文章介绍了无线通信系统中常用的两种信道估计方法——最小二乘(LS)和最小均方误差(MMSE)算法。LS算法简单但估计精度受噪声和导频序列限制，而MMSE算法考虑了噪声影响，提供更精确的估计。两者都需要导频序列，并且在实际应用中可通过多径信道模型等技术优化。
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⛄ 内容介绍
基于最小二乘（Least Squares, LS）和最小均方误差（Minimum Mean Square Error, MMSE）的导频信道估计是常用的信道估计方法之一，用于估计无线通信系统中的信道响应。下面将介绍LS和MMSE算法的基本原理和步骤。
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最小二乘（LS）算法： a. 发送导频序列：在发送端，周期性地插入已知导频序列到待传输的数据序列中。 b. 接收导频序列：接收端接收到包含导频序列的信号，并进行采样和解调。 c. 估计信道响应：使用接收到的导频序列和已知导频序列进行相关运算，得到信道响应的估计值。 d. 插值和外推：对于非导频位置，可以通过插值或外推方法获得信道响应的估计值。
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最小均方误差（MMSE）算法： a. 发送导频序列：同样在发送端周期性地插入已知导频序列到待传输的数据序列中。 b. 接收导频序列：接收端接收到包含导频序列的信号，并进行采样和解调。 c. 估计协方差矩阵：使用接收到的导频序列计算信道响应的协方差矩阵。 d. 计算MMSE估计：通过计算信道响应的协方差矩阵的逆矩阵与接收导频序列的乘积，得到信道响应的MMSE估计值。
LS算法是一种简单直接的信道估计方法，但在噪声较大或导频序列有限的情况下，其估计精度较低。而MMSE算法考虑了信道噪声的影响，可以提供更准确的信道估计结果。
需要注意的是，LS和MMSE算法都需要已知导频序列，因此在实际应用中，需要事先设计好导频序列并在发送端进行插入。此外，为了提高信道估计的准确性，可以采用多径信道模型、时频域插值等技术进行进一步优化。
⛄ 代码
%====================================================% Cobayashi Laboratory , Mie University, Japan%% Last Modified by tao,2001/05/17%====================================================function out = f_GetPoints(M)BPSKTable = f_EnGray(2);BPSKTable1 = [1+0i -1+0i];QPSKTable = f_EnGray(4);QPSKTable1 = [1 -1i 1i -1];QAM8Table7 = f_EnGray(8);QAM8Table = [ ...-1 + 1j*-1 ...-3 + 1j*0 ...-1 + 1j*1 ...0 + 1j*3 ...1 + 1j*-1 ...0 + 1j*-3 ...1 + 1j*1 ...3 + 1j*0 ]* sqrt(4/11);QAM8Table0 = [ ...3 + 1j ...1 + 1j ...-3 + 1j ...-1 + 1j ...3 + 1j*-1 ...1 + 1j*-1 ...-3 + 1j*-1 ...-1 + 1j*-1];QAM8Table6 = [ ...2 ...2+2j ...-2+2j ...2j ...2+1j*-2 ...1j*-2 ...-2 ...-2 + 1j*-2];QAM8Table5 = [ ...3+1j*1 ...1+1j*3 ...-3+1j*1 ...-1+1j*3 ...3+1j*-1 ...1+1j*-3 ...-3+1j*-1 ...-1+1j*-3 ];QAM8Table4 = [ ...1+1j*1 ...1+1j*-1 ...-1+1j*1 ...3+1j*-1 ...-3+1j*1 ...-1+1j*-3 ...1+1j*3 ...-1+1j*-1 ];QAM8Table3 = [ ...3 ...1+1j ...-1 + 1j ...3j ...1 + 1j*-1 ...1j*-3 ...-3 ...-1 + 1j*-1];QAM8Table2 = [ ...1 ...0.5+1j*0.5 ...-0.5 + 1j*0.5 ...1j ...0.5 + 1j*-0.5 ...1j*-1 ...-1 ...-0.5 + 1j*-0.5];QAM8Table1 = [ ...1 ...1+1j ...-1 + 1j ...1j ...1 + 1j*-1 ...1j*-1 ...-1 ...