Chen Chen

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WELCOME

• Chen Chen

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Simulation of MIMO Capacity Limits

• Professor Patric Östergård
• Supervisor Kalle Ruttik
• Communications Labortory

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Agenda

• Introduction to Multiple-In Multiple-Out(MIMO)
• MIMO Multiple Access Channel(MAC)
• Water-filling algorithm(WF)
• MIMO Broadcast Channel(BC)
• Zero-forcing method(ZF)
• Simulation results
• Conclusion

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What is MIMO
Input vector
Output vector
Noise vector
Hij is the channel gain from Txi to Rxj with
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MIMO MAC (uplink)
MAC is a channel which two (or more) senders send
information to a common receiver
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Water-filling algorithm
The optimal strategy is to pour energy
(allocate energy on each channel). In channels
with lower effective noise level, more energy
will be allocated.
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Iterative water filling algorithm

• Initialize Qi 0, i 1 K.
• repeat
• for j 1 to K

end until the desired accuracy is
reached
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MIMO MAC capacity
Single-user water filling
K-user Water-filling
When we apply the water filling QiQ.
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MIMO MAC capacity region
The capacity region of the MAC is the closure of
the set of achievable rate pairs (R1, R2).
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MAC sum capacity region (WF)
The sum rate converges to the sum capacity.
(Q1. Qk) converges to an optimal set of input
covariance matrices.
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MIMO BC (downlink)
Single transmitter for all users
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Zero-forcing method
To find out the optimal transmit vector, such
that all multi-user interference is zero, the
optimal solution is to force HjMj 0, for i? j,
so that user j does not interfere with any other
users.
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BC capacity region for 2 users

• The capacity region of a BC depends only on the
• Conditional distributions of

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BC sum capacity
1. Use water filling on the diagonal elements of
to determine the optimal power loading matrix
under power constraint P.
2. Use water-filling on the diagonal elements of
to calculate the power loading matrix that
satisfies the power constraint Pj corresponding
to rate Rj. (power control)
3. Let mj be the number of spatial dimensions
used to transmit to user j, The number of
sub-channels allocated to each user must be a
constant when K Nt/ mj ,
(known sub-channel)
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Examples of simulation results
Ergodic capacity with different correlations
(single user)
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Ergodic capacity (single user)
4 different set correlations magnitude
coefficient
Ergodic capacity Tx Rx 3 Tx Rx 3 Tx Rx 3 Tx Rx 3
Correlation (0, 0) (0, 0.2) (0.2, 0.95) (0.95, 0.95)
Max(SNR20) 16.37 16.26 11.68 8.07
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MIMO MAC sum capacity (2 users)
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MIMO MAC sum capacity (2 users)
3
2
1
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MIMO MAC sum capacity (2 users)
Ergodic capacity Tx Rx 3 Tx Rx 3 Tx Rx 3
sum capacity user 1 user2
Max(SNR20) 21.32 16.31 16.34
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MIMO MAC sum capacity (3 users)
Tx Rx 5 SNR20
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MIMO MAC capacity (3 users)
Ergodic capacity Tx Rx 3 Tx Rx 3 Tx Rx 3 Tx Rx 3
sum capacity user 1 user2 user3
Max(SNR20) 23.45 16.60 16.19 16.16
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MIMO MAC capacity (WF)(2 users)
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MIMO MAC capacity (WF) (2 users)
Ergodic capacity Tx Rx 3 Tx Rx 3 Tx Rx 3
With water filling sum capacity user 1 user2
Max(SNR20) 21.96 16.36 16.45
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MIMO MAC capacity (WF) (3 users)
Tx Rx 4 SNR20
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MIMO MAC capacity (WF) (3 users)
Ergodic capacity 4Tx X 4Rx, SNR20 4Tx X 4Rx, SNR20 4Tx X 4Rx, SNR20 4Tx X 4Rx, SNR20
sum capacity user 1 user2 user3
Max 39.60 27.57 27.58 27.78
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BC sum capacity
Tx4 Rx2 SNR20
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BC sum capacity with Power Control
Tx4 Rx2 SNR20
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BC sum capacity Coordinated Tx-Rx
Tx4 Rx2 SNR20 mj 2
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BC sum capacity
BC sum capacity Tx4, Rx2, mj 2 Tx4, Rx2, mj 2 Tx4, Rx2, mj 2
sum capacity user 1 user2
Max(SNR20) 27.03 15.67 14.81
With Power Control With Power Control With Power Control With Power Control
Max (SNR20) 28.18 16.68 17.03
Known sub-channel Known sub-channel Known sub-channel Known sub-channel
Max (SNR20) 31.79 16.61 18.43
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Conclusion

• MIMO capacity
• 1. It depends on H, the larger rank and eigen
  values of H, the
• more MIMO capacity will be.
• 2. If we understood better the knowledge of Tx
  and Rx, we can
• get higher channel capacity. With power
  control, the capacity
• will also be increased.
• 3. When water-filling is applied the capacity
  will be incresaing
• significantly.

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Main references

• 1. T. M. Cover, Elements if information theory,
  1991.
• 2. W. Yu, Iterative water-filling for Gaussian
  vector multiple access channels, 2004.
• 3. Quentin H.Spencer, Zero-forcing methods for
  downlink spatial multiplexing, 2004.

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THANK YOU!

• Any questions?