Null Space Mismatch in Cooperative Multipoint Cellular Networks

1. Null Space Mismatch in Cooperative Multipoint Cellular Networks AlexandrosManolakos Wireless Systems Laboratory, Electrical Engineering Stanford University Joint work with: Prof. Yair Noam, Prof. Andrea Goldsmith

2. Motivation • Cooperative Multipoint has emerged as an important feature of LTE-A • Obtaining global CSI is impractical: prohibitive system overhead, processing delays • CSI is typically available only inside a BSG • How often should we update the CSI estimate? Out-of-Group interference (OGI) RA-ENST algorithm

3. System Model Out of Group Interference UE BSG1 BSG2 Interference Level The received signal at UE1: The antennas of BSG2 and UE1.

4. Toy Example RA-ENST • Consider NT = 3 and NR = 1. Then, It suffices to learn these elements

5. Toy Example • Consider NT = 3 and NR = 1 BSG2 BSG1 Number of cycles needed:

6. Null Space variations • What is the null space consistency time? • What is the relation between the null space consistency time and channelcoherence time? • How often should weperform a RA-ENST sweep? eNodeB eNodeB

7. Precoding Matrix Equivalence • Let two precoding matrices. When can we say they are equivalent? • Definition 1: • For any transmitted signal interference is the same • i.e., • Definition 2: • The maximum interference is the same • i.e.,

8. Null Space mismatch Definition: The Null Space Mismatch of from the null space of is worst-case interference Interference temperature Normalized worst-case interference reduction

9. Null Space Consistency Time • Threshold in tolerable interference • Denote and • Definition: TheNull Space Consistency time is The time needed for the normalized worst case interference to reach a maximum threshold

10. Main Result • Assume evolves as a Gaussian process with time correlation function , then where For Rayleigh fading with Jakes’ model: We can now get a lower bound on the null space consistency time

11. “Asymptotic” behavior with many antennas NR=1, Lower bound on consistency time NR=1, MC estimate of consistency time

12. Numerical Results of RA-ENST in Rayleigh fading • NT= 6 and NR = 2 • Rayleigh fading Jakes’model • RA-ENST uses 1 msecfeedback

13. Numerical Results of RA-ENST in Rayleigh fading • NT= 8 and NR = 1 • Rayleigh fading Jakes’model • RA-ENST uses 1 msecfeedback

14. Numerical Results of RA-ENST in Rician fading • NT = 6 and NR = 2 • Rician fading Jakes’model, Fd= 3 Hz • RA-ENST uses 1msec feedback

15. Remarks NT=4,NR=1 NT=10, NR=1 NT=40,NR=4 NT=16,NR=4 The bound is loose for NR large

16. Main Takeaways • What is the null space consistency time? • The time needed the normalized interference to reach a predefined threshold • How often should we update the null space estimate? • In Rayleigh fading, with a perfect and instantaneous estimate, the update frequency should be as often as 3 - 8 times faster than the maximum Doppler frequency • How often should we perform a RA-ENST sweep? • Even faster than the above estimate () due to the noisy measurements

17. Ongoing Research • Exact formula of the null space consistency time • Understand how the null space changes in massive MIMO as a function of the antenna configuration • Approximate and fast null space learning in massive MIMO

18. Questions? Thank You