Why MIMO

Report
Presented by:
Joel Abraham
Anoop Prabha
Binaya Parhy
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Why MIMO
Different Arrangements of Antennas
Working
MIMO vs SIMO/MISO
Types of MIMO
◦ Diversity
◦ Spatial Multiplexing
◦ Uplink Collaborative MIMO Link
Actual Working
Channel Matrix
System Model
Advantages and Application


MIMO is an acronym that stands for Multiple Input Multiple
Output.
Motivation: current wireless systems
◦ Capacity constrained networks
◦ Signal Fading, Multi-path, increasing interference,
limited spectrum.
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MIMO exploits the space dimension to improve wireless
systems capacity, range and reliability
MIMO-OFDM – the corner stone of future broadband
wireless access
◦ – WiFi – 802.11n
◦ – WiMAX – 802.16e (a.k.a 802.16-2005)
◦ – 3G / 4G
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In short - Two or more data signals transmitted in the
same radio channel at the same time
It is an antenna technology that is used both in
transmission and receiver equipment for wireless
radio communication.
MIMO uses multiple antennas to send multiple
parallel signals (from transmitter).
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MIMO takes advantage of multi-path.
MIMO uses multiple antennas to send multiple parallel
signals (from transmitter).
In an urban environment, these signals will bounce off trees,
buildings, etc. and continue on their way to their destination
(the receiver) but in different directions.
“Multi-path” occurs when the different signals arrive at the
receiver at various times.
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With MIMO, the receiving end uses an algorithm or
special signal processing to sort out the multiple
signals to produce one signal that has the
originally transmitted data.
They are called “multi-dimensional” signals
There can be various MIMO configurations. For
example, a 4x4 MIMO configuration is 4 antennas
to transmit signals (from base station) and 4
antennas to receive signals (mobile terminal).

The total number of channel = NTx x NTr
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MIMO involves Space Time Transmit Diversity (STTD), Spatial
Multiplexing (SM) and Uplink Collaborative MIMO.
Space Time Transmit Diversity (STTD) - The same data is
coded and transmitted through different antennas, which effectively
doubles the power in the channel. This improves Signal Noise Ratio
(SNR) for cell edge performance.
Spatial Multiplexing (SM) - the “Secret Sauce” of MIMO. SM
delivers parallel streams of data to CPE by exploiting multi-path. It
can double (2x2 MIMO) or quadruple (4x4) capacity and throughput.
SM gives higher capacity when RF conditions are favorable and
users are closer to the BTS.
Uplink Collaborative MIMO Link - Leverages conventional single
Power Amplifier (PA) at device. Two devices can collaboratively
transmit on the same sub-channel which can also double uplink
capacity.
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Wireless throughput
scales as more radio
transmissions are
added
Only baseband
complexity, die
size/cost and power
consumption limits
the number of
simultaneous
transmission
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Each multipath route is
treated as a separate
channel, creating many
“virtual wires” over
which to transmit
signals
Traditional radios are
confused by this
multipath, while MIMO
takes advantage of
these “echoes” to
increase range and
throughput
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Consider a simple BPSK bit sequence 1,-1,1,1,-1
We code 1 as C1 and -1 as C2

