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OFDM Lecture 16 5 -Discrete Convolution, ISI and ICI on DMT/OFDM Systems

2022-08-05 05:12:00 【Ming Dynasty Bai Xiaosheng】

参考：

    

      The point of this article is very fresh and intuitive,Mainly from the linear algebra to explain the relevant principles

目录：

   1： 离散卷积

   2： ISI & ICI

一 离散卷积

   The convolution formula for continuous data was discussed earlier

   h(k)=x(k)\ast h(k)=\int_{-\infty}^{\infty}x(t)h(k-t)dt

  In fact, there is no continuous data, we generally use discrete convolution,

  y(k)=\sum_{0}^{\infty} x[n] \bullet h[k-n] 

   假设x的长度为n, h的长度为m, y的长度为n+m

  1.1 例子

   假设

    x=[x_0,x_1,x_2,x_3]

    h=[h_0,h_1,h_2,h_3]

  y_0=\sum_{n=0}^{3}x[n]\bullet h[0-n]

        =x_0h_0

y_1=\sum_{n=0}^{3}x[n]\bullet h[1-n]

      =x_0 \bullet h_1+x_1 \bullet h_0

y_2=\sum_{n=0}^{3}x[n]\bullet h[2-n]

   =x_2h_0+x_1h_1+x_0h_2

y_3=\sum_{n=0}^{3}x[n]\bullet h[3-n]

       =x_3h_0 +x_2h_1+x_1 h_2 +x_0h_3

  It's essentially the multiplication of two matrices

 Further representation method,如下图,Multiply and sum the corresponding column elements

二   CP(Cyclic prefix)  CS(Cyclic suffix)

     2.1 循环前缀,Cyclic suffix structure

    

 发送端

     经过IDFT After inverse discrete Fourier transform,得到长度为Ntime domain data

     Then insert a length of a 的cp, 以及长度为b 的 cs

 假设原始数据为

 X=[x_0,x_1,x_2,x_3]

a= b=2

cp=[x_2,x_3], cs=[x_0,x_1]

Finally the data becomes

 

2.2 ICI

 

 when decoding,We will Fourier transform it,对CP,CS 部分丢弃

 y_0=h_0 x_0+h_1x_3 +h_2x_2

如下

y_0=h_0x_0+h_1x_3+h_2x_2+ h_1x_1

One more noise was found h_1x_1

  y_0=y_{idle}+y_{ici}

  y_{ici}=h_1x_1,interference between other channels

下面是草图

 

 2.3   ISI 模型

     跟上面差不多

, 

 

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本文为[Ming Dynasty Bai Xiaosheng]所创，转载请带上原文链接，感谢
https://yzsam.com/2022/217/202208050509096410.html

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