带宽最优值.

4 仿真验证

 图 3 FLL-PLL不连续环路滤波器输出Fig. 3 Output of discontinuity FLL-PLL loop filter
 图 4 FLL-FPLL的环路滤波器输出Fig. 4 Output of FLL-FPLL loop filter

FLL-FPLL-PLL载波跟踪优化算法的环路滤波器频率输出如图 5所示,可以看出环路的状态转变和带宽调整过程:FLL牵引状态可以快速地消除捕获阶段剩余的多普勒频移,快速达到锁定状态,转换至FLL辅助PLL状态,误差减少至快捕带宽,转变至PLL精确跟踪状态,进而根据提出的环路优化调整策略对带宽进行了调整，将带宽调整至最优值，可以看出环路滤波器的输出误差值不断减少.

 图 5 FLL-FPLL-PLL环路输出Fig. 5 Output of FLL-FPLL-PLL loop filter

 图 6 不同C/N0带宽与噪声误差的关系Fig. 6 Relationship between bandwidth and noise error under different C/N0

 图 7 带宽试探调整算法的验证Fig. 7 Testing of tentative fitting bandwidth algorithm
 图 8 跟踪环路误差曲线Fig. 8 Loop tracking error curve
5 结 论

1) FLL和PLL的组合方式具有最佳组合方式,并分析确定了状态之间的转换时机,使状态转换更为连续.

2) 提出了试探法调整带宽和优化环路的方法,在高动态低信噪比的情况下,环路调整误差低至3 Hz,提高了跟踪精度,实现了高动态微弱信号精确跟踪.

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#### 文章信息

MU Weiqing, LIU Rongke, SONG Qingping, DUAN Ruifeng

Carrier tracking algorithm based on bandwidth optimization

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(10): 1918-1924.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0715