II International Workshop on Challenges and Trends on Broadband Wireless Mobile Access Networks – Beyond LTE-A

1. Associate Institute for Signal Processing Technische Universität München
Strategies to Combat Pilot Contamination in
Massive MIMO Systems
Michael Joham, David Neumann, and Wolfgang Utschick
Associate Institute for Signal Processing
Technische Universität München
2nd International Workshop on Challenges and Trends
of Broadband Wireless Mobile Access Networks — Beyond
LTE-A

2. Fifth Generation Wireless Systems (5G): Goals
◮ higher data rates
◮ better coverage
◮ lower latency
◮ lower battery consumption
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3. Fifth Generation Wireless Systems (5G): Approaches
◮ small (pico) cells
◮ device-to-device (D2D) communication
◮ multi-hop networks
◮ mm-wave technology
◮ massive MIMO
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4. Massive MIMO Setup
M antennas K users
◮ Large number of base station antennas
◮ About two orders of magnitude more antennas than users:
M ≫ K
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5. Law of Large Numbers
Let x ∈ CN and y ∈ CN be random with N i.i.d. entries.
Due to law of large numbers,
◮ limN→∞
1
N
1Tx = limN→∞
1
N
PN
i=1 xi
a.s.
= E[xi]
◮ limN→∞
1
N kxk22
a.s.
= E[|xi|2]
zero-mean x: limN→∞
1
N kxk22
a.s.
= var(xi)
◮ limN→∞
1
N yHx
a.s.
= E[y∗
i ]E[xi]
zero-mean x: limN→∞
1
N yHx
a.s.
= 0
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6. Benefits of Massive MIMO
Array Gain
M
SNR
Law of Large Numbers
◮ Asymptotic orthogonality: 1
M hHi
hj → 0
◮ Channel hardening: 1
M khik22
→ 2 for hi ∼ NC(0, 2I)
⇒ Robust spacial multiplexing with simple signal
processing methods
[Marzetta, 2010, Mohammed and Larsson, 2013]
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7. System Model
Uplink
yul
i =
XL
j=1
Hijsul
j + nul
i
Downlink: Linear Precoding
ydl
j =
XL
i=1
HT
ijWisdl
i + ndl
Wi = [wi1, . . . ,wiK] and Hij = [hij1, . . . ,hijK]
TDD: reciprocity of uplink and downlink channels
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8. CSI Acquisition
Uplink Training
ˆh
= h + n
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9. CSI Acquisition
Uplink Training
ˆh
= h+hI + n
◮ Pilot contamination:
interference during channel estimation
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10. CSI Acquisition
Uplink Training
ˆh
= h+hI + n
◮ Pilot contamination:
interference during channel estimation
◮ Focused downlink interference
◮ Ultimate limit on data SINR
[Marzetta, 2010]
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11. CSI Acquisition
Uplink Training
ˆh
= h+hI + n
◮ Pilot contamination:
interference during channel estimation
◮ Focused downlink interference
◮ Ultimate limit on data SINR
[Marzetta, 2010]
Multi-cell scenario
ˆH
i = Hii +
XL
j=1,j6=i
Hij +Ntr
i
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12. Achievable Rate
Lower bound on achievable rate [Medard, 2000]
rjk = log2(1 +
jk)
with
jk = |E[hHj
jkwjk]|2
1
dl
+ var[hHj
jkwjk] +
PL,K
i=1,n=1
(i,n)6=(j,k)
E[|hHj
jkwin|2]
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13. Achievable Rate
Lower bound on achievable rate [Medard, 2000]
rjk = log2(1 +
jk)
with
jk = |E[hHj
jkwjk]|2
1
dl
+ var[hHj
jkwjk] +
PL,K
i=1,n=1
(i,n)6=(j,k)
E[|hHj
jkwin|2]
Matched filter wjk = √jk
ˆh
jk and M → ∞
jk =
jk tr(Rjjk)2
PLi
=1
i6=j
ik tr(Rijk)2
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14. Dealing With Pilot-Contamination
◮ Pilot design, allocation of pilot sequences
[ITG WSA 2014], [IEEE SAM 2014]
◮ Non-linear semi-blind channel estimation
[IEEE SPAWC 2014]
◮ CoMP approach based on channel distribution information
[ITG SCC 2015]
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15. Pilot Allocation
Cell 1 Cell 2
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16. Pilot Allocation
Cell 1 Cell 2
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17. Pilot Allocation
T
Ttr Tul Tdl
◮ Fixed pilot sequence length
◮ Limited pool of orthogonal pilot sequences
◮ Allocation of one pilot sequence to each user
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18. Non-Cooperative Allocation
◮ Random allocation
◮ Fractional reuse of pilot sequences if Ttr K
◮ Position based allocation
◮ Group cells with a reuse pattern
◮ Assign pilots based on local channel quality and group
index
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19. NUM Based Allocation
◮ Use asymptotic rates to optimize pilot allocation
◮ Network utility maximization with respect to pilot
assignments
max
P1,...,PL∈{0,1}K×Ttr
U(r11, . . . , rLK) s.t. PiPT
i = I ∀i
◮ Network-wide combinatorial optimization problem
◮ Exhaustive search usually prohibitively complex
◮ Greedy methods are applicable
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20. Performance Gain
L = 21, K = 10,

