This paper is described intra-cell interference in case of multiuser access based on single-carrier frequency division multiple access signals (SC-FDMA), which is used in LTE networks for uplink control channel and virtual multiple-input multiple-output (V-MIMO) mode. It is shown the reason of intra-cell interference and performance degradation. Also it is discussed a gradient based solution for user alignment to minimize the interference. Keywords — interference, LTE, SC-FDMA, Gauss-Newton, optimization, SIR, mitigation.

1. Vladimir Lyashev, Mikhail Maksimov, Nikolai Merezhin
The Institute of Signal Processing and Control Systems Southern Federal University Rostov-on-Don – Taganrog, Russia
Non-Linear Optimization Scheme for Non-Orthogonal Multiuser Access
TELFOR – 2014 November 25-27, 2014

2. Page  2 The Institute of Signal Processing and Control Systems
Southern Federal University
Problem Definition
1
2
1
2
The reasons to lost orthogonality
 Birth & Death
 Channel Spread
 Low periodicity of Time Align
command – sync. problem
Future high capacity
communication systems
will require non-orthogonal
multiuser
access (METIS-2020)
Today communication systems are
based on orthogonal properties for
V-MIMO and WCDMA users.

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The Institute of Signal Processing and Control Systems Southern Federal University
Intra-cell Interference
Nuser = 6, td = 0 us
Nuser = 6, td = 1.56 us
Desired user
Interference
ξ
Desired user
Interference
ξ
23.7
0.11
-46 dB
14.41
4.12
-11 dB
12.52
0.67
-25 dB
11.23
2.63
-13 dB
13.37
0.95
-23 dB
16.91
1.01
-24 dB
9.83
0.65
-24 dB
2.42
3.15
2 dB
7.5
0.26
-29 dB
7.97
2.71
-9 dB
10.6
0.51
-26 dB
5.11
4.21
-1.7 dB
ETU channel (td=0us)
System model
This is equal power!

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Mathematical Model and Its Approximation
( , , ) ( , , , ) ( , ) ( , , ) ( , ) ( , , )
1
ˆ ( , , )
Y n l k H q n k l T q k P q k l X q l E n l k
Q
q
T n k l q
 


B-rank channel approximation:



B
H q n k l W q n S k
1
( , , , ) ( , , ) ( , )

 
 Rank-2 model basically gives a very good fit to the
experimental channel H(q, n, l, k), usually of a fit of order 95%.
 The rank-1 model also look promising, and can approximate
70% of the energy.

5. Page  5
The Institute of Signal Processing and Control Systems Southern Federal University
Non-linear Optimization Problem Formulation
Φ퐗=퐘− 퐓 푞퐏푞푋푞 푄 푞=12→min
Φ퐗:F퐓 ,퐗,퐏=퐘−퐘 퐓 ,퐗,퐏 2+휆1퐓 2+휆2퐗2+휆3퐏2
F퐓 +훿퐓 ,퐗+훿퐗,퐏+훿퐏=퐘−퐘 ,훿퐘
Assumption
Regulized minimization functional

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Southern Federal University
Tikhonov Regularization in Inverse Problem
2 2
Ax b  ε
Each least squares problem has to be regularized. In the linear case,
we want to solve minimization problem
after regularization
the solution is
Ax  b ε
 
A A I A b
x A A Γ Γ A b
H H
H H H
1
1


 
  

min
2 2
Ax b  Γx 
x  5

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Optimization Methods
Gauss-Newton method
Φ푥=Φ푥푖+Φ′푥푖훿푥
Trust-Region method
훿푥=T(푥푖+1−푥푖)
Levenberg-Marquardt approach (damped least-squares)
훿푥=−퐉퐻퐉+휇퐈−1퐉퐻퐅
Φ퐗=퐘− 퐓 푞퐏푞푋푞 푄 푞=12→min
D. Nion and L. De Lathauwer. Levenberg-Marquardt computation of the block factor model for blind multi-user access in wireless communications.In European Signal Processing Conference (EUSIPCO), Florence, Italy, September 4-8 2006.

8. Page  8
The Institute of Signal Processing and Control Systems Southern Federal University
Update strategy for 휇
t = 1.56 us
t = 0 us
The problem with the Levenberg-Marquandt method is that a single parameter 휇 is suited to deal with two distinct problems: first, it tries to control the step size, second it tries to avoid the possible ill-conditioning of the gradient matrix.

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Southern Federal University
Convergence
0 10 20 30 40 50
-8
-7.9
-7.8
-7.7
-7.6
-7.5
-7.4
-7.3
-7.2
-7.1
-7
Iteration #
EsN0, dB
[Convergence] EsN0 for FER=10-2
the method of gradient descent
Gauss-Newton
Gauss-Newton (휇 = 0)
Gradient descent (휇 → 푖푛푓)
Fix 휇 = 60
Adaptive 휇
If Λ > 0.0,
푠푒푡 휇 <= 휇 max
1
3
, 1 − 2Λ − 1 3 ;
Otherwise,
휇 <= 2휇.
Λ푖 = Λ푖−1 + 2휇 퐻 − 퐻 푅
20 iters.

10. Page  10 The Institute of Signal Processing and Control Systems
Southern Federal University
Simulation Results
-16 -14 -12 -10 -8 -6 -4
10
-4
10
-3
10
-2
10
-1
10
0
SNR, dB
BLER
MRC w/o interference
MRC
ALS
ALS with regularization
ALS Newton
SINR before -4.77 dB -10.4 dB
SINR after

11. Page  11
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Outlook
Pilot contamination problem in massive MIMO
Fast & distributed coherent signal processing
Joint multiuser detection
Joint sector/cell
Adaptive coupling scheme for relaxation based signal processing
MU-pairing for distributed MIMO System
Complexity Reduction of Proposed Method
Conjugate gradients: CG or BiCG
Decomposition methods: waveform relaxation

12. Page  12
The Institute of Signal Processing and Control Systems Southern Federal University
THE END
Any questions ?
Vladimir Lyashev, PhD lyashev@ieee.org