DIGITAL SPREAD SPECTRUM SYSTEMS

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DIGITAL SPREAD SPECTRUM SYSTEMS
ENG-737 Lecture 5

• 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 Gold
  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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DIFFERENTIAL ENCODING
Inversion
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 encodes provides 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 that 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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NEAR FAR PROBLEM FOR DSSS

• Major requirement for DSSS implementation is that
  one must maintain power control
• If one user has more power than others, at the
  receiver, the capacity of the system is degraded
• For maximum capacity, transmitters must maintain
  equal distance and equal power, i.e. mobile
  cellular must therefore maintain power control

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NEAR FAR PROBLEM ANALYSIS

• There are many ways in which the received powers
  can be unequal for a DSSS CDMA system
• For this analysis 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 / dia
• Where,
• Po received power at unit distance
• di distance from the ith transmitter to the
  jth receiver
• a propagation law
• The parameter a is the propagation law and
  depends upon the medium in which the transmission
  takes place

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NEAR FAR PROBLEM ANALYSIS (Cont.)

• In free space, a is the propagation law and
  depends upon the medium in which the transmission
  takes place
• In free space, a 2
• At UHF over an ideal earth, a tends to change to
  between 3 and 4 (determined experimentally)
• The above make it 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

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NEAR FAR PROBLEM ANALYSIS (Cont.)

• This is shown by
• Pi dj / dia Pj
• Pi / Pj (Po / dja) / (Po / dja) (dj / di)a
• The SNR at the output of the jth receiver may now
  be written as
• 2
  tm Beff Pj

2Eb / No (SNR)j
(SNR)o
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NEAR FAR PROBLEM ANALYSIS (Cont.)

• Solving for the term that is related to the
  distances gives
• The term (1/(SNR)j) subtracts off for the
  intended signal

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NEAR FAR PROBLEM ANALYSIS (Cont.)

• To find the capacity of a CDMA system where all
  powers are equal and the distances are the same,
  let
• Beff 20 x 106
• Tm 1/ 30,000
• SNRo 14
• SNRj 25
• Therefore, for all users U,
• U 2(20x106) / 30000(1/14) (1/25) 42
• Now if one user is 2.5 times closer than all
  other users but still with equal power,

Subtracts off closer user and intended user
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NEAR FAR PROBLEM ANALYSIS (Cont.)

• For a 3.68
• U 1 1 - (2.5)3.68 2 tm Beff (1/(SNR)o)
  (1/(SNR)j)
• U 1 1 - (2.5)3.68 2 x 20 x 106 /
  30000)(1/14 1/25)
• U 14
• The number of users has been reduced by a factor
  of 3 simply by one transmitter being 2.5 times
  closer than all of the others
• The system would completely fail as a multiple
  access system if dj / di gt 2.78, since only one
  user could be supported and none of the others
  would be received with the desired SNRo
• This is the Near Far Problem !

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PROCESSING GAIN PG
Processing gain is the improvement seen by a
spread spectrum system in SNR, within the
systems information bandwidth, over the SNR in
the transmission channel.
Typically Bi baud rate
PG BS / Bi BS / Ri PG(dB) 10 log (Bs / Ri)
Typical PG 20 to 60 dB
Bs
Typically Bs null-to-null
0
1/T
-4/T
-3/T
-2/T
-1/T
4/T
3/T
2/T
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JAMMING MARGIN

• In a general system with both noise and
  interference present, the receiver output SNR can
  be expressed as
• (SNR)o PG (SNR)i
• Where,
• PG processing gain
• (SNR)o Output SNR
• (SNR)I Input SNR
• The ability of a communication system to reduce
  the effects of jamming is called Jamming Margin

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JAMMING MARGIN MG
Jamming margin takes into account the requirement
for a useful system output SNR and allow for
internal losses.
MG GP Lsys (S/N)out , dB
Where, Lsys system implementation
losses (S/N)out SNR at information, despread,
output
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JAMMING MARGIN EXAMPLE

• Given,
• Chip rate 107 chips / sec
• Message bit rate 100 bits / sec
• Desired SNRo 25 14 dB
• System losses 2 dB
• Find MJ(dB)
• PG Bs / Ri 2 rc / Ri 2 x 107 / 100 2 x
  105
• PG (dB) 10 log (2 x 105) 53 dB
• MJ(dB) 53 dB 2 dB 14 dB 37 dB
• The required output SNR will be obtained if the
  jamming signal is less than 37 dB greater than
  the desired signal