On Tap Angular Spread and Kronecker Structure of WLAN Channel Models Month 2002 doc.: IEEE 802.11-02/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

Outline Motivation Measurement Environments Data Processing Month 2002 doc.: IEEE 802.11-02/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

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

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

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

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

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 2 300 250 400 200 350 150 300 100 250 200 50 150 100 Excess Delay (ns) Incident Angle ( o ) Q. Li (Intel), K. Yu (KTH), et al

Cluster Identification July 2003 Cluster Identification Power delay profile Single exponential decay curve RMS delay spread about 50 ns -80 -90 -100 -110 Average Received Power (dB) -120 -130 -140 -150 200 400 600 800 1000 1200 1400 1600 Excess Delay (ns) Q. Li (Intel), K. Yu (KTH), et al

Cluster Identification July 2003 Cluster Identification 3D multipath profile 50 100 150 200 250 300 350 1 2 3 4 5 x 10 -3 Path Magnitude Incident Angle ( o ) Excess Delay (ns) Q. Li (Intel), K. Yu (KTH), et al

Time Slice of Multipath Profile July 2003 Time Slice of Multipath Profile Multipath arrivals at delay 60 ns, 90 ns, and 120 ns 50 100 150 200 250 300 350 2 4 x 10 -3 60 ns 90 ns 120 ns Incident Angle (o) Q. Li (Intel), K. Yu (KTH), et al

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

Month 2002 doc.: IEEE 802.11-02/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 0.8 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

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

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

Measurement Results Normalized Residuals for data set 14 July 2003 30 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

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

Summary Large array measurements Month 2002 doc.: IEEE 802.11-02/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

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

Appendix (Cont’d) 3D multipath profile July 2003 50 100 150 200 250 300 350 400 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

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

Month 2002 doc.: IEEE 802.11-02/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