Simulation of the Spatial Covariance Matrix 802.11 TGn Channel - - PowerPoint PPT Presentation

November 2003

A.Forenza, et al - University of Texas at Austin Slide 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 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

November 2003

A.Forenza, et al - University of Texas at Austin Slide 2

doc.: IEEE 802. 11-03/925r0

Submission

Outline

• Analytical Model
• Performance Results
• Conclusions

November 2003

A.Forenza, et al - University of Texas at Austin Slide 3

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)

σ φ

σ φ

/ 2

2 1 ) (

−

= e p

φ

σ

π π, −

φ

November 2003

A.Forenza, et al - University of Texas at Austin Slide 4

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( ) ( ) ( ) (

1 i N i i m

m jD t g t s t r φ φ − − ⋅ ⋅ =

∑

=

λ π / 2 d D =

) (t gi

) (t s

1 } | ) ( {|

2 =

t s E

November 2003

A.Forenza, et al - University of Texas at Austin Slide 5

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]

[ ]

φ φ φ φ σ φ d p n m jD R

n m

) ( )) sin( ) ( exp( ) , (

,

⋅ − − ≈ ∫

+∞ ∞ −

[ ]

) , ( ) ( ) ( ) , ( σ φ φ φ σ φ B a a R ⊗ ⋅ ≈

H

) ( φ a

⊗

≈ φ

φ

November 2003

A.Forenza, et al - University of Texas at Austin Slide 6

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 Slide 7

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

v v R ⋅ = ⋅ λ

> < ⋅ − =

2 1,

2 2 v v NPI

1

v

2

v

November 2003

A.Forenza, et al - University of Texas at Austin Slide 8

doc.: IEEE 802. 11-03/925r0

Submission

Performance Results

• For AS<15o,

% 2 . ≈ NPI

November 2003

A.Forenza, et al - University of Texas at Austin Slide 9

doc.: IEEE 802. 11-03/925r0

Submission

CDF of the Mutual Information

• SNR = 15dB, AS<15o, mean-AoA

] , [ π π − ∈

November 2003

A.Forenza, et al - University of Texas at Austin Slide 10

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 Slide 11

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 Slide 12

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

π π, −

), 180 , min( φ ∆ − ) 180 , min( φ ∆

≈ ≈

November 2003

A.Forenza, et al - University of Texas at Austin Slide 13

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 Slide 14

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