Strategies to Combat Pilot Contamination in Massive MIMO Systems

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 ProcessingTechnische Universität München

2nd International Workshop on Challenges and Trends

of Broadband Wireless Mobile Access Networks — Beyond

LTE-A

Fifth Generation Wireless Systems (5G): Goals

◮ higher data rates

◮ better coverage

◮ lower latency

◮ lower battery consumption

Technische Universität München – Associate Institute for Signal Processing 2

Fifth Generation Wireless Systems (5G): Approaches

◮ small (pico) cells

◮ device-to-device (D2D) communication

◮ multi-hop networks

◮ mm-wave technology

◮ massive MIMO


Massive MIMO Setup

M antennas K users

◮ Large number of base station antennas

◮ About two orders of magnitude more antennas than users:

M ≫ K


Law of Large Numbers

Let x ∈ CN and y ∈ C

N be random with N i.i.d. entries.

Due to law of large numbers,

◮ limN→∞1N1Tx = limN→∞

1N

∑Ni=1 xi

a.s.= E[xi]

◮ limN→∞1N‖x‖22

a.s.= E[|xi|2]

zero-mean x: limN→∞1N‖x‖22

a.s.= var(xi)

◮ limN→∞1NyHx

a.s.= E[y∗i ] E[xi]

zero-mean x: limN→∞1NyHx

a.s.= 0


Benefits of Massive MIMO

Array Gain

M

SNR

Law of Large Numbers

◮ Asymptotic orthogonality: 1M

hHi hj → 0

◮ Channel hardening: 1M

‖hi‖22 → σ2 for hi ∼ NC(0, σ2I)

⇒ Robust spacial multiplexing with simple signal

processing methods

[Marzetta, 2010, Mohammed and Larsson, 2013]


System Model

Uplink

yuli =

L∑

j=1

Hijsulj + nul

i

Downlink: Linear Precoding

ydlj =

L∑

i=1

HTijWis

dli + ndl

Wi = [wi1, . . . ,wiK ] and Hij = [hij1, . . . ,hijK ]

TDD: reciprocity of uplink and downlink channels


CSI Acquisition

Uplink Training

h = h + n


CSI Acquisition

Uplink Training

h = h+hI + n

◮ Pilot contamination:

interference during channel estimation


CSI Acquisition

Uplink Training

h = h+hI + n



◮ Focused downlink interference

◮ Ultimate limit on data SINR

[Marzetta, 2010]


CSI Acquisition

Uplink Training

h = h+hI + n



◮ Focused downlink interference

◮ Ultimate limit on data SINR

[Marzetta, 2010]

Multi-cell scenario

Hi = Hii +

L∑

j=1,j 6=i

Hij +N tri


Achievable Rate

Lower bound on achievable rate [Medard, 2000]

rjk = log2(1 + γjk)

with

γjk =|E[hH

jjkwjk]|21ρdl

+ var[hHjjkwjk] +

∑L,Ki=1,n=1

(i,n)6=(j,k)

E[|hHjjkwin|2]


Achievable Rate

Lower bound on achievable rate [Medard, 2000]

rjk = log2(1 + γjk)

with

γjk =|E[hH

jjkwjk]|21ρdl

+ var[hHjjkwjk] +

∑L,Ki=1,n=1

(i,n)6=(j,k)

E[|hHjjkwin|2]

Matched filter wjk =√αjkhjk and M → ∞

γjk =αjk tr(Rjjk)

2

∑Li=1i 6=j

αik tr(Rijk)2


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]


Pilot Allocation

Cell 1 Cell 2


Pilot Allocation

Cell 1 Cell 2


Pilot Allocation

T

Ttr Tul Tdl

◮ Fixed pilot sequence length

◮ Limited pool of orthogonal pilot sequences

◮ Allocation of one pilot sequence to each user


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


NUM Based Allocation

◮ Use asymptotic rates to optimize pilot allocation

◮ Network utility maximization with respect to pilot

assignments

maxP1,...,PL∈{0,1}

K×Ttr

U(r11, . . . , rLK) s.t. PiPTi = I ∀i

◮ Network-wide combinatorial optimization problem

◮ Exhaustive search usually prohibitively complex

◮ Greedy methods are applicable


Performance Gain

L = 21, K = 10, β = d−α, α = 3.8

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.00.00

0.20

0.40

0.60

0.80

1.00

CDF of user downlink rates in Bit/s/Hz

Uncoordinated

Position Based

Greedy


Trade-Off between Pilot and Data Resources

L = 21, K = 10, T = 185, β = d−α, α = 3.8

10 14 18 22 26 30 34 38 42 46 50

1.00

1.20

1.40

1.60

1.80

2.00

Training resources Ttr

rate

of5

thp

erc

en

tile

Greedy

Position Based

Fractional Reuse

Uncoordinated


Non-Linear Channel Estimation

◮ Linear channel estimation based on pilots suffers from

pilot-contamination

◮ Reduce pilot-contamination by non-linear channelestimation based on data signals

◮ blind channel estimation[Mueller et al., 2013, Ngo and Larsson, 2012]

◮ semi-blind channel estimation[SPAWC 2014]


Blind Estimation

T

Tul Tdl

Uplink data:

