spread spectrum communication with cdma
TRANSCRIPT
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Communication Systems
Lecture 14
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Spread spectrum technique
The spread spectrum system (SSS) is one in which the transmitted
signal is spread over a wide frequency band, much wider, than the
minimum bandwidth required to transmit the information being
sent.
-A system is defined to be a speared spectrum system if it fulfills
the following requirements:
1-The signal occupies a bandwidth much in excess of the minimumbandwidth necessary to send the information.
2-Spreading is accomplished by means of a spreading signal, often
called a code signal, which is independent of the data.
3-At the receiver, despreading (recovering the original data) is
accomplished by the correlation of the received spread signal with a
synchronized replica of the spreading signal used to spread the
information.
Note
Standard modulation such as FM and PCM also spread the
spectrum of an information signal, but they do not qualify as spread
spectrum systems since they do not satisfy all the conditions above.
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The advantages of spread spectrum systems
-Interference suppression.
-White Gaussian noise is a mathematical model has infinite power
spread uniformly over all frequencies. The communication is
possible with this interfering noise (white Gaussian noise) of
infinite power because only the finite power noise components that
are present within the signal bandwidth can interfere with the
signal.-For a typical narrowband signal, this means that only the noise in
the signal bandwidth degrade performance.
The idea behind a spread spectrum anti-jam (AJ) system is as
follows:
a- consider that many orthogonal signal components are available to
a communication link and that only a small subset of these signal
coordinates are used at any time.
[Against white Gaussian noise, with infinite power, the use of
spreading offers no performance].
b-The noise from interferer (jammer) with a fixed finite power and
with uncertainty as to where in the signal space the signal
components (coordinates) are located, the jammers choices are
limited to the following:-
1-jam all the signal components (coordinates) of the system,
with equal amount of power in each one, with the result that a
little power is available for each component (coordinate).
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2-jam a few signal components (coordinates) with increased
power in each of the jammed coordinates.
Fig (14.1) compares the effect of spreading in the presence of white
noise with spreading in the presence of interferer (jammer). The
power spectral density of the signal is denoted G(F) before
spreading and Gss(f) after spreading.
Fig(14.1)
-Fig(14.1a) it can be seen that the single sided power spectral
density of white noise, is unchanged as a result of expanding the
signal bandwidth.
-Fig(14.1b) shows the case of received jammer power J, and power
spectral density where W is the unspread bandwidth.
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If interferer choice results in a reduction in interferer noise spectral
density by because
ssss W
WJ
W
JJ 0
0broadband jammer noise spectral density (14.1)
If interferer choice 2 results in a reduction in the number of signal
coordinates, that the jammer can increase its noise spectral density
from where is the portion of
interferer (jammer) bandwidth.
2-Energy density reduction.
Since in SSS, the signal is spread over many more signaling
components than conventional modulation schemes, the resulting
signal power is spread uniformly in the spread domain. Thus the
received signal is small, very difficult to detect by anyone except
the desired receiver (or intended receiver) systems designed for this
special task are known as low probability of detection (LPD) or low
probability of intercept (LPI).
3-Fine time resolution
Spread spectrum signals can be used for ranging or determination
of position location. Distance can be determined by measuring the
time delay between transmitted and received signal. Uncertainly in
the delay measurements is inversely proportion proportional to the
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bandwidth of the signal pulse as shown in fig (14.2). The
uncertainty of the measurement, t, is proportional to the rise time
of pulse, is given by
fig(14.1a)
Multiple access
-Multiple access refers to techniques that enable sharing a common
communication channel between multiple users.
-There is a difference between multiplexing and multiple access.
With multiplexing users requirements (or plans) are fixed, or atmost, slowly changing. The user allocation is assigned a priori and
the multiplexing (sharing) is usually a process that takes place
within the confines of a local site (e.g a circuit board). With
multiple access, usually involves the remote multiplexing (sharing)
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of a user and users requirements are changed (e.g satellite
communications).
