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6.4 Digital Modulation-An overviewModern Mobile communication uses digital modulation techniques.
Advancements in DSP and VLSI have made digital modulation more
cost effective than analog transmission systems
Advantages:1. Greater noise immunity
2. Robustness to channel impairments
3. Easier multiplexing of (voice, data & video)
4. Security 1
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5. Digital error- control codes detectand/orcorrect Tx errors
6. Complex signal conditioning &processing(encryption,equalization)
7. Programmable DSP Digital modulators,demodulators software
8. Modem design using embedded softwareimplementation(No redesign/replace Modem).
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Modulating (message) signal
Symbols/pulses
m finite states
Each symbol n bits of information
n = log m bits/symbol
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6.4.1 Factors that influence the choice
of Digital Modulation Desirable Modulation Scheme
low BER at low SNR
occupies min. BW
Easy & cost effective to implement
Performance of Modulation Scheme is measured interms of
power efficiency
BW efficiency
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Power Efficiencyp
Ability of modulation technique to preservethe
fidelity[Bit Error Prob] of msg evenat low power
levels
To Noise immunity by
signal power
Amountby which signal power to have certain
fidelitytype of modulation is used.
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Power efficiency : p: (Energy efficiency)
p= Signal energy per bit = Eb
Noise power spectral density No
Required at Rx to have certain Probability of
error
Power Efficiency
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Bandwidth efficiency
Ability of mod scheme to accommodate data
within a limited BW
How efficiently allocated BW is utilized
B = Throughput data rate = R bits/s bps/Hz
Hz in a given BW B BW of modulated RF
System capacity B B Tx more data in a
given spectrum
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Shannons Channel Coding theorem
For a given prob of error max possible BW
efficiency limited by noise in the channel
Channel capacity formula = Bmax = [C/B] =
log*1S/N+
C Channel capacity
B RF BW
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6.4.2 Bandwidth and Power Spectral Density of Digital
Signals
PSD of a random signal w(t) is
WT(f) FT of WT(t)
WT(t) = w(t) forT/2
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The PSD of a bandpass signal is related to PSD of
its baseband complex envelope
S(t) modulated (BandPass) signal
g(t) complex baseband envelope
S(t) = Re{g(t) exp(j2fct)}
Ps(f) = 0.25[Pg(f-fc)+Pg(-f-fc)]
Pg(f) = PSD of g(t)
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Absolute BW
Range of freq over which signal has nonzeroPSD.
But for rectangular pulses , PSD extends overinfinite range of frequencies
Simplermeasure of BW null-to-null BW = Widthof main spectral lobe
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Popular Measure of BW measures dispersion
of spectrum Half Power BW(3 dB Bandwidth)
HP BW(3 dB bandwidth) Interval b/w
frequencies at which PSD has dropped to one
half power or 3dB below the peak values.
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6.5 Line Coding
Digital baseband signals use line codes to Provide
particular spectral characteristics of a pulse train
Common line Codes for mobile comm.
Return-to-zero(RZ) non-return-to-zero(NRZ)
Manchester codes
Unipolar v/g levels 0 or v
Bipolar v/g levels -v or v13
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RZ pulse train returns to zero within every bitperiod
Spectral widening butimprovestimingsynchronization
NRZ dontreturn to zero during a bit period
signal constant throughout a bit period
more efficient than RZ but results in poorsynchronization
have large dc component
notused in dc blocking ckts such as
audio amplifiers or phone switching equipment15
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Manchester code
Spl NRZ line code
no dc comp simple synch used in phonelines and dc blocking ckts
Use 2 pulses for each binary symbol
zero-crossings are guaranteed in every bit perid
provide easy clock recovery
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Higher level mod (M-ary keying) signal set
more than 2 signals
Signal set size M No of bits/symbol logM
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Elements of S viewed as points in vector space
Finite set of physically realizable w/fs in vectorspace expressed as linear combination of N
orthonormal w/fs Form the basisof the vector
space
Representing modulation signal on a vector space
Find set of signals that form basis for thatvector space.
