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📁 通信原理的经典讲义
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      <P align=right><I><A 
      href="http://www.yobology.info/harbin/part1/index.htm">index</A></I></P>
      <P align=center>Part 1 </P>
      <P align=center>Chapter 3&nbsp;&nbsp;&nbsp;&nbsp;OFDM v.s, Correlative 
      PAM<BR><BR></P></TD></TR>
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      <P>Again let us take up metal cable transmission. As mentioned in previous 
      chapter, OFDM is able to achieve the fastest no-error transmission 
      (channel capacity). However, the process to make up the optimum power 
      distribution is very complicated, because we must find the best pair of 
      bit/symbol and rate of error correction for each sub-channels.</P>
      <P>We have another optimal transmission scheme called THP (Tomlinson 
      Harashima Precoder). </P>
      <P align=center><IMG height=480 src="Part1_3.files/img26.gif" width=746 
      border=0></P>
      <P>Remark that the received signal has discrete values. This scheme may be 
      difficult to implement in practical use too. An approximating method has 
      been fixed in IEEE P802.3an of 10GBASE-T, but several difficulties in 
      circuitry running at such high speed clock as 1GHz came out. Context of 
      the optimality is addressed in short as follows. </P>
      <P align=center>The precoder outputs random signal.&nbsp;<BR>The receiver 
      is possible to detect the correlated symbol <BR>without any signal 
      processing like equalization.</P>
      <P align=left>This optimality comes from the fact shown in previous 
      chapter, i.e., the uniform power spectrum of transmitting signal gives 
      good performance very close to the optimum.</P>
      <P align=left>Actual impulse response of 100 meter coaxial cable is 
      plotted as shown below, where each point shows value sampled 
      by&nbsp;symbol speed. It is seen that the first sample <IMG 
      src="Part1_3.files/part_1_3_htm_eqn17726.gif" border=0 NAMO_EQN__><!--NAMO_EQN__ 192 1h_{0}--> is very small, therefore, the 
      loop filter <IMG src="Part1_3.files/part_1_3_htm_eqn17972.gif" border=0 
      NAMO_EQN__><!--NAMO_EQN__ 192 1H(D)\slash h_{0}-1--> becomes very large. 
      From this reason the number of levels of the received signal bursts up and 
      information speed falls down. We must develop a practical design scheme 
      which gives maximum information speed by adjusting transmitting spectrum 
      and number of levels.</P>
      <P align=center><IMG height=351 src="Part1_3.files/img27.gif" width=568 
      border=0></P>
      <P align=left>Apart from actual cases, let us make a treatable model to 
      estimate net value of the information speed. Followings are attenuation 
      and impulse response of our model.</P>
      <P align=center><IMG height=396 src="Part1_3.files/fig28.gif" width=642 
      border=0></P>
      <P align=center><IMG height=387 src="Part1_3.files/img29.gif" width=626 
      border=0></P>
      <P align=left>Computer simulation of information speed for each levels 
      shows blue curve in next graph. Black line and red line show respectively 
      channel capacity&nbsp;by water pouring and maximum information speed of 
      conventional PAM.</P>
      <P align=center><IMG height=451 src="Part1_3.files/img30.gif" width=732 
      border=0></P>
      <P align=left><SPAN style="FONT-SIZE: 12pt"><FONT color=#660000>Note : The 
      black line is derived on Euclid distance and gives ideal maximum 
      information speed. In digital transmission, for example OFDM, the highest 
      speed must be less than it.</FONT></SPAN></P>
      <P align=left>Following graphs show transmitted and received signals.</P>
      <P align=center><IMG height=424 src="Part1_3.files/img31.gif" width=686 
      border=0></P>
      <P align=center><IMG height=431 src="Part1_3.files/img32.gif" width=698 
      border=0></P>
      <P align=center>&nbsp;</P></TD></TR></TBODY></TABLE>
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