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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

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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 2014 2

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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

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

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

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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

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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

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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

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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

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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 2014 10

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Asymptotic behavior with many antennas N R =1, MC estimate of consistency time N R =1, Lower bound on consistency time ICC 201411

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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 201412

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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 201413

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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 201414

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Remarks The bound is loose for N R large ICC 201415 N T =16,N R =4 N T =40,N R =4 N T =4,N R =1 N T =10, N R =1

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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 ICC 201416

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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 201417

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Questions? Thank You ICC 201418