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ICTP-ITU/BDT-URSI School on Radio-Based Computer Networking for Research and Training in Developing CountriesThe Abdus Salam International Centre for Theoretical Physics ICTP, Trieste (Italy), 7th February - 4th March 2005
Radiocommunication Channeland Digital Modulation: Basics
Prof. Dr. R. Struzakr.struzak@ieee.org
Note: These are preliminary notes, intended only for
distribution to participants. Beware of misprints!
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Outline
Radiocommunication channel Modulation
Spreading spectrum
Nonlinearities & intermodulation
Summary
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Microwave radio link
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Wireless Local Loop
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BSS
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PTP, PMP, Mesh A point-to-point (PTP) link is one station (node)communicating with another one
A point-to-multipoint (PMP) network is one node
(base station) communicating with more than one
other nodes Mesh network (fully connected): A network topology
in which there is a direct communication path between
any two nodes Mesh and PMP topologies share communication resources (media)
In a fully connected network with n nodes, there are n(n-1)/2 direct paths, i.e.,
branches.
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FDD radio links Two stations can talk and listen to each other at the same
time (time-sharing).
This requires separate (static) frequency channels a
technique known as Frequency Division Duplex (FDD)
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Station 1
TX RX
TXRX
Frequency
Channel 2
Station 2
Frequency
Channel 1
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TDD radio links Two stations can talk and listen to each other using the
same frequency channel (frequency-sharing), one after
another.
This requires time synchronization/ handshaking a
technique known as Time Division Duplex (TDD)
Station 1 Station 2
Single Frequency
ChannelTX
RX
TX
RX
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Radio Link model
Environ
ment
T-antenna
Propagation medium
R-antenna
Noise
Original message/ data
Reconstructed message/ data
EM waves:time-
distance-direction-polarization
ReceiverTime seriesProcessing/De-coding
TransmitterCoding/ProcessingTime series
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Transmitting station
Electrical signal is represented by a function of time.Radio wave transmitted is represented by a function of
time, distance, direction, and polarization.
Radiowave
Transmittingantenna
RF cable(signal attenuation)
Originalsignal
Transmitter(signal processing)
Electrical current EM wave
Focus of the school
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Receiving station
Radio
wave
Receiving
antenna
RF cable(signal attenuation)
Recovered
signal
Receiver(signal processing)
Electrical currentEM wave
Focus of the school
Radio wave received is represented by a function of time,distance, direction, and polarization that depends on signal-path environment
Electrical signal is represented by a function of time.Property of R. Struzak 11
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Modern radio: details
BASEBAND PROCESSING& PC INTERFACE
DAC
CRYSTALREFERENCE
FILTER
SYNTHETIZER
ADC
FILTER
IFFILTER
SYNTHETIZER
RFFILTER RFFILTER
ANTENNA
RFAMPLIFICATION
RFUP/DOWN
CONVERSION
IFGAIN&SELECTIVITY
SWITCH
TRANSMITTER COMMON PART RECEIVER
MOD
ULATION
&DEMO
DULATION
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Modern radio =combination of
radio and computerhardware &software
Software-definedradio
Systems withmost functionsdefined by
software Automatically
and/or at distance
RADIO WAVE PROPAGATION PATH
Beamforming
Freq. spread
Modulation
Multiplex
Format
Encryption
Encoding
Analog/Digital
Information source
Beamforming
Freq. despread
Demodulation
Demultiplex
Format
Decryption
Decoding
Digital/ Analog
Information sink
Fromo
th
ersources
Tootherdestinations
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Outline
Radiocommunication channel
Modulation
Spreading spectrum
Nonlinearities & intermodulation
Summary
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Modulation = process of translation
the message frombaseband signal tobandpass (modulatedcarrier) signal at
frequencies that are veryhigh compared to thebaseband frequencies.
Demodulation is the
reverse process Note: An information-bearing
signal is non-deterministic, i.e.it changes in an unpredictablemanner.
