1. On Tap Angular Spread and Kronecker Structure of WLAN Channel Models
Month 2002
doc.: IEEE /xxxr0
July 2003
On Tap Angular Spread and Kronecker Structure of WLAN Channel Models
Qinghua Li (Intel)
Kai Yu (KTH)
Minnie Ho (Intel)
Jeng Lung (Intel)
David Cheung (Intel)
Cliff Prettie (Intel)
Q. Li (Intel), K. Yu (KTH), et al
John Doe, His Company

2. Outline Motivation Measurement Environments Data Processing
Month 2002
doc.: IEEE /xxxr0
July 2003
Outline
Motivation
Measurement Environments
Data Processing
FD-SAGE algorithm
Estimation performance in synthetic channels
RMS Angular Spread
Cluster identification
Tap angular spread
Cluster angular spread
Verification of Kronecker Product Structure
Q. Li (Intel), K. Yu (KTH), et al
John Doe, His Company

3. Verification of Two Assumptions
July 2003
Verification of Two Assumptions
Tap angular spread — an important modeling assumption
5o tap angular spread
One path per tap within one cluster
Q. Li (Intel), K. Yu (KTH), et al

4. Kronecker Product Structure for Spatial Correlation
July 2003
Kronecker Product Structure for Spatial Correlation
The spatial correlation matrix of each tap is assumed to the Kronecker product of the transmit and receive correlation matrixes.
The spatially correlated channel matrix is given by
Q. Li (Intel), K. Yu (KTH), et al

5. Measurements Typical large office
July 2003
Measurements
Typical large office
Access point antenna is mounted under ceiling
Station antennas could be blocked by cubicle walls and file cabinets
3’ x 6’ and 1.5’ x 1.5’ antenna crosses 6’
AP (mounted under ceiling)
STA (at desk level)
Q. Li (Intel), K. Yu (KTH), et al

6. Signal Processing Algorithm
July 2003
Signal Processing Algorithm
Joint estimation of delay, angle, and channel gain
Maximum likelihood
Space-alternating generalized expectation-maximization (SAGE) : grouped coordinate ascent search algorithm
where
Q. Li (Intel), K. Yu (KTH), et al

7. Signal Processing Algorithm
July 2003
Signal Processing Algorithm
SAGE Performance in synthetic channels
About 3o angle resolution
o : synthetic
x : estimated 12 10 8
Path Magnitude 6 4 2
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200 50
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Excess Delay (ns)
Incident Angle ( o )
Q. Li (Intel), K. Yu (KTH), et al

8. Cluster Identification
July 2003
Cluster Identification
Power delay profile
Single exponential decay curve
RMS delay spread about 50 ns
-80
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-110
Average Received Power (dB)
-120
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Excess Delay (ns)
Q. Li (Intel), K. Yu (KTH), et al

9. Cluster Identification
July 2003
Cluster Identification
3D multipath profile 50
100
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200
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300
350 1 2 3 4 5
x 10 -3
Path Magnitude
Incident Angle ( o )
Excess Delay (ns)
Q. Li (Intel), K. Yu (KTH), et al

10. Time Slice of Multipath Profile
July 2003
Time Slice of Multipath Profile
Multipath arrivals at delay 60 ns, 90 ns, and 120 ns 50
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250
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350 2 4
x 10 -3
60 ns
90 ns
120 ns
Incident Angle (o)
Q. Li (Intel), K. Yu (KTH), et al

11. Cluster Identification
July 2003
Cluster Identification
2D filtering in angle-delay domain
Six clusters are identified
Incident Angle (o)
Q. Li (Intel), K. Yu (KTH), et al

12. Month 2002
doc.: IEEE /xxxr0
July 2003
RMS Angular Spread
Two sets of measurements with 50ns RMS delay spread, 112 taps, and 12 clusters
Cumulative distribution function of tap angular spread : mean 13.2o
Average cluster angular spread : 14.6o
Conclusion : Cluster AS ≈ Tap AS 5 10 15 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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0.9 1
CDF
The second is the same movie but cut to 17 to 22 ns in time (takes 5 seconds to watch in real-time).
These are probably the most visually appealing movies we have – nice distinctive wavefront arrivals from a few different directions.  Some things you can note as you show the movie: the movies were generated from data collected over 4 STA (desktop) positions and 37x37 AP (ceiling) positions in the 2-8 GHz band at a distance of about 3.5m, in SC12, 3rd floor (cubicle environment).  The 4 STA positions are at the corners of a 6” square.  The 37x37 AP positions are spaced over a grid with 0.5” spacing (total travel of 1.5’x1.5’).  The movie consists of 5476 actual vector network analyzer measurements (4*37*37) taken using an automated system (robotic positioners, etc.).  To generate the movie we took the inverse Fourier transform of each measurement (resulting in the impulse response at each point).  Each frame of the movie is a slice in time of all the impulse responses, the colors representing the intensity of the energy (in volts) at that point on the array. 
RMS angular spread for each tap (o)
Q. Li (Intel), K. Yu (KTH), et al
John Doe, His Company