-1 + 1j*-1];QAM16Table = f_EnGray(16);QAM16Table1 = [ ...1 + 1j*1 ...1 + 1j*3 ...3 + 1j*1 ...3 + 1j*3 ...-1 + 1j*1 ...-1 + 1j*3 ...-3 + 1j*1 ...-3 + 1j*3 ...1 + 1j*-1 ...1 + 1j*-3 ...3 + 1j*-1 ...3 + 1j*-3 ...-1 + 1j*-1 ...-1 + 1j*-3 ...-3 + 1j*-1 ...-3 + 1j*-3];QAM32Table2 = f_EnGray(32);QAM32Table = [ ...1 + 1j*1 ...3 + 1j*1 ...3 + 1j*5 ...5 + 1j*1 ...1 + 1j*3 ...3 + 1j*3 ...1 + 1j*5 ...5 + 1j*3 ...1 + 1j*-1 ...1 + 1j*-3 ...5 + 1j*-3 ...1 + 1j*-5 ...3 + 1j*-1 ...3 + 1j*-3 ...5 + 1j*-1 ...3 + 1j*-5 ...-1 + 1j*1 ...-1 + 1j*3 ...-5 + 1j*3 ...-1 + 1j*5 ...-3 + 1j*1 ...-3 + 1j*3 ...-5 + 1j*1 ...-3 + 1j*5 ...-1 + 1j*-1 ...-3 + 1j*-1 ...-3 + 1j*-5 ...-5 + 1j*-1 ...-1 + 1j*-3 ...-3 + 1j*-3 ...-1 + 1j*-5 ...-5 + 1j*-3 ...] * sqrt(1/10);QAM32Table1 = [ ...-3 + 1j*5 ...-5 + 1j*1 ...1 + 1j*5 ...5 + 1j*3 ...3 + 1j*-5 ...5 + 1j*-1 ...-1 + 1j*-5 ...-5 + 1j*-3 ...1 + 1j*1 ...-1 + 1j*5 ...5 + 1j*1 ...1 + 1j*-1 ...-1 + 1j*-1 ...1 + 1j*-5 ...-5 + 1j*-1 ...-1 + 1j*1 ...-3 + 1j*-3 ...-1 + 1j*-3 ...-3 + 1j*1 ...-3 + 1j*3 ...3 + 1j*3 ...1 + 1j*3 ...3 + 1j*-1 ...3 + 1j*-3 ...5 + 1j*-3 ...3 + 1j*1 ...1 + 1j*-3 ...-3 + 1j*-5 ...-5 + 1j*3 ...-3 + 1j*-1 ...-1 + 1j*3 ...3 + 1j*5 ...];QAM64Table = f_EnGray(64);QAM64Table1 = [ ...1 + 1j*1 ...1 + 1j*3 ...3 + 1j*1 ...3 + 1j*3 ...7 + 1j*1 ...5 + 1j*1 ...7 + 1j*3 ...5 + 1j*3 ...1 + 1j*7 ...3 + 1j*7 ...1 + 1j*5 ...3 + 1j*5 ...7 + 1j*7 ...5 + 1j*7 ...7 + 1j*5 ...5 + 1j*5 ...1 + 1j*-1 ...1 + 1j*-3 ...3 + 1j*-1 ...3 + 1j*-3 ...7 + 1j*-1 ...5 + 1j*-1 ...7 + 1j*-3 ...5 + 1j*-3 ...1 + 1j*-7 ...3 + 1j*-7 ...1 + 1j*-5 ...3 + 1j*-5 ...7 + 1j*-7 ...5 + 1j*-7 ...7 + 1j*-5 ...5 + 1j*-5 ...-1+ 1j*1 ...-1+ 1j*3 ...-3+ 1j*1 ...-3+ 1j*3 ...-7+ 1j*1 ...-5+ 1j*1 ...-7+ 1j*3 ...-5+ 1j*3 ...-1+ 1j*7 ...-3+ 1j*7 ...-1+ 1j*5 ...-3+ 1j*5 ...-7+ 1j*7 ...-5+ 1j*7 ...-7+ 1j*5 ...-5+ 1j*5 ...-1+ 1j*-1 ...-1+ 1j*-3 ...-3+ 1j*-1 ...-3+ 1j*-3 ...-7+ 1j*-1 ...-5+ 1j*-1 ...-7+ 1j*-3 ...-5+ 1j*-3 ...-1+ 1j*-7 ...-3+ 1j*-7 ...-1+ 1j*-5 ...-3+ 1j*-5 ...-7+ 1j*-7 ...-5+ 1j*-7 ...-7+ 1j*-5 ...