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Pilot Contamination Mitigation for Massive MIMO
Systems using Novel Channel Estimation Techniques
Hayder AL-Salihi
Centre for Telecommunications Research
Department of Informatics
King’s College London, University of London
London, UK
March, 2018
Hayder AL-Salihi (Centre for Telecommunications Research)
Pilot Contamination Mitigation for Massive MIMO Systems using Novel Channel Estimatio
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Outline
Introduction
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Outline
Introduction
Massive MIMO Main Challenge
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Outline
Introduction
Aims and Objectives
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Outline
Introduction
Aims and Objectives
Bayesian Compressed Sensing (BCS) Channel Estimation
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Outline
Introduction
Aims and Objectives
Sparse Bayesian Learning (SBL) Channel Estimation
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Outline
Introduction
Aims and Objectives
Optimal Pilot Design
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Outline
Introduction
Aims and Objectives
Channel Model
March, 2018 2 / 41

Outline
Introduction
Aims and Objectives
Channel Model
Discreate Fourier Transform (DFT) Based Channel Estimation
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Outline
Introduction
Aims and Objectives
Channel Model
Whitening Rotation (WR) Semi-blind Channel Estimation
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Outline
Introduction
Aims and Objectives
Channel Model
Simulation Results
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Outline
Introduction
Aims and Objectives
Channel Model
Simulation Results
Conclusion
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Introduction
The major targets for 5G of mobile communications, are to achieve
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Introduction
1000 times the system capacity.
March, 2018 3 / 41

Introduction
times the spectral efficiency, energy efficiency and data rate.
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Introduction
25 times the average cell throughput.
March, 2018 3 / 41

Introduction
25 times the average cell throughput.
Massive MIMO is a promising technology for 5G.
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What is MIMO?
SISO
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What is MIMO?
MIMO, Diversity
MIMO, Multiplexing
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Massive MIMO
Defined as a system using a large number of antennas at the base
station;
accordingly, a significant beamforming can be achieved and the
system capacity can serve a large number of users.
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Availability of accurate, instantaneous (CSI) at the base station.
Pilot Signal.
Channel estimation algorithm.
Pilot Reuse.
Pilot contamination.
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Aims and Objectives
Motivated by massive MIMO outstanding performance
And Considering Pilot Contamination Problem
We need to develop new techniques and approaches to address the pilot
contamination problem.
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Contribution
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Contribution
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Bayesian Channel Estimation
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Compressed Sensing (CS)
Compressed sensing (CS) techniques can recover the unknown signals
from only a small number of measurements,
significantly far fewer samples than via the conventional Nyquist rate,
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Sparse Nature
CS to exploit the sparse nature of signals (that is, only a small
number of components in a signal vector are non-zero).
CS allows for accurate system parameter estimation with less training,
thereby addressing the pilot contamination problem and improving
the bandwidth efficiency
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CS Shortages
However, the classical CS algorithms require prior knowledge of
channel sparsity.
The sampling matrix must satisfy the restricted isometry property
(RIP) to guarantee reliable estimation.
Several methods has been proposed to overcome the scarcity of
CS-based channel estimation.
These works assume dependency between antenna elements.
In realistic environments MIMO channel is generally correlated and
statistically dependent.
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Bayesian Estimation
In common literature, channel estimation methods are classified into:
Parametric approach.
Bayesian approach.
A standard parametric approach is the best linear unbiased estimator,
which is often referred to as least squares channel estimation.
In contrast to parametric methods, the Bayesian approach treats the
desired parameters as random variable with a-priori known statistics.
Clearly, the a-priori probability density function (PDF) of the channel
is assumed to be perfectly known at the receiver
Based on the Bayesian channel estimation philosophy, the estimation
of unknown parameters is the expectation of the posterior
probabilistic distribution.
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Bayesian Estimation
The posterior probabilistic distribution is proportional to the prior
probability and the likelihood of the unknown parameters.
