spread spectrum signals for digital communications
TRANSCRIPT
SPREAD SPECTRUM (SS)
SIGNALS FOR DIGITAL
COMMUNICATIONS
VERSION 1.1
Dr. Ali Muqaibel
Dr. Ali Hussein Muqaibel 1
Introduction
In Spread Spectrum, the bandwidth ๐ is much greater
than the info rate ๐ (bit/sec).
Bandwidth Expansion Factor ๐ต๐ =๐
๐ โซ 1
Redundancy is introduced to overcome interference
(Radio & Satellite)
Coding is an effective method for introducing
redundancy.
Pseudo randomness signals: appear like noise and are
difficult to receive by the non-intended receivers.
Narrow band signal
(data)
Wideband signal
(transmitted SS signal)
Dr. Ali Hussein Muqaibel 2
Major Applications of SS
1. Combating/Suppressing Jamming/interference due to other users/self-interference (Multipath).
2. Covert (hidden)/Secure Communication/Privacyโฆ Communication Security vs. information security
โฆ Spreading sequence can be very long -> enables low transmitted PSD-> low probability of interception (LPI)(especially in military communications)
3. CDMA: Coded division Multiple Access.. QUALCOMM lie!
โฆ CDMA allow multiple users to simultaneously use a common channel for transmission of information
โฆ Key=code
4. In Radar SS is used for time delay, velocity, and ranging.
Dr. Ali Hussein Muqaibel 3
How Tele-operators Market CDMA
Coverage
For Coverage, CDMA saves
wireless carriers from deploying
the 400% more cell site that
are required by GSM
CDMAโs capacity supports at
least 400% more revenue-producing
subscribers in the same spectrum
when compared to GSM
Capacity Cost
$$A carrier who deploys CDMA
instead of GSM will have
a lower capital cost
Clarity
CDMA with PureVoice
provides wireline clarity
Choice
CDMA offers the choice of simultaneous
voice, async and packet data, FAX, and
SMS.
Customer satisfaction
The Most solid foundation for
attracting and retaining subscriber
is based on CDMA
*From Samsumgโs narrowband CDMA (CDMAOneยฎ) marketing (2001)
Dr. Ali Hussein Muqaibel 4
Multiple access: FDMA, TDMA and CDMA
โขFDMA, TDMA and CDMA yield
conceptually the same capacity
โข However, in wireless communications
CDMA has improved capacity due to
โข statistical multiplexing
โข graceful degradation
โขPerformance can still be improved by
adaptive antennas, multiuser detection,
FEC, and multi-rate encoding
Dr. Ali Hussein Muqaibel 5
FDMA, TDMA and CDMA compared
TDMA and FDMA principle: โฆ TDMA allocates a time instant for a user
โฆ FDMA allocates a frequency band for a user
โฆ CDMA allocates a code for user
CDMA-system can be synchronous or asynchronous:โฆ Synchronous CDMA difficult to apply in multipath channels
that destroy code orthogonality
โฆ Therefore, in wireless CDMA-systems as in IS-95,cdma2000, WCDMA and IEEE 802.11 users are asynchronous
Code classification:โฆ Orthogonal, as Walsh-codes for orthogonal or
near-orthogonal systems
โฆ Near-orthogonal and non-orthogonal codes: Gold-codes, for asynchronous systems
Maximal length codes for asynchronous systems
Dr. Ali Hussein Muqaibel 6
Coverage Objective
Types of SS
1. Direct Sequence SS (DSSS)
PSK/QPSK+ pseudo-noise (PN) sequence
2. Frequency Hopping SS (FHSS)
M-ary FSK+PN
The pseudorandom sequence selects the frequency
of the transmitted sequence randomly
Anti-jamming (AJ) performance
Dr. Ali Hussein Muqaibel 7
Example of DS multiple access
waveforms
channel->
detecting A ... ->
polar sig.->
Dr. Ali Hussein Muqaibel 8
Frequency Hopping Spread Spectrum (FH-SS) (example: transmission of two symbols/chip)
2 levelsL
2 slotsk
:chip duration
: bit duration
: symbol duration
c
b
s
T
T
T
2 ( data modulator BW)
2 ( total FH spectral width)
L
d d
k
s d
W f
W W
bT
2L
4-level FSK modulation
Hopped frequency
slot determined by
hopping code
Dr. Ali Hussein Muqaibel 9
Model of SS Digital Comm. Sys.
The channel encoder: coding is usually employed to enhance the gain.
Synchronization (of the PN sequence)
โฆ Initially, training!, transmit a fixed PM bit pattern that the receiver will
recognize in the presence of interference with high probability.
