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WELCOME. Chen Chen. Simulation of MIMO Capacity Limits. Professor: Patric Ö sterg å rd Supervisor: Kalle Ruttik Communications Labortory. Agenda. Introduction to Multiple-In Multiple-Out(MIMO) MIMO Multiple Access Channel(MAC) Water-filling algorithm(WF) MIMO Broadcast Channel(BC)

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Chen Chen

Simulation of mimo capacity limits
Simulation of MIMO Capacity Limits

Professor: Patric Östergård

Supervisor: Kalle Ruttik

Communications Labortory


  • 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

What is mimo
What is MIMO

Input vector:

Output vector:

Noise vector :

Hij is the channel gain from Txito Rxj with

Mimo mac uplink
MIMO MAC (uplink)

MAC is a channel which two (or more) senders send information to a common receiver

Water filling algorithm
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.

Iterative water filling algorithm
Iterative water filling algorithm

Initialize Qi = 0, i = 1 …K.


for j = 1 to K;


until the desired accuracy is reached

Mimo mac capacity
MIMO MAC capacity

Single-user water filling

K-user Water-filling

When we apply the water filling Qi=Q.

Mimo mac capacity region
MIMO MACcapacity region

The capacity region of the MAC is the closure of the set of achievable rate pairs (R1, R2).

Mac sum capacity region wf
MAC sum capacity region (WF)

The sum rate converges to the sum capacity.

(Q1……. Qk) converges to an optimal set of input covariance matrices.

Mimo bc downlink
MIMO BC (downlink)

Single transmitter for all users

Zero forcing method
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.

Bc capacity region for 2 users
BC capacity region for 2 users

The capacity region of a BC depends only on the

Conditional distributions of

Bc sum capacity
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)

Examples of simulation results
Examples of simulation results

Ergodic capacity with different correlations (single user)

Ergodic capacity single user
Ergodic capacity (single user)

4 different set correlations magnitude coefficient

Bc sum capacity1
BC sum capacity




Bc sum capacity with power control
BC sum capacity: with Power Control




Bc sum capacity coordinated tx rx
BC sum capacity: Coordinated Tx-Rx




mj =2


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


Main references
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.

Thank you


Any questions?