MIMO Capacity and Duality Between MAC and BC
•
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I present the Multiple Input and Multiple Output (MIMO) channel capacity. Capacity regions for multiuser MIMO broadcast and multiple access channel are shown. Also, the duality relationship between multiple access and broadcast channel is presented.
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![Mul$ple
Input
Mul$ple
Output
(MIMO)
y = Hx + n
MIMO
Model
Transmit
Precoding
and
Receiver
Shaping
Singular
Value
Decomposi$on
(SVD):
H =UΣV H
y = Σx + n
Mul$plexing
gain
=
Rank
of
H
=
RH
Power
Noise
1 2 3
Subchannel
Water
Level
MIMO
Channel
Capacity
C = max
p(x)
I(X;Y) = max
p(x)
[H(Y)− H(Y | X)]
C = max
Pi:ΣiPi≤P
log2 1+
Piγi
P
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∑ γ = SNR
Pi
P
=
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γ0
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0
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γi <γ0
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γ0
!
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i:γi≥γ0
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- 1. Mul$user MIMO Gaussian Channels: Capacity Regions and Duality Shris$ Pradhan University of Bri.sh Columbia December 2011
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