-Spread spectrum methods can be used a multiple access technique,
in order to multiplex (share) a communication resource among
numerous users. The technique, termed code division multiple
access (CDMA), since each simultaneous user employ a unique
spread spectrum signaling code. One of the by products of this type
of multiple access is the ability to provide communication privacy
between users with different spreading signals. An unauthorized
user cannot easily monitor the communications of the authorized
users.
The basis of spread spectrum technology
-The basis of spread spectrum technology is expressed by Shannon
theorem in the form of channel capacity
)3.14.....(..........1log2
N
SWC
where
C=capacity in bit/sec, N=noise power
W=bandwidth in Hz, S=Signal power
This equation shows the relationship between the ability of a
channel to transfer errorfree information, compared with the signal
to noise ratio existing in the channel and the bandwidth used to
transmit the information.
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Letting C be the desired system information rate and changing
bases, we find
a)4.14(1log44.12
N
S
W
C
Note
11
4
1
3
1
2
11log
32
N
Sfor
N
S
N
S
N
S
N
S
N
S
e
and for S / N small, say 0.1,
)5.14(44.1
44.1
b)4.14(44.1
S
CNW
C
W
S
NN
S
W
C
Eq (14.5) shows that for any given noise to signal ratio we can have
a low information error rate by increasing the bandwidth used to
transfer the information. For example if we want a system to
operate in a link in which the interfering noise is 100 time greater
than the signal and if C=3k bit/s
MHzW 244.1
103100 3
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Spread spectrum techniques
The following techniques are used in spread spectrum systems:-
1-Direct sequence (DS)
2-Frequency hopping (FH)
3-Pulsed frequency modulation (chirp)
4-Time hopping (TH)
5-Hybrid forms [DS/FH, FH/TH and DS/FH/TH]
All the techniques mentioned above require a pseudo random noise(PN) code generator for bandwidth spreading. A (PN) generator
produces a binary sequence which is apparently random but can be
reproduced deterministically by the intended recipients.
Pseudonoise sequences
-A random signal cannot be predicted, its future variations can only
be described in a statistical sense. However, pseudorandom signal is
not random at all, it is deterministic, periodic signal that is known
to both transmitter and receiver.
Why the name Pseudonoise or pseudorandom? Even though the
signal is deterministic, it appears to have the statistical properties of
sampled white noise. It appears, to an unauthorized listener, to be a
truly random signal.
Randomness properties of a pseudorandom signal
-There are three basic properties that can be applied to any periodic
binary sequence as a test for appearance of randomness:-
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1-Balance property. Good balance requires as a sequence, the
number of binary ones differs from the binary zeros by at most one
digit
2-Run property. A run is defined as a sequence of a single type of
binary digit (or digits). The appearance of the alternate digit in a
sequence starts a new run. Among the runs of ones and zeros in
each period, it is desirable that about one half the runs of each type
are length 1, about one fourth are of length 2, one eight are of
length 3 and so on.
3-Correlation property. If a period of the sequence is compared
term by term with any cyclic shift of itself, it is best if the number
of agreements differs from the number of disagreements by not
more than one count.
Let us consider the output sequence of PN generator is
0001001101011111
1)No. of zeros =7, No. of ones =8
2)Consider the zero runs, there are four of them.
one half are of length 1 and
one fourth are length 2one fourth are length 3
Consider the linear shift register illustrated in fig(14.2). It is made
up of a four stage register for storage and shifting, a modulo-2
adder, and a feedback path from the adder to the input of the
register. The shift register operation is controlled by a sequence of
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clock pulses. At each clock pulse the contents of each state in the
register is shifted one stage to the right. The shift register sequence
is defined to the output of the last stage in this example.
