Presentacion us 2013_03_21

Multi-Dimensional Array Signal Processing
Applied to MIMO Systems

Prof. Dr.-Ing. João Paulo C. Lustosa da Costa
University of Brasília (UnB)
Department of Electrical Engineering (ENE)
Laboratory of Array Signal Processing
PO Box 4386
Zip Code 70.919-970, Brasília - DF

Universidade de Brasília
Homepage: http://www.pgea.unb.br/~lasp 1
Laboratório de Processamento de Sinais em Arranjos

Outline

 Universidade de Brasília: A Short Overview
 Research Areas: Laboratory of Array Signal Processing
 Multi-Dimensional Array Signal Processing
Motivation
Model Order Selection
UnB
Prewhitening
 MIMO-OFDM System
 Cooperative MIMO for WSN
 Conclusions

2

Outline

Motivation
UnB
Prewhitening
 Conclusions

3

Universidade de Brasília: A Short Overview (1)

 Universidade de Brasília (UNB)
One of the best federal universities in Brazil
The best university in the central-west region of Brazil
• Region with 12 million inhabitants
UNB is located in Brasília
• capital of Brazil
– political influence and cooperation with the Federal
Government 
• one of the most expensive cities in Brazil 
• one of the safest cities in Brazil 
• Great weather (avrg 22oC, min 17oC, max 28oC) 
• Several amazing waterfalls around Brasília 
– Itiquira, Pirinópolis, Chapada dos Veadeiros and others
• Cheap tickets to Rio de Janeiro and to the Northeast of Brazil 
4


5


In 2010, around 21000 candidates for approximately 3000 places
 Universidade de Brasília (UNB)
around 27000 students
around 3300 professors
(including all departments and all semesters)
 Department of Electrical Engineering
composed of three bachelor courses
• Communication Network Engineering
• Mechatronics
• Electrical Engineering (Electric Power Systems)
around 1500 students
around 70 professors

6

Outline

Motivation
UnB
Prewhitening
 Conclusions

7

Research areas (1)
Laboratory of Array Signal Processing (LASP)
http://www.pgea.unb.br/~lasp
Research topics:
• Telecommunications
– Cooperation with CityU of Hong Kong, TU Ilmenau, DLR, and UFC
– MIMO systems: Antenna array at TX and at RX
• Spatial domain: increase the exploitation of the frequency
spectrum
• Audio
– Cooperation with FAU in Nuernberg-Erlangen
(2 exchange students from Brazil – Science without Borders)
– Microphone array
• Business Intelligence: Projects with the Federal Government
• Ontology, Data Mining and Predictive Analytics
• Antenna Array Applications for Unmanned Aerial Vehicles (UAVs)
• Communications and Pose Estimation
8

Research areas (2)
Laboratory of Array Signal Processing (LASP)
• Side research topics applying antenna arrays or principal
component analysis or tensor calculus
• Magnetic Resonance Imaging (MRI)
• EEG
• Blind Malicious Traffic Detection in Networks
• Cooperative MIMO in Sensor Networks
• …

More information
• http://www.pgea.unb.br/~lasp

Exchange of Students
• Internship via DAAD RISE: TU Munich, Deggendorf and Freie U Berlin
• Internship via UnB scholarships: UPC
• Without scholarships: City U of HK
9

Outline

Motivation
UnB
Prewhitening
 Conclusions

10

Motivation (1)
 Malicious traffic detection

Amount of accesses
Time slots (10 min)

Detect if there is some malicious traffic
How many attackers and how many ports being attacked
Development of Intrusion Detection Systems (IDS)

Laboratório de Processamento de Sinais em Arranjos 3

Motivation (2)
 Business Intelligence (BI)

To support the decision making in the government and companies
Examples of data marts: personal, sales and logistic
Data mining: extract patterns from the data. For instance, increased
sales if beers and disposable diapers are close
Predictive analytics: predict the tendency and also support the decision

Motivation (3)
 Sound source localization

Sound source 1

Sound source 2
Microphone array

Applications: phone conference devices, bioacustics, computational
forensics and hearing aids.