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Once basis is found any pt in vector space
linear combination of basis signals
The basis signals are orthogonaltoone another in
time such that
Each of the basis signalsis normalizedto have
unit energy, i.e.,
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For BPSK scheme
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For BPSK scheme,
the basis signal
then, the BPSK signal set can be represented as
Eb-Energy per bit
Tb-Bit period
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constellation diagram
Graphical representation of the complex envelope of
each possible symbol state.
The X-axis represents the in-phase components
y-axisrepresents the quadrature component of
complex envelope22
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The number of basis signals required to represent
the complete modulationsignalsetis called thedimensionof the vector space.
No of basis signals
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Prob of bit error distance b/w closest point in
the constellation.
Modulation scheme densely packed less
energy efficient
Average probability of error for a particular
modulation signal,
NoNoise spectral density
dij Euclidean distance b/w ith& jthsignal points
Q-function
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Linear Modulation Techniques
In linear modulation techniques, the amplitude of the
transmitted signals, s(t), varies linearly with the modulatingdigital signal, m(t)(Hence non constant envelope).
Linear modulation techniques are bandwidth efficient, butmust be transmitted using linear RF amplifiers which havepoor power efficiency.
Using the power efficient nonlinear RF amplifiers could
cause severe adjacent channel interference, and results inthe loss of all the spectral efficiency gained by linearmodulation.
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Constant Envelop Modulation(Amplitude of carrier isconstant)
The constant envelop family of modulation has the
following advantages: Power efficient Class C amplifiers can be used without introducing
degradation in the spectrum occupancy.
Low out-of-band radiation(-60 to -70 dB)
Limiter-discriminator detection can be used, which simplifiesreceiver design and high immunity towards noise and fading effects.
But, they occupy a larger bandwidth than linearmodulation schemes.
Many practical mobile radio communication systems useNon linear modulation Schemes
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Binary Frequency Shift Keying (BFSK)
The frequency of a constant amplitude carrier signal is
switched between two values according to the two
possible message states(binary 1 or 0).
where is a constant offset from the nominal carrier
frequency
f2
27
G ti f FSK(di ti FSK)
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Generation of FSK(discontinuous FSK)
switchingb/w two independent oscillators
depending on databit is 1 or 0 and it isdiscontinuous at switching times (phase discontinuity)
Discontinuous FSK signal is represented as,
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Phase discontinuities several problems
spectral spreading
spurious transmissions
hence not used in highly regulated wireless systems
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Spectr m and BW of BFSK signals
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Spectrum and BW of BFSK signals
Complex envelope of FSK signal nonlinear function of
m(t)
PSDof FSK has discrete frequency components at fc,
fc+nf, fc-nf n is integer
PSDof continuous phase FSK falls off as inversefourth power of frequency offset from fc.
PSDof discontinuous phase FSK falls off asinverse square of frequency offset from fc.
1/[ 2f ]4
1/[ 2f ]2
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Transmission BW of FSK signal from Carsons rule
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Transmission BW of FSKsignal, from Carsons rule,
BT= 2f + 2B
B BWof digital baseband signal
If first null BW is used, BW of rectangular pulses,is B=R. FSK transmission BW = 2f + 2R = 2(f+R)
If raised cosine pulse-shaping filter is used,B = (1 + ) R/2 BT= 2f + (1+)R
roll off factor of the filter33
Coherent Detection of Binary FSK
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Coherent Detection of Binary FSK
Two Correlator with locally generated coherent
reference signals
Diff of Correlator o/p compared with threshold diff>Th1
diff
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Coherent Detection of Binary FSK
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Non coherent Detection of Binar FSK
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Detect FSK signal without coherent carrier
reference
Pair of matched filters envelope detectors
Filter in upper path matched to FSK signal of
frequency fL
Filter in lower path matched to FSK signal of
frequency fH
Non coherent Detection of Binary FSK
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Non coherent Detection of Binary FSK
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Non coherent Detection of Binary FSK
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Non coherent Detection of Binary FSK
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Matched filters BPFcentered at fH& fL