Assume that stage is initially filed with one and the remaining
stages are filled with zeros, that is the initial state of the register is
1000. The shift register states will be as follows:-
1X
2X
3X
4X
fig(14.2)
a-Since the last state, 1000 corresponds to the initial state 1000, we
see that the register repeats the forgoing sequence after 15 clock
pulse.
b-The o/p sequence is obtained by noting the contents of stage ateach clock pulse.
c-The output sequence: 00100110101111
-The shift register generator produces sequences that depend on the
number of stages, the feedback tap connections and initial
conditions. The output sequences can be classified as:-
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1-Maximal length, have the property that for an n stage linear
feedback shift register the sequence repetition period in clock pulse
P is
2-Nonmaximal length, if the sequence length is less than ( )
PN autocorrelation function-The autocorrelation function of a periodic waveform (t), with
period is given by
And the average power of a periodic signal (t) is given by
-The autocorrelation function of a periodic waveform (t),
with period in normalized from
Where (t) is a periodic pulse waveform representing a PN code,
we refer to each fundamental pulse as a PN code symbol or a chip.
-For a PN waveform of a unit chip duration and period P chips, the
normalized autocorrelation function may be expressed as
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(14.7)The normalized autocorrelation function for a maximal sequence ,
is shown plotted in fig(14.3), for three stages if reference sequence
1110010
Shift Sequence Agreement Disagreement
1 0111001 3 42 1011100 3 4
3 0101110 3 44 0010111 3 4
5 1001011 3 4
6 1100101 3 4
0 1110010 7 0 +1
1110010
daadadd
d=difference
a=agreement
fig(14.3)
Direct sequence spread spectrum systems
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-The block diagram in fig(14.4a) shows a direct sequence (DS)
modulator. Direct sequence is the name given to the spectrum
spreading technique whereby a carrier wave is modulated with a
data signal. (t), then the data modulated signal is again modulated
with a high speed (wideband) spreading signal g(t).
The ideal suppressed carrier binary phase shift keying BPSK
modulation results in instantaneous changes either 0 or radians
according to the data. Thus, the data phase modulated can be
expressed by
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fig(14.4)
Where P is the amplitude of the carrier . The transmitted
waveform can be expressed by
Where g(t) is an antipodal spreading code (signal) with +1or -1.
The modulator based on eq(14.8b) is shown in fig (14.4b).
-If the data input pulse (t) is binary value (either +1 or -1), then the
initial step in the DS/BPSK modulation can be accomplished by the
modulo-2 addition of the binary data sequence with the binary
spreading sequence.
-Demodulation of the DS/BPSK is accomplished by correlating or
remodulating the received signal with a synchronized replica of the
spreading signal g(t- d), where d is the receiver estimate of the
propagation delay from the transmitter to the receiver. In the
absence of noise and interference, the output signal from the
correlator can be written as
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Where the constant A is a system gain parameter and is a random
phase angle in the range (0,2). Since g(t)=1, the product
will be unity if , that is, if the code signal
at the receiver is exactly synchronized with the code signal at the
transmitter. When it is synchronized, the output of the receiver
correlator is the despread data modulated signal. The despreading
correlator is then followed by a conventional demodulator for
recovering the data.Let us consider an example of DS/BPSK modulation and
demodulation as a shown in fig(14.5) following the block diagrams
of fig(14.4b and d). The demodulation is a two steps:-
a-Despreading is accomplished by correlating the received signal
with a synchronized replica of the code.
b-Data demodulation, is accomplished by a conventional BPSK.
-In the example of fig(14.5) we see the code replica in
fig(14.5e) as the phase shift (either o or) that is produced at the
receiver by despreading code.
Fig(14.5f) shows the resulting estimate of the carrier phase
after despreading or after has been added to . At this
point the original data pattern can be recognized. The final step
shown in fig(14.5) can be obtained after BPSK demodulator.
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)(tx
)(tg
)()( tgtx
)()( ttxg
)( tg
)( tx
)(tx
fig(14.5)
Processing gain and jamming margin
A fundamental subject in spread spectrum systems is how much
protection spreading can provide against interfering signals with
finite power. The process gain of a processor is defined as the
difference between the output (S/N) ratio of the processor and the
input (S/N) of the processor.
-Spread spectrum develops its process gain in a sequential signal
bandwidth spreading and despreading operation. The process gain
of a spread spectrum processor can be defined as
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Where is the spread spectrum bandwidth (the total bandwidth
used by the spreading technique) R is the data rate.