Modulator/
Signal Processing
Carrier Generator
m(t)
s(t)
f(t)
s'(t)
Demodulator/
Signal Processing
m'(t)
RADIO ENVIRONMENT
TRANSMITTER RECEIVER
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CommunicationChannelOriginal messagem(t)
Transmitter
s(t) = U(m, f)m(t) = message (information, data)
s(t) = signal carrying the message
f = f(a,b,c,, t) (carrier function)
a,b,c, = modulation parameters
U, V, W= operators = noise, fading, perturbations
x(t) = perturbed signal at the receiver input
y(t) = reproduced message
Task: makey m (within anacceptable error)
Transport medium
x(t) = V(s, )
Receiver
y(t) = W(x)
Reproduced
(received) message
y = W{V[,U(m,f)]}
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Modulation Process( )1 2 3
1 2 3
, , ,... , (= carrier)
, , ,... (= modulation parameters)
(= time)
n
n
f f a a a a t
a a a a
t
=
Modulation implies varying one or morecharacteristics (modulation parameters a1, a2, an) ofa carrierfin accordance with the information-bearing(modulating) baseband signal
Each of the parameters a, b, c... carrying informationcan be modulated independently, increasingcommunication capacity at a cost of complexity.
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The carrier is generated in the transmitter
It may be a continuous (e.g. sinusoidal) current ofradio frequency, a sequence of short pulses, ornoise
Systems using pulse sequences are also calledcarrierless or impulse systems
It may also be a number of carriers, such as in
Orthogonal Frequency Division Multiplexing(OFDM) systems. For instance, one of standards Wireless Local Area Networks
(WLANs) foresees 52 carriers spaced 312.5 kHz apart
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Why Carrier?
To radiate EM waves effectively Radiation efficiency requires antenna dimensions to be
comparable with the radiated wavelength Antenna for 30 kHz would be 10 km long
Antenna for 3 GHz carrier is 10 cm long
To assure signal orthogonality (avoiding mutualinterference by using orthogonal frequencies) Note: There are also other methods of avoiding
interference (e.g. time- or code-orthogonality) Standards and RR impose limitations on carrier
frequencies (interference, intercommunications)
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Continuous carrier In the case of sinusoidal carrier, three modulation
parameters can be varied: the amplitude, the frequency,and the phase of the sinusoid (+ polarization). Thisgenerates three distinct modulation types: the amplitudemodulation
(AM), thefrequency modulation
(FM) and thephase modulation (PM)
Each of these may be continuous, when the instantaneousamplitude, frequency and phase of the sinusoid are
continuous functions of time, or may be pulsed, when thevariations occur instantaneously
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Amplitude modulation (AM)
A = A(t)
= const
= const
Frequency modulation (FM) A = const
= (t)
= const
Phase modulation (PM)
A = const
= const
= (t) Polarization modulation
Not used in radio
communications(used in some optical
communications)
Carrier:A sin[t +] + polarztn.; A, , , polarztn. = const
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Amplitude Shift Keying (ASK)
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1 10
Baseband
Data0 0
ASK
modulatedsignal
Acos(t) Acos(t)
Pulse shaping can be employed to remove spectral spreading
ASK demonstrates poor performance, as it is heavily affected by noise,fading, and interference
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Frequency Shift Keying (FSK)
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1 10 0
Baseband
Data
BFSK
modulatedsignalf0 f0f1 f1
where f0 =Acos(c-)t and f1 =Acos(c+)t Example: The ITU-T V.21 modem standard uses FSK
FSK can be expanded to a M-ary scheme, employing multiplefrequencies as different states
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Phase Shift Keying (PSK)
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1 10 0
s0 s0s1 s1
Baseband
Data
BPSK
modulatedsignal
where s0
=Acos(c
t) and s1
=Acos(c
t + )
Major drawback rapid amplitude change between symbols due to phasediscontinuity, which requires infinite bandwidth. Binary Phase Shift Keying(BPSK) demonstrates better performance than ASK and BFSK
BPSK can be expanded to a M-ary scheme, employing multiple phases and
amplitudes as different states
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PSK graphic representationThe two signals
s0 =Acos(t)s1 =Acos(t + )can be represented bytwo vectors (or points)
in the signal plane[Re(s), Im(s)]
Noise & interference
can change positions ofthe points and modifydecision: 0 or 1
A-A
Im(s)
Re(s)
Decision: s = s0 Decision: s = s1
10
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Differential Modulation
In the transmitter, each symbol is modulatedrelative to the previous symbol and modulatingsignal, for instance in BPSK 0 = no change,
1 = +1800
In the receiver, the current symbol is demodulatedusing the previous symbol as a reference. The
previous symbol serves as an estimate of thechannel. A no-change condition causes themodulated signal to remain at the same 0 or 1 stateof the previous symbol.
