Study on OTFS Channel Estimation Algorithms in High-Speed Mobile Communication Systems
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摘要: 针对高速移动环境中双色散信道会出现信道估计可靠性下降的问题，该文在正交时频空(OTFS)调制系统的输入-输出模型中提出一种基于压缩感知的信道估计算法。该算法利用信道中最大多普勒频移和最大时延确定导频发送矩阵的大小，相比传统的正交匹配追踪(OMP)信道估计算法，能够在保证相似信道估计准确度的情况下节省导频资源；并在此基础上，对OTFS调制符号做相位旋转，增加差分矩阵的秩，理论分析和仿真结果表明，该方案能够提升OTFS系统的分集阶数进而降低噪声的干扰。Abstract: In view of the problem that dual-dispersion channels will reduce the reliability of channel estimation in high-speed mobile environments, a channel estimation algorithm based on compressed sensing is proposed in the input-output model of Orthogonal Time-Frequency-Space (OTFS) modulation system. The maximum Doppler shift and the maximum delay in the channel are employed to determine the size of the pilot transmission matrix in the algorithm. Compared with the traditional Orthogonal Matching Pursuit (OMP) channel estimation algorithms, the pilot resources can be saved in the proposed algorithm while the accuracy of similar channel estimation is guaranteed. Furthermore, the phase rotation of the OTFS modulation symbols is used to improve the rank of the differential matrix. Theoretical analysis and simulation results show that the diversity order of the OTFS system is improved and noise interference is reduced.
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表 1 本文PRS-OMP信道估计算法步骤
步骤 操作 描述 1 初始化 传感矩阵${\boldsymbol{X}}_{\bf{p}}^{\rm{T}}$，采样向量${\boldsymbol{y}}_{\bf{p}}^{\rm{T}}$，残差能量阈值为$\varepsilon $(足够小)；残差${{\boldsymbol{r}}_0} = {\boldsymbol{y}}_{\bf{p}}^{\rm{T}}$，索引集${ { \boldsymbol{\varLambda } }_{\rm{0} } } = \varphi$(空集)，$t = 1$ 2 时延多普勒路径匹配 找出残差${\boldsymbol{r}}$和传感矩阵${\boldsymbol{X}}_{\bf{p}}^{\rm{T}}$列向量内积中最大值所对应的脚标${\lambda _t} = \arg {\max _{j = \left( {1, \cdots ,N} \right)}}\left| {\left\langle {{{\boldsymbol{r}}_{t - {\rm{1}}}},{\boldsymbol{X}}_{\bf{p}}^{\rm{T}}\left[ j \right]} \right\rangle } \right|$ 3 记录路径，并建立路径对应的传感矩阵列向量集合 更新索引集${{\boldsymbol{\varLambda}} _t} = {{\boldsymbol{\varLambda}} _{t - 1}} \cup \{ {\lambda _t}\} $，记录找到的传感矩阵中的重建原子集合${\boldsymbol{X}}_{{\bf{p}},t}^{\rm{T}} = \left[ {{\boldsymbol{X}}_{{\bf{p}},t{\rm{ - 1}}}^{\rm{T}},{\boldsymbol{X}}_{_{\bf{p}}}^{\rm{T}}\left[ {{\lambda _t}} \right]} \right]$ 4 计算信道增益 由最小二乘[21]得到${\hat {\boldsymbol{h}}'_{{\bf{p}},t}} = \arg \min {\left\| {{\boldsymbol{y}}_{\bf{P}}^{\rm{T}} - {\boldsymbol{X}}_{{\bf{p}},t}^{\rm{T}}{{\hat {\boldsymbol{h}}'}_{{\bf{p}},t}}} \right\|_2}$ 5 更新残差 ${{\boldsymbol{r}}_t} = {\boldsymbol{y}}_{\bf{P}}^{\rm{T}} - {\boldsymbol{X}}_{{\bf{p}},t}^{\rm{T}}{\hat {\boldsymbol{h}}'_{{\bf{p}},t}}$, $t = t + 1$ 6 判断迭代条件 判断是否满足${\left\| {{{\boldsymbol{r}}_t}} \right\|_2} \le \varepsilon $，若满足，则停止迭代；若不满足，则执行步骤2 7 输出对应路径的信道增益 输出：${{\boldsymbol{h}}'_{\bf{p}}}$的$P$-稀疏的逼近元${\hat {\boldsymbol{h}}'_{{\bf{p}},t}}$ 
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表 2 仿真参数设置
系统 载波频率(GHz) 子载波间隔(kHz) $M$ $N$ 路径数$P$ 调制方式 最大速度(km/h) PRS-OMP降导频资源率(%) 系统1 4 3.75 2 2 4 BPSK 506.250 100.00 系统2 4 3.75 4 2 4 BPSK 506.250 56.25 系统3 4 3.75 4 4 4 BPSK 253.125 14.06
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