-For direct sequence systems, is approximately the code chip
rate and the processing gain can be expressed as
This process gain does not mean that the processor can perform
satisfactorily when faced with an interfering signal having a power
level larger than the desired signal by the amount of the available
process gain. For this reason, jamming Margin ( ) is used to
express the capability of the spread spectrum system under
interference conditions. can be expressed as
Frequency Hopping system (FH)-In a frequency hopping system spread spectrum, the frequency of
the modulating signal shift by a PN code. The frequency shifting is
performed by a frequency mixer (converter).
-The modulation most commonly used with this technique is M-ary
frequency shift keying (MFSK), where information bits
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are used to determine which one of M frequencies is to be
transmitted. The position of the M-ary signal set is shifted
pseudorandomly by the frequency synthesizer over a hopping
bandwidth . A typical FH/MFSK system block diagram is
shown in fig(14.6). In a conventional MFSK system, the data
symbol modulates a fixed frequency carrier, in an FH/MFSK the
data symbol modulates a carrier whose frequency is
pseudorandomly determined. In either case, a single tone is
transmitted:-
-The FH system in fig(14.6) contains two step modulation process-
data modulation and frequency hopping modulation.
-Also FH system can be implemented as a single step whereby the
frequency synthesizer produces a transmission tone based on the
simultaneous the desired PN code and the data.
-At each frequency hop time, a PN generator feeds the frequency
synthesizer a frequency word (as a sequence of chips), which
selects one of symbolset positions.
The frequency hopping bandwidth , and the minimum
frequency spacing between hop positions f, determine theminimum of chips necessary in the frequency word. Thus
Number of tones contained in (14.11a)
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-Note
-The receiver for FH system reverses the signal processing steps ofthe transmitter. The received signal is first FH demodulated
(dehopping) by mixing it with the same sequence of
pseudorandomly selected frequency tones that was used for
hopping. Then the dehopped signal is applied to a conventional
bank of M noncoherent energy detectors to select the most likely
symbol.
fig(14.6)
-The processing gain in FH is larger than DS because the SS
technology permits FH bandwidth larger than implementable DS
bandwidth ( ).
-Since FH techniques operate over such wide bandwidths, it is
difficult to maintain phase coherence from hop to hop. Therefore,
noncoherent demodulation is used for HF.
-Let us consider the FH example illustrated in fig(14.7). The input
data consist of a binary sequence with data rate R=150 bit/s. The
modulation is 8-ary FSK.
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The symbol rate is
The symbol duration (T)= =20 msec
The frequency is hopped once per symbol
The hopping rate=50 hop/sec
Fig(14.7) shows the time-bandwidth plane of the communication
resource.
The tone separationWhich corresponds to the minimum required tone spacing for the
orthogonal signaling.
fig(14.7)
-In a conventional 8-ary MFSK scheme, a single tone (offset from
, the fixed center frequency of the data band). The only difference
in this FH/MFSK example is that the center frequency of the data
band is not fixed, the center frequency is changed according PN
code as indicated in the dashed line.
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Robustness of FH
Robustness characterizes a signals ability to withstand
impairments from the channel, such as noise, jamming, fading and
so on. A signal configured with multiple replicate copies, each
transmitted on a different frequency, has a greater likelihood of
survival than does a single such signal with equal total power and
frequency (i.e one single frequency). The greater the diversity
(multiple transmissions, at different frequencies, spread in time),the more robust the signal against random interference. The
following example should clarify the concept. Consider a message
consisting of three symbols: . If a diversity technique is used
with repeating the message N times. Let us choose N=4. Then, the
repeated symbols called chips can be written
Each chip is transmitted at a different hopping frequency (the center
of the data bandwidth is changed for each chip). The resulting
transmissions at frequencies yield a more robust signal
than without such diversity as shown in fig(14.8).
