Globecom 2015, San Diego, USA

1. Pilot Contamination Mitigation for Wideband
Massive MMO: Number of Cells Vs Multipath
T. E. Bogale+
, L. B. Le+
, X. Wang++
and L. Vandendorpe+++
Institute National de la Recherche Scientifique (INRS), Canada+
University of Western Ontario (UWO), Canada++
University Catholique de Louvain (UCL), Belgium+++
Dec. 07, 2015 (Globecom 2015)

2. Presentation outline
Presentation Outline
1 Existing Channel Estimation (Summary)
OFDM Approach
Non-OFDM Approach
2 Multicell Channel Estimation and Objective
3 Proposed Channel Estimation and Beamforming: Main Results
4 Proposed Joint Channel Estimation and Beamforming: Details
5 Simulation Results
6 Conclusions
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 2 / 10

3. Existing Channel Estimation (Summary) OFDM Approach
Existing Channel Estimation: OFDM
Assumptions
Pilot duration Tp, bandwidth B and delay spread Td are known
Existing Channel Estimation Technique:
OFDM Approach (i.e., Frequency domain approach)
Non-OFDM Approach (i.e., Time domain approach)
OFDM Approach:
If To is OFDM duration and Tu is useful symbol duration, maximum number of UEs are
[Marz TWC 10] and [Fern JSAC 13]
K =
Tp
Td
Tu
To
Example: LTE signal with ∆f = 15KHz, Tu = 1
∆f = 66.7µs, Tp = To, Td = 4.69µs,
K = Tu
Td
≈ 14 (L = Ns
K sub-carriers per UE)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 3 / 10

4. Existing Channel Estimation (Summary) OFDM Approach
Existing Channel Estimation: OFDM
Assumptions
Pilot duration Tp, bandwidth B and delay spread Td are known
Existing Channel Estimation Technique:
OFDM Approach (i.e., Frequency domain approach)
Non-OFDM Approach (i.e., Time domain approach)
OFDM Approach:
If To is OFDM duration and Tu is useful symbol duration, maximum number of UEs are
[Marz TWC 10] and [Fern JSAC 13]
K =
Tp
Td
Tu
To
Example: LTE signal with ∆f = 15KHz, Tu = 1
∆f = 66.7µs, Tp = To, Td = 4.69µs,
K = Tu
Td
≈ 14 (L = Ns
K sub-carriers per UE)
.
...
...
...
0 14
1
2
K
..
.
...
Ns-1
Ns-1
Ns-1
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 3 / 10

5. Existing Channel Estimation (Summary) Non-OFDM Approach
Existing Channel Estimation: Non-OFDM
Same settings as OFDM (i.e., Ts = Tu
Np
, L = Td
Ts
=
Np
K multipaths
between kth UE and nth BS antenna ¯hkn = [¯hk1n, ¯hk2n, · · · , ¯hkLn])
rn =
K
k=1
Xk ¯hkn + wn = X¯hn + wn
where X = [X1, X2, · · · , XK ], ¯hn = [¯h1n, ¯h2n, · · · , ¯hKn] and
Xk =










xk1
0 · · · 0 0
xk2
xk1
· · ·
...
...
xk3
xk2
· · · 0 0
...
... · · ·
...
...
xk(Np−1)
xk(Np−2)
· · · xk(Np−L+1)
xk(Np−L)
xkNp
xkNp−1
· · · xk(Np−L+2)
xk(Np−L+1)










If K =
Np
L = Ns
Np
, X is full row-rank (i.e., ¯hn is estimated reliably)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 4 / 10

