ECE 6640
Digital Communications
Dr. Bradley J. Bazuin
Assistant Professor
Department of Electrical and Computer Engineering
College of Engineering and Applied Sciences
Chapter 12
Chapter 12:
12.1
12.2
12.4
12.5
12.6
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Spread Spectrum Signals for Digital Communications
Model of Spread Spectrum Digital Communication System
Direct Sequence Spread Spectrum Signals
Other Types of Spread Spectrum Signals
Synchronization of Spread Spectrum Systems
Bibliographical Notes and References
Problems
Notes and figures are based on or taken from materials in the course textbook:
J.G. Proakis and M.Salehi, Digital Communications, 5th ed., McGraw-Hill, 2008.
762
763
765
814
815
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Chapter Content
•
Spread spectrum signals used for the transmission of digital information are
distinguished by the characteristic that their bandwidth W is much greater than
the information rate R in bits/s. That is, the bandwidth expansion factor Be
=W/R for a spread spectrum signal is much greater than unity.
– The large redundancy inherent in spread spectrum signals is required to overcome
the severe levels of interference that are encountered in the transmission of digital
information over some radio and satellite channels.
•
Spread spectrum signals are used for
– Combating or suppressing the detrimental effects of interference due to jamming,
interference arising from other users of the channel, and self-interference due to
multipath propagation.
– Hiding a signal by transmitting it at low power and, thus, making it difficult for an
unintended listener to detect in the presence of background noise.
– Achieving message privacy in the presence of other listeners.
•
General applications:
–
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Sonar, radar, GPS, Bluetooth, Military communications, narrowband interference
communications (all forms of jamming), multiuser communications (CDMA cell phones),
maintain average power in a link (telephony).
3
Classes of Systems
• Direct Sequence Spread Spectrum (DSSS)
– A pseudorandom “chipping” sequence is used to spread an
underlying binary data stream. The chip rate defines the spectrral
bandwidth.
• Frequency Hopping
– A narrower bandwidth communication signal is periodically
moved to different centers frequencies in a defined fraquency band
in a pseudorandom way.
– Systems may be characterized as slow or fast hopping based on the
time spent at each frequency (or the number of symbols
transmitted during each dwell time at a frequency).
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Spread Spectrum Model
• “Spreading” performed by a pseudorandom sequence
generator.
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– The pattern/sequence must be known to both ends and
synchronization must occur.
– Often an initial contact is made (link entry and establishment) and
then a new code or sequence would be used for the
communications.
5
Direct Sequence Signaling
• Binary Symbols {+1, -1} multiplied by a chipping
code consisting of a pseudo-random binary symbol
x t   xt   ct 
sequence.
DSS
– The symbol modulates a lengthy chip sequence by +/- 1.
– But multiplying by the chip sequence again the original
signal returns.
xt   xDSS t   ct   xDSS t    xt   ct 
PN Code and Data
• Encoding involves
“multiplying” an
integer number of
PN code chips for
each bit of data.
• Typically the chip
rate is significantly
higher than the data
bit rate!
– Bandwidth
expansion
– Spreading gain
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Autocorrelation
• If we transmit the DSS signal, there is a time delay due to
distance. Thus, we must time align the received DSS with
the chip sequence in order to receive it.
Tc

R()
A2
(1 - |  | / Tc) for |  |  Tc
elsewhere
= - A2 /N
= A2
-Tc
-NTc
Tc
NTc
DSS Transmitter System
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Figure 15.1-1
Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
DSS Bandwidth
• The bandwidth is based on the chip rate
  
Rc         Trep 
 TC 

1 
2

Gc  f   TC  sinc f  TC    f 

Trep 


Rx     
T 
Gx  f   T  sinc f  T 
RDSS    E xt   ct   xt     ct  
 E xt   xt    ct   ct  
 E xt   xt   E ct   ct   
   
 
  
RDSS        Trep       
 TC 
  TC 
 T 
Bandwidth Expansion Factor
• For DS spreading of the signal, the bandwidth has gone
from R=1/T to 1/Tc
g BWex 
Tb WC

TC
R
Correlation Receiver
• Use the PN sequence as an optimal “filter” or correlator
sequence
Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
DSS Inherent Anti-Jam
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Figure 15.1-2
Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
An Alternate Modulator Concept
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Demodulators
• Simplified receiver
diagrams.
• The matched or
correlating filter
elements must be
related to the
“chip” being
received, prior to
chip correlation
with the pseudo
random sequence.
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Simplified Receiver Noise & SNR
• The noise power is filtered by the correlation receiver
– Mix by PN sequence
– Integrate for the Bit Period, Tb
– The effective noise bandwidth is related to the data bit period due
to the summation performed by the received signal correlator
Rnn   N 0  BT  sincBT  
 f
S nn  f   N 0  
 BT
SNRD 
SR
N 0  Wx



 2  Eb
Pe  Q
 N0




Uncoded DS Performance
• The bit error rate for a basic DSSS signal (Like GPS) is
defined as


2  Eb 
Pe  Q

 J0 
– where J0 is used instead of N0 to describe interference power
instead of noise power.
• If average signal power is considered, this can be written
as