21. = d−, = 3.8
1.00
0.80
0.60
0.40
0.20
0.00
Uncoordinated
Position Based
Greedy
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
CDF of user downlink rates in Bit/s/Hz
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22. Trade-Off between Pilot and Data Resources
L = 21, K = 10, T = 185,

23. = d−, = 3.8
2.00
1.80
1.60
1.40
1.20
1.00
10 14 18 22 26 30 34 38 42 46 50
Training resources Ttr
rate of 5th percentile
Greedy
Position Based
Fractional Reuse
Uncoordinated
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24. Non-Linear Channel Estimation
◮ Linear channel estimation based on pilots suffers from
pilot-contamination
◮ Reduce pilot-contamination by non-linear channel
estimation based on data signals
◮ blind channel estimation
[Mueller et al., 2013, Ngo and Larsson, 2012]
◮ semi-blind channel estimation
[SPAWC 2014]
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25. Blind Estimation
T
Tul Tdl
Uplink data:
Y ul
i =
XL
j=1
HijSul
j +Nul
i
◮ Estimate all channels Hij at base station i
◮ MAP approach
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26. Blind Estimation
Let Hi = [Hi1, . . . ,HiL]
Conditional density
i |Hi(Y ul
fY ul
i |Hi) ∝
exp
h
−tr
h
Y ul
i
H
ulHiHH
−1
i + I
Y ul
i
ii
detTul
ulHH
i Hi + I
∝
exp
tr
Y ul
i Y ul
i
H
Hi
HH
i Hi + 1
ul
−1
I
HH
i
detTul
ulHH
i Hi + I
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27. Blind Estimation
MAP Formulation
Hblind
i = argmax
Hi
tr
Y ul
i Y ul
i
H
Hi
HH
i Hi +
1
ul
I
−1
HH
i
##
− Tul log det
ulHH
i Hi + I
− tr(HiD−1
i HH
i )
hijk ∼ NC(0,

28. ijk I) and Di = diag(

29. i11, . . . ,

30. iLK)
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31. Blind Estimation
with the singular value decomposition Hi = UiiV H
i
MAP Formulation
Hblind
i = argmax
Hi
tr
UH
i Y ul
i Y ul
i
H
Ui2
i
2
i +
1
ul
I
−1
#
− Tul log det
ul2
i + I
i D−1
− tr(V H
i Vi2
i )
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32. Blind Estimation
Left Singular Vectors
tr
UH
i Y ul
i
i Y ul
H
Ui2
i
2
i +
1
ul
I
−1
#
⇒ Ui: principal eigenvectors of Y ul
i Y ul
i
H
Right Singular Vectors
i D−1
−tr(V H
i Vi2
i )
i D−1
⇒ Vi: permutation such that diagonal of V H
i Vi is sorted
ascendingly
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33. Blind Estimation
⊕ Analytical solution for MAP estimator
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34. Blind Estimation
⊕ Analytical solution for MAP estimator
⊖ Large amount of uplink data necessary
⊖ Not applicable in practical systems
⊖ Performance disappointing
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35. Semi-blind Estimation
T
Ttr Tul Tdl
◮ Use both training signals and uplink data
◮ MAP approach
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36. Semi-blind Estimation
Additional Training Based Term
−
Y tr − √trHii i −
XL
j=1
j6=i
√trHij j
2
F
◮ No analytical solution
◮ Gradient based optimization
◮ Accurate initial guess via heuristic based on projection of
least squares estimate on eigenvectors of Y ul
i Y ul
i
H
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37. Results
L = 21, M = 100, K = 5, Tul = 200
channel model based on urban macro scenario in [ITU-R, 2009]
1.00
0.80
0.60
0.40
0.20
0.00
0.0 1.0 2.0 3.0 4.0 5.0 6.0
User rates
Linear MMSE
Blind
Subspace Projection
Semi-blind Heuristic
Semi-blind MAP
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38. CDI Precoding
◮ Additional static precoding step
◮ Reduction of interference based on structure in the
propagation environment and/or a coordinated multi-point
approach
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39. CDI structure
CoMP
d11
d21
d12
d22
◮ Structure of channel covariance matrix depends on
terminal position
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40. CDI structure
Multi-path propagation
◮ Structure of channel covariance matrix depends on
terminal position
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41. CDI Precoding
Equivalent Single Cell Scenario
hi ∼ NC(0,Ri) with Ri6=

