Sub-Nyquist Sampling of Wideband Signals

Itai Friedman Tal Miller

Supervised by:

Deborah Cohen

Technion – Israel Institute of Technology

Optimization of the choice of mixing sequences

Presentation Outline

System Description Project ObjectiveMain Project Stages

Spectrum Sparsity

Spectrum is underutilizedIn a given place, at a given time, only a small number of PUs transmit concurrently

Shared Spectrum Company (SSC) – 16-18 Nov 2005

Model

Input signal in Multiband model:

Signal support is but it is sparse.N – max number of transmissionsB – max bandwidth of each transmission

Output:

Reconstructed signalBlind detection of each transmission

Minimal achievable rate: 2NB << fNYQ

~ ~~~

Mishali & Eldar ‘09

NYQf

The Modulated Wideband Converter (MWC)

~ ~~~

ip t

iy n

Mishali & Eldar ‘10

1

2 sT

1

2 sT

1

2 sT

snT

snT

snT

MWC – Recovery

Sz f

~~~~

z f

SA

y f

A

S Sz f A y f †

1

2 sT

1

2 sT

1

2 sT

1

2 sT

Now we can solve a linear set of equations for input signal:

MWC – Recovery System

MWC – Mixing & AliasingSystem requirement:

are periodic functions with period called “Mixing functions”

Examples for :…

ip t

1

-1

pT

Frequency domain

ip t

Project Objective

Questions:What are the best Mixing functions ?Focusing on {+1,-1} functions, what properties should the sequences have?

Main Objective: Finding optimal Mixing function sequences for effective reconstruction

ip t

What is our part in the system?

Analog signal generation

Mixing

Filtering

Sampling

Recovery

The code already exists, we modify the mixing functions generator

Main Project StagesDeepening the understanding of the theory behind the systemUnderstanding the current achievements in the mixing functions fieldDefining sequences criteria for optimal system performanceSimulating the different sequences in the MWC system using MatlabDetermining what are the optimal sequences based on simulations and publicating the findings

Gantt (5 weeks)Week 5

Week 4

Week 3

Week 2

Week 1

Achievements

Understanding the fundamentals of CS

Literature review of sequences

Going over the simulation code and being able to run a simulation

Thank youFor listening

And thanks Debby for the basis to our presentation