1. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin1 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.eduforenza@ece.utexas.edudjlove@ece.utexas.edurheath@ece.utexas.edu

2. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin2 Outline Analytical Model Performance Results Conclusions

3. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin3 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)

4. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin4 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 N 0 =1) : transmitted signal (with )

5. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin5 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]

6. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin6 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]

7. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin7 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

8. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin8 Performance Results For AS<15 o,

9. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin9 CDF of the Mutual Information SNR = 15dB, AS<15 o, mean-AoA

10. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin10 Ergodic Capacity AS<15 o (EP=Equal Power, WF=Water-Filling)

11. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin11 Computational Time “Fast-R” is ~200 times faster than 802.11n 18taps/user (model C) and 34taps/user (model F)

12. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin12 Modifications to the Current Standard Assume Laplacian distribution defined in the domain [ ], instead of [ ] as in [1] Assume Tap-AS < 15 o, for any value of Cluster-AS. In [3]: Tap-AS Cluster-AS 13 o No evidence for AS > 13 o

13. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin13 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).

14. doc.: IEEE 802. 11-03/925r0 Submission November 2003 A.Forenza, et al - University of Texas at Austin14 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