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ESTIMATION AND DETECTION OF COHERENT SIGNALS

BACHELOR OF ENGINEERING

Electronics and Communication Engineering

By

SHAIK MOHAMMED NAWAZ 04-08-4023SHAIK ASWATH HUSSAIN 04-08-4142L

MOHAMMED KHADEER 04-07-4046

Department of Electronics and Communication Engineering

Muffakham Jah College of Engineering and Technology

(Affliated to Osmania University)

Banjarahills Hyderabad

2009-2010

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ESTIMATION AND DETECTION OF COHERENT SIGNALS

A project submitted in partial fulfillment of the requirement of the degree of

BACHELOR OF ENGINEERING

of theOsmania University

Hyderabad, Andhra Pradesh

BySHAIK MOHAMMED NAWAZ 04-08-4023

SHAIK ASWATH HUSSAIN 04-08-4142L

MOHAMMED KHADEER 04-07-4046

Muffakham Jah College of

Engineering and Technology

Department of Electronics & Communication Engineering

MUFFAKHAM JAH COLLEGE OF ENGINEERING & TECHNOLOGY

Mount Pleasant, 8-2-249, Road No.3, Banjarahills,Hyderabad - 500 035, Andhra Pradesh, India.

2009-2010

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Department of Electronics and Communication Engineering

Certificate

This is to certify that

SHAIK MOHAMMED NAWAZ 04-08-4023

SHAIK ASWATH HUSSAIN 04-08-4142LMOHAMMED KHADEER 04-07-4046

Belonging to B.E. ECE 4/4 of Muffakham Jah College of Engineering and

Technology, has successfully completed their project work entitled during

the academic year 2010-2011 for the partial fulfillment of award of bachelor

of engineering in the field of ECE as presented by Osmania University, Hyd.

This is a bonafide record of the work carried under our guidance and

supervision.

Dr. KALEEM FATIMA Mrs. AYESHA NAAZ

H.O.D.ECE Associate Professor MJCET, ECED

PROJECT GUIDE

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ACKNOWLEDGEMENT

Firstly, we would like to express our deepest sense of gratitude to Associate

Professor Mrs Ayesha Naaz for giving us the opportunity to work on this project. She

was always there to provide the insightful thinking needed for completion of the Project.

She has been a constant source of inspiration and guidance. We are also greatly indebted

to MJCET ECED for allowing us to complete our project in the labs. It has really been an

enriching experience for us. We would like to thank Mrs Ayesha Naaz for the

innumerable discussions we had with her during course of project.

We would also like to thank Dr Kaleem Fatima and Dr C. Rangaiah for their

constant support and help, without the help form them our project would have taken us

much longer than the final four months from start to finish. We are also indebted to thelab incharge Mr M.A. Majeed Zubair sir for his constant cooperation and help he has

provided.

We would once again like to thank Mrs Ayesha Naaz as she is not only expert in

signal processing, but also gave us engineering insight into the detailed engineering level

of our design. The really cool thing is that we took the basic data of ULA and continued

it up to the final 3D geometry and it matched up. This is some of the stuff engineers

dream of. Mrs Ayesha Naaz, as far as we are concerned, is the best signal processing

engineer we have worked with. we would recommend her to anyone.

Thanks are also due to our Lab mates for making our stay there a memorable one.

They were real fun to work with.

Finally I offer my heartiest gratitude to my family members for their selfless

blessings.

With sincere regards,

SHAIK MOHAMMED NAWAZ

SHAIK ASWATH HUSSAIN

MOHAMMED KHADEER

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CONTENTSAbstract i

List of Symbols ii

List of abbreviation iii

1. Introduction to array signal processing.

2. Direction of arrival estimation

3. Esprit

4. Applications of DOA

5. Conclusions

6. References

ABSTRACT

Direction finding denotes the direction from which usually apropagatingwave

arrives at a point, where usually a set of sensors are located. Direction finding cannot be

implemented using a single sensor. To accomplish this task we need an array of sensors.

The processing of signal received by an array of sensors is known as array signal

processing

Array signal processing deals with the processing of signals received by an array

of sensors placed at different points in a field of interest which may be an

electromagnetic field. A sensor array is used to measure the wave field and extract

information about the sources, the medium and the properties of the sources. It has varied

fields of applications, such as Tomography, Seismology, Sonar, Radar communication,

Medical diagnosis etc.

