Null Space Mismatch in Cooperative Multipoint Cellular Networks Joint work with: Prof. Yair Noam, Prof. Andrea Goldsmith Alexandros Manolakos Wireless Systems Laboratory, Electrical Engineering Stanford University ICC 20141

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 ICC

System Model The received signal at UE 1 : The antennas of BSG 2 and UE 1. BSG 1 BSG 2 UE Interference Level Out of Group Interference ICC 20143

Toy Example RA-ENST Consider N T = 3 and N R = 1. Then, It suffices to learn these elements ICC 20144

Number of cycles needed: Consider N T = 3 and N R = 1 Toy Example BSG 1 BSG 2 ICC 20145

Null Space variations What is the null space consistency time? What is the relation between the null space consistency time and channel coherence time? How often should we perform a RA-ENST sweep? eNodeB ICC 20146

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., ICC 20147

Null Space mismatch Definition: The Null Space Mismatch of from the null space of is Normalized worst-case interference reduction Interference temperature worst-case interference ICC 20148

Null Space Consistency Time Threshold in tolerable interference Denote and Definition: The Null Space Consistency time is The time needed for the normalized worst case interference to reach a maximum threshold ICC 20149

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 ICC

“Asymptotic” behavior with many antennas N R =1, MC estimate of consistency time N R =1, Lower bound on consistency time ICC

Numerical Results of RA-ENST in Rayleigh fading N T = 6 and N R = 2 Rayleigh fading Jakes’ model RA-ENST uses 1 msec feedback ICC

Numerical Results of RA-ENST in Rayleigh fading N T = 8 and N R = 1 Rayleigh fading Jakes’ model RA-ENST uses 1 msec feedback ICC

Numerical Results of RA-ENST in Rician fading N T = 6 and N R = 2 Rician fading Jakes’ model, F d = 3 Hz RA-ENST uses 1msec feedback ICC

Remarks The bound is loose for N R large ICC N T =16,N R =4 N T =40,N R =4 N T =4,N R =1 N T =10, N R =1

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 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 ICC

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 ICC

Questions? Thank You ICC