 4 W
R
Pe  Q
 J avg

Pavg






– Where W/R describes the bandwidth ratio or spreading gain.
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Example 12.2-3
• Desired BER 10-6, available bandwidth expansion 1000.
What is the maximum narrowband jamming power that be
encountered and maintain communications?
– antipodal signaling requires 10.5 dB Eb/No for 10-6 BER
– coding gain provides 1000 or 30 dB

 4 W
– based on the previous equation


W
 4 R 

  10.5dB
J
 avg

Pavg 

dB
 J avg

 6dB  30dB  10.5dB  25.5dB

Pavg 
dB
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Pe  Q





R 
J avg

Pavg 
Note: dB(4) ≈ 6 not 3
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DSSS with Coding
• The text suggests multiple ways to either directly encode
the data or generate a concatenated code to provide further
enhancements in interference or jamming.
• If interested, study the textbook.
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GPS Signal Characteristics
•
Two Principal Frequencies
– L1 Band at 1575.42 MHz with C/A and P(Y) codes
– L2 Band at 1227.60 MHz with P(Y) code
– L5 Band at 1176.45 MHz with “new” C/A code
•
Direct Sequence Spread Spectrum Communications
– Data Message at 50 bps consisting of 1500 bit pages (30 sec.)
– C/A-code spreads the data using 1023-bit Gold codes at a chipping rate of
1.023 Mcps (C/A – coarse-acquisition code)
– P(Y)-code spreads the data using a code that Does not repeat at a chipping
rate of 1.0.23 Mcps (P – precision code)
•
Code Transmission
– The C/A- and P(Y)-codes are transmitted in quadrature on L1
– The P(Y)-code is transmitted on L2
GPS Receiver Characteristics
• Receive up to 12 satellites simultaneously
• User Minimum received power
L1 C/A-Code:
L1 P-Code:
L2 P-Code:
kTB (20 MHz):
-100
–130 dBm
–133 dBm
–136 dBm
–101 dBm
Therm al Noise P ower
C/A Code
P (Y ) Code
-110
-120
dB m / Hz
–
–
–
–
-130
-140
-150
-160
-10
-5
0
Frequancy (M Hz )
5
10
Nominal Power Levels
• Reference noise power: -174 dBm/Hz
– C/A code bandwidth 2 MHz: 63 dB
– Nominal thermal noise floor in band: -111 dBm
– Receiver Noise Figure (estimate 10 dB)
• Minimum detectable signal level: -101 dBm
• C/A Signal: -130 dBm
– Coding gain 1023,000/50=2046043.1 dB
– (P-Code coding gain is 10x better)
• Margin (-130 + 43.1 +6?) – (-101) = 20.1 dB
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– Note that initial signal was 29 dB below the noise floor!
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GPS User Position Computation
Satellite
r
s
u
Earth
SV to User Distance
r = || s – u ||
r = c x t
Measured Pseudorange
 = r + c x tu
Unknowns
r(x, y, z), t
Use 4 SVs to
solve
• GPS uses the triangulation of signals from the
satellites to determine locations on earth.
• GPS satellites know their location in space and
receivers can determine their distance from a
satellite by using the travel time of a radio
message from the satellite to the receiver.
• After calculating its relative position to at least 4
satellites, a GPS receiver can calculate its position
using triangulation.
• They also have a database (or almanac) of the
current and expected positions for all of the
satellites that is frequently updated from earth.
Code Division Multiple Access
•
CDMA in the US is associated with Qualcomm, San Diego, CA.
– Early related standards IS-95 and IS-2000 or CDMA2000
•
IS-95 (https://en.wikipedia.org/wiki/IS-95)
– In the forward direction, radio signals are transmitted by base stations
(BTS's). All forward transmissions are QPSK with a chip rate of
1,228,800 per second. Each signal is spread with a Walsh code of length
64 and a pseudo-random noise code (PN code) of length 215, yielding a PN
roll-over period of 80/3 ms.
– For the reverse direction, radio signals are transmitted by the mobile.
Reverse link transmissions are OQPSK in order to operate in the optimal
range of the mobile's power amplifier. Like the forward link, the chip rate
is 1,228,800 per second and signals are spread with Walsh codes and the
pseudo-random noise code, which is also known as a Short Code.
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IS-95 Forward Link
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IS-95 Receiver Link
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Frequency Hopping
• In a frequency-hopped (FH) spread spectrum
communication system the available channel bandwidth is
subdivided into a large number of contiguous frequency
slots. In any signaling interval, the transmitted signal
occupies one or more of the available frequency slots. The
selection of the frequency slot(s) in each signaling interval
is made pseudorandomly according to the output from a
PN generator.
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Typical FH Modulation Type
• Although PSK modulation gives better performance than
FSK in an AWGN channel, it is sometimes difficult to
maintain phase coherence in the synthesis of the
frequencies used in the hopping pattern and, also, in the
propagation of the signal over the channel as the signal is
hopped from one frequency to another over a wide
bandwidth. Consequently, FSK modulation with
noncoherent detection is often employed with FH spread
spectrum signals.
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FH-SS System.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Figure 15.2-1
(a) Transmit
(b) Receive
Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
FH System Block Diagram
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Comparison FH to DSSS
• FH spread spectrum signals are used primarily in digital
communication systems that require AJ protection and in
CDMA, where many users share a common bandwidth.
• In most cases, an FH signal is preferred over a DS spread
spectrum signal because of the stringent synchronization
requirements inherent in DS spread spectrum signals.
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