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DPSK = Differential phase-shift keying: In the
transmitter, each symbol is modulated relative to
the phase of the immediately preceding signal
element transmitted Differential modulation is theoretically 3dB
poorer than coherent. This is because the
differential system has 2 sources of error: acorrupted symbol, and a corrupted reference (the
previous symbol)
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Pulse trains as Carrier A carrier = a train of identical
pulses regularly spaced in time
Example 2003 : Ultra Wideband(UWB) systems Systems that use time-domain
modulation and signal processingmethods (e.g.,pulse-positionmodulation)
Used for sensing, short-range radar,and telecommunication applications
Employ short pulses (duration of ~1 to10 ns), occupying the bandwidth ofmore than 1.5 GHz (or more than 25%of the center frequency)
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Inpulse-frequency modulation (PFM), the pulse
repetition rate is varied in accordance with the
modulating signal; in Pulse-Amplitude Modulation
(PAM), the amplitude of individual pulses in thepulse train is varied
Inpulse-time modulation (PTM) generic class, the
time of occurrence of some characteristic of thepulsed carrier is varied, eg. Duration (PDM) or
position (PPM)
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Inpulse-position
modulation (PPM),the temporal
positions of
individual pulses arevaried in relation tothe reference
positions, inaccordance themodulating signal
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Noise (random processes), and pseudo-random
processes can also be used as carriers
Example: spread-spectrum systems
In some systems, the carrier and modulation formatchange during the transmission
Independently of the modulation type, spectra of
signals used in radiocommunications are,contained between 9 kHz and 275 GHz, as defined
in ITU Radio Regulations
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Demodulation & Detection
Demodulation
Is process of removing the carrier signal to
obtain the original signal waveform
Detection extracts the symbols from thewaveform
Coherent detection Non-coherent detection
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Coherent (synchronous) Detection
Signal change introduced by the channel (phase
and attenuation) is estimated. It is then possible to
reproduce the transmitted signal and demodulate.
Requires a replica carrier wave of the samefrequency and phase to be delivered at the
receiver.
The received signal and replica carrier are cross-correlated using information contained in their
amplitudes and phases.
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Carrier recovery methods include
Pilot Tone (such as Transparent Tone in Band) Less power in the information bearing signal, High peak-to-
mean power ratio
Carrier recovery from the information signal E.g. Costas loop
Applicable to
Phase Shift Keying (PSK) Frequency Shift Keying (FSK)
Amplitude Shift Keying (ASK)
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Geometric Representation
Digital modulation involves choosing a particular
signal si(t) form a finite set S of possible signals.
For binary modulation schemes a binary
information bit is mapped directly to a signal andS contains only 2 signals, representing 0 and 1.
For M-ary keying S contains more than 2 signals
and each represents more than a single bit ofinformation. With a signal set of size M, it is
possible to transmit up to log2Mbits per signal.
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Any element of set S can be represented as a point
in a vector space whose coordinates are basis
signals j(t) such that
( ) ( )
( )
( ) ( )
2
1
0, ; (= are orthogonal)
1; ( normalization)
Then
i j
i
N
i ij j
j
t t dt i j
E t dt
s t s t
=
=
= = =
=
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Example: BPSK Constellation Diagram
( ) ( ) ( ) ( )
( ) ( )
1 2
1
2 2cos 2 , cos 2 ; ; 0
energy per bit; bit period
For this signal set, there is a single basic signal
2 cos 2 ; 0
b bBPSK c c b
b b
b b
c b
b
BPSK
E ES s t f t s t f t t T
T T
E T
t f t t T T
S E
= = =
= =
=
= ( ) ( ){ }1 1,b bt E t -Eb Eb
Q
I
Constellation diagram
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Constellation diagram
= graphical representation of the complex
envelope of each possible symbol state The x-axis represents the in-phase component
and the y-axis the quadrature component of thecomplex envelope
The distance between signals on a constellation
diagram relates to how different the modulationwaveforms are and how easily a receiver can
differentiate between them.
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QPSK
Quadrature Phase Shift Keying (QPSK) can
be interpreted as two independent BPSK
systems (one on the I-channel and one on
Q), and thus the same performance buttwice the bandwidth efficiency
Large envelope variations occur due toabrupt phase transitions, thus requiring
linear amplification
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QPSK Constellation Diagram
Carrier phases
{0, /2, , 3/2}
Q
Carrier phases
{/4, 3/4, 5/4, 7/4}
I
Q
I
Quadrature Phase Shift Keying has twice the bandwidth efficiency ofBPSK since 2 bits are transmitted in a single modulation symbol
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Types of QPSK
I
Q
Property of R. Struzak 44
Conventional QPSK has transitions through zero (i.e. 1800phase transition). Highlylinear amplifiers required.
