July 2006

Cong Shen, UCLA

Slide 1

doc.: IEEE 802.11-06/0979r0

Submission

MIMO-OFDM Beamforming for Improved Channel Estimation in 802.11n WLAN

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Date: 2006-07-18

Name Company Address Phone email Cong Shen University California,

Los Angeles 420 Westwood Plaza, Los Angeles, CA 90066

+310-206-6718 congshen@ee.ucla.edu

Michael P. Fitz University California, Los Angeles

420 Westwood Plaza, Los Angeles, CA 90066

Authors:

July 2006

Cong Shen, UCLA

Slide 2

doc.: IEEE 802.11-06/0979r0

Submission

Abstract

• MIMO-OFDM Beamforming for Improved Channel

Estimation in 802.11n WLAN

July 2006

Cong Shen, UCLA

Slide 3

doc.: IEEE 802.11-06/0979r0

Submission

Problem Formulation

• System model

• Beamforming: SVD of the channel matrix– BF & water-filling maximize the capacity

– BF & U(k) simplify the receiver detection/decoding.

Beamformer MIMO ChannelReceiverDetection

( , )k lX

( , )k lZ

( , )k lY

( )kV ( )kH

( , )k lN

k-th subcarrier, l-th time interval,2Tx, 2Rx

July 2006

Cong Shen, UCLA

Slide 4

doc.: IEEE 802.11-06/0979r0

Submission

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

July 2006

Cong Shen, UCLA

Slide 5

doc.: IEEE 802.11-06/0979r0

Submission

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:

1 0 1 0

0 1 0 1

1 1 11

1 1 12

A V

A E V

July 2006

Cong Shen, UCLA

Slide 6

doc.: IEEE 802.11-06/0979r0

Submission

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 802.11 TGn models we found this happens very rarely. Thus it is not dominant in performance.

July 2006

Cong Shen, UCLA

Slide 7

doc.: IEEE 802.11-06/0979r0

Submission

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

(1) (1) (1) (1)HΛ U H V

(2) (1) , (2) (1) U VU U W V V W

July 2006

Cong Shen, UCLA

Slide 8

doc.: IEEE 802.11-06/0979r0

Submission

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.

2 2

* * where 1A

* *1 1* *2 2

1 1(2) (1) (1 ) and (2) (1) (1 )

1 1

Q PQ Q P P

Q P

U U V V

(2) (2) (2)HU H V

July 2006

Cong Shen, UCLA

Slide 9

doc.: IEEE 802.11-06/0979r0

Submission

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

1-2

1-2

1-2

1-2

HH

U

H

HH

V

H

(I + Q Q) 0I QW =

Q I0 (I + QQ )

(I + P P) 0I PW =

P I0 (I + PP )

July 2006

Cong Shen, UCLA

Slide 10

doc.: IEEE 802.11-06/0979r0

Submission

Frequency Smoothed Beamformer Design Based on Smoothed SVD

Input:

Initialize:

Repeat:

Output: beamforming matrices

( ), 1, pk k DH

[ (1), (1), (1)] svd (1)U Λ V H

for 2 to dopi D

[ ( ), ( ), ( )] ssvd ( 1), ( ), ( 1), ( 1) ;i i i i i i i U Λ V H H U V

end for ( ), 1, pk k DV

July 2006

Cong Shen, UCLA

Slide 11

doc.: IEEE 802.11-06/0979r0

Submission

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.

( )kH

( )kH

July 2006

Cong Shen, UCLA

Slide 12

doc.: IEEE 802.11-06/0979r0

Submission

Simulation Results

• 2 X 2 MIMO-OFDM preamble

• OFDM structure identical to 802.11a/g (i.e., 52 subcarriers)

• BICM Spatial multiplexing, with ML detection and Viterbi hard decoding

• 64 QAM

• IEEE 802.11n channel model D

• Wiener Filtering channel estimation

6 8 10 12 14 16 18 20 22 24 2610

-5

10-4

10-3

10-2

10-1

100

SNR per receive antenna, dB

Bit

Err

or R

ate

64QAM BICM MIMO-OFDM, channel D

perfect CSI at the receiverFSB with smoothing across all subcarriersno FSB with single-subcarrier CE

July 2006

Cong Shen, UCLA

Slide 13

doc.: IEEE 802.11-06/0979r0

Submission

Simulation Results (2)

• 2 X 2 MIMO-OFDM preamble

• OFDM structure identical to 802.11a/g (i.e., 52 subcarriers)

• BICM Spatial multiplexing, with ML detection and Viterbi hard decoding

• 256 QAM

• IEEE 802.11n channel model D

• Wiener Filtering channel estimation

12 14 16 18 20 22 24 26 2810

-5

10-4

10-3

10-2

10-1

100

SNR per receive antenna, dB

Bit

Err

or R

ate

256QAM BICM MIMO-OFDM, channel D

perfect CSI at the receiverFSB with smoothing across all subcarriersno FSB with single-subcarrier CE