Sub-NyquistReconstruction

Midterm PresentationWinter 2010/2011

By: Yousef Badran

Supervisors:Asaf ElronIna Rivkin

TechnionIsrael Institute of Technology

Project Overview

• Part of the Modulated Wideband Converter project cluster.– A system for sub-Nyquist sampling of multiband

signals.• Sub-module of the reconstruction block. • To be implemented on Altera Stratix III

(EP3SE260) FPGA device, using a single FPGA out of 4 available FPGAs.

Project Block Diagram

Input and Output

Input:Sequences z[n] representing spectrum slices

At most N sequences, one per slice

Spectral support slices s Bnt

lBtjl thetxnz

|)())((][ 2

Problem:Spectral support and carrier frequencies of bands are unknown.A single slice may contain more than one band (at most N/2).A single band might be divided between two slices.

Input and Output

Output:• A sequence of numbers, at most N/2 pairs of numbers per spectral slice.• Each pair of numbers describes the beginning and end of energy in a slice• Requires high resolution vectors for accurate results.

Welch’s Method for Power Estimation

Algorithm— Divide the time signal into successive, overlapping blocks.— Form the periodogram for each block:

— The Welsh estimate of the power spectral density is given by:

(K= # of blocks)

Contradiction: Maximize M for spectral resolution vs. Maximize K for better averaging results and greater spectral stability.

Typical choice:

21( ) | ( ) |kx kP f FFT x

M

1

1( ) ( )k

k

X xi

S f P fK

_ _M K Length of vector

Welch’s Method (Cont.)Demands

– 18-bit fixed-point representation.• 17 bit word length• 1 bit fraction length

Problem?MATLAB’s FFT does not support fixed point operations.

Solution:Use Simulink FFT block instead.

Problem?Simulink Fixed-point block-set license keys was not acquired by the Technion .

Alternatives:Use Altera FFT MATLAB model (?)Find an alternative fixed point FFT calculation published on the internet.

Welch’s Method for Power EstimationComparision between MATLAB’s PWELSH, and my own: (M=256, R=128)

Welch’s Method for Power EstimationComparision between MATLAB’s PWELSH, and my own: (M=256, R=128)

Quantization

Uniform Quantization and Dynamic Range:Map amplitude values into a set of discrete values, depending on the dynamic range of the signal values and perceptual sensitivity.

- Useful for band recognition and band level separation.- Helps identify and recognize weak signals.- Helps identify strong signals that exceed the domain range.- Helps separate different signals located on the same band.

ALTERA FFT MegaCore FunctionThe FFT MegaCore function is a high performance, highly-parameterizable Fast Fourier transform (FFT) processor. The FFT MegaCore function implements a complex FFT or inverse FFT (IFFT) for high-performance applications.

Features (resolution of 4096 bits):+ Bit-accurate MATLAB models.+ Reduced memory requirements.+ Maximum system clock frequency >300 MHz (vs. Input freq. of 20 MHz).+ Low multipliers usage (~20/384 Mul. Blocks)

- High Logic Registers usage (~7-10%).

Resources

Mathematical Tools

Project WorkflowAlgorithm

• Resources & requirements• Understand theory and reference implementation• Propose alternative and equivalent calculation

MATLAB

• Floating-point representation• 18-bit fixed point representation

• Find an alternative fixed point FFT Solution• Find implementations of required mathematical operations in VHDL

VHDL Design

• Creating a block diagram• Altera DSP designer• Implement missing mathematical tools in VHDL

Design Simulation

• ModelSim• Creat testbench for each VHDL design• Simulations

Synthesis & Debug

• Synthesis • Timing simulations using Altera Stratix III libraries

• Debugging the system

Next Steps

Thank you!