12- OFDM with Multiple Antennas

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12- OFDM with Multiple Antennas
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Multiple Antenna Systems (MIMO)
TX
RX
Receive Antennas
Transmit Antennas
Different paths

• Two cases
• Array Gain if all paths are strongly correlated
  to which other the SNR can be increased by array
  processing
• Diversity Gain if all paths are uncorrelated,
  the effect of channel fading can be attenuated by
  diversity combining

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Recall the Chi-Square distribution
1. Real Case. Let
Then
with
2. Complex Case. Let
Then
with
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Receive Diversity
RX
TX
Transmit Antennas
Receive Antennas
Different paths
Noise PSD
Energy per symbol
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Assume we know the channels at the receiver. Then
we can decode the signal as
signal
noise
and the Signal to Nose Ratio
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In the Wireless case the channels are random,
therefore is a random variable
Now there are two possibilities 1. Channels
strongly correlated. Assume they are all the same
for simplicity
Then
assuming
and
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From the properties of the Chi-Square
distribution
better on average
but with deep fades!
Define the coefficient of variation
In this case we say that there is no diversity.
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2. Channels Completely Uncorrelated.
Since
Diversity of order
with
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Example overall receiver gain with receiver
diversity.
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Transmitter Diversity
TX
RX
Transmit Antennas
Receive Antennas
Different paths
Equivalent to one channel, with no benefit.
Total energy equally distributed on transmit
antennas
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However there is a gain if we use Space Time
Coding (2x1 Alamouti) Take the case of
Transmitter diversity with two antennas
TX
RX
Given two sequences code them within the two
antennas as follows
antennas
time
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This can be written as
To decode, notice that
Use a Wiener Filter to estimate s
with
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It is like having two independent channels
Apart from the factor ½, it has the same SNR as
the receive diversity of order 2.
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2x2 MIMO with Space Time Coding (2x2 Alamouti)
TX
RX
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Same transmitting sequence as in the 2x1 case
antennas
time
Received sequences
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Write it in matrix form
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Combined as
to obtain
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After simple algebra
with
diversity 4
This yields an SNR
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WiMax Implementation
Subscriber Station
Base Station
Down Link (DL) BS -gt SS Transmit
Diversity Uplink (UL) SS-gtBS
Receive Diversity
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Down Link Transmit Diversity
Use Alamouti Space Time Coding
Transmitter
IFFT
TX
Data in
Error Coding
M-QAM
buffer
STC
IFFT
TX
Space Time Coding
Block to be transmitted
time
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Receiver
Data out
S/P
P/S
Error Correction
FFT
M-QAM
STD
2
2
Space Time Decoding For each subcarrier k
compute
with
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Preamble, Synchronization and Channel Estimation
with Transmit Diversity (DL)
The two antennas transmit two preambles at the
same time, using different sets of subcarriers
EVEN subcarriers
CP
128


128
64
128
CP
128

ODD subcarriers
-
128
64
128
frequency
time
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Both preambles have a symmetry
received signal from the two antennas

• Problems
• time synchronization
• estimation of both channels

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Symmetry is preserved even after the channel
spreading
CP
128


128
64
128
CP
128

-
128
64
128
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One possibility use symmetry of the preambles
The two preambles can be easily separated
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MIMO Channel Simulation
Take the general 2x2 channel
Rayleigh
Rayleigh
Correlation at the transmitter
Correlation at the receiver