Dr. Ali Hussein Muqaibel 10
Interference & jamming
It ch/s depends on its origin (military)
1. Tone
2. Multi-tone
3. Partial band (Narrowband)
4. Broadband
5. Continuous/Pulsed (discontinuous)
6. Fixed/ time variant
1 to 4 have similar effects on DSSS
If the interference is broadband , it may be characterized as an equivalent AWGN
In CDMA we can have multi user interference.
๐๐ ๐
Tone
๐๐ ๐
Multi-Tone
๐๐ ๐
Partial band
๐๐ ๐
Broad band๐ฝ0
๐๐
Pulsed
๐๐๐
time
Dr. Ali Hussein Muqaibel 11
Objective (more details)
Performance evaluation of SS in the
presence of NB/broadband interference.
Two types of modulation are considered:
โฆ PSK if phase coherence is possible for time
longer than 1
๐.
โฆ FSK if phase coherence is not possible for
time longer than 1
๐. Like the time varying
channels (aircrafts)
Dr. Ali Hussein Muqaibel 12
Tone Jamming (cont.) Despreading spreads the jammer power
and despreads the signal power:
Dr. Ali Hussein Muqaibel 14
Tone Jamming (cont.)
Filtering (at the BW of the phase modulator)
after despreading suppresses the jammer
power:
Dr. Ali Hussein Muqaibel 15
DSSS
Revisit the model, and assume BPSK
๐ผ๐๐๐๐๐๐๐ก๐๐๐ ๐ ๐๐ก๐ = ๐ ๐๐๐ก๐ /sec.
๐ด๐ฃ๐๐๐๐๐๐๐ ๐ต๐๐๐๐ค๐๐๐กโ = ๐ ๐ป๐ง.
The phase of the carrier is shifted
pseudo-randomly according to the
pattern from PN generator at a rate
๐ ๐ก๐๐๐๐ /sec.๐ = 1/๐๐
๐๐ : duration of the phase chip interval (Basic
element in DSSS)
๐๐ = 1/๐
๐๐ : duration of a rectangular pulse (time of
transmission for a bit)
Dr. Ali Hussein Muqaibel 16
Bandwidth Expansion Factor
Bandwidth Expansion Factor:
๐ต๐ = ๐/๐ = ๐๐ /๐๐
In practice ๐๐ /๐๐ is integer.
๐ฟ๐ = # ๐๐ ๐โ๐๐๐ ๐๐๐ ๐๐๐๐. ๐๐๐ก. =
# of phase shifts during one bit
transmission.
Using (๐, ๐) = (๐๐ฟ๐ , ๐) code.
To transmit ๐ chips, the time available
in ๐ ๐๐
The code rate (block, convolutional):
๐ ๐ =๐
๐=
1
๐ฟ๐
Dr. Ali Hussein Muqaibel 17
โข Bandwidth of ๐ ๐ก =1
๐๐
โข Bandwidth of ๐ ๐ก =1
๐
โข Bandwidth of ๐ ๐ก ๐ ๐ก =1
๐+
1
๐๐
โ1
๐๐ถDr. Ali Hussein Muqaibel 19
Forming the DS (Modulator)
Let ๐๐ = ๐๐กโ bit of PN sequence. (0,1)
๐๐ = ๐๐กโ bit from the encoder.
๐๐ = ๐๐ + ๐๐ (same โ ๐๐ = 0, otherwise ๐๐ = 1)
then use a BPSK modulator.
๐๐ ๐ก = ๐ ๐ก โ ๐๐๐ (๐๐ = 0)
โ๐ ๐ก โ ๐๐๐ (๐๐ = 1)
(kLc ,k)
encoder
Modulation
g(t)+
Info.
sequence
k bits/unit
time
Coded
sequence
kLc
bits /time
PN Seq.
kLc bits/time
๐๐
๐๐
๐๐
Dr. Ali Hussein Muqaibel 20
Alternative Modulator Modulation of ๐๐โs first
๐๐ (๐ก) = (2 ๐๐ โ 1) ๐(๐ก โ ๐๐๐)
output of PN sequence
๐๐ (๐ก) = (2 ๐๐ โ 1) ๐(๐ก โ ๐๐๐)
Multiplying Both
๐๐ (๐ก) = (2 ๐๐ โ 1) (2 ๐๐ โ 1) ๐(๐ก โ ๐๐๐)
Modulation
g(t)+
PN Seq. waveform
with square pulse
shape
Coded
Seq.
Dr. Ali Hussein Muqaibel 21
x
๐๐(๐ก)
๐๐ (๐ก)๐๐ (๐ก)
Equivalence of the two modulators
๐๐ ๐๐ ๐๐ = ๐๐ โจ ๐๐ ๐๐
(1) (2 ๐๐ โ 1) (2 ๐๐ โ 1) ๐๐(๐)
0 0 0 ๐(๐ก) 1 ๐(๐ก)
0 1 1 โ ๐(๐ก) -1 โ ๐(๐ก)
1 0 1 โ ๐(๐ก) -1 โ ๐(๐ก)
1 1 0 ๐(๐ก) 1 ๐(๐ก)
โข The two modulators are equivalent and can be used for coded or uncoded
systems
โข The first is easier to implement.