Envelope detectors O/P sampled at t=kTb
compared
If envelope detector o/p> or < threshold
o/p 1/0
Non coherent Detection of Binary FSK
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Probability of error of an FSK system non
coherent detection,
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6 9 2 Minimum Shift Keying
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6.9.2 Minimum Shift Keying
Special type of Continuous phasefrequency shift keying(CPFSK)
Peak frequency deviation = (Bit rate)/4
Frequency difference between the logical one and logical
zero statesequal to half the data rate MSKContinuous phase FSK with modulation index = 0.5
Modulation Index of FSK = FMmodulation index
F peak RF frequency deviation
Rb Bit rate
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Modulation index = 0 5
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Modulation index = 0.5
min frequency spacing b/w fH& fL
that allows two FSK signals to be coherently
orthogonal
Two FSK signals vH(t) & vL(t) are orthogonaliff,
MSK fast FSK frequency spacing used =1/2of[used in noncoherent FSK]
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MSK used in mobile radio comm system
constant envelope
spectral efficiency
good BER performance
selfsynchronizing capacity
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MI(t) & MQ(t)
odd & evenbits of bipolar data stream
1
feed the In-phase& Quadrature arms of
modulator at a rate of Rb/2
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MSK special type of continuous phase FSK of
above SMSK(t) is rewritten using trigonometric
identities as,
If k 0 or mI(t) is 1 or -1
MSK constant amplitude
45
h i i b d d
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Phase continuity at bit transition period is ensured
by choosingcarrier frequency fc integral
multiple of one fourth the bit period 1/4T
Compare SFSK& SMSK MSKsignal is an FSKsignal
with binary signaling frequencies fc+1/4T & fc-1/4T
phaseof MSKsignal varies linearly during each
bit period
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N li d PSD i
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Normalized PSD is,
From PSD of MSK
MSK has lower side
lobethan QPSK & OQPSK
99%of MSK power is
contained within B = 1.2/T
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99% of QPSK & OQPSK is contained within B = 8/T
MSKhas faster rolloff due to smoother pulse
functions
Main lobe of MSK is wider than QPSK & OQPSK
MSK is less spectrally efficient than PSK techniqueswhen compared in terms of first null bandwidth
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No change in phase at bit transition periods
MSKhas continuous phase property
Envelopeis constanteven after band limiting
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Small variations in envelope removed by hard
limiting at the Rx without raising the out-of-
band radiation levels
Amplitudeis constant MSK signals are amplified
using nonlinear amplifiers
MSK simple demodulation & synchronization
ckts. Hence popular among mobile radiocommunications
51
MSK Transmitter
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MSK Transmitter
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MSK Transmitter and Receiver
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MSK Transmitter and Receiver
CarrierXlied with cos[t/2T] produce two
phase-coherent signals at fc+1/4T & fc-1/4T
2 FSK signals separated using 2 NBPF combinedto form in-phase x(t) & quadrature
y(t) carrier components
These carriers are Xliedwith odd & even bit
streams mi(t) & mq(t) produce MSK signal
SMSK(t)53
MSK Receiver
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MSK Receiver
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S (t) Xlied by in phase x(t) & quadrature y(t)
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SMSK(t) Xliedby in-phase x(t)& quadrature y(t)
carriers
o/p of Xliersare integratedover two bit periods
dumped to decision ckt at the end of each two
bit periods
Based on o/p of integrator threshold detector
o/p is 0/1
o/p data streams mi(t)/mq(t) offset combined
to get demodulated signal.55
6 9 3 Gaussian Minimum Shift Keying (GMSK)
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6.9.3 Gaussian Minimum Shift Keying (GMSK)
Simple Binary modulation scheme derivative of
MSK
Sidelobe levels by passing modulating NRZ
data waveform through premodulation Gaussianpulseshaping filter
NRZ data w/f Gaussian Filter Smoothened o/p
stabilizesthe instantaneous frequency variationsover time which reduces the sidelobe levels in
Transmitted spectrum 56
GMSKcan be
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detected using coherent detector(as MSK)
detectedusing noncoherent detector (as FSK)
Has excellent power efficiency(due to constant
envelope) & spectral efficiency
Premodulation gaussian filtering Introduces ISIin
the Tx signal but degradationis not severe if 3dBbandwidthbit duration product (BT)of filter
is greater than 0.5
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GMSK d l ti filt h i l
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GMSK premodulation filter has impulse response,
Transfer function,
GMSK filter defined by B & baseband symbol
duration T.
