WELCOME Chen Chen

Simulation of MIMO Capacity Limits

Professor: Patric stergrd

Supervisor: Kalle Ruttik

Communications Labortory

AgendaIntroduction 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 MIMOHij is the channel gain from Txi to Rxj with Input vector: Output vector: Noise vector :

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

Water-filling algorithmThe 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 Initialize Qi = 0, i = 1 K.repeat;for j = 1 to K; end;until the desired accuracy is reached

MIMO MAC capacity Single-user water filling When we apply the water filling Qi=Q.K-user Water-filling

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

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)Single transmitter for all users

Zero-forcing methodTo 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 usersThe capacity region of a BC depends only on the Conditional distributions of

BC sum capacity1. 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 resultsErgodic capacity with different correlations (single user)

Ergodic capacity (single user)4 different set correlations magnitude coefficient

MIMO MAC sum capacity (2 users)

123 MIMO MAC sum capacity (2 users)

MIMO MAC sum capacity (2 users)

MIMO MAC sum capacity (3 users)Tx = Rx= 5SNR=20

MIMO MAC capacity (3 users)

MIMO MAC capacity (WF)(2 users)

MIMO MAC capacity (WF) (2 users)

MIMO MAC capacity (WF) (3 users)Tx= Rx =4SNR=20

MIMO MAC capacity (WF) (3 users)

BC sum capacity

Tx=4; Rx=2;SNR=20;

BC sum capacity: with Power ControlTx=4; Rx=2;SNR=20;

BC sum capacity: Coordinated Tx-Rx Tx=4; Rx=2;SNR=20;mj =2

BC sum capacity

ConclusionMIMO 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.

Main references1. 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?