Why MIMO - EEWeb

klapdorothypondMobile - Wireless

Nov 23, 2013 (3 years and 6 months ago)

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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
-
>