-5+ 1j*-5];QAM128Table1 = f_EnGray(128);QAM128Table = [ ...1 + 1j*1 ...3 + 1j*1 ...1 + 1j*3 ...3 + 1j*3 ...7 + 1j*1 ...5 + 1j*1 ...7 + 1j*3 ...5 + 1j*3 ...7 + 1j*9 ...5 + 1j*9 ...7 + 1j*11 ...5 + 1j*11 ...9 + 1j*1 ...11 + 1j*1 ...9 + 1j*3 ...11 + 1j*3 ...1 + 1j*7 ...3 + 1j*7 ...1 + 1j*5 ...3 + 1j*5 ...7 + 1j*7 ...5 + 1j*7 ...7 + 1j*5 ...5 + 1j*5 ...1 + 1j*9 ...3 + 1j*9 ...1 + 1j*11 ...3 + 1j*11 ...9 + 1j*7 ...11 + 1j*7 ...9 + 1j*5 ...11 + 1j*5 ...-1 + 1j*1 ...-1 + 1j*3 ...-3 + 1j*1 ...-3 + 1j*3 ...-1 + 1j*7 ...-1 + 1j*5 ...-3 + 1j*7 ...-3 + 1j*5 ...-9 + 1j*7 ...-9 + 1j*5 ...-11 + 1j*7 ...-11 + 1j*5 ...-1 + 1j*9 ...-1 + 1j*11 ...-3 + 1j*9 ...-3 + 1j*11 ...-7 + 1j*1 ...-7 + 1j*3 ...-5 + 1j*1 ...-5 + 1j*3 ...-7 + 1j*7 ...-7 + 1j*5 ...-5 + 1j*7 ...-5 + 1j*5 ...-9 + 1j*1 ...-9 + 1j*3 ...-11 + 1j*1 ...-11 + 1j*3 ...-7 + 1j*9 ...-7 + 1j*11 ...-5 + 1j*9 ...-5 + 1j*11 ...-1 + 1j*-1 ...-3 + 1j*-1 ...-1 + 1j*-3 ...-3 + 1j*-3 ...-7 + 1j*-1 ...-5 + 1j*-1 ...-7 + 1j*-3 ...-5 + 1j*-3 ...-7 + 1j*-9 ...-5 + 1j*-9 ...-7 + 1j*-11 ...-5 + 1j*-11 ...-9 + 1j*-1 ...-11 + 1j*-1 ...-9 + 1j*-3 ...-11 + 1j*-3 ...-1 + 1j*-7 ...-3 + 1j*-7 ...-1 + 1j*-5 ...-3 + 1j*-5 ...-7 + 1j*-7 ...-5 + 1j*-7 ...-7 + 1j*-5 ...-5 + 1j*-5 ...-1 + 1j*-9 ...-3 + 1j*-9 ...-1 + 1j*-11 ...-3 + 1j*-11 ...-9 + 1j*-7 ...-11 + 1j*-7 ...-9 + 1j*-5 ...-11 + 1j*-5 ...1 + 1j*-1 ...1 + 1j*-3 ...3 + 1j*-1 ...3 + 1j*-3 ...1 + 1j*-7 ...1 + 1j*-5 ...3 + 1j*-7 ...3 + 1j*-5 ...9 + 1j*-7 ...9 + 1j*-5 ...11 + 1j*-7 ...11 + 1j*-5 ...1 + 1j*-9 ...1 + 1j*-11 ...3 + 1j*-9 ...3 + 1j*-11 ...7 + 1j*-1 ...7 + 1j*-3 ...5 + 1j*-1 ...5 + 1j*-3 ...7 + 1j*-7 ...7 + 1j*-5 ...5 + 1j*-7 ...5 + 1j*-5 ...9 + 1j*-1 ...9 + 1j*-3 ...11 + 1j*-1 ...11 + 1j*-3 ...7 + 1j*-9 ...7 + 1j*-11 ...5 + 1j*-9 ...5 + 1j*-11] * sqrt(1/41);QAM256Table = f_EnGray(256);switch M,case 0, table = [0];case 2, table = BPSKTable;case 4, table = QPSKTable;case 8, table = QAM8Table;case 16, table = QAM16Table;case 32, table = QAM32Table;case 64, table = QAM64Table;case 128, table = QAM128Table;case 256, table = QAM256Table;otherwise, error('No such MQAM!');endout = table;
⛄ 运行结果
⛄ 参考文献
[1] 朱竞.基于导频的MB-LSF算法的OFDM系统信道估计研究[D].华东理工大学,2014.
[2] 王宏宇.快时变信道下OFDM系统频率同步与信道估计技术研究[D].西南交通大学,2014.
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