Research on OTSM Iterative Detection Algorithm in High-speed Mobile Environment
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摘要: 正交时序复用( Orthogonal Time Sequency Multiplexing, OTSM)通过级联时分和沃尔什-哈达玛(WHT)复用将信息符号在时延和序列域进行复用。由于WHT在调制解调过程不需要进行复杂的乘法运算，相比于正交时频空(OTFS)调制有更低的调制复杂度。该文针对高速移动环境下的OTSM系统提出了一种二级均衡器：首先利用信道矩阵的稀疏性和带状结构在时域逐块进行低复杂度MMSE检测；随后采用高斯-赛德尔(GS)迭代检测进一步消除残余符号干扰。仿真结果表明，所提算法与基于单抽头频域均衡的GS迭代检测算法相比，采用16QAM调制且误码率为10–4时有1.8 dB性能增益。
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关键词:
- 正交时序复用 /
- 时延-序列域 /
- 沃尔什-哈达玛变换 /
- 高斯-赛德尔迭代检测
Abstract: Orthogonal Time Sequency Multiplexing (OTSM) multiplexes information symbols in the delay-sequence domain through concatenated time division and Walsh-Hadamard multiplexing. Due to the Walsh-Hadamard Transform (WHT) does not require complex multiplication operations in the modulation and demodulation process, it has lower modulation complexity than Orthogonal Time-Frequency Space (OTFS). In this paper, a two-stage equalizer is proposed for OTSM systems in high-speed mobile environments. First, low-complexity MMSE detection is performed block-by-block in the time domain by utilizing the sparsity and band structure of the channel matrix; Then Gauss-Seid (GS) iterative detection further removes residual symbol interference. The simulation results show that, compared with the GS iterative detection algorithm based on single-tap frequency domain equalization, the proposed algorithm has a performance gain of 1.8 dB when 16QAM modulation is used and the bit error rate is 10–4. -
算法1 前向替换算法 计算${{\boldsymbol{r}}^{(1)} } = {{\boldsymbol{L}}^{ - 1} }{\boldsymbol{r}}$ 1：输入：下三角矩阵${{\boldsymbol{L}}_{M \times M} }$和${{\boldsymbol{r}}_{M \times 1} }$ 2：输出：${\boldsymbol{r}}_{M \times 1}^{(1)} = {\boldsymbol{L}}_{M \times M}^{ - 1}{{\boldsymbol{r}}_{M \times 1} }$ 3：${{\boldsymbol{r}}^{(1)} }(0) = {\boldsymbol{r}}(0)$ 4：for$k = 1:\alpha - 1$ do
5：${{\boldsymbol{r}}^{(1)} }(k) = {\boldsymbol{r}}(k) - \displaystyle\sum _{i = 1}^k{\boldsymbol{L}}(k,k - i){{\boldsymbol{r}}^{(1)} }(k - i)$6：end 7：for$k = \alpha :M - 1$ do
8：${{\boldsymbol{r}}^{(1)} }(k) = {\boldsymbol{r}}(k) - \displaystyle\sum _{i = 1}^{\alpha - 1}{\boldsymbol{L}}(k,k - i){{\boldsymbol{r}}^{(1)} }(k - i)$9：end 
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算法2 后向替换算法 计算${{\boldsymbol{r}}^{(2)} } = {{\boldsymbol{U}}^{ - 1} }{{\boldsymbol{r}}^{(1)} }$ 1：输入：上三角矩阵${{\boldsymbol{U}}_{M \times M} }$和${{\boldsymbol{r}}^{(1)} }_{M \times 1}$ 2：输出：${\boldsymbol{r}}_{M \times 1}^{(2)} = {\boldsymbol{U}}_{M \times M}^{ - 1}{\boldsymbol{r}}_{M \times 1}^{(1)}$ 3：${{\boldsymbol{r}}^{(2)} }(M - 1) = \frac{ { {{\boldsymbol{r}}^{(1)} }(M - 1)} }{ {{\boldsymbol{U}}(M - 1,M - 1)} }$ 4：for$k = M - 2:M - \alpha $do
5：${ {\boldsymbol{r} }^{(2)} }(k) = \dfrac{1}{ { {\boldsymbol{U} }(k,k)} }[{ {\boldsymbol{r} }^{(1)} }(k) - \displaystyle\sum _{i = 1}^{M - k - 1}{\boldsymbol{U} }(k,k + i){ {\boldsymbol{r} }^{(2)} }(k + i)]$6：end 7：for$k = M - \alpha - 1:0$do 8：${ {\boldsymbol{r} }^{(2)} }(k) = \dfrac{1}{ { {\boldsymbol{U} }(k,k)} }[{ {\boldsymbol{r} }^{(1)} }(k) - \displaystyle\sum _{i = 1}^{\alpha - 1}{\boldsymbol{U} }(k,k + i){ {\boldsymbol{r} }^{(2)} }(k + i)]$ 9：end
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表 1 所提接收机中不同操作的计算复杂度
操作 所需复乘次数 低复杂度LU分解 $[{\alpha ^2} + 2\alpha ]MN$ 前向替换算法 $N \left[M\alpha - \dfrac{ { {\alpha ^2} } }{2} + \dfrac{\alpha }{2} - 1 \right]$ 反向替换算法 $N \left[M(\alpha - 1) - \dfrac{ { {\alpha ^2} } }{2} + \dfrac{\alpha }{2}\right]$ 稀疏矩阵向量乘法 $P(\beta + 1)MN$
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