Doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at...
14
Novembe r 2003 A.For enza, et a 1 doc.: IEEE 802. 11-03/925r0 Submission Simulation of the Spatial Covariance Matrix 802.11 TGn Channel Model Special Committee November 11 th , 2003 Antonio Forenza, David J. Love and Robert W. Heath Jr. The University of Texas at Austin Department of Electrical and Computer Engineering Wireless Networking and Communications Group 1 University Station C0803 Austin, TX 78712-0240 Phone: +1-512-425-1305 Fax: +1-512-471-6512 E-mail: forenza @ ece . utexas . edu , djlove @ ece . utexas . edu , rheath @ ece . utexas . edu
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Transcript of Doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at...
November 2003
A.Forenza, et al - University of Texas at Austin
1
doc.: IEEE 802. 11-03/925r0
Submission
Simulation of the Spatial Covariance Matrix
802.11 TGn Channel Model Special Committee
November 11th, 2003
Antonio Forenza, David J. Love and Robert W. Heath Jr.
The University of Texas at AustinDepartment of Electrical and Computer EngineeringWireless Networking and Communications Group
1 University Station C0803Austin, TX 78712-0240
Phone: +1-512-425-1305Fax: +1-512-471-6512
E-mail: [email protected], [email protected], [email protected]
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Outline
• Analytical Model
• Performance Results
• Conclusions
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Analytical Model
• Each channel tap exhibits Laplacian power azimuth spectrum (PAS) in the domain [ ]:
: AoA offset with respect to the mean AoA ( ) of
the tap
: RMS Angular Spread (AS)
/2
2
1)(
ep
,
0
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Analytical Model• Received signal at the m-th sensor of the array
antenna for one channel tap:
D : normalized distance between array elements ( )
N : number of rays for one tap : complex Gaussian fading coefficient
(with variance N0=1)
: transmitted signal (with )
))sin()1(exp()()()( 01
i
N
iim mjDtgtstr
/2 dD
)(tg i
)(ts 1}|)({| 2 tsE
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Analytical Model• Correlation of the signals at the sensors m and n:
• Closed form for the correlation coefficients
(Approx: ) [5]:
: array response (column vector) for the mean azimuth AoA ( )
B : matrix with coefficients depending on the AoA and AS of the tap
: Shur-Hadamard (or elementwise) product [4]
dpnmjDR nm )())sin()(exp(),( 0,0
),()()(),( 0000 BaaR H
)( 0a
0
0
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Performance Results
• We compared 3 different models:
1) 3GPP: sum of rays (model of reference) [2]
2) 802.11n: approximation with series of Bessel
functions of the first kind [1]
3) “Fast-R”: approximation for low per-tap AS [5]
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Performance Results• Eigenvalue decomposition of the spatial
covariance matrix:
• Normalized Phase-Invariant [6]:
: dominant eigenvector for 802.11n or Fast-R
: dominant eigenvector for 3GPP
vvR
21 ,22 vvNPI
1v
2v
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Performance Results• For AS<15o, %2.0NPI
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
CDF of the Mutual Information
• SNR = 15dB, AS<15o, mean-AoA ],[
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Ergodic Capacity
• AS<15o (EP=Equal Power, WF=Water-Filling)
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Computational Time• “Fast-R” is ~200 times faster than 802.11n
18taps/user (model C) and 34taps/user (model F)
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Modifications to the Current Standard
• Assume Laplacian distribution defined in the domain
[ ], instead of [ ]
as in [1]
• Assume Tap-AS < 15o, for any value of Cluster-AS.
In [3]: Tap-AS Cluster-AS 13o
No evidence for AS > 13o
, ),180,min( )180,min(
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
Conclusions
• The “Fast-R” method is a practical alternative to computing the covariance R using [1].
• The “Fast-R” method generates covariances that are close to that generated by [1], when the per-tap AS is less than 15 degrees.
• The computational reduction is significant (factor of ~200).
November 2003
A.Forenza, et al - University of Texas at Austin
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doc.: IEEE 802. 11-03/925r0
Submission
References[1] IEEE 802 11-03/161r2, TGn Indoor MIMO WLAN Channel Models[2] 3GPP TS Group,”Spatial Channel Model, SCM-121 Text V3.3, Spatial
Channel Model AHG (Combined ad-hoc from 3GPP and 3GPP2), March 14, 2003
[3] Q. Li, K.Yu, M. Ho, J. Lung, D. Cheung, and C.Prettie, “On the tap angular spread and Kronecker structure of the WLAN channel model,” Presentation, July 2003.
[4] R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, New York,
March 2001.[5] A.Forenza, D.J.Love, and R.W.Heath Jr., “Simulation of the Spatial
Covariance Matrix for MIMO Systems”, WNCG Tech. Report, Sept.2003 (also submitted to VTC Spring 2004).
[6] D.J.Love, and R.W.Heath Jr., “Equal Gain Transmission in Multiple-Input Multiple-Output Wireless Systems”, IEEE Transactions on Communications, vol.51, n.7, July 2003
