Presented by:
Joel Abraham
Anoop Prabha
Binaya Parhy
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.
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
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).
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.
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
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.
Wireless throughput
scales as more radio
transmissions are
added
Only baseband
complexity, die
size/cost and power
consumption limits
the number of
simultaneous
transmission
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
Consider a simple BPSK bit sequence 1,

1,1,1,

1
We code 1 as C1 and

1 as C2
C1 =
c
2 =
1

1
Dimension of C is determined by the Number of
Tx
and Rx
H = Channel Matrix
n = Noise
Rx
1
= h
11
Tx
1
+ h
21
Tx
2
+ h
31
Tx
3
+ n
1
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
◦
WLAN
–
WiFi
802.11n
◦
Mesh Networks (e.g.,
MuniWireless
)
◦
WMAN
–
WiMAX
802.16e
◦
4G
◦
RFID
◦
Digital Home
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
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
w
c
t
+
∑
N
n
=1
r
n
cos
(
w
c
t
+
f
n
)
Examples
Vehicle to vehicle communication
Satellite channels
Indoor communication
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.
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.
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
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
MIMO Wireless Communications
Capacity of MIMO
9
Well known STBC codes
–
Criteria to be a good ST BC code.
–
Cyclic and Unitary STBC
²
Orthogonal STBC
²
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
ρ
:SNR, h: Channel gain
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
M
t
xM
r
channel coefficients.
)


1
(
log
2
2
h
E
C
h
)
1
(
log
2
SNR
C
Block Diagram Of a MIMO communication
system
2
1
Mt
1
2
Mr
H
1,1
h
1,2
H
1,M
r
H
2,1
h
2,2
H
2,Mr
h
Mt,1
h
Mt,2
h
Mt,Mr
Mr
Mt
Mt
Mt
Mr
Mr
h
h
h
h
h
h
h
h
h
,
2
,
1
,
,
2
2
,
2
1
,
2
,
1
2
,
1
1
,
1
.
.
.
.
.
.
.
.
Channel Matrix H=
MIMO Capacity
◦
Four Cases
1.
M
t
=
M
r
=1 Reduces to SISO
2.
M
r
=1, M
t
>1
3.
M
t
=1,
M
r
>1
4.
M
r
>1, M
t
>1
)
det(
log
2
H
t
MrxMr
H
HH
M
I
E
C
Case:2(
M
r
=1, M
t
>1)
Mr
Capacity
Case:3(
M
t
=1, M
r
>1)
Mt
Capacity
ρ
=10 dB
ρ
=5 dB
ρ
=1 dB
Case:4(
M
t
>1, M
r
>1)
Mt
Capacity
ρ
=10 dB
ρ
=5 dB
ρ
=1 dB
Conclusion:
M=min(M
t
,M
r
)
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.
)
1
(
log
2
M
C
The maximum probability of error (also called PEP

Piece wise error probability)
of a MIMO system is given by
r

> rank of and
λ
i
’s are the eigen valus of
Based on the PEP code design criteria were proposed by Tarokh in 1998.
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.
Product criterion or Coding gain criterion
The minimum value of the product over all pairs of distinct code
word difference should be as large as possible.
r
r
rM
t
M
r
i
i
M
H
C
C
4
2
1

~
Pr
1
C
C
~
C
C
C
C
H
~
~
r
i
i
1
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
Where T=M
t
and 0<
γ
<1
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.
t
M
c
c
t
C
C
M
1
'
)
det(
min
2
1
'
MIMO Tran receiver can be modeled as
C is the ST code is one among the signal constellation.
So we will conclude that
Square size i.e. T=M
t
C
l

2
=M
t
2
(This is for normalization to have a fair comparison)
The difference matrix between any two distinct code
C
l
and C
l
’
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.
r
r
t
t
r
TxM
xM
M
TxM
t
TxM
N
H
C
M
Y
Cyclic and Unitary STBC
Orthogonal STBC
Diagonal algebric
BLAST(V

BLAST & D

BLAST)
Differential STBC(Non coherent detection)
l
t
M
l
l
ju
ju
ju
t
l
e
e
e
M
C
.
.
0
0
0
.
.
0
0
0
.
.
.
0
0
.
.
0
0
.
.
0
2
1
•
Proposed by
Hochwald
&
Sweldens
in 2000.
1
,.......
2
,
1
,
0
.,
,.........
,
1
.....,
2
,
1
,
0
),
2
(
2
1
L
u
u
u
L
l
L
l
t
M
l
•
Why Cyclic?
C
l
=
C
L+l
i.e. the code regenerates itself.
•
Sqrt
(M) is to satisfy the energy criterion 
C
l

