Anjela Y' Govan

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Finding Signal In the Noise Direct-Sequence
Spread Spectrum Methods
Anjela Y. Govan Mathematician Northrop
Grumman Morrisville, NC 919.465.5000
University of Tennessee October 23, 2009
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Digital Signal Processing

• Applications communications, image processing,
  RADAR, SONAR, seismology, biomedicine, etc.
• Academic disciplines electrical and computer
  engineering, computer science, mathematics
• Math probability (e.g. random processes), linear
  algebra, calculus, abstract algebra (e.g. Galois
  fields), discrete math, differential equations,
  etc.
• Jobs Communications industry, Defense sector

Problem
accurately transfer data from point A to point B
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Basic Communications Chain
Micro- phone
Analog To Digital
Digital Modulation
Channel Encoding
Source Encoding
Channel
Speaker
Digital To Analog
Digital De- Modulation
Channel Decoding
Source Decoding
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• Why Digital (discrete and finite)
• computational, capacity of the computers
• mathematical, linear algebra

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Sending signals

• Message HELLO
• Source encode binary message (ASCII), 40 bits
• 01001000 01000101 01001100 01001100 01001111
• Modulate Quadrature phase-shift keying (QPSK),
• four analog signals to carry the data sin(?t?)
• s0(t) 00, s1(t) 01, s2(t)
  10, s3(t) 11
• Sent message
• s1s0s2s0 s1s0s1s1 s1s0s3s0 s1s0s3s0 s1s0s3s3

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Receiving signals

• (attenuated, Doppler shifted) Signal (noise)
• s1s0s2s0
• Analog-to-Digital (A/D) sampling
• 01001000
• Received H

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Time and Frequency Domains

• Time h(t)
• Multiplication - h(t)g(t)
• Convolution - h(t)?g(t)
• Periodic
• Discrete

• Frequency H(f)
• Convolution - H(f)?G(f)
• Multiplication - H(f)G(f)
• Discrete
• Periodic

Fourier transform
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Signal Spectrum Time vs Frequency

• Two different ways of looking at the same thing

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Direct-Sequence Spread Spectrum (DSSS) Signals

• In time domain multiply x(t)d(t)c(t) (data,
  spread code)
• In frequency domain convolution X(f)D(f)?C(f)

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Why spread spectrum?

• Hard to find
• Resistant to jamming
• Multiple users in the same frequency band (Code
  Division Multiple Access)

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Extracting the DSSS signal

• Let the spread code c(t)1
• Wrong spread code c(t)

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Extracting the DSSS signal

• Let the spread code c(t)1
• Right spread code c(t), wrong phase

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Extracting the DSSS signal

• Let the spread code c(t)1
• Right spread code c(t)
• Synchronization is a must!

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Dominant Mode Despreading Algorithm

• Brian Agee, Roland J. Kleinman, Jeffrey H.
  ReedIEEE, 1996

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DMDS Algorithm (Theory)
STEP 4
STEP 3
STEP 2
STEP 1

• Despread

Dominant Mode w of the autocorrelation ?
maximum eigenvalue
Autocorrelation Matrix H Hermitian T
time-averaging
Frequency-channelize data signal x(t) fr
spread code repeat rate Ld LTI lowpass filter
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DMDS Implementation

• x(t) c(t)d(t) ? xtctdt
• s number of symbols transmitted
• p number of samples per symbol
• m number of chips per data symbol
• n number of chips per spread code repeat
• xt(x0, x1, , xn-1, xn, xn1, ,
  x2n-1, , xms-1)

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Implementation A/D

• Spread Signal x(t) ? xt

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Implementation Simple Example

• p m (samples per symbol chips per symbol)
• m 15, then fd 1/15
• n 32, then fr 1/32
• DEMO

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