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fig(14.8)
Fast hopping versus slow hopping
-For frequency hopping systems, the term chip is used to
characterize the shortest continuous waveform in the system. FH
system is classified as:-
1-Slow frequency hopping (SFH), in which the symbol rate is
an integer multiple of the hop rate. That is several symbols are
transmitted on each frequency hop.
2-Fast frequency hopping (FFH), in which the hop rate . That is,
the carrier frequency will change or hop several times during the
transmission of one symbol.
fig(14.9) shows FFH and SFH.
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1f
2f
3f
4f
1f
fig(14.9)
Processing gain for FH
The processing gain for FH can be expressed by the general
equation for processing gain as
Time hopping(TH)
Time hopping is pulse modulation with PN code sequence is used
to key the transmitter on and off as shown in fig(14.10). Transmitter
on and off times are there for pseudorandom, like the code, which
give an average transmit duty cycle of as much as 50%.
12 nPT
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fig(14.10)
-TH has found major application in combination with frequency
hopping. The fine difference separating time frequency and plain
frequency hopping is that in FH systems the transmitted frequency
is changed at each code bit time, whereas a TH/FH system may
change frequency only at one/zero transitions in the PN code (or
change both frequency and time of transitions). Fig(14.11) shows a
time hopping system.
fig(14.11)
-TH is used for ranging and multiple access applications.
Pulsed FM (chirp) systems
-One type of spread spectrum modulation that does not necessarily
employ coding but does use a wider bandwidth than that absolutely
required so that it can realize processing gain is chirp modulation.
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-Chirp modulation has found its main application in radar but it also
applicable to data communications.
-Chirp transmission are characterized by pulse RF signals whose
frequency varies in some known way during each pulse period. The
advantage of these transmission for radar is that significant power
reduction is possible.
-The receiver used for chirp signals is a matched filter, matched to
the angular rate of change of the transmitter frequency-swept
signal.
-The transmitted signal can be generated by using VCO and
matched filter used in the receiver as dispersive delay line (DDL).
Fig(14. 12) shows typical waveform and block diagram for chirp
system.
t
tB
B/2
where
fig(14.12)
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-The chirp matched filter compresses a frequency sweep, usually
linear, which provides an improvement in output signal (voltage) to
noise ratio equal to , Where the compression ratio
Where transmitted pulse duration
For example in radar system
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t
tB
fig(14.12a)
Synchronization for SSSFor both DS and FH spread spectrum systems, a receiver must
employ a synchronized replica of the spreading or code signal to
demodulate the received signal successfully. The process of
synchronizing the locally generated spreading signal with the
received SS signal is usually accomplished in two steps:-
a-Acquistion, consists of bringing the two spreading signals into
coarse alignment with one another.
b-Tracking, takes over and continuously maintains the best possible
waveform fine alignment by means of a feedback loop.
Acquisition
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-The acquisition problem is one of searching a limited region of
time and frequency uncertainty in order to synchronize the received
spread spectrum signal with the locally generated spreading signal.
Acquisition process can be classified as:-
a)coherent. B)noncoherent.
-Since the dispreading process typically takes place before carrier
synchronization, and therefore the carrier phase is unknown at this
point, most acquisition process utilized noncoherent detection.
-When determining the limits of the uncertainty in time and
frequency, the following items must be considered:-
1-uncertainty in the distance between the transmitter and receiver
translates into uncertainty in the amount of propagation delay.
2-Uncertainty of the receiver relative velocity with respect to the
transmitter translates into uncertainty in the value of Doppler
frequency offset of the incoming signal.
3-Relative oscillator instabilities between the transmitter and the
receiver result in frequency offset between the two signals.
Correlator structures method for acquisition
-A common feature of all acquisition methods is that the receiver
signal and the locally generated signal are first correlated to
produce a measure of similarity between the two. This measure is
then compared with a threshold to decide if the two signals are in
synchronism. If they are in synchronism, the tracking loop takes
over. If they are not in synchronism, the acquisition procedure
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provides for a phase or frequency change in the locally generated
uncertainty region, and another correlation process is started again.