Motivation (4)
 Wind tunnel evaluation

Array

Improvement of the aerodynamics of vehicles


Motivation (5)
 Channel model
Direction of Departure (DOD)
Transmit array: 1-D or 2-D

Direction of Arrival (DOA)
Receive array: 1-D or 2-D

Frequency Delay
Time Doppler shift


Goal

Model order Is the noise No Parameter
Measurements
selection colored? Estimation
Yes
Subspace
Prewhitening

 Measurements or data from several applications, for instance,
MIMO channels, EEG, stock markets, chemistry, pharmacology, medical imaging,
radar, and sonar
 Model order selection
estimation of the number of the main components (total number of parameters)
often assumed known in the literature
 Parameter estimation techniques
extraction of the parameters from the main components
 Subspace prewhitening schemes
application of the noise statistics to improve the parameter estimation

16

Goal: Model Order Selection

Measurements
Yes
Subspace
Prewhitening

 What is the best model order selection (MOS) scheme?
several schemes in the literature
Answer depends on data size and structure, and noise type
Is the multi-dimensional structure of the data taken into account?

 The right model order
crucial for the parameter estimation and subspace prewhitening

17

Goal: Parameter Estimation

Measurements
Yes
Subspace
Prewhitening
 Parameter estimation
mapping between the main components and the parameters

 In the literature, in case of arbitrary array geometries
the solutions are iterative, e.g., SAGE and Alternating Least Squares (ALS)
no guarantee of convergence

 The closed-form schemes in literature, e. g., R-D ESPRIT
restricted to shift invariant arrays
without robustness to arrays with positioning errors and to the violation of the
narrow band assumption
18

Goal: Subspace Prewhitening

Measurements
Yes
Subspace
Prewhitening

 Subspace prewhitening
improve the parameter estimation in the presence of colored noise

 We consider the cases:
structure of the noise statistics with respect to the correlation level
multi-dimensional structure of the noise statistics, common for certain MIMO
and EEG applications
unavailability of samples without the presence signal components to obtain
the noise statistics

19

Outline

Motivation
UnB
Prewhitening
 Conclusions

20

Model Order Selection: State of the Art (1)
 A large number of model order selection (MOS) schemes have been proposed in the
literature. However,
most of the proposed MOS schemes are compared only to Akaike’s Information
Criterion (AIC) and Minimum Description Length (MDL);
the Probability of correct Detection (PoD) of these schemes is a function of the array
size (number of snapshots and number of sensors).

21

Data model and Goal
 Noiseless case

= + +

 Matrix data model

Our objective is to estimate d from the noisy observations .

22

Analysis of the Noise Eigenvalues Profile
 The eigenvalues of the sample covariance matrix

10
d = 2, M = 8, SNR = 0 dB, N = 10
 Finite SNR, Finite N
8
M - d noise eigenvalues follow a
Wishart distribution. 6

i
d signal plus noise eigenvalues 4

2

0
1 2 3 4 5 6 7 8
Eigenvalue index i

23

Exponential Fitting Test (EFT)
 Observation is a superposition of noise and signal
The noise eigenvalues still exhibit the exponential profile
We can predict the profile
of the noise eigenvalues
to find the “breaking point”
Let P denote the number
of candidate noise eigenvalues.
• choose the largest P
such that the P noise
eigenvalues can be fitted
with a decaying exponential
d = 3, M = 8, SNR = 20 dB, N = 10

24

Comparison of MOS Schemes (1)
 Case that M and N are close

25

Comparison of MOS Schemes (2)
 Case that M >> N

26

Data Model and Goal
Noiseless data representation

= + +

Problem

where is the colored noise tensor.

Our objective is to estimate d from the noisy observations .

27

R-D Exponential Fitting Test
 R-D exponential profile

We can define global eigenvalues

28

R-D Exponential Fitting Test
 R-D exponential profile
Comparison between the global eigenvalues profile and the profile
of the last unfolding

29

Closed-form PARAFAC based
 For P = 2, i.e., P < d  For P = 4, i.e., P > d

= + = + + +

= + = + + +
 We assume d = 3 and we consider only solutions with the
two smallest residuals of the SMD, i.e., b = 1 and 2.
 Due to the permutation ambiguities, the components of
different tensors are ordered using the amplitude based
approach.