C1 =

1
-1
Dimension of C is determined by the Number of Tx and Rx

c2 =
H = Channel Matrix
n = Noise

Rx1 = h11Tx1 + h21Tx2
+ h31Tx3 + n1
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Using the space dimension (MIMO) to boost data
rates up to 600 Mbps through multiple antennas and
signal processing.
Target applications include: large files backup, HD
streams, online interactive gaming, home
entertainment, etc.
Backwards compatible with 802.11a/b/g
Application
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WLAN – WiFi 802.11n
Mesh Networks (e.g., MuniWireless)
WMAN – WiMAX 802.16e
4G
RFID
Digital Home
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http://en.wikipedia.org/wiki/4G
http://en.wikipedia.org/wiki/MIMO#MIMO_literature
http://www.wirelessnetdesignline.com/howto/wlan/185300393;jsessionid=3R20PO41A
V3Y1QE1GHRSKHWATMY32JVN?pgno=1
www.ieeeexplore.com
http://www.ece.ualberta.ca/~HCDC/mimohistory.html
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.13.4732&rep=rep1&type=p
df
Anoop Madhusoodhanan Prabha
36576876
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Rayleigh Model
Statistical Modeling of wireless channels.
Magnitude of signal varies randomly as it propagates in the
medium.
Best fit for tropospheric and ionospheric signal propagation.
Fits fine for Urban environments too.
Highlight – No dominant light of sight communication
between transmitter and receiver.
Rate of channel fade – Studied by Doppler shift. 10Hz to 100
Hz is the shift considered in GSM phones modeling for an
operating frequency of 1800 MHz and speed between 6km/h
to 60 km/h
Racian Fading
 Comes into picture when there is a dominant
component present (especially line of sight way)
 v(t) = C cos wct + ∑Nn=1 rn cos (wct + fn)
 Examples
 Vehicle to vehicle communication
 Satellite channels
 Indoor communication
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Nakagami fading
 Reason for modeling – Empirical results matched
with short wave ionospheric propagation.
 If amplitude – Nakagami distributed, power –
gamma distributed and ‘m’ is the shape factor in this
distribution.
 For m=1, its Rayleigh fading (amplitude
distribution) and corresponding power distribution is
exponential.
 These days many recent papers recommend this
model as an approx. to Rician model.
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The fading and shadowing effects are overcome by
spatial diversity i.e. my installing multiple antennas.
 Antennas separated by 4 – 10 times the wavelength to
ensure unique propagation paths.
 As a part 4G, one of important emphasis is on
throughput improvement.
 This stressed on better modulation techniques and
coding practices.
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For transmit/receive
beamforming we have a
diversity order of MN, referred
to as full diversity.
M – Number of transmitting
antennas
N – Number of receiving
antennas
v – beamforming vector for
receiver
u – beamforming vector for
transmitter
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The design goal of 802.11n was “HT”, High throughput.
Speed – 600 Mbps unlike the 802.11g (54Mbps)
The achievement of this speed is as follows:
More Subcarriers (OFDM) – from 48 (802.11g) to 52 thus speed
increased to 58.5Mbps
FEC squeezing to a coding rate of 5/6 instead of ¾ boosted the link
rate to 65Mbps.
Guard interval of 800ns in 802.11g was reduced to 400ns thus
increasing the throughput to 72.2Mbps.
MIMO with a max of 4X4 architecture which means 72.2X4 =
288.9Mbps
Channel width of 802.11g was 20Mhz each which was increased to
40MHz which eventually resulted in 600MHz throughput.
http://www.wirelesscommunication.nl/
 Wikipedia
 http://www.intel.com/technology/itj/2006/volume10is
sue02/art07_mimo_architecture/p04_mimo_systems_
reliability.htm
 http://www.wirevolution.com

Binaya Parhy
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MIMO Wireless Communications
Capacity of MIMO
Well known STBC codes
–
–
–
–
–
–
Criteria to be a good ST BC code.
Cyclic and Unitary STBC
Orthogonal STBC
Diagonal algebric
BLAST(V-BLAST & D-BLAST)
Differential STBC(Non coherent
detection)
Summarize
• SISO Capacity
– Capacity of any communication system is given
by the most famous equation
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C  Eh log2 (1   | h | )
ρ:SNR, h: Channel gain
2
C  log2 (1  SNR)
Note: Since channel is assumed to be N(0,1), this reduces to just
• MIMO Capacity Equation
It is similar but when it is MIMO we have MtxMr channel coefficients.
1
Block Diagram Of a MIMO communication
system
H1,1
H2,1
2
h2,2
h1,2
1
2
H2,Mr
hMt,1
Mt
H1,M
hMt,2
r
Mr
hMt,Mr
Channel Matrix H=
 h1,1
h
 2,1
 .

