November 2003 doc.: IEEE 802. 11-03/925r0 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 Submission Slide 1 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Outline • Analytical Model • Performance Results • Conclusions Submission Slide 2 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Analytical Model • Each channel tap exhibits Laplacian power − π , π azimuth spectrum (PAS) in the domain [ ]: 1 − φ σ 2 / φ = p ( ) e σ 2 φ φ : AoA offset with respect to the mean AoA ( ) of 0 the tap σ : RMS Angular Spread (AS) Submission Slide 3 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Analytical Model • Received signal at the m -th sensor of the array antenna for one channel tap: N ∑ = ⋅ ⋅ − φ − φ r ( t ) s ( t ) g ( t ) exp( jD ( m 1 ) sin( )) m i 0 i = i 1 D : normalized distance between array elements D = π / λ ( ) 2 d N : number of rays for one tap : complex Gaussian fading coefficient g i ( t ) (with variance N 0 =1 ) 2 = : transmitted signal (with ) s ( t ) E {| s ( t ) | } 1 Submission Slide 4 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Analytical Model • Correlation of the signals at the sensors m and n : +∞ ≈ ∫ [ ] φ σ − φ − φ ⋅ φ φ R ( , ) exp( jD ( m n ) sin( )) p ( ) d 0 0 m , n − ∞ • Closed form for the correlation coefficients φ ≈ (Approx: ) [5]: 0 [ ] φ σ ≈ φ ⋅ φ ⊗ φ σ H R ( , ) a ( ) a ( ) B ( , ) 0 0 0 0 φ φ : array response (column vector) for the mean azimuth AoA ( ) a ( ) 0 0 B : matrix with coefficients depending on the AoA and AS of the tap ⊗ : Shur-Hadamard (or elementwise) product [4] Submission Slide 5 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 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] Submission Slide 6 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Performance Results • Eigenvalue decomposition of the spatial covariance matrix: ⋅ = λ ⋅ R v v • Normalized Phase-Invariant [6]: = − ⋅ < > NPI 2 2 v 1 , v 2 v : dominant eigenvector for 802.11n or Fast-R 1 v : dominant eigenvector for 3GPP 2 Submission Slide 7 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Performance Results ≈ NPI 0 . 2 % • For AS<15 o , Submission Slide 8 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 CDF of the Mutual Information ∈ − π π • SNR = 15dB, AS<15 o , mean-AoA [ , ] Submission Slide 9 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Ergodic Capacity • AS<15 o (EP=Equal Power, WF=Water-Filling) Submission Slide 10 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Computational Time • “Fast-R” is ~200 times faster than 802.11n 18taps/user (model C) and 34taps/user (model F) Submission Slide 11 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 Modifications to the Current Standard • Assume Laplacian distribution defined in the domain − π , π min( φ ∆ − min( φ ∆ [ ], instead of [ , 180 ) ] , 180 ), 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 Submission Slide 12 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 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). Submission Slide 13 A.Forenza, et al - University of Texas at Austin
November 2003 doc.: IEEE 802. 11-03/925r0 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 Submission Slide 14 A.Forenza, et al - University of Texas at Austin
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