1-Direct sequence parallel search acquisitions.
Fig(14.12) shows DS parallel search acquisitions. The locally
generated code g(t) is available with delays that are spaced
one-half chip ( ) apart. If the time uncertainty between the
local code and the received code is chips, and a complete
parallel search of the entire time uncertainty region is to be
accomplished in a single search time, 2 correlators are
used. Each carrelator simultaneously examines a sequence of
chips, after which the 2 correlator outputs are compared.
The locally generated code, corresponding to the correlator
with the largest output is chosen.
fig(14.12)
2-Frequency hopping parallel search acquisition.
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Fig(14.13) shows a simple parallel search acquisition. Assume
that a sequence of N frequencies from the hop sequence is
chosen as a synchronization pattern (without data
modulation). The N noncoherent matched filters each consists
of a mixer followed by a bandpass filter (BPF) and a square
law envelope detector(an envelope detector followed by a
square law device). If the frequency hopping sequence is
delays are inserted into the matched filters sothat when the correct frequency hopping sequence appear, the
system produces a large out, indicating detection of the
synchronization. Acquisition can be accomplished rapidly
because all possible code offsets are examined
simultaneously.
fig(14.13)
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Since the required number of correlator or matched filters are
large, fully acquisition techniques are not usually used.
Serial search acquisition techniques are used instead of
parallel acquisition technique.
3-Direct sequence serial search acquisition.
-A popular technique for the acquisition of spread spectrum
signals is to use a single correlator or matched filter to serially
search for the correct phase of the DS code signal or the
correct hopping pattern of the FH signal.
-In a stepped serial acquisition scheme for a DS systems, the
timing of the local PN code is set, and the locally generated
PN signal is correlated with the incoming PN signal. At fixed
examination intervals of , where. , the output signal
is compared to a preset threshold. If the output is below the
threshold, the phase of the locally generated code signal is
incremented by a fraction(usually one half) of a chip and the
correlation is reexamined. When the threshold is exceeded,
the PN code is assumed to have been acquired, the phase
incrementing process of the local code is stopped, and the
code tracking procedure will be initiated.
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fig(14.14)
4-FH serial search acquisition.
Fig(14.15) shows, the PN code generator controls the
frequency hopper. Acquisition is accomplished when the local
hopping is aligned with that of the received signal, in a similar
procedure to DS.
fig(14.15)
Tracking
-Once acquisition or coarse synchronization is completed, tracking
or fine synchronization takes place.
Tracking code loops can be classified as:-
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1. Coherent tracking loops: The carrier frequency and phase are
known exactly so that the loop can operate on a baseband
signal.
2. Noncoherent tracking loops: The carrier frequency is not
known exactly (due to Doppler effects, for example), nor is
the phase.
-In most instances, since the carrier frequency and phase are not
known exactly, a noncoherent code loop is used to tract the
received PN code.
1)Full time earlylate tracking loop [often referred to as a delay
locked loop (DLL)].
-A basic noncoherent DLL loops for a direct sequence spread
spectrum system using binary phase shift keying (BPSK) is shown
in fig(14.16). The data and the code g(t) each modulate the
carrier using BPSK, and as before in the absence of noise and
interference, the received waveform can expressed as
(14.14)
Where A is a system gain parameter and is a random phase angle
in the range (.0.2). The locally generated code of the tracking loop
is offset in phase from the incoming g(t) by a time , where
[ is the chip duration of PN code]. The loop provides
fine synchronization by first generating two PN code sequences
delayed from each other by one chip. Two bandpass
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filters are designed to pass the data and to average the product of
g(t) and the two PN sequences .
fig(14.14)
-The square law envelop detector eliminates the data since
. The output of each envelope detector is given by
Where is the autocorrelation of the PN waveform.
-The feedback signal instructs the VCO either to increase or
decrease its frequency, then forcing to either increase or decrease.
-When , is a small number, , yielding the
despread signal Z(t), which is applied to the input of a conventional
data demodulator.