Therefore GMSK is defined by its BT product58
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GMSK Bit E R t
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GMSK Bit Error Rate
Bit error probability for GMSK is,
61
GMSK Transmitter & Receiver
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GMSK Transmitter :
Pass a NRZ message bit stream through aGaussian baseband filter having impulse
response
followed by FM modulator 62
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Usedin US Cellular Digital Packet Data (CDPD)
& Global System for mobile (GSM) system.
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GMSK Receiver :
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GMSK Receiver :
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GMSK Receiver :
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GMSK Receiver :
Orthogonal coherent detectors
Or
Use simple noncoherent detectors FMdiscriminators
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Pbm
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6.10 Combined Linear & Constant Envelope Modulation
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Techniques
Digital BB data is sent by varying both
envelope & phase (or frequency) of carrier
M-ary modulation
71
M i li h
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M-ary signaling scheme
two or more bits are grouped together
symbols
one of M signals S1(t), S2(t),,SM(t) is Tx during
each symbol period of duration Ts
No. of possible signals= M = 2 ; n integer
amplitude, phase or frequency of carrier is
varied M-ary ASK, M-ary PSK or M-ary FSK72
M-ary Modulation Schemes
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y
Achieve better BW efficiency than PowerEfficiency
Eg: 8-PSK BW = log8 = 3 times smaller thanBPSK
BER performance worse than BPSK
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6.10.1 M-ary Phase Shift Keying (MPSK)
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M-ary PSK carrier phase takes on one of M
possible values
Modulated waveform,
Energy per symbol
symbol period
74
Si(t) can be rewritten in quadrature form as,
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( ) q ,
i = 1,2,..,M
Choose the basis signals,
Over 0 t Ts
75
M-ary PSK signal is
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M-ary PSK signal is,
i=1,2,..,M
There are 2 basis signals(therefore constellation is
2 dimensional)
M-ary msg points equally spaced on a circleof
radius Es centered at origin
76
Fig 6 45 constellation diagram of 8-ary PSK
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Fig 6.45 constellation diagram of 8-ary PSK
M-ary PSK ampof Tx signal const circular
constellation
MPSK const envelope signal when no pulse shaping
used
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= 6.62
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Fig 6.45 distance b/w adjacent symbols =2Es(sin(/M)) &
Average symbol error probability ofcoherent M-aryPSK is,
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Power Spectra of M-ary PSK
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Ts symbol duration
Tb Bit duration
Ts= TblogM
PSD of M-ary PSK signal with rectangular pulses is,
81
Fig 6.46A M fi t ll
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As M first nullBW Rb = const
M BWefficiency
Fixed Rb M B B
M constellationisdensely packed power efficiency
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6 10 2 M ary Quadrature Amplitude Modulation (QAM)
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6.10.2 M-ary Quadrature Amplitude Modulation (QAM)
QAM Hybrid modulation Technique: Vary both A& Phase
Fig 6.47 constellation diagram
16ary QAM
square lattice of signal points
84
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General M-ary QAM is,
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y
Emin energy of signal with lowest amplitude
Closest point has min energy
ai & bi pair of independent integers
M-ary QAM
doesnthave const energy per symbol,
doesnt have const dist b/w symbol states
86
Si(t)in terms of 2 basis fns,
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(ai,bi) element of L by L matrix, gives location
87
Eg: 16-QAM signal constellation Fig 6.47,
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LXL matrix is,
L=16=4
88
Average prob of error M-ary QAM, using
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g p y Q , gcoherent detection,
In terms of average signal energy, Eav
Power spectrum & BW efficiency of QAM identical to M-ary PSK modulation
Power efficiency of QAM superior to M-ary PSK89
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6.10.3 M-ary Frequency Shift Keying (MFSK) and OFDM
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M-FSK signals,the transmitted signal is defined as
M Tx signals
equal energy
equal duration signal frequencies are separated by 1/2Ts Hz
& signals are orthogonal
91
Coherent detection of M-ary FSK:
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has bank of M correlators
matched filters tuned to M distinct carriers Avg prob of error =
Noncoherent detection: Using matched filters followed by envelope
detectors,
Avg probability of error is,
92
Using only leading terms of binomial expansion,
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the prob of error,
BW of coherentM-ary FSK signal,
BW of noncoherentMSK is,
93
BW efficiency of M-ary FSK with M
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M-FSK BW inefficient
All M signals are orthogonal no crowding insignal space power effi with M , It can be
amplified using nonlinear amplifiers
Orthogonality characteristic of MFSK led toOFDM power efficient signaling for a large no. ofusers on the same channel.