13. Covariance Matrices Assume N x M channel matrix H, we estimate
July 2003
Covariance Matrices
Assume N x M channel matrix H, we estimate
Channel covariance matrix for tap L:
Covariance matrix at Tx for tap L:
Covariance matrix at Rx for tap L:
Q. Li (Intel), K. Yu (KTH), et al

14. Mismatches in Kronecker Structure
July 2003
Mismatches in Kronecker Structure
To evaluate the Kronecker Structure of MIMO channel covariance matrix, we define:
Normalized Residual for each tap
Wideband Model Error
Q. Li (Intel), K. Yu (KTH), et al

15. Measurement Results Normalized Residuals for data set 14 July 200330
Data set 14, 2x2 case 25 20
Normalized Residuals (%) 15 10 5 30 40 50 60 70 80 90
100
110
120
Tap Index
Q. Li (Intel), K. Yu (KTH), et al

16. Wideband Model Errors Error increases with number of antennas
July 2003 1 2 3 4 5 6 7 8 10 15 20 25
Number of Receive Antenna Elements
Wideband Model Error (%)
Data set 14: NLOS
Data set 7: roughly LOS
Wideband Model Errors
Error increases with number of antennas
Q. Li (Intel), K. Yu (KTH), et al

17. Summary Large array measurements
Month 2002
doc.: IEEE /xxxr0
July 2003
Summary
Large array measurements
Joint angle, delay, and gain estimation (SAGE)
Multiple clusters may arrive within few taps and they can’t be identified from a single exponential decay curve
Cluster Angular Spread ≈ Tap Angular Spread.
Model error introduced by Kronecker structure increases with the number of antennas
Q. Li (Intel), K. Yu (KTH), et al
John Doe, His Company

18. Appendix Power delay profile (STN) Single exponential decay curve
July 2003
Appendix
Power delay profile (STN)
Single exponential decay curve
RMS delay spread about 54 ns
-80
-90
-100
-110
Average Received Power (dB)
-120
-130
-140
-150
200
400
600
800
1000
1200
1400
1600
Time Delay (ns)
Q. Li (Intel), K. Yu (KTH), et al

19. Appendix (Cont’d) 3D multipath profile July 200350
100
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200
250
300
350
400 5 10 15 20 25 30 35 1 2 3 4
x 10 -3
Path Magnitude
Excess Delay (ns)
Incident Angle ( o )
Q. Li (Intel), K. Yu (KTH), et al

20. Appendix (Cont’d) 2D filtering in angle-delay domain
July 2003
Appendix (Cont’d)
2D filtering in angle-delay domain
Manually identified 7 clusters together with 3D-image
Q. Li (Intel), K. Yu (KTH), et al

21. Month 2002
doc.: IEEE /xxxr0
July 2003
Appendix (Cont’d)
Cumulative distribution function of tap angular spread ; mean value: 11.5o
Average cluster angular spread : 14.1o
Conclusion : Cluster AS ≈ Tap AS 1
0.9
0.8
0.7
0.6
The second is the same movie but cut to 17 to 22 ns in time (takes 5 seconds to watch in real-time).
These are probably the most visually appealing movies we have – nice distinctive wavefront arrivals from a few different directions.  Some things you can note as you show the movie: the movies were generated from data collected over 4 STA (desktop) positions and 37x37 AP (ceiling) positions in the 2-8 GHz band at a distance of about 3.5m, in SC12, 3rd floor (cubicle environment).  The 4 STA positions are at the corners of a 6” square.  The 37x37 AP positions are spaced over a grid with 0.5” spacing (total travel of 1.5’x1.5’).  The movie consists of 5476 actual vector network analyzer measurements (4*37*37) taken using an automated system (robotic positioners, etc.).  To generate the movie we took the inverse Fourier transform of each measurement (resulting in the impulse response at each point).  Each frame of the movie is a slice in time of all the impulse responses, the colors representing the intensity of the energy (in volts) at that point on the array. 
Cumulative Distribution Function
0.5
0.4
0.3
0.2
0.1 5 10 15 20 25 30
Angular Spread for each tap (degree)
Q. Li (Intel), K. Yu (KTH), et al
John Doe, His Company