ee359 final projectchannel estimation in a mimo-ofdm system.htm

mimo-ofdm信道估计matlab程序

LS and MMSE estimation. <SPAN style="mso-spacerun: yes">&nbsp;</SPAN>The 
simulated system has 64 subcarriers and uses 16 pilot tones.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>For the interpolation, a low-pass 
interpolation is performed by taking the IFFT of the estimated subcarriers, 
zero-padding, and the taking the FFT. <SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN>The channel in this simulation is a 
Rayliegh fading channel.</P>
<P class=MsoNormal><SPAN style="mso-spacerun: yes"></SPAN>&nbsp;</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" 
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"21600,21600"><v:imagedata o:title="fig1" src = 
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<P class=MsoNormal style="TEXT-ALIGN: center" align=center>Fig 1.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>Normalized estimation error vs. SNR</P>
<H4>Channel Estimation for a MIMO-OFDM system</H4>
<P class=MsoNormal>In the case of channel estimation for a MIMO-OFDM system with 
M<SUB>T</SUB> transmitters and M<SUB>R</SUB> receivers, there are 
M<SUB>T</SUB>xM<SUB>R</SUB> channels to be estimated.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>As all transmitters send their signals 
simultaneously, the received signal at each receiver is a superposition of the 
transmitted signals that are distorted by the channel.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>Hence in the estimation process of 
channel between i抰h transmitter and j抰h receiver the signal transmitted by 
other transmitters are interference.<SPAN style="mso-spacerun: yes">&nbsp; 
</SPAN>So in the MIMO channel estimation, whenever a pilot tone is inserted in a 
subcarrier, all other transmitters don抰 send anything in that subcarrier.</P>
<P class=MsoNormal>This is the proposed method in [4].<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>This method is proposed for the cases 
that the time interval between two consecutive symbols is larger than channel 
coherence time, or the case that we have no information about temporal 
correlation of the channel.</P>
<P class=MsoNormal>In [5] the channel estimation is based on this assumption 
that the delay profile of the channel is known, and it doesn抰 change much 
between two consecutive symbols. <SPAN style="mso-spacerun: yes">&nbsp;</SPAN>If 
the interval between two consecutive symbols is less than the channel coherence 
time, it is possible to use this correlation to improve the channel 
estimation.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>Assume 
<I><U>H</U>(k,n)</I> is the estimate of the channel at time k and n抰h pilot 
tone frequency.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>Also assume 
<I>H(k+1,n)</I> is the LS estimate of the channel at time <I>k+1</I> and pilot 
tone frequency <I>n</I>. <SPAN style="mso-spacerun: yes">&nbsp;</SPAN>The best 
linear mean square estimator of the <I><U>H</U>(k+1,n)</I> given 
<I><U>H</U>(k,n)</I> and <I>H(k+1,n)</I> is</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal><I><U>H</U>(k+1,n)</I> = <I>a.<U>H</U>(k,n)+b.H(k+1,n)</I> 
<SPAN style="mso-spacerun: yes">&nbsp;</SPAN>for<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN><I>a = ( R<SUB>hh</SUB><SUP>2</SUP>(0) - 
R<SUB>hh</SUB><SUP>2</SUP>(1) ) / ( R<SUB>hh</SUB><SUP>2</SUP>(0) - 
R<SUB>hh</SUB><SUP>2</SUP>(1) + &#963;<SUP>2</SUP>R<SUB>hh</SUB><SUP>2</SUP>(0) 
)<SPAN style="mso-spacerun: yes">&nbsp; </SPAN></I>and <I><SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN>b = <SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN>&#963;<SUP>2</SUP>R<SUB>hh</SUB><SUP>2</SUP>(1) 
/ ( R<SUB>hh</SUB><SUP>2</SUP>(0) - R<SUB>hh</SUB><SUP>2</SUP>(1) + 
&#963;<SUP>2</SUP>R<SUB>hh</SUB><SUP>2</SUP>(0) )<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN><SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN><o:p></o:p></I></P>
<P 
class=MsoNormal><I><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></I></P>
<P class=MsoNormal>Note that although MMSE shows a better performance than LS, 
the computational complexity of this method is the main problem of using that 
for this simulation.</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal>To compare these two cases a MIMO system with 2 transmitters 
and 2 receivers in a Rayleigh fading channel is simulated in Matlab.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>All channel impulse responses are 