โข The second is easier to relate to demodulation
(kLc ,k)
encoder
Modulation
g(t)+
Info.
sequence
k bits/unit
time
Coded
sequence
kLc
bits /time
PN Seq.
kLc bits/time
Modulation
g(t)+
PN Seq. waveform
with square pulse
shape
Coded
Seq. x
Dr. Ali Hussein Muqaibel 22
๐๐(๐ก)
๐๐ (๐ก) ๐๐(2)
๐๐
๐๐
๐๐
๐๐1
Demodulator
The received signal for the ๐๐กโ code element
โ no de-spreading yet โ
๐๐ (๐ก) = ๐๐ (๐ก) ๐๐ (๐ก) + ๐ง (๐ก)
= (2 ๐๐ โ 1) (2 ๐๐ โ 1) ๐ (๐ก โ ๐ ๐๐) + ๐ง (๐ก)
๐ง(๐ก) assumed to be stationary random process
with zero mean)
Dr. Ali Hussein Muqaibel 23
Demodulation
Multiply by (2๐๐ โ 1) takes out the effect of the PN sequence.
In modulator (b) we are multiply before filtering.
In modulator (c) we are using a correlatorinstead of a matched filter.
Optimality of matched filter assume โGaussianityโโฆ If ๐ง(๐ก) is not Gaussian>>> no optimality
โฆ If noise distribution is not known, we still can use it.
Dr. Ali Hussein Muqaibel 25
Error Rate Performance of
Detector of the DecoderThe processing gain & the Jamming margin.
๐ธ๐ = ๐๐๐ฃ ๐๐ =๐๐๐ฃ
๐ ๐ธ๐ : Energy per bit in term of average power (๐๐๐ฃ).
๐๐ : bit interval.๐๐๐ฃ
๐ฝ๐๐ฃ
: signal to jamming power ratio.
๐ฝ0 : the power spectral density (PSD) for the jamming signal. (+๐0)
๐ฝ0 =๐ฝ๐๐ฃ
๐.
๐ธ๐
๐ฝ0
= ๐๐๐ฃ
๐ / ๐ฝ
๐๐ฃ
๐=
๐
๐ /(๐ฝ๐๐ฃ/๐๐๐ฃ)
๐/๐ = ๐๐/ ๐๐ = ๐ต๐ = ๐ฟ๐ = ๐บ๐
๐๐๐๐๐๐ ๐ ๐๐๐ ๐บ๐๐๐ (๐บ๐)
Dr. Ali Hussein Muqaibel 26
Processing Gain, SJR, and Jamming
Margin Processing gain (๐บ๐) : the advantage gained over the jammer that
is obtained by expanding the BW of the transmitted signal.
Let ๐ธ๐
๐ฝ0
be interpreted as SNR (SJR) required for a specific error
rate performance and
๐
๐ available bandwidth expansion factor.
๐ฝ๐๐ฃ
๐๐๐ฃ
Jamming margin of DSSS system i.e the largest value that ๐ฝ๐๐ฃ
๐๐๐ฃ
can take and still satisfy the probability of error, ๐๐ .
The total average interference power is ๐ฝ๐๐ฃ = 2๐ฝ0๐, where ๐ฝ0 is
the value of the power spectral density of an equivalent wideband
interference.
๐ธ๐
๐ฝ0= 2
๐
๐ /
๐ฝ๐๐ฃ
๐๐๐ฃ
Dr. Ali Hussein Muqaibel 27
Example (To be checked)
Suppose we wish to maintain ๐๐ โค 10โ6 , the system has ๐/๐ = 500. What is the Jamming margin ?
For ๐๐ = 10โ6 we require ๐ธ๐ / ๐ฝ0 = 10.5 ๐๐ต.
๐บ๐ = 30 ๐๐ต
So , Jamming margin = 33 โ 10.5 = 22.5 ๐๐ต.
That is the received signal can be detected reliably (at 10โ6) even when the interference is up to 100times the received signal.
One can design the system for a given Jamming margin.
Dr. Ali Hussein Muqaibel 28
In Class Exercise
A user is communicating with a satellite using a
signal of power = 20๐๐ต๐. A jammer is
transmitting 60๐๐ต๐ (continuous, full-band).
The needed transmission rate is 100 ๐/๐ . The
required ๐ธ๐
๐ฝ0
is 10 ๐๐ต.
Find the required bandwidth?
Dr. Ali Hussein Muqaibel 29
User