Y uli =

L∑

j=1

HijSulj +Nul

i

◮ Estimate all channels Hij at base station i

◮ MAP approach


Blind Estimation

Let Hi = [Hi1, . . . ,HiL]

Conditional density

fY

uli|Hi

(Y uli |Hi) ∝

exp[

− tr[

Y uli

H (ρulHiH

Hi + I

)−1Y uli

]]

detTul(

ρulHHi Hi + I

)

∝exp

[

tr

[

Y uli Y ul

i

HHi

(

HHi Hi +

1ρul

I

)−1HH

i

]]

detTul(

ρulHHi Hi + I

)


Blind Estimation

MAP Formulation

Hblindi = argmax

Hi

[

tr

[

Y uli Y ul

i

HHi

(

HHi Hi +

1

ρul

I

)−1

HHi

]]

− Tul log det(

ρulHHi Hi + I

)

− tr(HiD−1i HH

i )

hijk ∼ NC(0, βijk I) and Di = diag(βi11, . . . , βiLK)


Blind Estimation

with the singular value decomposition Hi = UiΣiVHi

MAP Formulation

Hblindi = argmax

Hi

tr

[

UHi Y ul

i Y uli

HUiΣ

2i

(

Σ2i +

1

ρulI

)−1]

− Tul log det(

ρulΣ2i + I

)

− tr(V Hi D−1

i ViΣ2i )


Blind Estimation

Left Singular Vectors

tr

[

UHi Y ul

i Y uli

HUiΣ

2i

(

Σ2i +

1

ρulI

)−1]

⇒ Ui: principal eigenvectors of Y uli Y ul

i

H

Right Singular Vectors

− tr(V Hi D−1

i ViΣ2i )

⇒ Vi: permutation such that diagonal of V Hi D−1

i Vi is sorted

ascendingly


Blind Estimation

⊕ Analytical solution for MAP estimator


Blind Estimation

⊕ Analytical solution for MAP estimator

⊖ Large amount of uplink data necessary

⊖ Not applicable in practical systems

⊖ Performance disappointing


Semi-blind Estimation

T

Ttr Tul Tdl

◮ Use both training signals and uplink data

◮ MAP approach


Semi-blind Estimation

Additional Training Based Term

−∥

∥

∥

∥

Y tr −√ρtrHiiΨi −

L∑

j=1j 6=i

√ρtrHijΨj

∥

∥

∥

∥

2

F

◮ No analytical solution

◮ Gradient based optimization

◮ Accurate initial guess via heuristic based on projection of

least squares estimate on eigenvectors of Y uli Y ul

i

H


Results

L = 21, M = 100, K = 5, Tul = 200channel model based on urban macro scenario in [ITU-R, 2009]

0.0 1.0 2.0 3.0 4.0 5.0 6.00.00

0.20

0.40

0.60

0.80

1.00

User rates

Linear MMSE

Blind

Subspace Projection

Semi-blind Heuristic

Semi-blind MAP


CDI Precoding

◮ Additional static precoding step

◮ Reduction of interference based on structure in the

propagation environment and/or a coordinated multi-point

approach


CDI structure

CoMP

d11

d21

d12

d22

◮ Structure of channel covariance matrix depends on

terminal position


CDI structure

Multi-path propagation

◮ Structure of channel covariance matrix depends on

terminal position


CDI Precoding

Equivalent Single Cell Scenario

hi ∼ NC(0,Ri) with Ri 6= βi I

Identical Pilot Sequences

least squares estimate: hi =∑L

j=1 hj + ni

CDI precoder

wi = Aihi


Achievable Rate

SINR

γi =ui

1ρdl

+ vi + ti

with

ui = |tr[RiAi]|2

vi =

K∑

j=1

tr

[

RiAj

(

1

ρtrI+

K∑

n=1

Rn

)

AHj

]

ti =

K∑

j=1j 6=i

|tr[RiAj]|2

◮ For large M the quadratic terms are dominant

◮ Choose Ai such that tr(RiAj) = 0


CDI Zero-forcing


Vectorization

ri = vec(Ri)

R = [r1, . . . , rK ]and

ai = vec(Ai)

A = [a1, . . . ,aK ]


CDI Zero-forcing


Vectorization

ri = vec(Ri)

R = [r1, . . . , rK ]and

ai = vec(Ai)

A = [a1, . . . ,aK ]

Pilot-contamination Suppressing Precoder

RHA!= 0 ⇒ A = R+


Single-cell Scenario

K = 9, Ttr = 3channel model based on urban macro scenario in [ITU-R, 2009]

200 400 600 800 1,000 1,200 1,4000.00

2.00

4.00

Number of Antennas

Sp

ectr

ale

fficie

ncy

pe

ru

se

rin

Bit/s

/Hz

No CDI precoding

MMSE estimation

CDI zero-forcing

Time sharing


Multi-cell Scenario

L = 7, K = 2

100 200 300 4000.00

2.00

4.00

6.00

Number of Antennas

Sp

ectr

ale

fficie

ncy

pe

ru

se

rin

Bit/s

/Hz

No CDI precoding

MMSE estimation

CDI zero-forcing

PCP zero-forcing


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


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 theChannel.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).


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 International Workshop 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.


Technology

Strategies to Combat Pilot Contamination in Massive MIMO Systems