1 2 3 4 5
P

30

Simulations
Model Order Selection in Additive White Gaussian Noise Scenario
Probability of correct Detection vs. SNR

 White Gaussian noise


31

Simulations
Model Order Selection in Additive Colored Gaussian Noise Scenario
Probability of correct Detection vs. SNR

 Colored Gaussian noise


32

Outline

Motivation
UnB
Prewhitening
 Conclusions

33

Motivation
 Colored noise is encountered in a variety of signal processing applications, e.g.,
SONAR, communications, and speech processing.
 Without prewhitening the parameter estimation is severely degraded.

 Traditionally, stochastic prewhitening schemes are applied.

 By prewhitening the subspace via our proposed deterministic prewhitening
scheme, an improvement of the parameter estimation is obtained compared to the
stochastic prewhitening schemes.

34

Noise Analysis
 Analysis via SVD

Stochastic
prewhitening schemes

With colored
noise the d main
components are
more affected.

Deterministic
prewhitening scheme

35

Simulations
Subspace Prewhitening for Colored Noise with Structure
RMSE vs. Correlation Level

The noise correlation
is known.
SE – Standard ESPRIT

36

Sequential GSVD
 These matrix based prewhitening schemes have a worse accuracy for
multidimensional colored noise or interference with Kronecker correlation
structure,
when applied in conjunction with the subspace-based parameter estimation
techniques, such as R-D Standard ESPRIT and R-D Standard Tensor-ESPRIT

 Therefore, we propose the Sequential Generalized Singular Value
Decomposition (S-GSVD) of the measurement tensor and of the
multidimensional noise samples
enables us to improve the subspace estimation
based on the prewhitening correlation factors estimation
has a low complexity and a high accuracy version

37

Simulations

Subspace Prewhitening for Multi-dimensional Colored Noise
RMSE vs. Number of Samples without Signal Components (Nl)

STE – Standard
Tensor-ESPRIT

38

Iterative S-GSVD
 In some multidimensional applications,
the noise samples without the presence of signal components are not
available
 For these cases, we propose the Iterative Sequential GSVD (I-S-GSVD)
jointly estimation of the signal data and of the noise statistics via a proposed
iterative algorithm in conjunction with the S-GSVD
low computational complexity of the S-GSVD
for intermediate and high SNR regimes similar accuracy as the S-GSVD, where
is required
convergence with two or three iterations
applied in conjunction with the subspace-based parameter estimation techniques,
e.g., R-D Standard Tensor-ESPRIT (R-D STE)

39

Simulations
RMSE vs. Correlation Level

STE – Standard
Tensor-ESPRIT
40

Simulations
RMSE vs. Number of Iterations

STE – Standard
Tensor-ESPRIT
41

Outline

Motivation
UnB
Prewhitening
 Conclusions

42

MIMO-OFDM System (1)


MIMO-OFDM System (2)

M: number of transmit antennas.
N: number of time-slots in the whole time frame.
P: number of symbol periods in each time-slot.

Known.
K: number of receive antennas.
Known. F: number of subcarriers

Our objective is to estimate S and H from the noisy observations Y.
.

State-of-the-art MIMO-OFDM Schemes
 Existing Solution: Alternating Least Squares (ALS) Receiver
Drawback: iterative, higher complexity, requires pilot symbols (loss
in transmission efficiency)

 Proposed Solution I: Least Squares Khatri-Rao factorization (LS-KRF)
Closed-form, lower complexity for medium-to-high SNRs, requires
pilot symbols (loss in transmission efficiency)

 Proposed Solution II: Simplified Closed-form PARAFAC
Avoid the knowledge on the first row in the symbol matrix
Closed-form, lower complexity, same performance of the pilot
symbols based schemes for intermediate and high SNR regimes
(high transmission efficiency)

45

MIMO-OFDM Simulations (1)
Bit Error Rate vs. SNR @ K=2, M=4, F=4, N=5, P=3

-1
ALS ( 1= 2=0.0001)
(P-)LS-KRF
Parameter Settings:
10

K=2, M=4, F=4, N=5, P=3
-2
10 Channel estimate NMSE vs. SNR @ K=2, M=4, F=4, N=5, P=3

ALS ( 1= 2=0.0001)
0 (P-)LS-KRF
10
-3
10

-1
-4 10
10

-15 -10 -5 0 5 10 15 20 25 30 NMSE -2
SNR (dB) 10

-3
10

-15 -10 -5 0 5 10 15 20 25 30
SNR (dB)