94
6.11 Spread spectrum modulation techniques.
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Modulation & demodulation
techniques BW efficiency
power efficiency
Spread spectrum
pseudorandom
BW =>BW inefficient (disadvantage)
noiselike properties Advantage :multiple users use same BW
simultaneously.
95
Spreading of waveform is controlledby:
P d i (PN)
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o Pseudo noise(PN) sequence or
o Pseudo noise code.
At Rx-> SS signals demodulatedusing locally
generated pseudo random carrier.
cross correlation with PN sequence->
despreads the spread spectrum signal=> restores
the message.
96
Advantage:
I t f j ti bilit
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Interference rejection capability
o Each user is given a unique PN code-> orthogonalto
the code of other users.
o Rx separates each user based on their codes, even
though they occupy the same spectrum at all times.
Narrowband interference-> removed using notch
filtering.
97
Advantage:
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Eliminates freq planning since all cells can use the
same channels.
SS signals have uniform energy over a large BW->
hence at a given time only a small portion of the
spectrum will undergo fading.
98
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6.11.1 pseudo-noise (PN) sequences.
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Binary sequence with an autocorrelationthat
resembles the autocorrelation of a random binary
sequence.
A.C->also resemblesthe A.Cof band limited white
noise
100
Characteristics of PN sequences:
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Characteristics of PN sequences:
Equal number of 0s & 1s.
Very low correlation b/w shifted versions of the
sequence.
Very low cross correlation b/w any two sequences.
101
PN sequence is generated using-> sequential logiccircuits
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circuits.
Has consecutive stages of two state memory.
Feedback logic.102
Binary sequence are shiftedthrough shift registers
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y q g g
wrt clock pulse
Output of various stages are logically combined&
fedback as the i/pto the first stage.
If feedback logic->has ex-or gates-> shift register is
called a linear PN sequence generator.
103
Initial contentsof memory stages and the feed
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back logic -> decides>successive contents ofmemory.
If linear S.R reaches zero state at some time->always remain in the zero state-> o/p all 0s.
There are (2^m)-1 non zero states for m-stage F/Bregisters.
Sequence ->linear F/B register-> maximal length(ML) sequence.
104
6.11.2 direct sequence spread spectrum(DS-SS).
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DS-SS->system->spreadsthe baseband data bymultiplying BB data pulseswith PN sequence.
Single pulse/symbol of PN waveform-> chip.
105
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106
Data symbols Rectangular pulses v=+1/-1.
information bits
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information bits
added in modulo 2fashion.
chips before being phase modulated
At Rx-> use coherent/differentially coherent PSKdemodulation.
The received spread spectrum signal for singleuser:
Diff user have diff p(t)107
m(t)rectangular pulses of amplitude+1/-1each symbol duration=Ts
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each symbol duration Ts
P(t) PN sequence each pulsechip(Narrower than the bit) rectangular pulse+1/-1and duration=Tc.[Tc BW of spread spectrum.
B->BWof m(t)cos2 fct-> Bw of modulatedsignal.108
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109
Rx signal passes through wideband filter
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Multipliedby local replica of PN code sequence p(t).
If p(t)=+1/-1=>P^2(t)=1
multiplication-=>yields despread signal s(t). BWNB Signal
-at input of demodulator.
Coherent PSK/differential PSK demodulator -> givesm(t).
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WBF O/P NB interference
Rx Correlator o/p after despreading->Signal BW=B
Interference get spread
Interference BW >Bss
Strong interference/weak signal STRONG SIGNAL & WEAK
INTERFERENCE111
Filteringaction of demodulator-> removes most
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of interference spectrum.
Interference rejection ratio=Bss/B.
Greater the PG=> greater the ability to suppress
in-band interference.
112
Direct Sequence Spread Spectrum
E l
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Example
113
Approximate Spectrum of DSSS Signal
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114
6.11.3 frequency hopped spread spectrum.
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It involves a periodic change of transmission frequency
hopset-set of possible carrier frequencies.