In Offset QPSK, the phase transitions are limited to 900, the transitions on the I and Qchannels are staggered.
In /4 QPSK the set of constellation points are toggled each symbol, so transitionsthrough zero cannot occur. This scheme produces the lowest envelope variations.
All QPSK schemes require linear power amplifiers
I
I
Conventional QPSK Offset QPSK /4 QPSK
M lti l l (M ) Ph d
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Multi-level (M-ary) Phase and
Amplitude Modulation
16 QAM 16 PSK 16 APSK
Amplitude and phase shift keying can be combined to transmit several bits persymbol. (Often referred to as linearas they require linear amplification. More
bandwidth-efficient, but more susceptible to noise.)
For M=4, 16QAM has the largest distance between points, but requires verylinear amplification. 16PSK has less stringent linearity requirements, but hasless spacing between constellation points, and is therefore more affected bynoise.
Simulation: http://www.educatorscorner.com/index.cgi?CONTENT_ID=2478Property of R. Struzak 45
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Decision region
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DistortionsDecision region
Perfect channel White noise Phase jitter
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i
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Eye Diagram
Eye pattern is an oscilloscopedisplay in which digital data
signal from a receiver isrepetitively superimposed onitself many times
(sampled and applied to thevertical input, while the datarate is used to trigger thehorizontal sweep).
It is so called because thepattern looks like a series ofeyes between a pair of rails.
Time (symbols)
Magnitude
If the eye is not
open at the samplepoint, errors will occurdue to signalcorruption
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GMSK Gaussian Minimum Shift Keying (GMSK) is a form of
continuous-phase FSK in which the phase change ischanged between symbols to provide a constant envelope.Consequently it is a popular alternative to QPSK
The RF bandwidth is controlled by the Gaussian low-passfilter bandwidth. The degree of filtering is expressed bymultiplying the filter 3dB bandwidth (B) by the bit periodof the transmission (T), i.e. by BT
GMSK allows efficient class C non-linear amplifiers to beused
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Outline
Radiocommunication channel
Modulation
Spreading spectrum
Nonlinearities & intermodulation
Summary
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Modulation Spectra The Nyquist bandwidth is the
minimum bandwidth that cancarry a given volume ofinformation
The spectrum occupied by asignal is usually larger and
spill over adjacent channelscausing interference
The spectrum occupied by asignal can be reduced byapplication of filters
Technical standards and RRimpose limits on spectralmasks
Nyquist MinimumBandwidth
Frequency
RelativeMagnitude(dB
)
AdjacentChannel
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Capacity of communication system
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Capacity of communication system
C = B*log2{1 + [S/(No*B)]}
Bandwidth, Hz
Noise density, W/Hz
Received signal power, W
Capacity, bit/s
The capacity to transfer error-free information is enhancedwith increased bandwidth B, even though the signal-to-noise
ratio is decreased because of the increased bandwidth.
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SS communications basics
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SS communications basics
Original
information
Propagation effects Transmission
Reconstructed
information
Original signal Spread signal
Spread signal+ Reconstr. signal
Spreading
De-spreading
Unwanted signals + Noise
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SS: basic characteristics
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SS: basic characteristics
Signal spread over a wide bandwidth >> minimum
bandwidth necessary to transmit information
Spreading by means of a code independent of the data
Data recovered by de-spreading the signal with asynchronous replica of the reference code TR: transmitted reference (separate data-channel and reference-channel, correlation detector)
SR: stored reference (independent generation at T & R pseudo-random identical waveforms,synchronization by signal received, correlation detector)
Other (MT: T-signal generated by pulsing a matched filter having long, pseudo-randomly controlledimpulse response. Signal detection at R by identical filter & correlation computation)
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SS communication techniques
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SS communication techniques
FH: frequency hoping (frequency synthesizer controlled by pseudo-random sequence of numbers)
DS: direct sequence (pseudo-random sequence of pulses used forspreading)
TH: time hoping(spreading achieved by randomly spacing transmitted pulses)
Random noise as carrier
Hybrid combination of the above
Other techniques (radar and other applications)
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Multiple-access techniques
FDMA: frequency-division multiple access
TDMA: time-division multiple access
CDMA: code-division multiple access
Other (e.g. OFDM)
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FDMA
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FDMA
Freque
ncy
Time
Power density
FDMA
Freq
uency
Property of R. Struzak 57
TimeFrequency channel
Bm
Bc
Transmission is organized
in frequency channels.