6. Multicell Channel Estimation and Objective
Existing Channel Estimation: Mult-cell
∴ In Tu duration, CSI of K UE can be learned (i.e., each UE uses L
”net” sub-carriers (time-slots) in OFDM (Non-OFDM))
(Same resource in both freq and time domain CSI acquisitions)
Each BS equipped with massive (N → ∞) antennas serve K UEs
(i.e., use Tp to learn CSI)
No CoMP transmission is required (Advantageous)
Reusing of CSI pilots over multiple cells: ”Pilot contamination” (each UE
SINR will be bounded) (Disadvantage)
(i.e., only one cell Nc = 1 can serve its UEs without Pilot contamination)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 5 / 10

7. Multicell Channel Estimation and Objective
Existing Channel Estimation: Mult-cell
∴ In Tu duration, CSI of K UE can be learned (i.e., each UE uses L
”net” sub-carriers (time-slots) in OFDM (Non-OFDM))
(Same resource in both freq and time domain CSI acquisitions)
Each BS equipped with massive (N → ∞) antennas serve K UEs
(i.e., use Tp to learn CSI)
No CoMP transmission is required (Advantageous)
Reusing of CSI pilots over multiple cells: ”Pilot contamination” (each UE
SINR will be bounded) (Disadvantage)
(i.e., only one cell Nc = 1 can serve its UEs without Pilot contamination)
OBJECTIVE
For fixed B, L, Tp and each cell serves K UEs, can we
increase Nc more than one ensuring that each UE
achieve unbounded sub-carrier SINR when N → ∞?
(i.e., mitigate (cancel) pilot contamination)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 5 / 10

8. Proposed Channel Estimation and Beamforming: Main Results
Proposed Design (Summary)
Three step approach
Allow pilot transmission in time domain (i.e., Non-OFDM)
Express estimate of each sub-carrier channel as linear
combination (LC) of received signal in CSI acquisition phase
Optimize Nc, pilots and LC terms ensuring unbounded SINR
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 6 / 10

9. Proposed Channel Estimation and Beamforming: Main Results
Proposed Design (Summary)
Three step approach
Allow pilot transmission in time domain (i.e., Non-OFDM)
Express estimate of each sub-carrier channel as linear
combination (LC) of received signal in CSI acquisition phase
Optimize Nc, pilots and LC terms ensuring unbounded SINR
Main Results
Using the proposed design, Nc = L cells can reliably estimate the CSI
while ensuring unbounded SINR
There is a Non-zero gap between the rate achieved by proposed
design (i.e., CSI estimation and beamforming) and perfect CSI
⇒ ONLY mitigating pilot contamination
Multipath taps L, analogous to OFDM CP size, increases with B
∴ Wideband massive MIMO helps increase Nc
A total of Np = KNc UEs are served in all cells
∴ Each UE effectively uses one ”net” pilot for any B (interpretation)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 6 / 10

10. Proposed Joint Channel Estimation and Beamforming: Details
Proposed Design: Details
Rx signal from CSI acquisition (nth antenna in ith BS)
rin =
K
k=1
(Xki ¯hkiin +
Nc
j=1,j=i
Xkj ¯hkjin) + win
Introduce LC vector and express ˆhkiins = rT
invkis
Beamforming phase
yins =
K
k=1
Nc
j=1
hkjinsdkjs + ˜wins, ⇒ ˆdkis = aH
kiisyis
SINR ˆdkis
¯γkis =
E|hH
kiisakiis|2
(m,j)=(k,i) E|hH
mjisakiis|2 + E| ˜wH
isakiis|2
(11)
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11. Proposed Joint Channel Estimation and Beamforming: Details
MRC Beamforming
MRC receive beamformer akiis
E|wH
i akiis|2
=vH
kis
K
m=1
Nc
j=1
X∗
mj Cmji XT
mj + σ2
I vkis
E|hH
mjisakiis|2
=vH
kis X∗
mj Cmji f∗
s fT
s Cmji +
K
u=1
Nc
v=1,(u,v)=(m,j)
Cmjuvis XT
mj + σ2
tr{Cmjis}I vkis
where C(.) is related to channel covariance information
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 7 / 10