 .
hMt ,1

h1, 2
.
.
h2, 2
.
.
hMt , 2
.
.
h1, Mr 
h2, Mr 



hMt , Mr 
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MIMO Capacity

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C  EH log2 det(I MrxMr 
HH H )
Mt


◦ Four Cases
1.
2.
3.
4.
Mt=Mr=1 Reduces to SISO
Mr=1, Mt>1
Mt=1, Mr>1
Mr>1, Mt>1
Case:2(Mr=1, Mt>1)
Capacity
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Mr
Case:3(Mt=1, Mr>1)
ρ =10 dB
Capacity
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ρ =5 dB
ρ =1 dB
Mt
Case:4(Mt>1, Mr>1)
ρ =10 dB
ρ =5 dB
Capacity

ρ =1 dB
Mt

Conclusion:
C  M log2 (1   )
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M=min(Mt,Mr)
The capacity of the MIMO system increases linearly with
the minimum of transmitter and receiver antenna.
To achieve the potential huge capacity, new coding and
modulation called Space Time coding or ST-modulation is
developed since 1998.
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The maximum probability of error (also called PEP- Piece wise error probability)
of a MIMO system is given by

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
1
~
P r C   C | H    i 
2  i 1 
r
M r
 

 4M t



 rM r

~

C  C
r-> rank of

Based on the PEP code design criteria were proposed by Tarokh in 1998.
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~
~

C  C  C  C 
and λ ’s are the eigen valus of
H
i
Rank criterion or Diversity criterion
The minimum rank of difference of any 2 code word over all possible pairs
should be should be as large as possible. If there are L signals then there are
L(L-1)/2 pairs.
 r

Product criterion or Coding
gain
i  criterion
 
i 1

The minimum value of the product
over all pairs of distinct code
word difference should be as large as possible.
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Q: Among these two criteria which one is more
important?
A: Diversity is the more important one.
Accordingly lets define two terms that define the
wellness of a ST code
1. Diversity order = rxMr
2. Normalized coding gain
1

min' det(C  C ' )
2 M t c c
Where T=Mt and 0<γ<1

1
Mt
When r=Mt, the ST code is called to achieve full
diversity. The condition T=Mt is a necessary and
sufficient condition for achieving full diversity.
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MIMO Tran receiver can be modeled as
YTxM r 
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
Mt
CTxM t H M t xM r  NTxM r
C is the ST code is one among the signal constellation.
So we will conclude that
Square size i.e. T=Mt
||Cl||2=Mt2 (This is for normalization to have a fair comparison)
The difference matrix between any two distinct code Cl and Cl’ should
be full rank.
 The coding gain γ should be as large as possible. γ is a measure of
the minimum Euclidian distance between two codes.
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 Cyclic and Unitary STBC
 Orthogonal STBC
 Diagonal algebric
 BLAST(V-BLAST & D-BLAST)
 Differential STBC(Non coherent detection)
• Proposed by Hochwald & Sweldens in 2000.
 e ju1l

 0
Cl  M t  0

 0

 0
0
. .
e ju2l
.
. .
. .
0
. .
0
. .
0 

0 

0 
0 
ju  
e Mt l 
l
(2 ), l  0,1,2.....,L  1
L
u1 , u2 ,.........., uM t  0,1,2,.......L  1
l 
•
•
•
•
•
•
•
•
•
•
Why Cyclic?
Cl=CL+l i.e. the code regenerates itself.
Sqrt(M) is to satisfy the energy criterion ||Cl||2=Mt2.
Achieves full diversity.
To maximize coding gain ui’s should be chosen carefully.
Exhaustive search methodology is used to find ui’s.
For Mt=2, L=4, [u1 u2]=[1 1], coding gain=.707
For Mt=2, L=16, [u1 u2]=[1 7]
For Mt=4, L=16, [u1 u2 u3 u4]=[1 3 5 7], coding
gain=.4095
As Cl is a diagonal matrix, at a time slot only one Tx
transmits.
Why Unitary?
An unitary matrix satisfies AHA=I (Identity Matrix).
Cyclic ST is an unitary code.
• Cyclic ST code is not the optimum unitary code.
There are others which can give lesser coding
gain for e.g. Mt=2, L=4 C  2  j 1  j C  2   j 1  j 
0
3  1  j
j
1
3 1  j

1  j
2   j 1 j
2 j
C2 
C3 



j 
 j 
3  1  j
3 1  j
j
• The coding gain for above ST code is 0.8165.
The upper bound is given by

L
2( L  1)
• For L=8, the optimal code is not yet discovered.
• No new ST coding techniques has to be
explored.
• Orthogonal STBC achieve full diversity and offer
fast ML decoding. Proposed by Alamouti in 1998
for two Tx.
 X1
G2 ( X 1 , X 2 )  
*

X
2

X2 
*
X 1 
• X1, X2 are any two complex symbols.
• Fast ML decoding means for ML X1, X2 can be
minimized separately therefore decreasing the
complexity of the minimization problem.
• For more transmitters, Orthogonal design can be
used.
• Orthogonal design with k variables X1, X2,…… Xk
is a pxn matrix such that
• The entries of G are 0,+/- X1, +/- X2 ,……., +/Xk or their conjugates.
• The columns are orthogonal to each other. i.e.