Hopping occurs over a frequency band that includes a
number of channels.
BW of channel used in hopset-> instantaneous BW. B
BW of spectrum over which hopping occurs-> total
hopping BW. Bss
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If single carrier frequency(single channel) is usedon each hop >single channel modulation
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on each hop-> single channel modulation
Time duration b/w hop->hop duration/hoppingperiod(Th).
Bss->total hopping BW.
B->instantaneous BW
PG=Bss/B.
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6.11.3 frequency hopped spread spectrum.
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Carrier frequency abruptly change(hop)in
accordance with PN code sequence.
The set of possible carrier frequencies is called the
hopset
Hopping occurs over a frequency band that
includes a number of channels
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The frequency of the carrier is periodically modified(hopped) following a specific sequence of frequencies
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(hopped) following a specific sequence of frequencies.
In FHSS systems, the spreading code is this list offrequencies to be used for the carrier signal, a.k.a. thehopping sequence
The amount of time spent on each hop is known as dwelltime and is typically in the range of 100 ms.
Redundancy is achieved through the possibility to
execute re-transmissions on different carrier frequencies(hops).
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If only a single carrier frequency is used on
h h d l i i ll d i l h l
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each hop, Modulation is called single channel
modulation
The time duration between hops is called the
hop duration or the hopping period and is
denoted by Th
The total hopping bandwidth and the
instantaneous bandwidth are denoted by Bssand B respectively.
The processing gain = Bss/B for FHSS systems
Dehopped signal->hoppingis removedfrom Rx
signal
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signal.
If the Frequency synthesizer produced by the
receiver synthesizer is synchronized with the
frequency pattern of the received signal ,then the
mixer output is a dehopped signal.
It is possible to have collisions in an FH system
where an undesired user transmits in the channel
at the same time as the desired user
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Frequency hopping-fast/slow.
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fast frequency hopping
more than one frequency hop during eachtransmitted symbol.
hopping rate information symbol rate.
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6.11.4 performance of direct sequence spreadspectrum.
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direct sequence spread spectrum with k users.
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Each user-> PN sequence->N chips/ message symbol period T
NTc=T
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Transmitted signal of Kth user,
Pk(t)->PN code sequence of Kth user.
mk(t)->data sequence of Kth user.
Rx signal will consist of sum of k different transmitted signals->[one desired user & k-1 undesired user]+additive noise.
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Reception Decision variable of ith Tx bit of user 1
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if m1,i=-1=> bitis received in error if Zi(1)>0.
Probability of error=
Rx signal r(t)-> linear combination of signals plusadditive noise
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Response of receiver due to the desired signal from user
1:
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1:
Gaussian random variable representing noise with zero
mean & variance: with n(t) Additive Gaussian Noise
Multiple access interferencefrom user k,
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Ik-> has cummulative effects of N random chipsfrom kthinterferer over the integration period Tof one bit
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of one bit.
From central limit theorem-> sum of these effectswill tend toward gaussian distribution
(k-1)->users which serve as identically distributedinterferers=> total multiple access interference
Average probability of error is,
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Single user=> k=1=> Peexpression=expression for
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g e p p
BPSK modulation.
Interference limited case-> No ->Eb/No->
Therefore
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6.11.5 Performance of frequency hopping spreadspectrum.
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FH-SS systems-> many users hop their carrier frequencies
using BFSK modulation.
If 2 users are notsimultaneously utilizing the same
band=> prob of error for BFSKis
If 2 users Tx simultaneously in the same frequency
band-> collision/ hitoccurs.
Overall prob of error,
Ph->prob of a hit. Prob that hit doesnt occur135
If there are M hopping channels(slots)=>
h / b h f ll b
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There is 1/M prob that a given interferer will bepresent in the desired users slot.
If there are (k-1)interfering users=> prob that atleast one is present in the desired frequency slot
When M is too large.
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If k=1,
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If Eb/No->,
Till now assumption:
All users hoptheir carrier frequencies
synchronously. =>slotted frequency hopping
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Asynchronous case when,
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Radio signals will not arrive synchronously[sametime] to each user due to various propagationdelays.
Prob of hit for asynchronous case is,
->Nb: number of bits per hop.
-> prob of hit is increased.
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