??????? ??????? ?????? ??? (Spread Spectrum) Chapter 2b

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Chapter 2b

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Chapter 2b Frequency- Hop Spread Spectrum
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1. Basics of Frequency Hopping

• Method to change the carrier frequency
  periodically

• Typically, modulation code is k-bits that select
  1-out-2k frequencies (or frequency bands) which
  are spaced approximately

• Rx removes the FH by mixing (down-converting)
  with LO signal which is hopping synchronously
  with the received signal.
• Usually coherent FH is not implemented since
  carrier phase estimation is required per each hop.

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1.1 Classification of Frequency Hopping Systems

• Academic Classification
• Slow Frequency Hopping
• In every hop there are more than
  one symbol
• Fast Frequency Hopping
• In every hop there is one symbol
  or less
• Industrial Classification
• Slow Frequency Hopping Less
  then 50hps
• Medium Frequency Hopping 50hps to
  500hps
• Fast Frequency Hopping More
  then 500hps

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2.1 Coherent slow FH Spread Spectrum
Tx implementation for Coherent slow FH Spread
Spectrum
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Coherent slow FH Spread Spectrum Receiver
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Analysis of Coherent slow FH Spread Spectrum

• Output of freq. synthesizer at Tx is the hop
  carrier hT(t) bandpass signal with random
  sequence of tones fn, of duration Th

(1)
Coherent assumption the same phase is used
each time
returns to the same frequency
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Analysis of Coherent slow FH Spread Spectrum
cont.

• PSD of transmitted slow FH

(2)
is the convolution of the two signals
(3)
(4)
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Analysis of Coherent slow FH Spread Spectrum
cont.

• Notations

(5)
(6)
(7)
PSD Sh(f) can be simplified by assuming
This assumption is valid whenever 1/Th is small
compared to the minimum frequency spacing i.e.
Slow FH
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Analysis of Coherent slow FH Spread Spectrum
cont.

• Simplified PSD further assume

(8)
Note PSD has discrete components, due to the
coherent FH assumption. The same phase is used
each time hT(t) returns to frequency fm . If
Then - the discrete components are negligible.
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Example

• Calculate the PSD of a transmitted coherent slow
  FH signal with the following parameters.Modulatio
  n BPSK, Rb1Mbps, Rh100Khops/sec, 4
  frequencies are employed, minimum spacing equals
  data rate.
• Solution
• Since minimum spacing gtgt hop rate
• we can use simplified PSD formula.

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Receiver for slow FH

• The received signal

(9)
This signal is down converted using hR(t)
(10)
Assuming
No tracking errors
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Receiver for slow FH
(11)
Recovered data-modulated carrier
Usually- there are tracking errors and
Thus the recovered carrier is phase modulated
by terms with the form
(12)
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Dealing with tracking errors in slow FH

• Need means for coherent carrier tracking,
  independent of the FH tracking loop.
• Possible way estimating Rx phase every hop
• feed forward carrier phase estimation using
  known sync. Word
• Need to protect sync. word to avoid hostile
  jammer (I.e., by changing periodically the sync
  word)

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Non coherent slow FH

• Coherent FH are complex to implement
• Non-coherent
• Differentially coherent
• When freq. synthesizer phase is random for each
  successive time interval, PSD of hT(t)

(13)
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Typical Example of Slow non coherent FH

• Data modulation
  2L-ary FSK
• Each TsLTb sec. the modulator
  outputs 1-out-2L tones
• Spacing between the tones 1/LTb
• Bd, Bandwidth of modulated signal Bd 2L/LTb
• Each Th the data modulated signal is translated
  to a new frequency by a FH modulator, 2k
  frequency bands of wide Bd
• Total BW of system
  Bss2kBd
• Th gt LTb slow FH condition

Plot this for k3 and L2. That is 4-FSK and 8
bands for the FH signals
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Non Coherent fast FH

• Here

• Hop-bands can change many times per symbol
• Data modulator can operate in different modes
  with different complexities. Can use the K hops
  per symbol based on majority vote or Maximum
  Likelihood sequence estimation.

• Benefits frequency diversity gain on each
  transmitted symbol
• Partial-band jammer
• improving performance in fast fading
  multipath channel

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Typical Example of Fast non coherent FH

• Data modulation
  2L-ary FSK
• Each Th(1/K) Ts sec. the modulator
  outputs 1-out-2L tones. That is the tones are
  subdivided into K chips
• Spacing between the tones 1/Th
  K / LTb K / Ts
• Bd, Bandwidth of modulated signal Bd 2L /
  Th K2L / LTb
• Each Th the data modulated signal is translated
  to a new frequency by a FH modulator, 2k
  frequency bands of wide Bd
• Total BW of system
  Bss2kBd
• Th lt LTb fast FH condition

Plot this for LKk 2. That is 4-FSK and 4
bands for the FH signals
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Combined DS-FH spread spectrum transmitter DPSK
data modulator
Data modulated carrier
NRZ data
Differential encoder
Bandpass filter
Frequency synthesizer
Code GENERATOR
FH code clock
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Combined DS-FH spread spectrum receiver DPSK
data demodulator
Bandpass filter
BP filter
Bandpass filter
Frequency synthesizer
Code GENERATOR
FH code clock