Presentacion us 2013_03_21

Universidade de Brasília

Laboratório de Processamento de Sinais em Arranjos

1

Multi-Dimensional Array Signal Processing

Applied to MIMO Systems

Prof. Dr.-Ing. João Paulo C. Lustosa da CostaUniversity 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



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Outline

Universidade de Brasília: A Short Overview

Research Areas: Laboratory of Array Signal Processing


Motivation

Model Order Selection

Prewhitening

MIMO-OFDM System

Cooperative MIMO for WSN

Conclusions

UnB



3

Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



4

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



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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



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Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



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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



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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



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Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



Motivation (1)

Malicious traffic detection

3

Time slots (10 min)

Am

ou

nt

of

acc

esses

Detect if there is some malicious traffic

How many attackers and how many ports being attacked

Development of Intrusion Detection Systems (IDS)



Motivation (2)

Business Intelligence (BI)

3

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

Microphone array

Sound source 1

Sound source 2

Applications: phone conference devices, bioacustics, computational

forensics and hearing aids.

3



Motivation (4)

Wind tunnel evaluation

Improvement of the aerodynamics of vehicles

Array

4



Receive array: 1-D or 2-D

Frequency

Time

Transmit array: 1-D or 2-D

Direction of Arrival (DOA)

Delay

Doppler shift

Direction of Departure (DOD)

Motivation (5)

Channel model

5



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Goal

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

MeasurementsModel order

selection

Subspace

Prewhitening

Parameter

EstimationIs the noise

colored?

Yes

No



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Goal: Model Order Selection

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


selection

Subspace

Prewhitening

Parameter


colored?

Yes

No



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Goal: Parameter Estimation

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


selection

Subspace

Prewhitening

Parameter


colored?

Yes

No



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Goal: 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


selection

Subspace

Prewhitening

Parameter


colored?

Yes

No



20

Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



21

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).



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Data model and Goal

Noiseless case

Our objective is to estimate d from the noisy observations .

Matrix data model

+ +=



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1 2 3 4 5 6 7 80

2

4

6

8

10

Eigenvalue index i

i

Analysis of the Noise Eigenvalues Profile

Finite SNR, Finite N

M - d noise eigenvalues follow a

Wishart distribution.

d signal plus noise eigenvalues

d = 2, M = 8, SNR = 0 dB, N = 10

The eigenvalues of the sample covariance matrix



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Exponential Fitting Test (EFT)

Observation is a superposition of noise and signal

The noise eigenvalues still exhibit the exponential profile

We can predict the profileof the noise eigenvaluesto find the “breaking point”

Let P denote the number of candidate noise eigenvalues.

• choose the largest Psuch that the P noise eigenvalues can be fitted with a decaying exponential

d = 3, M = 8, SNR = 20 dB, N = 10



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Comparison of MOS Schemes (1)

Case that M and N are close



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Comparison of MOS Schemes (2)

Case that M >> N



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Data Model and Goal

Noiseless data representation

Problem

where is the colored noise tensor.

= ++

Our objective is to estimate d from the noisy observations .



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R-D Exponential Fitting Test

We can define global eigenvalues

R-D exponential profile



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R-D Exponential Fitting Test

Comparison between the global eigenvalues profile and the profile

of the last unfolding

R-D exponential profile



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Closed-form PARAFAC based

Model Order Selection For P = 2, 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.

For P = 4, i.e., P > d

+=

+=

= +

= +

P

1 2 3 4 5

+ +

+ +



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Simulations

White Gaussian noise

Model Order Selection in Additive White Gaussian Noise Scenario

Probability of correct Detection vs. SNR



32

Simulations

Colored Gaussian noise

Model Order Selection in Additive Colored Gaussian Noise Scenario

Probability of correct Detection vs. SNR



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Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



34

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.



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Noise Analysis

Stochastic

prewhitening schemes

With colored

noise the d main

components are

more affected.

Analysis via SVD

Deterministic

prewhitening scheme



36

Simulations

The noise correlation

is known.

SE – Standard ESPRIT

Subspace Prewhitening for Colored Noise with Structure

RMSE vs. Correlation Level



37

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

Sequential GSVD



38

Simulations

Subspace Prewhitening for Multi-dimensional Colored Noise

RMSE vs. Number of Samples without Signal Components (Nl)

STE – Standard

Tensor-ESPRIT



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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)



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Simulations


RMSE vs. Correlation Level

STE – Standard

Tensor-ESPRIT



41

Simulations


RMSE vs. Number of Iterations

STE – Standard

Tensor-ESPRIT



42

Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



MIMO-OFDM System (1)



MIMO-OFDM System (2)

K: number of receive antennas.

M: number of transmit antennas.

N: number of time-slots in the whole time frame.

P: number of symbol periods in each time-slot.

F: number of subcarriers

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

.

Known.

Known.



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)

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-15 -10 -5 0 5 10 15 20 25 30

10-4

10-3

10-2

10-1

SNR (dB)

Bit E

rror

Rate

Bit Error Rate vs. SNR @ K=2, M=4, F=4, N=5, P=3

ALS (1=

2=0.0001)

(P-)LS-KRF

-15 -10 -5 0 5 10 15 20 25 30

10-3

10-2

10-1

100

SNR (dB)

NM

SE

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

ALS (1=

2=0.0001)

(P-)LS-KRF

Parameter Settings:

K=2, M=4, F=4, N=5, P=3



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-15 -10 -5 0 5 10 15 20 25 300

0.02

0.04

0.06

SNR (dB)

Mean P

rocessin

g T

ime (

s)

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

-15 -10 -5 0 5 10 15 20 25 30

5

10

15

20

SNR (dB)

Num

ber

of

Itert

ations

Number of Iterations in ALS vs. SNR @ K=2, M=4, F=4, N=5, P=3

ALS (1=

2=0.0001)

LS-KRF

P-LS-KRF

No. of Iters. Outer (1=0.0001)

No. of Iters. Inner (2=0.0001)




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Parameter Settings I:

K=2, M=4, F=4, N=5, P=3

-15 -10 -5 0 5 10 15 20 25 30

10-3

10-2

10-1

SNR (dB)

Bit E

rror

Rate


(P-)LS-KRF (w/ Overhead)

S-CFP w/ Pairing (w/o Overhead)

-15 -10 -5 0 5 10 15 20 25 30

10-3

10-2

10-1

100

101

SNR (dB)

NM

SE


(P-)LS-KRF (w/ Overhead)





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Parameter Settings II:

K=2, M=4, F=3, N=3, P=5

-15 -10 -5 0 5 10 15 20 25 30

10-2

10-1

SNR (dB)

Bit E

rror

Rate


ALS (w/ Overhead)


-15 -10 -5 0 5 10 15 20 25 30

10-3

10-2

10-1

100

101

SNR (dB)

NM

DS

E


ALS (w/ Overhead)





50

Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



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



56

Outline




Motivation


Prewhitening

MIMO-OFDM System


Conclusions

UnB



57

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


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



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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



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Thank you for your attention!

Gracias por su atención!

Prof. Dr.-Ing. João Paulo C. Lustosa da CostaUniversity 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

Documents

Presentacion us 2013_03_21