Posterior = Prior × Liklihood
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In order to accurately estimate the CSI with the aid of the limited
pilot resources, we operate the conventional minimum mean square
error (MMSE) channel estimation process using an optimally designed
pilot set to improve the performance of the proposed technique.
The optimal pilots are designed to minimize the mean square error
(MSE) under the total transmit power constraint based on
optimization problem formulation.
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Channel Model
Most of the studies of massive MIMO systems assume the channel
condition to be an independent and identically distributed (i.i.d)
Rayleigh fading.
To evaluate massive MIMO efficiently in more realistic scenarios, we
need models that capture important massive MIMO channel
characteristics,
for example the Rician fading channel that is used to model the direct
of line-of-sight (LOS) paths in mobile radio channels, as well as
indoor wireless.
The millimetre-wave (mm-wave) operating of interesting aspects of
near-LOS propagation that would mitigate the effect of pilot
contamination is being considered as a candidate for new radio bands
for 5G mobile communication systems.
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Channel Model
It can be found that, as the the LOS components are increased, the
estimation accuracy in terms of the MSE of the LMMSE is enhanced.
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Discreate Fourier Transform (DFT) Based Channel
Estimation
DFT Channel Estimation
Iterative DFT Channel Estimation
Most Significant Taps (MST) DFT Channel Estimation
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Semi-blind based channel estimation
The aim is to construct a channel estimation scheme with a limited
number of pilots to alleviate the potential shortcomings of a blind
scheme of complexity,
while also employing statistical blind information for pilot
decontamination and bandwidth efficiency. Such a scheme is
semi-blind in nature since it employs both pilot and blind information.
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Semi-blind based channel estimation
We will apply the WR based channel estimation for massive
MIMO-OFDM to address the pilot contamination problem.
The WR technique consist of two steps: 1) estimation of a whitening
matrix using information data; and 2) estimation of unitary matrix
using pilots.
Also, we combined the DFT-based channel estimator with WR
technique.
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System Model
Multi-Cell
Multi-User
Time Division Duplex (TDD)
Massive MIMO-OFDM
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System Model
Each cell comprises M antennas at the BS
and N single-antenna mobile stations.
Uplink channel estimation
The received signal Yc∗,i at the i-th antenna element in the cell c∗
can be expressed as
Yc∗,i [v, k] =
N
X
n=1
Hn
c∗,c∗,i [v, k]Xn
c∗ [v, k]
+
C
X
c=1,c6=c∗
N
X
n=1
Hn
c∗,c,i [v, k]Xn
c [v, k] + Wc∗,i [v, k], (1)
for 1 ≤ i ≤ M and 1 ≤ c ≤ C,
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System Model
By compacting the above equation, we get
Yc∗ = Xc∗ Hc∗,c∗ +
C
X
c=1,c6=c∗
XcHc∗,c + Wc∗ , (2)
Hc∗,c = Fhc∗,c, (3)
Yc∗ = Ac∗ hc∗,c∗ + Zc∗ . (4)
where the term Zc∗ =
PC
c=1,c6=c∗ XcFh0n
c∗,c + Wc∗ in (4) represents
the net sum of inter-cell interference plus the receiver noise.
If Ac∗ has more rows than columns, i.e. the number of the pilot is
greater than the number of the path, then (10) )is a standard LS
problem with the estimated CIR given by
ĥc∗,c∗ = (AH
c∗ Ac∗ )−1
AH
c∗ Yc∗ . (5)
However, we are more interested in the case of the number of the
path is greater than the number of the pilot.
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CS-based estimation for Massive MIMO
Based on the physical properties of outdoor electromagnetic
propagation, the channel impulse response (CIR) in wireless
communications usually possesses several significant channel taps as
it shown in Fig. 2, i.e. the CIR are sparse,
So, the number of non-zero channel taps is much smaller than the
channel length, hence CS techniques can be applied for sparse
channel estimation [13]-[15].
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CS-based estimation for Massive MIMO
This sparsity feature can be exploited to reduce the necessary channel
parameters needing to be estimated.