2
=M
t
2
.
•
Achieves full diversity.
•
To maximize coding gain
u
i
’s
should be chosen carefully.
•
Exhaustive search methodology is used to find
u
i
’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
C
l
is a diagonal matrix, at a time slot only one
Tx
transmits.
•
Why Unitary?
An unitary matrix satisfies A
H
A=I (Identity Matrix).
Cyclic ST is an unitary code.
j
j
j
j
C
j
j
j
j
C
j
j
j
j
C
j
j
j
j
C
1
1
3
2
1
1
3
2
1
1
3
2
1
1
3
2
3
2
1
0
•
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
•
The coding gain for above ST code is 0.8165.
The upper bound is given by
•
For L=8, the optimal code is not yet discovered.
•
No new ST coding techniques has to be
explored.
)
1
(
2
L
L
•
Orthogonal STBC achieve full diversity and offer
fast ML decoding. Proposed by Alamouti in 1998
for two Tx.
•
X
1
, X
2
are any two complex symbols.
•
Fast ML decoding means for ML X
1
, X
2
can be
minimized separately therefore decreasing the
complexity of the minimization problem.
•
For more transmitters, Orthogonal design can be
used.
*
1
*
2
2
1
2
1
2
)
,
(
X
X
X
X
X
X
G
•
Orthogonal design with k variables X
1
, X
2
,…… X
k
is a pxn matrix such that
•
The entries of G are 0,+/

X
1
, +/

X
2
,……., +/

X
k
or their conjugates.
•
The columns are orthogonal to each other. i.e.
•
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.
n
k
H
I
X
X
X
G
G
2
2
1
2
1
........
•
In general n=2
l
an orthogonal design of size n by n can be given as
•
Rate is given by l+1/2
l
•
With increase in l the rate decreases, so 2x2
Alemouti
is normally
used.
H
l
l
l
l
l
X
X
X
G
I
X
I
X
X
X
X
G
X
X
X
G
l
l
l
l
l
)
,....
,
(
)
,....
,
(
)
,....
,
(
2
1
2
2
*
1
2
1
2
1
2
1
2
1
2
1
1
•
Vandermonde
transformation is used.
•
S1,S2…
Sk
are the k information symbols. 
θ
k=1. The code word is
formed as
diag
[X1,X2,…
Xk
].
•
Θ
k=exp(j(4k

3)/2K) k=1,2..K
•
Achieves full diversity.
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
2
1
.
.
.
.
.
.
1
.
.
1
1
)
,......,
,
(
.
.
)
,......,
,
(
.
.
k
k
k
k
k
k
k
k
k
k
V
S
S
S
V
X
X
X
•
The first MIMO system proposed by
Tuschini
from Bell Lab to verify the
potential MIMO capacity.
•
V

Blast
Systme
•
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.
..a3,a2,a1,a0
Mt
1
2
Mr
..
b3,b2,b1,b0
•
The first MIMO system proposed by
Tuschini
from Bell Lab to verify the
potential MIMO capacity.
•
V

Blast
Systme
•
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.
..a3,a2,a1,
a0
Mt
1
2
Mr
..b3,b2,b1,b0
•
Coding is done with in each data stream but no
coding across different streams.
•
At the 1
st
time slot only 1 transmitted sends
other send nothing. At 2
nd
only 1
st
and 2
nd
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.
So
at first a dump (identity matrix is sent)
t
M
t
l
t
t
I
M
S
S
C
M
S
N
H
S
M
Y
0
1
,
,
1
•
For stability unitary ST coding is used.
•
ML Detection

:
•
•
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.
2
1
,
1
..
1
,
0
,

1

min
arg
ˆ
Y
C
M
Y
C
l
t
L
l
l
CSI
Known at Tx
and Rx
Known at Tx
and unknown
at Rx
Unknown at both
Tx, Rx
Transmissio
n Signal
ML
Demodulatio
n
STBC
Arbitrary STBC
Arbitrary
Unitary STBC
2
1
,
1
..
1
,
0

1

min
arg
Y
C
M
Y
l
t
L
l
2
1
..
1
,
0


min
arg
H
C
M
Y
l
t
L
l
2
1
..
1
,
0


min
arg
WH
C
M
Y
l
t
L
l
GW
S
l
C
S
1
,
1
S
C
M
S
l
t
<

Coherent


<

NonCoherent

>
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