1. MIMO-OFDM Beamforming for Improved Channel Estimation in 802.11n WLAN
July 2006
doc.: IEEE /0979r0
July 2006
MIMO-OFDM Beamforming for Improved Channel Estimation in n WLAN
Date:
Authors:
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Cong Shen, UCLA
Cong Shen, UCLA

2. July 2006
doc.: IEEE /0979r0
July 2006
Abstract
MIMO-OFDM Beamforming for Improved Channel Estimation in n WLAN
Cong Shen, UCLA
Cong Shen, UCLA

3. Problem Formulation System model
July 2006
doc.: IEEE /0979r0
July 2006
Problem Formulation
System model
Beamforming: SVD of the channel matrix
BF & water-filling maximize the capacity
BF & U(k) simplify the receiver detection/decoding.
Cong Shen, UCLA
Cong Shen, UCLA

4. Problem Formulation (cont’d)
July 2006
doc.: IEEE /0979r0
July 2006
Problem Formulation (cont’d)
Channel Estimation
Interpolation and Smoothing (Wiener Filtering)
the MIMO channel H(k) are ‘smooth’ over subcarriers
What happens to channel estimation when BF is incorporated?
Can we design BF such that the equivalent channel after BF, are still ‘smooth’ over subcarriers?
Yes: interpolation and smoothing, good performance
No: single-subcarrier-based CE, performance degradation
Cong Shen, UCLA
Cong Shen, UCLA

5. Challenges and Hopes SVD of a complex-valued matrix is not unique
July 2006
doc.: IEEE /0979r0
July 2006
Challenges and Hopes
SVD of a complex-valued matrix is not unique
Lemma: Valid U’s (V’s) differ by unitary rotations
Hope: pick up the right ones
Challenge: how?
Several issues when singular values become close
How to determine the corresponding singular vectors?
In some extreme situations, there is no way to maintain the smoothness, e.g., a famous example in matrix perturbation theory:
Cong Shen, UCLA
Cong Shen, UCLA

6. Our Solution SVD of a complex-valued matrix is not unique
July 2006
doc.: IEEE /0979r0
July 2006
Our Solution
SVD of a complex-valued matrix is not unique
Smoothed SVD algorithm.
Several issues when singular values become close
How to determine the corresponding singular vectors?
SSVD algorithm can automatically deal with it.
In some extreme situations, there is no way to maintain the smoothness.
When this happens, there is nothing we can do. BUT using the IEEE TGn models we found this happens very rarely. Thus it is not dominant in performance.
Cong Shen, UCLA
Cong Shen, UCLA

7. Smoothed SVD Algorithm
July 2006
doc.: IEEE /0979r0
July 2006
Smoothed SVD Algorithm
This is a piece-wise smoothing SVD algorithm for two adjacent H’s.
Assume H(1) has a valid SVD:
We want a valid SVD of H(2) such that U(2) and V(2) are obtained by some unitary rotations of U(1) and V(1):
The target is to make U(2) / V(2) close to U(1) / V(1). An easy way to obtain one unitary matrix from another one is by unitary rotation;
Exhaustive search for Wv / Wu is infeasible
Too many variables
Real-time application
Cong Shen, UCLA
Cong Shen, UCLA

8. Smoothed SVD algorithm (cont’d)
July 2006
doc.: IEEE /0979r0
July 2006
Smoothed SVD algorithm (cont’d)
Add extra (reasonable) constraints on Wv and Wu
Special unitary matrix, SU(2)
is real.
Thus, Wv / Wu only has two degrees of freedom:
Solve P and Q such that has zero off-diagonal elements
Two complex variables, two equations, closed-form solution available.
Cong Shen, UCLA
Cong Shen, UCLA

9. Extension to more than 2 antennas
July 2006
doc.: IEEE /0979r0
July 2006
Extension to more than 2 antennas
Possible ways
Use the representation theory of SU(n), and similarly reduce the number of unknowns and solve them.
Use the same argument as before, but
matrices instead of scalars
Complexity issue, only feasible for small number of antennas
Cong Shen, UCLA
Cong Shen, UCLA

10. Frequency Smoothed Beamformer Design Based on Smoothed SVD
July 2006
doc.: IEEE /0979r0
July 2006
Frequency Smoothed Beamformer Design Based on Smoothed SVD
Input:
Initialize:
Repeat:
Output: beamforming matrices
Cong Shen, UCLA
Cong Shen, UCLA

11. Statistics of the equivalent channel
July 2006
doc.: IEEE /0979r0
July 2006
Statistics of the equivalent channel
H(k) has very nice statistical behaviors
However, strictly speaking, loses almost all the nice properties
Not Gaussian
Spatially correlated
Frequency autocorrelation functions are difficult to get
For simplicity we assume to be
Gaussian
No cross-subchannel correlation
Obtain the frequency autocorrelation functions via simulation
Then, Wiener Filtering CE can be directly applied.
Cong Shen, UCLA
Cong Shen, UCLA

12. Simulation Results July 2006 2 X 2 MIMO-OFDM preamble
doc.: IEEE /0979r0
July 2006
Simulation Results
2 X 2 MIMO-OFDM preamble
OFDM structure identical to a/g (i.e., 52 subcarriers)
BICM Spatial multiplexing, with ML detection and Viterbi hard decoding
64 QAM
IEEE n channel model D
Wiener Filtering channel estimation
Cong Shen, UCLA
Cong Shen, UCLA

13. Simulation Results (2) July 2006 2 X 2 MIMO-OFDM preamble
doc.: IEEE /0979r0
July 2006
Simulation Results (2)
2 X 2 MIMO-OFDM preamble
OFDM structure identical to a/g (i.e., 52 subcarriers)
BICM Spatial multiplexing, with ML detection and Viterbi hard decoding
256 QAM
IEEE n channel model D
Wiener Filtering channel estimation
Cong Shen, UCLA
Cong Shen, UCLA