In this case, we can address the pilot contamination problem by using
fewer pilots than the unknown channel coefficients [13]-[15].
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SBL-Based Channel Estimator
In this section, the pattern-coupled sparse Bayesian learning method
is presented in the context of massive MIMO channel estimation.
Based on Bayesian channel estimation philosophy, estimated unknown
parameters of interest are an expectation of the posterior probability.
As such, to obtain the estimated channel, we need to infer the
posterior probability of the unknown parameters.
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Bayesian Inference Model
Following the pattern-coupled sparse Bayesian learning model and
based on Bayes’ rule [10], the full posterior distribution of hc∗,c∗ over
unknown parameters of interest for the problem at hand is
proportional to the prior probability and the likelihood of the unknown
parameters, that can be computed as
P(hc∗,c∗ |α, γ, Yc∗ ) = P(hc∗,c∗ |α)P(Yc∗ |hc∗,c∗ ), (6)
where γ represents the inverse of the net sum of the noise and
interference covariance matrices and α are non-negative
hyperparameters controlling the sparsity of the channel hc∗,c∗ .
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According to probability theory, the term P(Yc∗ |hc∗,c∗ ) can be
written as
P(Yc∗ |hc∗,c∗ ) = (
1
√
2πγ−1
)exp(−
||Yc∗ − hc∗,c∗ Ac∗ ||2
2
2γ−1
), (7)
The statistical properties of the sparse multipath structure of the
channel is following Gaussian distribution based on the central line
theorem [...]. So, the Gaussian prior for each channel coefficient
P(hc∗,c∗ |α) in the pattern-coupled model is given by
P(hc∗,c∗ |α) =
M
Y
i=1
P(Hc∗,c∗,i [v, k]|αi , αi+1, αi−1) (8)
March, 2018 30 / 41

=(2π)
−M
2
M
Y
i=1
((αi , βαi+1, βαi−1))
1
2
exp[
−1
2
(Hn
c∗,c∗,i [v, k])T
((αi , βαi+1, βαi−1))Hn
c∗,c∗,i [v, k]],
i = 1, ..., M (9)
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where 0 ≤ β ≤ 1 is a parameter indicating the pattern relevance
between the channel coefficient Hn
c∗,c∗,i [v, k] and its neighboring
coefficients {Hn
c∗,c∗,i+1[v, k], Hn
c∗,c∗,i−1[v, k]}.
For β = 0, the Gaussian prior distribution in (10) is reduced to the
prior for the conventional sparse Bayesian learning (which represents
the uncorrelated channel scenario).
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We now proceed to perform Bayesian inference for the proposed
pattern-coupled SBL-based estimator. The posterior
P(hc∗,c∗ |α, γ, Yc∗ ) ∼ N(µ, Σ) follows a Gaussian distribution with
its mean and covariance given respectively by
µ = γΣAc∗
H
Yc∗ , (10)
Σ = (D + γ(Ac∗ )H
Ac∗ )−1
, (11)
where D is a diagonal matrix with its ith diagonal element is given by
[αi , βαi+1, βαi−1], for i = 1, ..., M. The maximum a posterior (MAP)
estimate of hc∗,c∗ is the mean of its posterior distribution, i.e.,
ĥc∗,c∗ = µ = ((Ac∗ )H
Ac∗ + γ−1
D)−1
(Ac∗ )H
Yc∗ . (12)
To obtain the term ĥc∗,c∗ , we need to jointly estimate the
hyperparameters α and γ, which can be achieved by exploiting the
expectation-maximization (EM) approach (we refer interested readers
to [10] for detailed derivations).
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Enhanced SBL-Based Estimator
In contrast to the proposed SBL-based estimator, the performance of
the proposed SBL-based estimator can be improved through the
principle of thresholding, which can be applied to retain the most
significant taps.
The proposed algorithm therefore implements a threshold approach by
conserving the channel taps that have energies above a threshold
value of % and setting the other taps to zero.
The value of % is the energy of the CIR.
