1. Channel Coherence Time
April 2007
doc.: IEEE /0570r0
July 2009
Channel Coherence Time
Date:
Authors:
Eldad Perahia, Intel Corporation
Eldad Perahia, Intel Corporation

2. April 2007
doc.: IEEE /0570r0
July 2009
Introduction
For features like beamforming, SDMA, etc. that require feedback, the coherence time of the channel is the actual parameter that is important in determining the timeliness of the feedback
Objective of this presentation is to compute the coherence time of the measured data in [1] and compare it to the 11n channel model
Eldad Perahia, Intel Corporation
Eldad Perahia, Intel Corporation

3. July 2009
Analysis Methodology
In the 11n channel model, Doppler was set to 1.2 km/hour (which sets the coherence time of the channel) but the estimate of Doppler was based on the amplitude of measured data
Doppler function resulted in a coherence time of 57 ms based on equation in [2]
Coherence time typically defined as time over which the time correlation function is above 0.5 [3]
We will examine autocorrelation functions of the 11n channel model and the measured data [1] using both complex data and amplitude data
As will be shown, Doppler and coherence time analysis needs to be based on complex data
Eldad Perahia, Intel Corporation

4. TGn Channel Model Example
July 2009
TGn Channel Model Example
Example of the time progression of a single subcarrier of 11n channel model D
Eldad Perahia, Intel Corporation

5. Autocorrelation of TGn Channel Model (1/2)
July 2009
Autocorrelation of TGn Channel Model (1/2)
Autocorrelation of complex data at 0.5 = 54 ms
Coherence time computed by equation in [2] = 57 ms
Very close agreement
Eldad Perahia, Intel Corporation

6. Autocorrelation of TGn Channel Model (2/2)
July 2009
Autocorrelation of TGn Channel Model (2/2)
Autocorrelation of the amplitude of the data results in long autocorrelation time ( )
Phase of the data is critical to accurate computation of the autocorrelation function
0.5 = 35 ms
Eldad Perahia, Intel Corporation

7. Example of Measured Data
July 2009
Example of Measured Data
Measured data is comprised of 3x3 link
This is an example of the time progression of a single subcarrier of a single Tx and Rx antenna combination
i.e. H[1,2] for subcarrier 1
Eldad Perahia, Intel Corporation

8. Autocorrelation of Complex Measured Data
July 2009
Autocorrelation of Complex Measured Data
Eldad Perahia, Intel Corporation

9. Autocorrelation of Measured Data
July 2009
Autocorrelation of Measured Data
Top figure is the autocorrelation function of the amplitude of the data
Bottom figure is the autocorrelation function of the phase of the data
In comparison to the previous slide, in this example the phase of the data dominates the autocorrelation function
Eldad Perahia, Intel Corporation

10. July 2009
Data Processing (1/2)
For each pair of Tx and Rx antennas in the 3x3 link, an autocorrelation function was computed for time progression of a each subcarrier of the complex data, as illustrated in slide 8
Time over which the time correlation function is above 0.5 (coherence time) was found from these autocorrelation functions
Eldad Perahia, Intel Corporation

11. July 2009
Data Processing (2/2)
These values were grouped to form a CDF of coherence times for each link
CDFs were computed for the data for all the links in [1]
90% probability and 50% probability points are examined
Eldad Perahia, Intel Corporation

12. Coherence Time Results
July 2009
Coherence Time Results
As described in [1], the type of motion between the transmitter and receiver is categorized as follows
someone waving their hands in front of the device at both ends of the link (Double Motion, DM)
someone waving their hands in front of the device at one end of the link (Single Motion, SM)
many people known to be walking around (People Motion, PM)
typical motion in office environment (Light Motion, LM)
90% probability coherence times are averaged together for links with the same type of motion
50% probability coherence times are averaged together for links with the same type of motion
Eldad Perahia, Intel Corporation

13. July 2009
Conclusion
Channel coherence time of the measured data is twice as long as the 11n channel even in the highest motion case where someone was waving their hands in front of the device at both ends of the link
In typical office environment, the channel coherence time was 5-10x longer than the 11n channel model
11ac channel model must be modified to better match measured channel coherence times
We welcome further measurements from other companies in order to properly model channel coherence time for TGac channel model
Eldad Perahia, Intel Corporation

14. July 2009
References
[1] Perahia, E., Kenney., T., Stacey, R., et. al., Investigation into the n Doppler Model, IEEE /538r0, May 11, 2009
[2] Erceg, V., Schumacher, L., Kyritsi, P., et al., TGn Channel Models, IEEE /940r4, May 10, 2004
[3] Rappaport, T. S., “Wireless Communications: Principles and Practice,” Prentice Hall, 1996
Eldad Perahia, Intel Corporation