Rayliegh fading channels with the Bessel autocorrelation function (Jakes 
model).<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>Figure 2 shows the envelope 
of one of the paths in the multipath channel generated for this simulation.</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" 
align=center><!--[if gte vml 1]><v:shape id=_x0000_i1052 
style="WIDTH: 6in; HEIGHT: 324pt" type = "#_x0000_t75" coordsize = 
"21600,21600"><v:imagedata o:title="fig2" src = 
"./project1_files/image003.emz"></v:imagedata></v:shape><![endif]--><![if !vml]><img border=0 width=576 height=432
src="./project1_files/image004.gif" v:shapes="_x0000_i1052"><![endif]></P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center>Fig 2. A typical 
amplitude variation for one path of a multipath channel</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal>Figure 3 shows the performance of these two methods for 
several signal to noise ratios.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>In 
this simulation, maximum Doppler frequency is 10 Hz, the bandwidth of each 
subchannel is 20kHz, total number of subcarriers is 64 and the number of pilots 
is 32. <SPAN style="mso-spacerun: yes">&nbsp;</SPAN></P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" 
align=center><!--[if gte vml 1]><v:shape id=_x0000_i1056 
style="WIDTH: 6in; HEIGHT: 324pt" type = "#_x0000_t75" coordsize = 
"21600,21600"><v:imagedata o:title="fig3" src = 
"./project1_files/image005.emz"></v:imagedata></v:shape><![endif]--><![if !vml]><img border=0 width=576 height=432
src="./project1_files/image006.gif" v:shapes="_x0000_i1056"><![endif]></P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center>Fig 3. Normalized 
estimation error vs. SNR for two different methods</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal>Increasing the maximum Doppler frequency, decreases the 
coherence time of the channel, so it is expected that the performance of the 
second method degrades by increasing the maximum Doppler frequency.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>Figure 4 shows the results of simulation 
of the method for the three different Doppler frequencies.<SPAN 
style="mso-spacerun: yes">&nbsp; </SPAN>The degradation is clear from this 
figure.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>The parameters for this 
simulations are the same as last simulation. <SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN><SPAN 
style="mso-spacerun: yes">&nbsp;</SPAN></P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" 
align=center><!--[if gte vml 1]><v:shape id=_x0000_i1057 
style="WIDTH: 6in; HEIGHT: 324pt" type = "#_x0000_t75" coordsize = 
"21600,21600"><v:imagedata o:title="fig4" src = 
"./project1_files/image007.emz"></v:imagedata></v:shape><![endif]--><![if !vml]><img border=0 width=576 height=432
src="./project1_files/image008.gif" v:shapes="_x0000_i1057"><![endif]></P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center>Fig 4. Normalized 
estimation error of second method</P>
<P class=MsoNormal style="TEXT-ALIGN: center" align=center>for different SNR抯 
and different Doppler frequencies</P>
<P class=MsoNormal><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></P>
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<H3>References</H3>
<P class=MsoNormal>[1] G. J. Foschini, and M. J. Gans, "On Limits of Wireless 
Communication in a Fading Environment when Using Multiple Antennas," <I>Wireless 
Personal Communications,</I> No. 6, 1998, pp. 315-335. </P>
<P>&nbsp;[2] Y. Li, J. H. Winters, and N. R. Sollenberger, "MIMO-OFDM for 
Wireless Communications: Signal Detection with Enhanced Channel Estimation," 
<I>IEEE Tran. Commun.</I>, vol. 50, No. 9, pp. 1471-1477, September 2002. </P>
<P>&nbsp;[3] B. Yang, K. B. Letaief, R. S. Cheng, and Z. Cao, "Channel 
Estimation for OFDM Transmission in Multipath Fading Channels Based on 
Parametric Channel Modeling," <I>IEEE Tran. Commun.</I>, vol. 49, No. 3, pp. 
467-479, March 2001. </P>
<P>&nbsp;[4] Y. Li, N. Seshadri, and S. Ariyavisitakul, "Channel Estimation for 
OFDM Systems with Transmitter Diversity in Mobile Wireless Channels," <I>IEEE J. 
Select. Areas Commun.</I>, vol. 17, No. 3, pp. 461-471, March 1999. </P>
<P>&nbsp;[5] V. K. Jones, and G. C. Raleigh, "Channel Estimation for Wireless 
OFDM Systems," <I>Proc. GLOBCOM'98</I>, pp. 980-985. </P>
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