Each link is assigneda separate channel.
Example: Telephony Bm = 3-9 kHz
TDMAP d it
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TDMA
Tim
e
Power densityTDMA
Freque
ncy
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Frequency
TimeTime slot
Time-frame
Transmission is organized in repetitive
time-frames. Each frame consists of
groups of pulses - time slots. Each user/
link is assigned a separate time-slot.
Example: DECT (Digital enhanced cordless phone) Frame lasts 10 ms, consists of 24 time slots (each 417s)
FH SS (CDMA)
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FH SS (CDMA)
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Freq
uency
CDMA
Time
Power density
Frequency
Time-frequency slot
Bm
Bc
Transmission is organized intime-frequency slots. Each link
is assigned a sequence of the slots,
according to a specific code.
Time
DS SS: transmitter
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Modulator X Antenna
[A(t), (t)]Information
[g1(t)]
Modulated signal
S1(t) = A(t) cos(0t + (t))band Bm Hz
Spread signal
g1(t)S1(t)
band Bc Hz
Bc >> Bm
Carrier
cos(0t)
gi(t): pseudo-random noise (PN) spreading functions that spreads the energy of S1(t) over a bandwidth
considerably wider than that of S1(t): ideally gi(t) gj(t) = 1 ifi =j and gi(t) gj(t) = 0 ifi j
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DS SS-receiver
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Spreadingfunction
[g1(t)]
Correlator&
bandpass
filter
Xantenna
Tod
emodulator
Linear
combination
g1(t)S1(t)g2(t)S2(t)
.
gn(t)Sn(t)N(t) (noise)
S(t)
g1(t) g1(t)S1(t)
g1(t) g2(t)S2(t)
.
g1(t) gn(t)Sn(t)
g1(t) N(t)g1(t) S(t)
S1(t)
Property of R. Struzak 61
SS-receivers Input
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SS receiver s Input
Unwanted signalsSS s.: g2(t)S2(t); ; gn(t)Sn(t)
Other s. : S(t)
Noise: N(t)
W/Hz
Wanted (spread) signal: g1(t)S1(t)
BcHz
Signal-to-interference ratio (S/ I)in = S/ [I()*Bc]
Property of R. Struzak 62
Bc = Input correlator bandwidth
I() = Average spectral power density of unwanted signals in BcS = Power of the wanted signal
SS-correlator/ filter output
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Bm
Bc
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(S/ I)out = S/ [I()*Bm]Bc = Input correlator bandwidth
Bm = Output filter bandwidth
I() = Average spectral power density of unwanted signals & noise in BmS = power of the wanted signal at the correlator output
Wanted (correlated) signal: de-spread to its original bandwidth
as g1(t) g1(t)S1(t) = S1(t) with g1(t) g1(t) = 1
Uncorrelated (unwanted) signalsspread & rejected by correlator + noise
g1(t) S(t); g1(t) N(t); g1(t) gj(t)Sj(t) = 0as gi(t) gj(t) = 0 fori j
Signal-to-interference ratio
Spreading = reducing spectral power density
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SS Processing Gain == [(S/ I)in/ (S/ I)out ] = ~Bc/ Bm
Example: GPS signal
RF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz
Processing gain ~20000 (+43 dB)
Input S/N = -20 dB (signal power = 1% of noise power)
Output S/N = +23 dB (signal power = 200 x noise power)
(GPS = Global Positioning System)
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Outline
Radiocommunication channel
Modulation
Spreading spectrum
Nonlinearities & intermodulation Summary
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Sources of undesired nonlinear effects:
Receiver RF input/ mixing stage Transmitter output stages
Vicinity of the equipment (usually of the
transmitter)
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Types of undesired nonlinear effects:
Receiver blocking
Transmitter spurious radiations & intermodulation
Receiver spurious responses & intermodulation Note: Several nonlinear interactions may occur
simultaneously
(Source: ITU/ CCIR Rep. 524-1, Vol. 1, p. 30, 1986)
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Non-ideal wideband
memory-less linear devicesare often treated byexpressing the output (Y) ofthe system as a power series
of the total input signalX:Y a a X a X a X a X
n
n= + + + + + +0 1 2
2
3
3 ... ...