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ESPRIT algorithm is used to estimate the number and directions of arrival

(DOA) of the sources. The algorithm uses the orthogonal property for the estimation of

direction of arrival. It performs the Eigen value decomposition of the sample covariance

matrix of received signal at array of sensors.

ESPRIT is implemented on 1 D and 2 D array geometries such as triangle, square, circle.

List of Abbreviation

DOA Direction Of Arrival

MUSIC MUlti SIgnal Classification

SNR Signal to Noise Ratio

ULA Uniform Linear Array

UCA Uniform Circular Array

List of Symbols

D Distance between sensors

Azimuth angle

Wavelength

W White additive noise

r(t) Received signal at array element

s(t) Source signal

n(t) Random noise

A Steering vector

R Covariance Matrix of received signal

Hermit transform

Variance of additive noise

M Number of sensors

D Number of source signals

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N Number of snapshots

Signal Subspace

Noise Subspace

Music Spectrum

elevation angle

INTRODUCTION TO ARRAY SIGNAL PROCESSING

Array signal processing is a part of signal processing that uses sensors that are

organized in patterns, or arrays, to detect signals and to determine information about

them. An array of sensors is used to receive a propagating wave field with the following

objectives:

1) To localize a source.

2) To receive a message from a distant source.

3) To image a medium through which the wave field is propagating.

An array of sensors is often used in many diverse fields of science and engineering,

particularly where the goal is study the propagating wave fields. Various fields of

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d

1

Signal Source 1

Receive Signals

Sensor Array

(ULA )

Signal Source 2

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application of array signal processing are tomography, seismology, sonar, radar,

communication, medical diagnosis etc.

The most common application of array signal processing involve estimating

direction of arrival (DOA), which our project investigates In signal processing,

direction of arrival denotes the direction from which usually apropagatingwave arrives

at a point, where usually a set of sensors are located.

We aim merely to demonstrate the potential that array geometries have in estimating

direction of arrival (DOA).

There are various DOA estimation algorithms available of which we are using

ESPRIT algorithm. ESPRIT is used to describe the experimental and theoretical

techniques involved in the determining the parameters of multiple wave fronts arriving at

an sensor array from measurements made on the signals received at the array. MUSIC

algorithm uses the orthogonal relation between signal subspace and noise subspace for

estimating the direction of arrival of the signal. ESPRIT performs the Eigen-

decomposition of the covariance matrix of received signal at the sensor array.

Direction of Arrival Estimation Algorithm

2.1 Introduction

We know that there is a one-to-one relationship between the direction of a signal

and the associated received steering vector. It should therefore be possible to invert the

relationship and estimate the direction of a signal from the received signals. An antenna

array therefore should be able to provide for direction of arrival estimation.

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Fig 2.1: Antenna array and DOA estimation algorithm

In practice, the estimation is made difficult by the fact that there are usually an

unknown number of signals impinging on the array simultaneously, each from unknown

directions and with unknown amplitudes. Also, the received signals are always corrupted

by noise. Nevertheless, there are several methods to estimate the number of signals andtheir directions. Figure 2 shows some of these several spectral estimation techniques.

BASIC CONDITIONS OF DOA ALGORITHMS

The DOA algorithm must satisfy the following conditions :

Low computational intensity (MIPS/MFLOPS)

High accuracy (RMSE)

High speed

Easy implementation

Good performance at low SNRs

Works on a 2 microphone array system with 4cm separation between

them.

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2.2 CLASSIFICATION OF METHODS OF DOA ESTIMATION

Figure 2.2: Some of the several spectral estimation techniques

Most of the antenna array direction of arrival(DOA) estimation methods are based

on the sub-space concept and require the Eigen-decomposition of the input correlation

matrix. State-space method, MUSIC, and ESPRIT are examples of these techniques.

