The document discusses the basic mathematics behind MIMO (Multiple Input Multiple Output) technology used in wireless communications. It contains the following key points: 1) MIMO systems use multiple antennas at both the transmitter and receiver to enhance performance. This allows for transmitting and receiving multiple data streams simultaneously. 2) There are two main MIMO modes - spatial multiplexing provides throughput/capacity gains by transmitting different data symbols from each transmitter, while space-time block coding provides diversity gains through redundant transmission to improve reliability. 3) The MIMO system can be modeled by a channel matrix relating the transmitted and received signals, where each element represents fading between an antenna pair. Techniques like zero-forcing equalization are used

1. Basic Mathematics of MIMO
Technology
By
DR. Pravinkumar Patil
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2. Wireless communication challenges.
• Spectrum Limitations
• Signal Interference
• Multipath Fading
• Power Consumption
• Security Concerns
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3. Introduction to MIMO Technology
• Multiple Input Multiple Output (MIMO) is a technology
used in wireless communication systems to enhance
performance by transmitting and receiving multiple data
streams simultaneously. This technique is particularly
beneficial in the field of wireless communications, where
channel conditions can be challenging and subject to
fading, interference, and other impairments.
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4. MIMO Technology
MIMO systems:
• Multiple Antennas at the transmitter and receiver.
• MIMO modes
- Spatial Multiplexing MIMO systems provides
Capacity/throughput gain
(improves spectrum efficiency or data rate)
- STBC MIMO systems offers diversity gain
(improves reliability of transmission)
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5. MIMO System Model
y = Hx + n
User data stream
.
.
User data stream
.
.
.
.
Channel
Matrix H
x1
x2
xM
s
y1
y2
yN
y
Transmitted vector Received vector
.
.
h11
h21
Where H =
h11 h21 ….. .hn1
h12 h22 …… hn2
h1m h2m ….. .….hnm
. . .
Nr
Nt
hij is a Complex Gaussian
random variable that models
fading gain between the i th
receive and j th transmit
antenna
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Fig.5: MIMO system model

6. Spatial Multiplexing MIMO System
Zero Forcing receiver:
11
h
22
h
21
h
12
h
Tx Antenna 1
Tx Antenna 2
Rx Antenna 1
Rx Antenna 2
1 11 1 12 2 1
2 21 1 22 2 2
1 11 12 1 1
2 21 22 2 2
1 1
2 2
1
1 11 12 1
2 21 22 2
ˆ
ˆ
ˆ
ˆ
y h x h x n
y h x h x n
y h h x n
y h h x n
x y
x y
x h h y
x h h y
W

  
  
       
 
       
       
   
 

   
 
 
   
     

     
     
For ZF receivers
1
W H 

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• A spatial multiplexing MIMO system transmits different data symbols from
each transmitter.
• Zero Force Equalization:
• The signals from each transmitter combine over the air and are received by
multiple receive antennas.
• SM systems have capacity gain=Min
Fig.6: 2X2 MIMO model
( , )
t r
N N

7. Space Time Block Code (STBC)
MIMO system
– Considers redundant data transmission
– Offers diversity gain
– 2 X1 MIMO STBC coding also known as “Alamouti Code”
– Improves BER performance
Information
Source
Constellation
Mapper Alamouti ST
block code
h1
h2
Symbol
Period 2
Symbol
Period 1
STBC
Decoder
ML Decision
ML Decision
Soft decision for
c1
Soft decision for
c2
1 1 1 2 2
y x x
h h
 
* *
2 1 2 2 1
( ) (x )
y h x h
  
STBC Transmitter (Encoder)
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Figure: MIMO STBC
1
t r
L N N
  

8. MIMO-OFDM technology
 MIMO OFDM: A Combination of MIMO and OFDM appears
like many parallel SISO transmissions on orthogonal
subcarriers.
-OFDM may be combined with MIMO for improved
performance
-It is considered as most suitable candidate for next generation
wireless systems.
 MIMO- OFDM improves both throughput (data rate) and
reliability (better QOS)
-Supported by most of the modern wireless standards
(WLAN,WMAN,4G,LTE etc.)
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9. Need for adaptive controller
Figure: Block diagram of a general adaptive wireless system
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10. Thank You!
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