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
Slide 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 ICC 2014 2
Slide 3
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
Slide 4
Toy Example RA-ENST Consider N T = 3 and N R = 1. Then, It
suffices to learn these elements ICC 20144
Slide 5
Number of cycles needed: Consider N T = 3 and N R = 1 Toy
Example BSG 1 BSG 2 ICC 20145
Slide 6
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
Slide 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., ICC 20147
Slide 8
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
Slide 9
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
Slide 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 ICC 2014 10
Slide 11
Asymptotic behavior with many antennas N R =1, MC estimate of
consistency time N R =1, Lower bound on consistency time ICC
201411
Slide 12
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
Slide 13
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
Slide 14
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
Slide 15
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
Slide 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 ICC 201416
Slide 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 ICC 201417