Based on the Eigen- decomposition of covariance matrix of the array output, they offer

high resolution and give accurate estimates. In this work, Music algorithm for direction

of arrival estimation (DOA) is proposed. Of all techniques shown in Fig. 2, ESPRIT is

probably the most popular technique

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Estimation of Signal Parameters via Rotational

Invariance Techniques

The ESPRIT method for DOA estimation was first proposed by Roy and Kailath .Assumethat the array ofNsensors consists ofN/2 pairs called doublets. The displacement vector

from one sensor in the doublet to its pair is identical for all the doublets. The first and

second members of the doublets can be separated and grouped to form two N/2 element

subarrays. The vectors x and y are the data vectors corresponding to each of the

subarrays. The output of the subarrays x and y can be expressed as:

Xn=ASn+Vn(x)

Yn=Asn+Vn(x)

is a digonal matrix rxr

Zn= | Xn | = AbSn+Vn

| Yn |

R is the covarience matrix of z.

2.3.3 Characteristics of ESPRIT algorithm

1. The algorithm has good performance and can be used with a variety of array

geometries.

2. The algorithm requires the knowledge of sensor element characteristics.

3. It can be used to estimate multiple parameters (Azimuth, Elevation, range etc.,)per source.

4. The performance of this algorithm improves when SNR and / or the number of

snapshots (i.e., the total information content) is increased above a particular threshold.

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5. This algorithm encounters difficulties in presence of fully correlated sources (i.e.,

Multi path propagation) and is computationally expensive because it involves a search

over the function for the peaks. Spatial smoothing can be introduced to overcome

this problem. In fact, spatial smoothing is essential in a multipath propagation

environment . To perform spatial smoothing, the array must be divided up into smaller,

possibly overlapping subarrays and the spatial covariance matrix of each subarray is

averaged to form a single, spatially smoothed covariance matrix. The MUSIC algorithm

is then applied on the spatially smoothed matrix

6.

2.4ESPRIT

Algorithm flow chart

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The unitary ESPRIT

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QR ESPRIT

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*( ) ( ) ( ) P a S a =

*

1( )

( ) ( ) ( )P

a in v s a

=

*

* *

( ) ( )( )

( ) ( )N N

a aP

a E E a

=

'( )

' 'N N

a aP

a E E a =

{ }1 0s in . ( ) / ( )K c a n g le z d

=

{ }10

sin a rg ( ) /( )K K

c d

=

Applications of doa

DOA estimation is a very important technique both in wirelesstelecommunication system and audio/speech processing system

The estimated DOAs of incoming signals can be used to suppress the

interference and enhance the desired signal in an adaptive array sensor system

Another applicable field of DOA estimation is robotics

It can deal with signals up to the number of sensors, and because its unnecessary

to search nulls of directivity patterns, the calculation cost is reduced.

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. CONCLUSION

The conclusions based on the results of this simulation study are summarized as follows:

1. The ESPRIT method estimates signal DOA by finding the roots of two independentequations closest to the unit circle. This method does not require using a scan vector

to scan over all possible directions like the MUSIC (Multiple Signal Classification)

algorithm.2. Estimation error is relatively independent of signal azimuth angle if the signal

impinging the array from low elevation angle.

3. When the signal impinging the array from high elevation angle, there are some criticalazimuths angles that yield a very large estimation error. This is due to the fact that at

those critical azimuth angles, the received data vectors are very close. Thus there is not

sufficient information to process the received data. To avoid large estimation

error, we suggest to alternatively choosing a different subset and shifting the subset indifferent directions.

4. Estimation error can be reduced by (a) using an array containing a large number of

elements, (b) increasing the number of temporal averaging in matrix element

estimation.5. Array element position may deviate from the ideal position. Position deviation will

degrade DOA performance. Sensitivity analysis due to imprecise element position will becarried out in future study.

REFRENCES

1. SCHMIDT,R.O: Multiple emitter location and signal parameter estimation, IEEE

transactions on Antennas and propagation, vol . AP-34, march 1986

2. CHOI, Y.H: Subspace based coherent sources localization with forward and

backward covariance matrices, IEEE proceeding on radar sonar and Navigation, vol-

149, june 2002

3. USHA PADMINI,C. PRABHAKARNAIDU,S: CIRCULAR ARRAY AND

STIMATION OF DIRECTION OF ARRIVAL OF A BROADBAND SOURCE, signal

processing, vol-37, 1994

Books

1. Sensor array signal processing---- Prabhakar s.naidu

2. Digital spectral analysis--------Marple

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