DIGITAL SPREAD SPECTRUM SYSTEMS

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DIGITAL SPREAD SPECTRUM SYSTEMS
ENG-737

• Wright State University
• James P. Stephens

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GOLD CODE IMPLEMENTATION

• Gold Codes are used by GPS and are constructed by
  the linear combination of two m-sequences of
  length n10
• There are 1023 possible codes possible for n10
• Each different code is generated by inputting a
  different initial fill into the G2 Coder
• Each GPS satellite is assigned a different code

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GPS C/A CODER
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KASAMI CODES

• Kasami sequences are one of the most important
  types of binary sequence sets because of their
  very low cross-correlation and their large number
  of available sets
• There are two different sets of Kasami sequences,
  Kasami sequences of the small set and sequences
  of the large set
• A procedure similar to that used for generating
  Gold sequences will generate the small set of
  Kasami sequences with M 2n/2 binary sequences
  of period N 2n/2 1
• In this procedure, we begin with an m-sequence
  a and we form the sequence a by decimating a
  by 2n/2 1
• It can be verified that the resulting sequence a
  is an m-sequence with period 2n/2 - 1

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KASAMI CODE IMPLEMENTATION
X4 X 1 q 2n/2 1 5 m 2n/2 - 1
3 Where, q decimation value m period of a
a
a 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0
a 1 1 0

• a xor b 0 0 1 0 1 1 1 0 1 1 1 1
  1 1 0

• Kasami codes are generated by cyclically
  shifting a 2n/2 -2 2 times
• Including a and b there are 2n/2 4 sequences

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KASAMI CODE IMPLEMENTATION

• Example
• Let n10, therefore, N2n - 1 1023 (length of
  a)
• The decimation value is 2n/2 1 33 which is
  used to create a
• 1023/33 31 which will be the length of a
• If we observe 1023 bits of sequence a, we will
  see 33 repetitions of the 31-bit sequence which
  we will call sequence b
• Now taking 1023 bits of sequence a and b we
  form a new set of sequences by adding (modulo-2
  addition) the bits from a and the bits from b
  and all 2n/2 2 cyclic shifts of the bits from
  b
• By including a in the set, we obtain a set of
  2n/2 32 binary sequences of length 1023
• All the elements of a small set of Kasami
  sequences can be generated in this manner

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KASAMI CODE IMPLEMENTATION

• The autocorrelation and cross-correlation
  functions provide excellent properties, as good
  or better, than Gold Codes
• The large set of Kasami sequences is generated
  in a similar manner with the addition of another
  register
• The two registers are a preferred pair as in Gold
  Code and therefore when combined with the
  decimated sequence, produce all the associated
  Gold Codes and the Kasami sequences for an even
  larger let of sequences

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FACTORS FOR DETERMINING SIGNALING FORMAT

• Signal spectrum
• Synchronization
• Interference and noise immunity
• Error detection capability
• Cost and complexity

Before we begin a more in-depth discussion of
direct sequence spread spectrum, it will be
helpful to compare various encoding and / or
signaling techniques used in digital
communications
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DIGITAL SIGNAL ENCODING FORMATS

• Biphase-Space
• Always a transition at beginning of interval
• 1 no transition in middle of interval
• 0 transition in middle of interval
• Differential Manchester
• Always a transition at middle of interval
• 1 no transition at beginning of interval
• 0 transition at beginning of interval
• Delay Modulation (Miller)
• 1 transition in middle of interval
• 0 no transition if followed by 1, transition at
  end of interval if followed by 1
• Bipolar
• 1 pulse in first half of bit interval,
  alternating polarity from pulse to pulse
• 0 no pulse

• Nonreturn to zero-level (NRZ-L)
• 1 high level
• 0 low level
• Nonreturn to zero-mark (NRZ-M)
• 1 transition at beginning of interval
• 0 no transition
• Nonreturn to zero-space (NRZ-S)
• 1 no transition
• 0 transition at beginning of interval
• Return to zero (RZ)
• 1 pulse in first half of bit interval
• 0 no pulse
• Biphase-Level (Manchester)
• 1 transition from hi to lo in middle of
  interval
• 0 transition from lo to hi in middle of
  interval
• Biphase-Mark
• Always a transition at beginning of interval
• 1 transition in middle of interval
• 0 no transition in middle of interval

