Subsystem Blocks
CHAPTER 5. SUBSYSTEM BLOCKS
5.2 Matrix Blocks
5.2 Matrix Blocks
MIMO can be regarded as a baseband technique, where the transmitted signals are recovered by advanced signal processing. This requires a total redesign of the ADS 802.lla receiver, which was out of the scope of this project.
Therefore influence of the channel and channel correction was modeled using the following correlation and decorrelation blocks. Although, that does not model the fading MIMO channel, it does indicate the influence of channel correlation and allows the use of the standard 802.lla ADS receiver blocks.
Hence for designing a MIMO system, some undeveloped blocks should be done first. Those blocks are about building a MIMO channel and for recovering back the signal from the channel.
For that intention the next two blocks are presented.
5.2.1 Correlation
The correlation block (or correlation matrix block, see figure 5.12) will take all the signals from the sources and mix them with each others.
G~,nM;fIt.1...(ii~t CorretMalnX20
...
,mo 1=tho 1
mo)=rno)
rho_3"'rho_3
Figure 5.9: Correlation matrix block
This block has four inputs, one for each stream and 6 outputs, one per stream and two tor testing.
The correlation block builds the pseudo channel matrix previously explained in the theoretical chapter of this report. At the output of this block each stream will be formed by of all signal
CHAPTER 5. SUBSYSTEM BLOCKS
streams. Hence, this block is implementing the following matrix.
(
a p i P2 P3)
H(t)
=
PI a PI P2P2 PI a PI P3 P2 PI a
So, at the output of the block, for the first stream for instance, there will be:
A = SOUrCel
*
a+
SOUrCe2*
PI+
SOUrCe3*
P2+
SOUrCe4*
P3(5.1 )
But several considerations are taken about this H matrix. The first one is concerning the path losses, the a. In this case they are not considered so the a will be equal to one because any signal component is lost. The other assumption done is that the influence of the non desired streams in the desired one is equal for all streams, which means:PI
=
P2=
P3 and called simply p. Usually used to be a percentage value.After those considerations the H matrix will be like the following.
Using the previous example and a correlation value of 20%, the first stream will be A = Source1
+
0.2Source2+
0.2Source3+
0.2Source4(5.2)
5.2. MATlliX BLOCKS
The internal scheme of the correlation block is shown in the figure 5.10.
---0
cr---Figure 5.10: Correlation matrix block scheme
This block presents 4 inputs and 6 instead of 4 outputs. That is because there will be 4 normal (namely crossed) outputs and two for measuring. A remark should be done about the upper two measuring outputs.
The first normal output is just the signal of the first source with a certain correlated com-ponent coming from the other sources. From this point there will be impossible to separate the correlated component -called distortion- from the desired signal. Due to that, two extra (and equal) ports are used. Inthose ports the desired signal will be suppressed and only the distortion will pass by. After this block noise will be added to one of those paths (exactly the same added noise of the first stream).
That two measuring paths will be used for measuring the signal to distortion (SND) and the signal to noise and distortion ratio (SNDR).
CHAPTER 5. SUBSYSTEM BLOCKS
5.2.2 Decorrelation
The correlation matrix inverse block or decorrelation block (see figure 5.11) will take the 4 streams at its input and recover the transmitted signal from them. Thus, it is doing the same task as the channel estimation block in a MIMO receiver. Mathematically this is the inverse matrix of the H matrix, namely, inverting the Correlation block.
r./.,r~MOllln...4 d':s.1 CorreiMatrill:;·9
..
,rho'-rhD 1
mo:2smD:2
mo_3-rtlO_3
Figure 5.11: Correlation matrix inverse block
It is important to notice that this block is done after doing a channel estimation. With that process, the system "knows" the channel (H matrix) and then design this correlation matrix inverse according with that estimation for extracting the signal. Although it is one of the main issues of the study of MIMO systems, and due to the fact that it is not the aim of this project, this lines will not pay attention to how is the channel estimation done.
So at this point is placed this block, done after the channel estimation process. Each stream will be extracted from the total signal received in each antenna.
Ifthere is no correlation between those streams at the same antenna, this extraction would be perfect but, obviously in the real world it never happens. That is the intention of the next blocks.
They will introduce non-linearities, noise, correlation, etc in order to build a more real design.
5.2. MATRIX BLOCKS
Returning to the actual block, the following figure 5.12 is the internal design. The used algorithm have been calculated first and optimized afterwards with Mathematica 5.
CorrMatlnv4_dist 0
-C>---.--.---.---.--t-"-t--~
PA Num,,'0
Port 13 measures tIle contribution of the channels 2,3 and 4.
Also it i. possible to measure them with an extra signal (PortA), tyoically noise.
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.,
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.,
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Num=:1
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.,
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~VN'~
lrMtroP.rllnwl.""14
...',
."=<.r-ltl0J)·(-2"rtIo_,-;z ..l""(r+rtID_2))
.,2""----r-2"rho_'.I""I'tlo_2"{I1'Io_'trho_3J+!'ho_'"(rtlc_'-7-rho_~.(rtID_'·rho_J»
.'31:-{r.rho_2r(11'10_2"(r"mo.)l· rhD_,O(rho_'trtID_J)}
.'4&-mO_"rtlD_'~"rho_2"(-2"ttrl'lc..,2)"(.nt11"D_'-;zrrtlo_J '121..,2
122=r-3" (2"rtIIU·rho_2"rho_il-l""(rtlo_'-Z·rho_2'"'2'trtlD_J-;;!) a23=(-r'mo_'r(r-2"rtlo_2 ).(mo_3,rtto_''"'2'trho_2''"'2» t(rho_1"rho_:r21 .24a-(f~_2)·(moy(J"I'lhoJl. rl'IO_"(rho_'+rho_3»
."".,3
.U--023
"J=oZ1I~mo_'"I""rI'IO_2"imo_'ofrtlD_3)trtvJ_,"(1f'IO_1-:Z-rho_r2-trtlo_'"rtvJ_J)
&04.1"'4
-...,.
Figure 5.12: Correlation matrix inverse diagram
The four lower inputs/outputs are for each stream. The upper two are for measuring signal-to-noise ratio and signal-to-distortion ratio respectively (see Measurement Techniques chapter).
CHAPTER 5. SUBSYSTEM BLOCKS