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CRB For SBL-Based Estimator
To quantify the best performance that can be achieved by the
proposed algorithm, in this section, we derive the CRB of the
pattern-coupled SBL channel estimation.
The CRB on the covariance of any estimator θ̂ can be given as
E{(θ̂ − θ)(θ̂ − θ)H} ≥ J−1(θ), where J(θ) is the Fisher information
matrix (FIM) corresponding to the observation f , and can be given as
J(θ) = E(
∂
∂θ
logl(θ, f ))(
∂
∂θ
logl(θ, f ))T
, (13)
where l(θ, f ) is the likelihood function corresponding to the
observation f , parametrized by θ [16].
Theorem 1: The closed form expression of the Bayesian CRB for the
proposed SBL can be given as
J(hc∗,c∗ ) ≥ (
1
(αi , βαi+1, βαi−1)
+
Ac∗ (Ac∗ )H
γ
)−1
.
i = 1, ..., M. (14)
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Following (19), we can write the FIM as
J(hc∗,c) ≥ E(
∂2log(phc∗,c /Yc∗ (hc∗,c, Yc∗ ))
∂2hc∗,c
). (15)
Based on Bayes’ rule in (8), the FIM can be decomposed into two
terms
E(
∂2log(phc∗,c /Yc∗ (hc∗,c, Yc∗ ))
∂2hc∗,c
) =
E(
∂2log(pYc∗ /hn
c∗,c
(Yc∗ , hc∗,c))
∂2Hc∗,c
)+
E(
∂2log(phc∗,c
(hc∗,c))
∂2hc∗,c
). (16)
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Which can be expressed in matrix form as
J = JD + JP. (17)
where J, JD and JP represent the Bayesian FIM, data information
matrix and prior information matrix, respectively.
Using (9), the data information matrix JD can be given as
JD = E(
∂2log(pYc∗ /hc∗,c
(Yc∗ , hc∗,c))
∂2hc∗,c
) =
Ac∗ (Ac∗ )H
γ
. (18)
Considering (10), the prior information matrix JD can be given as
JP = E(
∂2log(phc∗,c
(hc∗,c))
∂2hc∗,c
) = (αi , βαi+1, βαi−1)−1
. (19)
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Simulation Results
The proposed SBL approach provided significant performance
enhancement as a result of exploiting the correlation between the
antennas. The results showed that the thresholding approach strengthened
the estimation accuracy of conventional SBL as the CIR possessed so
many taps without a significant energy. By setting the threshold and
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Simulation Results
It can be observed that estimation accuracy is improved when employing
the antennas correlation on a large scale.
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Conclusion
We proposed a SBL-based channel estimation algorithm for multi-cell
massive MIMO systems.
The simulation results revealed that the SBL-based channel
estimation algorithm had a tremendous advantage over conventional
estimators.
Furthermore, the proposed technique can be enhanced by
thresholding the CIR to a specific value.
In addition, the results demonstrated that the estimation accuracy is
enhanced by employing the correlation between antennas on a large
scale.
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For Further Reading I
M. Carlin, P. Rocca, G. Oliveri, F. Viani, and A.
Massa,”Directions-of-arrival estimation through Bayesian compressive
sensing strategies”,IEEE Trans. Antennas Propagat., vol.61, no. 7, pp.
38283838, July 2013.
R. G. Baraniuk, ”Compressive sampling”, IEEE Signal Process. Mag.,
vol. 24, no. 4, pp. 118-124, July 2007.
J. Fang, Y. Shen, H. Li and P. Wang, ”Pattern-Coupled Sparse
Bayesian Learning for Recovery of Block-Sparse Signals”, IEEE
Transaction on Signal Processing, vol. 63, no. 2, pp. 360-372, 2015.
Y. Shen, H. Duan, J. Fang, H. Li, ”Pattern-coupled sparse bayesian
learning for recovery of block-sparse signals”, Acoustics Speech and
Signal Processing (ICASSP) 2014 IEEE International Conference on,
pp. 1896-1900, May 2014.
March, 2018 41 / 41

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