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DIGITAL SIGNAL ENCODING FORMATS
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DIFFERENTIALLY ENCODING AND DECODING
Encoder
1s are converted to 180o phase shifts, 0s are
unchanged
Decoder
1s are inserted for every transition, 0s if
no transition
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DIFFERENTIAL ENCODING
1 0 1 1 0 0 0 1 1 0 1
1 0 1 1 0 0 0 1 1 0 1
0 0 1 0 0 0 0 1 0 0 1
1 0 0 0 1 0 1 1 1 0 0
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DIGITAL SIGNAL ENCODING FORMATS

• Phase-encoding schemes are used in magnetic
  recording systems, optical communication, and in
  some satellite telemetry links
• Schemes with transitions during each interval are
  self-clocking
• Schemes that transition in the middle are
  naturally shorter pulses and require greater
  bandwidth
• Differential encoding supports non-coherent
  detection

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DIRECT SEQUENCE SYSTEMS

• DSSS is the most common commercially
• Sometimes called PN spread spectrum
• Used in CDMA Cellular systems, GPS, some earlier
  cordless telephones, and 802.11(b)
• DSSS directly modulates a carrier with a high
  rate code that is combined with data
• DSSS usually employs PSK and the code is often
  combined with data by mod-2 addition, i.e. code
  inversion keying
• Predominantly, in practice, a DSSS transmitted
  signal is either
• BPSK (Binary Phase Shift Keyed)
• QPSK (Quadrature Phase Shifted Keyed)
• MSK (Minimum Shifted Keyed)

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BINARY SHIFT KEYING

• This technique is implemented with a Balanced
  Modulator
• Two basic types of modulators are
• Single balanced
• Double balanced
• Three port devices in which ? 1s on the code
  data input cause 180 degree phase shifts of the
  carrier

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BINARY PHASE SHIFT KEYING (BPSK)
Data Code
Typically more than one cycle per chip
1800 Phase Shifts
BPSK
Carrier
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BPSK POWER SPECTRAL DENSITY
Suppressed Carrier
Discrete spectral lines
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SUPPRESSED CARRIER

• Reasons that make suppressed carrier desirable
  are
• More difficult for adversary to detect signal
• Power not wasted on carrier
• Signal has constant envelop level so that power
  efficiency is maximized for the bandwidth used
• Bi-phase modulators are simple, stable, low cost
  devices

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BPSK CIRCUIT IMPLEMENTATION
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PHASOR REPRESENTATION

• BPSK is called antipodal
• Antipodal means that two symbols meet the
  following criteria
• s1 -s2
• BPSK other than 1800 is not antipodal

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QUADRATURE PSK OR QPSK

• QPSK does not degrade as seriously as BPSK when
  passed through non-linearity simultaneous with
  interference
• Bandwidth is one-half required by BPSK at same
  data rate (or twice the data rate in the same
  bandwidth)

AB ?
00 0
01 90
10 180
11 270
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QPSK BLOCK DIAGRAM
m1(t)cos(2pft)
Code 1
cos(2pft)
Data 1
Carrier
SQPSK
sin(2pft)
Code 2
m2(t)sin(2pft)
m2(t)
Data 2
SQPSK(t) m1cos(2pft) m2sin(2pft)
m1(t)
Twice the data same BW
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ALTERNATIVE IMPLEMENTATION OF QPSK
2-bit serial to parallel
Code
Data
QPSK
Half the BW same data rate
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BALANCED MODULATORS
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BPSK MODULATION
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CARRIER SUPPRESSION

• Carrier suppression may be expressed in dB in
  accordance with the following expression
• V 10 log B/ (A sin ? A sin ?)
• Where,
• B amplitude of the correct output signal
• (i.e. when AA
  and ? ? 00)
• A 00 signal
  amplitude
• A 1800 signal amplitude
• ? A phase offset
• ? A phase offset