42. i I
Identical Pilot Sequences
least squares estimate: ˆh
i =
PL
j=1 hj + ni
CDI precoder
wi = Aiˆh
i
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43. Achievable Rate
SINR
i =
ui
1
dl
+ vi + ti
with
ui = |tr[RiAi]|2
XK
vi =
j=1
tr
RiAj
1
tr
I+
XK
n=1
Rn
!
AHj
#
ti =
XK
j=1
j6=i
|tr[RiAj ]|2
◮ For large M the quadratic terms are dominant
◮ Choose Ai such that tr(RiAj) = 0
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44. CDI Zero-forcing
◮ Choose Ai such that tr(RiAj) = 0
Vectorization
ri = vec(Ri)
¯R
= [r1, . . . , rK]
and
ai = vec(Ai)
¯A
= [a1, . . . , aK]
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45. CDI Zero-forcing
◮ Choose Ai such that tr(RiAj) = 0
Vectorization
ri = vec(Ri)
¯R
= [r1, . . . , rK]
and
ai = vec(Ai)
¯A
= [a1, . . . , aK]
Pilot-contamination Suppressing Precoder
¯R
H ¯A
!=
0 ⇒ ¯A
= ¯R
+
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46. Single-cell Scenario
K = 9, Ttr = 3
channel model based on urban macro scenario in [ITU-R, 2009]
200 400 600 800 1,000 1,200 1,400
4.00
2.00
0.00
Number of Antennas
Spectral efficiency per user in Bit/s/Hz
No CDI precoding
MMSE estimation
CDI zero-forcing
Time sharing
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47. Multi-cell Scenario
L = 7, K = 2
100 200 300 400
6.00
4.00
2.00
0.00
Number of Antennas
Spectral efficiency per user in Bit/s/Hz
No CDI precoding
MMSE estimation
CDI zero-forcing
PCP zero-forcing
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48. Conclusions
◮ huge antenna gain
◮ law of large numbers: orthogonalization hardening
◮ limited number of pilot sequences: pilot contamination
◮ reduction of pilot contamination:
coordination and semi-blind channel estimation
◮ potentially suppression of pilot contamination:
decontamination by channel distribution precoding
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49. References I
[ITU-R, 2009] ITU-R (2009).
Guidelines for evaluation of radio interface technologies for IMT-Advanced.
Technical Report Report ITU-R M.2135-1, International Telecommunication Union (ITU).
[Marzetta, 2010] Marzetta, T. (2010).
Noncooperative cellular wireless with unlimited numbers of base station antennas.
IEEE Transactions on Wireless Communications, 9(11).
[Medard, 2000] Medard, M. (2000).
The Effect Upon Channel Capacity in Wireless Communications of Perfect and Imperfect Knowledge of the
Channel.
IEEE Transactions on Information Theory, 46(3):933–946.
[Mohammed and Larsson, 2013] Mohammed, S. and Larsson, E. (2013).
Per-antenna constant envelope precoding for large multi-user MIMO systems.
IEEE Transactions on Communications, 61(3):1059–1071.
[Mueller et al., 2013] Mueller, R. R., Vehkaperae, M., and Cottatellucci, L. (2013).
Blind pilot decontamination.
In 17th International ITG Workshop on Smart Antennas (WSA).
[Neumann et al., 2014a] Neumann, D., Gründinger, A., Joham, M., and Utschick, W. (2014a).
On the amount of training in coordinated massive MIMO networks.
In 8th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), pages 293–296.
Invited paper.
[Neumann et al., 2014b] Neumann, D., Gründinger, A., Joham, M., and Utschick, W. (2014b).
Pilot coordination for large-scale multi-cell TDD systems.
In 18th International ITG Workshop on Smart Antennas (WSA).
Technische Universität München – Associate Institute for Signal Processing 35

50. References II
[Neumann et al., 2014c] Neumann, D., Joham, M., and Utschick, W. (2014c).
Channel Estimation in Massive MIMO Systems.
In preparation.
[Neumann et al., 2014d] Neumann, D., Joham, M., and Utschick, W. (2014d).
Suppression of pilot-contamination in massive MIMO systems.
In 15th IEEE InternationalWorkshop on Signal Processing Advances in Wireless Communications (SPAWC),
pages 11–15.
[Neumann et al., 2015] Neumann, D., Joham, M., and Utschick, W. (2015).
CDI precoding for massive MIMO.
In 10th International ITG Conference on Systems, Communications and Coding (SCC).
[Ngo and Larsson, 2012] Ngo, H. Q. and Larsson, E. (2012).
EVD-based channel estimation in multicell multiuser MIMO systems with very large antenna arrays.
In 37th International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 3249–3252.
Technische Universität München – Associate Institute for Signal Processing 36