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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Professor: Patric Östergård
Supervisor: Kalle Ruttik
Noise vector :
Hij is the channel gain from Txito Rxj with
MAC is a channel which two (or more) senders send information to a common receiver
The optimal strategy is to ‘pour energy’ (allocate energy on each channel).
In channels with lower effective noise level, more energy will be allocated.
Initialize Qi = 0, i = 1 …K.
for j = 1 to K;
until the desired accuracy is reached
Single-user water filling
When we apply the water filling Qi=Q.
The capacity region of the MAC is the closure of the set of achievable rate pairs (R1, R2).
The sum rate converges to the sum capacity.
(Q1……. Qk) converges to an optimal set of input covariance matrices.
Single transmitter for all users
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.
The capacity region of a BC depends only on the
Conditional distributions of
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)
Ergodic capacity with different correlations (single user)
4 different set correlations magnitude coefficient
MIMO MAC sum capacity (2 users)
Tx = Rx= 5
Tx= Rx =4
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
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.