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CARRIER SUPPRESSION

• Example
• Compute the carrier suppression of
  biphase-balanced modulation in dB if the
  amplitude of the correct signal (B) is 10, the
  zero and 1800 signal amplitude is 5 (A and A),
  and the phase offsets (? and ?) are
• (a) 90 degrees
• V 10 log 10/(5 sin 900 5 sin 900) 0 dB
  (no carrier suppression)
• (b) 60 degrees
• V 10 log 10/(5 sin 600 5 sin 600) 0.62
  dB
• (c) 1 degree
• V 10 long 10/5 sin 10 5 sin 10) 17.58 dB

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QPSK MODULATOR
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BPSK AND QPSK SPECTRA
66
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MQPSK / OQPSK / SQPSK

• Modified QPSK such that by shifting the I and Q
  clocks, no phase transition will occur larger
  than 900

QPSK
SQPSK

• 00 00
• 01 900
• 1800
• 2700

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MINIMUM SHIFT KEYING
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DSSS MODULATION COMPARISON
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WHICH MODULATION WOULD YOU CHOOSE ?

• Depends upon
• Effects on synchronization
• Sidelobe energy / bandwidth
• Complexity of modulator / demodulator
• Effects of jamming in interference
• Impact on size, weight, power, and reliability

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DETERMINING THE NUMBER OF SIMULTANEOUS USERS

• Many DSSS users can transmit messages
  simultaneously over the same channel bandwidth
  provided each user has his own PN code sequence
• Digital communications in which each
  transmitter/receive user pair has its own
  distinct signature code is called Code Division
  Multiple Access (CDMA)
• In cellular systems, a base station transmits
  signals to Nu mobile receivers using Nu
  orthogonal PN sequences, one for each receiver
• These Nu signals are perfectly synchronized so
  that they can arrive in synchronism due to the
  orthogonality of the codes
• However, this synchronization cannot always be
  achieved, particularly in the uplink (mobile to
  base station)

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DETERMINING THE NUMBER OF SIMULTANEOUS USERS

• In demodulation of each DSSS signal at base
  station, the signals from the other simultaneous
  users of the channel appear as additive
  interference
• Assume equal power of all simultaneous users at
  the base station (achieved via adaptive power
  control), the desired SNR is
• In determining the maximum number of users, we
  assumed that the codes are orthogonal and the
  interference from the other users adds on a power
  basis and dominates the noise term
• This is why the design of a large set of PN
  sequences with good correlation properties is
  important

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DETERMINING THE NUMBER OF SIMULTANEOUS USERS

• Example
• Desired level of performance for a user in a
  CDMA system requires Eb/Jo 10 dB
• Determine the maximum number of simultaneous
  users that can be accommodated in a CDMA system
  if the bandwidth-to-bit ratio is 100 (PG) and the
  coding gain is 6 dB

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NEAR FAR PROBLEM FOR DSSS

• There are many ways in which the received powers
  can be unequal for a DSSS multiple access system
• For the analysis that follows, assume that all
  users transmit with equal power, but are
  different distances from the jth receiver
• Then the received power from the ith
  transmitter may be represented as
• Pi Po / di?
• Where,
• Po received power at unit distance
• di distance from the ith transmitter to the
  jth receiver
• ? propagation law
• The parameter ? is the propagation law and
  depends upon the medium in which the transmission
  takes place
• In free space ? 2, at UHF over an ideal earth ?
  tends to change between 3 and 4 (determined
  experimentally)

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NEAR FAR PROBLEM FOR DSSS

• It is possible to represent the ratio of the
  power received from the ith transmitter to that
  received from the jth transmitter, which is the
  desired signal
• This is shown by
• The SNR at the output of the jth receiver may now
  be written as

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NEAR FAR PROBLEM FOR DSSS

• Solving for the term that is related to the
  distances gives
• The term subtracts off for the intended
  signal
• To find the capacity of a CDMA system where all
  powers are equal and the distances are the same,
  let

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NEAR FAR PROBLEM FOR DSSS

• Therefore, for all users U,

Subtracts off closer user and intended user