-The main problem with the DDL is that the early and late arms
must be precisely gain balanced or else the feedback signal
will be offset and will not zero signal when the error is zero. This
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problem is solved by using a time shared tracking loop in place of
the full time locked loop.
-The main advantages are that only one correlator need be used in
the design of the loop.
2)Tuadither tracking loop.
-A problem with some control loops is that if things are going well
and the loop is tracking accurately, the control signal is essentially
zero. When the control signal is zero, the loop can get confused and
do mistakable things. One type of time shared tracking loop, called
the tau-dither loop (TDL), shown in fig(14.17).
-Intentionally injecting a small error in the tracking correction, so
that the loop kind vibrates around the correct answer. This vibration
is typically small, so that the loss in performance is minimal. This
design has the advantage that only one correlator is needed to
provide the code tracking function and the despreading function.
-As Shown in fig (14.17), the PN code generator is driven by a
clock signal whose phase is dithered back and forth with a square
wave switching function, this eliminates the necessity of ensuring
identical transfer functions of the early and late paths. The S/Nperformance of the TDL is only about 1.1dB worse than that of the
DLL.
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fig(14.17)
SS Commercial applications
1-Code division multiple access
-Fig(14.18) shows the communication resource(CR) plane being
partitioned by the use of a hybrid combination of FDMA and
TDMA known as code division multiple access (DMA).
CDMA is an application of spread spectrum (SS) techniques. Since
SS techniques can be classified into two major categories, direct
sequence SS and frequency hopping FHSS, thus CDMA can be also
classified into two major parts.
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Code division multiplexing
fig(14.18)
a-FH-CDMA
At each time slot whose duration is usually short, the frequency
band are divided (i.e band assignments) in FH-CDMA as shown in
the fig(14.18). In fig(14.18), during time slot 1, signal 1, occupies
band 1, signal 2 occupies band 2 and the signal 3 occupies band 3.
During time slot 2, signal 1 hops to band 3, signal 2 hops to band 1,
and so on. The CR can thus fully utilized, but the participants,
having their frequency bands reassigned at each time slot. Each user
employs a specific pseudnoise (PN) code orthogonal control their
frequency bands and time slot.
-The block diagram in fig(14.19) shows CDMA frequency hopping.
At each frequency hop time the PN generaor feeds a code sequence
to a device called frequency hopper. The frequency synthesizer is
used to generate one of the allowable hop frequencies according PN
code. MFSK modulation is used with FH, the data symbol
modulates a carrier wave that hops across the total CR bandwidth.
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AtA
cos ]cos[ ttnA
hopsfrequency
lfundamenta
stepfrequencyFSK
k2
fig(14.19)
b-DS-CDMA
In DS-CDMA, each of N user groups is given its own code,
wherei=1,2,3,N. The user codes are approximately orthogonal, so
that the cross correlation of two different codes is near zero.
Fig(14.20) shows a DS/CDMA. The first lock shows the data
modulation of a carrier . The output of the data modulatorbelonging to a user from group 1 is
(this is a general form independent modulation)
The next block, the data modulated signal is multiplied by the
spreading signal belonging to user group 1, and the resultingsignal is transmitted over the channel. Simultaneously,
users from group 2 through N multiply their signals by their own
code functions. Frequently, each ode function is kept secret, and its
use is restricted to the community of authorized users. The signal
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present at the receiver is the linear combination of the received
signals from N users
The first stage of the receiver multiples the incoming signals by
[for user 1]. The output of the multiplier will yield the signal
-If the code functions are chosen with orthogonal properties,
the desired signals can be extracted perfectly in the absence of noise
since and the undesired signals are easily rejected,
since
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fig(14.20)
Multipath channels
-fig (14.21) shows a communication link with two discrete paths.
The multipath wave is delayed by some time , compared with the
direct wave.