12. Proposed Joint Channel Estimation and Beamforming: Details
MRC Beamforming
MRC receive beamformer akiis
E|wH
i akiis|2
=vH
kis
K
m=1
Nc
j=1
X∗
mj Cmji XT
mj + σ2
I vkis
E|hH
mjisakiis|2
=vH
kis X∗
mj Cmji f∗
s fT
s Cmji +
K
u=1
Nc
v=1,(u,v)=(m,j)
Cmjuvis XT
mj + σ2
tr{Cmjis}I vkis
where C(.) is related to channel covariance information
Observation
X∗
mj Cmji f∗
s fT
s Cmji XT
mj : Scales with N2
(dominant)
Other terms scale with N, L or Np (can be ignored for very large N)
⇒ γkis ≈
vH
kis X∗
ki Ckii f∗
s fT
s Ckii XT
ki vkis
vH
kis
K
m=1
Nc
j=1,(m,j)=(k,i) X∗
mj Cmji f∗
s fT
s Cmji XT
mj vkis
large N
(12)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 7 / 10

13. Proposed Joint Channel Estimation and Beamforming: Details
Determination of number of cells Nc
Choose Nc ensuring γkis → ∞ as N → ∞ (i.e., get no. of cells)
max
Nc
|fT
s Ckii XT
ki vkis|, s.t fT
s Cmji XT
mj vkis = 0, ∀(m, j) = (k, i)
Using rank analysis, vkis = 0 exists iff Nc ≤ L for any C(.) (i.e., if Nc > L,
equality constraints may not be satisfied) (see Theorem 1 of paper)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 7 / 10

14. Proposed Joint Channel Estimation and Beamforming: Details
Determination of number of cells Nc
Choose Nc ensuring γkis → ∞ as N → ∞ (i.e., get no. of cells)
max
Nc
|fT
s Ckii XT
ki vkis|, s.t fT
s Cmji XT
mj vkis = 0, ∀(m, j) = (k, i)
Using rank analysis, vkis = 0 exists iff Nc ≤ L for any C(.) (i.e., if Nc > L,
equality constraints may not be satisfied) (see Theorem 1 of paper)
Optimization of Pilots and LC terms (Xmj and vkis)
For given Nc, optimize vkis, Xmj to get max ¯γkis(γkis) for arbitrary N
For fixed Nc, Xmj , maxvkis
¯γkis(γkis) is RQ (closed form)
Choose noise like orthogonal xmj ∈ CNp×1
, ∀m, j (suboptimal)
(Ensures balanced sub-carrier rate, e.g., random QPSK samples)
xmj from Zadoff Chu seq. achieves superior rate (not used in paper)
(Zadoff Chu sequences: Flat spectrum and used in LTE Ref. signal)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 7 / 10

15. Simulation Results
Simulation Results
2 3 4 5 6 7 8 9 10
0
0.5
1
1.5
2
2.5
Normalized number of antennas (N
0
)
R
kis
(inb/s/hz)
Proposed
LS (Pilot reuse)
MMSE (Pilot reuse)
LS (Orthogonal pilot)
MMSE (Orthogonal pilot)
EVD approach in [7]
Approach in [9]
2 4 6 8 10 12 14 16 18
0
2
4
6
8
10
12
14
15
Normalized number of antennas (N
0
)
R
kis
(inb/s/hz)
Proposed approach
Perfect CSI
Rg
<< c0
R
g
≈ c
0
REREFENCES
[7]: Q. N. Hien and E. G. Larsson,
”EVD-based channel estimation in multicell
multiuser MIMO systems with very large
antenna arrays”, in ICASSP, 2012, Kyoto,
Japan, 2012, pp. 3249 - 3252.
[9]: T. X. Vu, T. A. Vu, and T. S.Q Quek,
”Successive pilot contamination elimination in
multi-antenna multi-cell networks,” IEEE
Wireless Commun. Letters, Nov. 2014.
PARAMETER SETTINGS
Multipath components L = 4, SNR=0dB
Pilot: Np = 16 (random QPSK symbols)
Number of cells Nc = L = 4, K = 4
Total number of BS antenna N=2N0
All multipath channels are i.i.d with gains
gk1i = 1, gk2i = 0.9, gk3i = 0.6, gk4i = 0.7, ∀k
First UE in cell i is the target UE
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 8 / 10

