1

MID-SEMESTER PRESENTATION

ANAT KLEMPNERSPRING 2012

SUPERVISED BY: MALISA MARIJAN YONINA ELDAR

A Compressed Sensing Based UWB

Communication System

2

Contents

Background UWB – Ultra Wideband Project Motivation Compressed Sensing

Project overview Project Goals Project Tasks

Channel Estimation Theoretical Analysis

What’s Next?

3

UWB

A technology for transmitting information in bands occupying over 500 MHz bandwidth.

Used for short-range communicationVery low Power Spectral Density

4

UWB - Advantages

Useful for communication systems that require: High bandwidth Low power consumption Shared spectrum resources

5

UWB - Applications

In communications: High speed, multi-user wireless networks. Wireless Personal Area Networks / Local Area

Networks Indoor communication

6

UWB - Applications

Radar Through-wall imaging and motion sensing radar Underground imaging

Long distance , Low data rate applications Sensor networks High precision location systems

7

Project Motivation

The problem: The UWB signal has very high bandwidth, and

therefore the UWB receiver requires high-speed analog-to-digital converters.

High sampling rates are required for accurate UWB channel estimation.

8

Project Motivation

The proposed approach relies on the following UWB signal properties: The received UWB signal is rich in multipath

diversity.

The UWB signal received by transmitting an ultra-short pulse through a multipath UWB channel has a sparse representation.

9

Compressed Sensing

The main idea: A signal is called M-sparse if it can be written

as the sum of M known basis functions:

1

M

i ii

x

10

Compressed Sensing

An M-sparse signal can be reconstructed using a few number of random projections of the signal into a random basis which is incoherent with the basis in which the signal is sparse, thus enabling reduced sampling rate.

Where Φ is the random projection matrix (measurement matrix).

y x

11

Project Goals

We wish to build a simulation environment for an UWB communication system with compressed sensing based channel estimation.

The system will be based on the IEEE 802.15.4a standard for UWB communication.

The simulation environment will be used to compare different compressed sensing strategies.

12

Simulation Environment

Block-Diagram of the system:

Signal Generat

or

Multipath

ChannelDetection

Channel Estimation

To be implemented according to

IEEE 802.15.4a standard

Correlator Based Detector/ Rake

Receiver

13

Project Tasks

Phase 1 - Simulate the system and perform the channel estimation. Performance parameter: MSE of the estimation error as a function of the number of measurements.

Phase 2 - Simulate signal detection methods: correlator-based detector and the RAKE receiver .Performance parameter: BER vs. input SNR for different sampling rates and number of pilot symbols.

14

Project Tasks

Phase 3- Compare the MSE and BER performance for the different sampling schemes: the randomized Hadamard scheme, Xampling method, and the random filter.

Phase 4 -Compare the MSE and BER performance for the different sampling schemes and the reconstruction algorithms (e.g. , OMP, eOMP, and CoSaMP).

15

Currently: Phase I – Channel Estimation

Block-Diagram of the process:

Signal Generat

or

Multipath

Channel

Analog pre-

processing

A/D Conversio

n

Reconstruction Algorithm

To be implemented according to

IEEE 802.15.4a standard

Randomized Hadamard Scheme/ Random

Filter

Variants of the MP

algorithm

16

Channel Estimation - Theory

The signal:Each block of data contains pilot symbols,

which are used to estimate the channel parameters, and can be described as:

where is the transmission pulse. (Shape defined in the standard).

1

0

pN

fi

s t p t iT

17

Channel Estimation - Theory

Multipath Channel:A fading channel can be described as:

where is the number of multipaths, is the l-th propagation path, and is the delay of the l-th propagation path.

The goal of channel estimation is to estimate channel parameters .

1

0

L

l ll

h t t

18

Channel Estimation - Theory

Channel output:The received pilot waveform:

where is the channel noise.

The pilot waveform in each frame:

rs t s t h t w t

1

0

L

l ll

x t p t h t p t

19

Channel Estimation - Theory

Signal Model:An arbitrary signal can be described as a

vector of its samples.

The received signal in our case, can be written as a vector in the form:

where the non-zero coefficients of represent the channel gains, and is a Toeplitz Matrix with the elements:

x

,k j sp k j T

20

Channel Estimation - Theory

Analog Pre-Processing: Our goal is to achieve random projections of the

signal.

There are several ways to achieve random projections, the first method that will bet tested is the Randomized Hadamard Scheme.

21

Channel Estimation - Theory

Analog Pre-Processing – Randomized Hadamard Scheme: The sampling matrix: is used to create the sampled

signal:

R is a sub-sampling matrix – contains only one (Randomly chosen) non-zero value in each row.

H is the Hadamard matrix. S is a diagonal matrix with a random binary

modulation sequence on its digonal.

22

Channel Estimation - Theory

Reconstruction Problem: The problem of finding unknown channel parameters

can be described as:

This problem can be solved using variants of the Matching Pursuit (MP) Algorithm.

We will first try to use the OMP Algorithm – Orthogonal Matching pursuit.

1min . .s t y

23

What’s Next?

Simulate system according to IEEE 802.15.4a standard.

Perform channel estimation and evaluate performance.

Simulate signal detection methods.

24

Thank You!