46


Mean Processing Time vs. SNR @ K=2, M=4, F=4, N=5, P=3

Mean Processing Time (s)
0.06
ALS ( 1= 2=0.0001)
0.04 LS-KRF
P-LS-KRF

0.02

0
-15 -10 -5 0 5 10 15 20 25 30
SNR (dB)
Number of Iterations in ALS vs. SNR @ K=2, M=4, F=4, N=5, P=3
Number of Itertations

20 No. of Iters. Outer ( 1=0.0001)

No. of Iters. Inner ( 2=0.0001)
15

10

5
-15 -10 -5 0 5 10 15 20 25 30
SNR (dB)

47


(P-)LS-KRF (w/ Overhead) Parameter Settings I:
S-CFP w/ Pairing (w/o Overhead)
-1
10 K=2, M=4, F=4, N=5, P=3
Channel estimate NMSE vs. SNR @ K=2, M=4, F=4, N=5, P=3
1
10
-2 (P-)LS-KRF (w/ Overhead)
10
S-CFP w/ Pairing (w/o Overhead)

0
10

-3
10
-1
10

-15 -10 -5 0 5 10 15 20 25 30 NMSE -2
10
SNR (dB)

-3
10

-15 -10 -5 0 5 10 15 20 25 30
SNR (dB)

48


Parameter Settings II:
K=2, M=4, F=3, N=3, P=5
-1
10
Channel estimate NMSE vs. SNR @ K=2, M=4, F=3, N=3, P=5

ALS (w/ Overhead)
1
10 S-CFP w/ Pairing (w/o Overhead)

0
-2 10
10

NMDSE
ALS (w/ Overhead)
-1
S-CFP w/ Pairing (w/o Overhead) 10

-15 -10 -5 0 5 10 15 20 25 30
SNR (dB) -2
10

-3
10

-15 -10 -5 0 5 10 15 20 25 30
SNR (dB)

49

Outline

Motivation
UnB
Prewhitening
 Conclusions

50

Cooperative MIMO Applied to WSN (1)
 Wireless Sensor Networks
Several applications: agriculture, defense and environment
Energy limitations: small batteries and no replacement of them
Communication consumes most of the energy


 Simulation scenario
The cooperative MIMO channels generated using the IlmProp
50 sensors placed in an area of 400 × 400 m2
Sensors distributed following a random pattern following Poisson
distribution in two dimensions
Perfect synchronization among sensors assumed
Pilots with 30 data symbols
The transmitted data with 1000 data symbols
Stationary channel
The carrier frequency 2.4GHz
Fat fading over the transmission bandwidth
The simulation ranges from -10 to 10 dB SNR and 1000
independent Monte Carlo runs for each SNR


 Simulation scenario


 SNR vs BER


 Normalized energy consumption
5 hops for multi-hop scheme


Outline

Motivation
UnB
Prewhitening
 Conclusions

56

Conclusions
 In this presentation, we have present our state-of-the-art proposed schemes for
model order selection (MOS)
subspace prewhitening
joint symbol and channel estimation for MIMO-OFDM systems
Cooperative MIMO for WSN
 Important contributions in the MOS field
Modified Exponential Fitting Test (M-EFT): Matrix data contaminated by
white noise
R-D EFT: Tensor data contaminated by white noise
Closed-Form PARAFAC based Model Order Selection (CFP-MOS)
scheme: Tensor data contaminated by white and colored noise
 Important contributions in the subspace prewhitening field
Deterministic prewhitening: Matrix data and noise with correlation structure
Sequential GSVD: Tensor data and noise with tensor structure
Iterative Sequential GSVD: Tensor data and noise with tensor structure
No availability of noise samples
57

Conclusions

 In the MIMO-OFDM field:
Simplified closed-form PARAFAC based scheme: no overhead (w/o pilots)

 In the WSN field:
Cooperative MIMO: instead of single and multi-hop

58

Thank you for your attention!

Gracias por su atención!

Prof. Dr.-Ing. João Paulo C. Lustosa da Costa
University of Brasília (UnB)
Department of Electrical Engineering (ENE)
Laboratory of Array Signal Processing
PO Box 4386
Zip Code 70.919-970, Brasília - DF

Homepage: http://www.pgea.unb.br/~lasp 59

Presentacion us 2013_03_21

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