16. Simulation Results
Simulation Results
2 4 6 8 10 12 14 16 18 20
0
0.5
1
1.5
2
2.5
3
Normalized number of antennas (N
0
)
R
kis
(inb/s/hz)
N
c
=5 (v
kis
with (11))
N
c
=5 (v
kis
with (12))
N
c
=6 (v
kis
with (11))
N
c
=6 (v
kis
with (12))
REREFENCES
[7]: Q. N. Hien and E. G. Larsson,
”EVD-based channel estimation in multicell
multiuser MIMO systems with very large
antenna arrays”, in ICASSP, 2012, Kyoto,
Japan, 2012, pp. 3249 - 3252.
[9]: T. X. Vu, T. A. Vu, and T. S.Q Quek,
”Successive pilot contamination elimination in
multi-antenna multi-cell networks,” IEEE
Wireless Commun. Letters, Nov. 2014.
PARAMETER SETTINGS
Multipath components L = 4, SNR=0dB
Pilot: Np = 16 (random QPSK symbols)
Number of cells Nc = L = 4, K = 4
Total number of BS antenna N=2N0
All multipath channels are i.i.d with gains
gk1i = 1, gk2i = 0.9, gk3i = 0.6, gk4i = 0.7, ∀k
First UE in cell i is the target UE
OBSERVATIONS
Proposed design achieves better rate than
existing designs in massive MIMO regime
There is a rate gap between proposed and
perfect CSI designs even if N → ∞
As expected, we have pilot contamination
when Nc > L = 4 (i.e., bounded rate)
Also Np = KNc confirms that our design
spends only one ”net” pilot per UE irrespective
of bandwidth (which is reduced by a factor of L
compared to existing design)
∴ Treating wideband channel as it is helps
increasing number of cells in massive MIMO
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 8 / 10

17. Conclusions
Conclusions
We propose new joint channel estimation and beamforming
design for multicell massive MIMO systems
The proposed design exploits multipath components of frequency
selective wireless channels
The proposed design allows Nc = L cells utilize the same
time-frequency resources while efficiently mitigating pilot
contamination
The proposed design is applicable for arbitrary channel statistics
both i.i.d and correlated (see also [Boga TSP 15])
The proposed design can also be extended straightforwardly to
other channel and beamformings (see [Boga TSP 15] for more details )
The proposed design is simple to implement as the main
complexity arises from Rayleigh quotient problem (similar
complexity as matrix SVD)
(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 9 / 10

18. References
References
T. E. Bogale, L. B. Le, X. Wang, and L. Vandendorpe, Pilot contamination
in wideband massive MIMO system: Number of cells vs multipath, IEEE
Trans. Signal Process. (submitted) (2015).
F. Fernandes, A. Ashikhmin, and T. L. Marzetta, Inter-cell interference in
noncooperative TDD large scale antenna systems, IEEE J. Select. Areas
in Commun. 31 (2013), no. 2, 192 – 201.
Q. N. Hien and E. G. Larsson, EVD-based channel estimation in multicell
multiuser MIMO systems with very large antenna arrays, ICASSP, 2012
(Kyoto, Japan), 2012, pp. 3249 – 3252.
T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers
of base station antennas, IEEE Trans. Wireless Commun. 9 (2010),
no. 11, 3590 – 3600.
T. X. Vu, T. A. Vu, and T. S.Q Quek, Successive pilot contamination
elimination in multi-antenna multi-cell networks, IEEE Wireless Commun.
Letters (2014), 617 – 620.
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