G H G  X 1  X 1  ........ X k
2
2
2
I
n
• n is related to the number of transmitter antenna
and p to the time delay.
• The rate of orthogonal design is k/p i.e a code
word of time delay p carries k information
symbols.
•In general n=2l an orthogonal design of size n by n can be given as

 G2l ( X 1 , X 2 ,....X l )
G2l ( X 1 , X 2 ,....X l 1 )  
*

X
l 1 I 2l 1



H
G2l ( X 1 , X 2 ,....X l ) 

X l 1 I 2l1
•Rate is given by l+1/2l
•With increase in l the rate decreases, so 2x2 Alemouti is normally
used.

•Vandermonde transformation is used.
1
 X1 
 S1 
 1
X 
S 

1
 2
 2
 12
 .   V (1 ,  2 ,......, k )  . V (1 , 2 ,......, k )   1
12
 
 

.
.
.
 
 
 .
 X k 
 S k 
1k 1 1k 1
.
.
.
1 
.  k 
2
. k 


k 1
 k 
.
•S1,S2…Sk are the k information symbols. |θk|=1. The code word is
formed as diag[X1,X2,…Xk].
•Θk=exp(j(4k-3)/2K) k=1,2..K
•Achieves full diversity.
•The first MIMO system proposed by Tuschini from Bell Lab to verify the
potential MIMO capacity.
• V-Blast Systme
..a3,a2,a1,a0
.b3,b2,b1,b0
Mt
1
2
Mr
•Each data stream layer for each Tx.
•No coding across different layer. Decoding by nulling and cancellation
method. Ymr is used to obtain Ymr-1 and so on.
•Disadvantage- error propagation.
•The first MIMO system proposed by Tuschini from Bell Lab to verify the
potential MIMO capacity.
• V-Blast Systme
..a3,a2,a1,
a0
b3,b2,b1,b0
Mt
1
2
Mr
•Each data stream layer for each Tx.
•No coding across different layer. Decoding by nulling and cancellation
method. Ymr is used to obtain Ymr-1 and so on.
•Disadvantage- error propagation.
• Coding is done with in each data stream but no
coding across different streams.
• At the 1st time slot only 1 transmitted sends
other send nothing. At 2nd only 1st and 2nd Tx
sends and so on. After Mt time slots all Tx
starts sending.
• Achieves full diversity.
• Better performance than V-BlAST.
• Decoding is same as V-BLAST.
•



There are 3 scenarios.
CSI is not available at Tx but available at Rx---ST coding
CSI is not available at both Tx and Rx--- Differential Coding
CSI is available at both Tx and Rx--- Beam forming or Smart
Antenna
•


Differential Encoding/Decoding
Proposed by Hughes, Hochwald and Swelden in 2000.
Non coherent detection ideal for slow fading channels.
Y 
S 

Mt
S H   N
1
Cl , S 1 , S 0  M t I M t
Mt
 So at first a dump (identity matrix is sent)
• For stability unitary ST coding is used.
• ML Detection-:
•
1
ˆ
Cl ,  arg min || Y 
Cl , Y 1 ||2
l 0,1..L 1
Mt
• Performance of Non-coherent detection is 3 dB below
then coherent case dute to noise.
• The received vector at the previous slot is used for
detection of present information symbol.
CSI
<------------Coherent---------
Known at Tx
and Rx
<--NonCoherent->
Known at Tx
and unknown
at Rx
Unknown at both
Tx, Rx
Transmissio
S  Cl
S  GW
n Signal

ML
arg min || Y 
CH

M
arg min || Y 
C WH ||
M
Demodulatio
n
STBC
Arbitrary STBC Arbitrary
1
S 
Cl , S 1
Mt
l  0 ,1..L 1

l

2
l  0 ,1..L 1

l
t

||
2
arg min || Y 
l 0,1..L 1
1
Cl , Y 1 ||2
Mt
t
Unitary STBC

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