In a DS, if we assume that the receiver is synchronized to the time
delay and RF phase of the direct path, the received signal can be
expressed as
Where x(t) is the data signal, g(t) is the code signal, n(t) is a zero
mean Gaussian noise process, and is the differential time delay
between the two paths. The angle is a random phase and is the
attenuation of the multipath signal relative to the direct path. The
output of the correlator can be written as
Where =1. Also for , g(t)g( )0. Therefore, if is
less than the differential time delay between the multipath and
direct path signals, we can write
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Where is a zero mean Gaussian noise. We see that the SSS
effectively eliminates the multipath interference by virtue of its
code correlation receiver.
fig(14.21)
Note
If FH is used against the multipath problem, using another
mechanism to the improvement by rapid frequency change.
Advantages of CDMA
1-Privacy, When the code for a particular user group is only
distributed among authorized users, the CDMA process provides
privacy, since the transmission cannot easily be intercepted by
unauthorized users without the code.
2-Fading channels: If A particular portions of the spectrum is
characterized by fading signals in that frequency rage are
attenuated. In a FH/CDMA, only during the time a user hops into
the affected portion of the spectrum will user experience
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degradation. However, in a DS/CDMA only a part from the
spreaded bandwidth is affected.
3-Jam resistance according the processing gain .
4-Flexibility: All users can share the full spectrum of the resources
(frequency and time) asynchronously, that is the transition times of
the different users symbols do not have to coincide.
Ex14.1
A hopping bandwidth of 400 MHz and a frequency step size of 100Hz are specified. What is the minimum number of PN chips that are
required for each frequency word?
Slution
Number of tones contained in
Minimum number of chips
Ex14.2
Consider the DS BPSK spread spectrum transmitter. Let the input
sequence 100110001, arriving at a rate of 75 bit/s, where the
leftmost bit is the earliest bit. Let g(t) be generated by the shift
register with initial state of 1111 and a cock rate of 225Hz.
a-Sketch the final transmitted sequence x(t)g(t).
b-What is the bandwidth of the transmitted (spread) signal.
c-What is the processing gain?
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d-Suppose that the estimated delay is too large by one chip time.
Sketch the despread chip sequence?
solution
x(t)=100110001 with data rate=75 bits
g(t) =111100010011010 with clock rate=225 Hz
Let
b-Bandwidth of
c-processing gain
d-x(t)g(t) 000100010100101111100010100
g(t) advanced by 1chip 01110001001101011110001001
O/P sum 01101001110100010001001110
Ex14.3
A total of 24 equal power terminals are to share a frequency band
through a code division multiple access (CDMA) system. Each
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terminals information at 9.6 kbit/s with a direct sequence spread
spectrum BPSK modulated signal. Calculate the minimum chip rate
of the PN code in order to maintain a bit error probability of
solution
from table of error function x=3.09
4.77=
W=4.77x23x9.6 kbit/s=1.05 MHz
minimum chip rate
where bit energy, bit duration
S=received signal power, R=data rate
where =averages signal power to average noise power
=Noise power spectral density
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W=bandwidth of the system
Ex14.4
Consider an FH/MFSK system .Let the PN generator be defined by
a 20 stage linear feedback shift register with a maximal length
sequence. Each state of the register dictates a new center frequency
within the hopping band. The minimum step size between center
frequencies is 200Hz. The register clock rate is 2KHz. Assume that
8-ary FSK modulation is used and that the data rate is 1.2kbit/s.a-What is the hopping bandwidth.
b-What is the chip rate.
c-How many chips are there in each data symbol.
d-What is the processing gain.
solution
Hopping bandwidth=
Wss=number of statesminimum step between frequencies
b-chip rate =hop rate=2000chip/s
c-chip/symbol:
d-processing gain:
Ex14.5
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A feedback shift register PN generator produces a 31 bit PN
sequence at a clock rate of 10MHz. What are the equation and
graphical form of the autocorrelation function and power spectral
density of the sequence? Assume that pulses have values of 1v.
Solution
The 31 bit sequence has autocorrelation function with a maximum
value at
Decreasing linearly to -1/31 at for T equal to a chip
interval
[total agreements total disagreements in one full period of
the sequence with a position cyclic shift]
)12( 31P
R() repeates for offset times= for
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