X(t) Y(t)
X(t) = A1sin(w1t) + A2sin(w2t) + The coefficients a are presumed to be real andindependent onX.
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In practice, one focus only on those impairments
that fall in the desired frequency channel The lowest from these (and often the dominant
one) is the third-order nonlinearity
The second-order nonlinearity may also be a
critical performance parameter for a receiver. Theapproach presented here can easily be extended tothe evaluation of the second-order and othernonlinearities of a receiver.
30 1 3Y a a X a X = + +
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Blocking dynamic range (BDR)
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Blocking dynamic range (BDR)2 3
0 1 2 3 ...y a a x a x a x= + + + +
Noise Floor
Output
power(dBm
)
Input
power (dBm)P1dB-inMDS
1dBP1dB-out
BDR
(Blocking Dynamic Range)
MDS = Minimum
Detectable Signal
(Output Noise Floor)
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IP1dB_b
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Two-signal Input Referred Blocking 1 dB
Gain Compression Point
Refers to the condition when there are 2 single-
frequency input signalsx(t) = [A1 cos(1t) + A2 cos(2t) and one of
them (the blocker) is significantly stronger than
the other, that is A2 >> A1.( )20 1 3 2 1
3( ) cos 1 ...
2y t a a a A A t
= + + +
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If a3 < 0, the weaker signal A1cos(1t)
experiences progressively less gain as the
stronger signal A2cos(2t) gets stronger.
The gain drops by 1 dB from its ideal valuewhen the blocker amplitude reaches
11 _
3
0.0725IP dB b aAa
=
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Assume a small signal test, i.e. A small enough
such that
The input level for which the output componentsat 1 and 2 have the same amplitude as those at
(212) and (221) is the input referred third-
order intercept point:
2
1 3
9
4a a A
13
3
3
4
3IIP
aA
a=
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Intermodulation Intermodulation spurious signals can be generated
when two or more RF signals are applied to a non-linear device
They could produce interference
The magnitude of the spurious signals depends onthe power of the original signals and on the degreeof device nonlinearity
Technical standards and RR impose limits on out-of-band (spurious) radiations
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Intermodulation products The frequency (Fi) of an intermodulation
product Fi = C1*F1+C2*F2+ .. +Cn*Fn {C1, C2, ...,Cn} are positive or negative integers or
zero, and
{F1, F2, ..., Fn} are the frequencies of the signals
applied to the device
The order of the intermodulation product isthe sum: {|C1| + |C2| + ... + |Cn|}
Property of R. Struzak 75
IIP3
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Two-signal Input-Referred Third-order Intercept
Point
A third-order intermodulation component (IM3)
due to two sinusoidal input signals of equal
amplitude (Acos1t, Acos2t)[ ] [ ]
[ ] ( ) ( )
3
0 1 1 2 3 1 2
2 3 3
0 1 3 1 2 2 3 1 2 3 2 1
( ) cos( ) cos( ) cos( ) cos( )
9 3 3
cos( ) cos( ) cos 2 cos 24 4 4
y t a a A t A t a A t A t
a a a A A t A t a A a A
= + + + + =
= + + + + +
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Example: 3rd order intermodulation Two real signals of frequencies F1 and F2 when applied
to a nonlinearity, produce six false signals (3-rd orderintermodulation products) at the following frequencies:
Fia = 2*F1 - F2
Fib = 2*F2 - F1 Fic = 2*F1 + F2
Fid = 2*F2 + F1
Fie = 3F1
Fif = 3F2
Even if F1 and F2 do not interfereone with another, intermodulationproducts can interfere with one oranother.Frequencies Fia, Fib, can be close
to F1 or F2.More real signals, more thenumber of false signals
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F1 F2
2F1-F2 2F2-F1
2F22F1
2F1+F2 2F2+F1
3F13F2
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All above parameters are defined under assumptions of
small-signal and systems with third-order nonlinearity IP1dB and IP1dB_b can be directly measured
IIP3 and IIP3_h cannot be directly measured: they canonly be extrapolated from small signal measurements asthey are defined under small signal assumptions.
The numerical values of the parameters are inter-related: IP1dB = IIP3 9.6 dB
IP1dB_b = IIP3 12.6 dB IIP3_h = IIP3 + 5 dB
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Summary Radiocommunication channel
Modulation
Spreading spectrum
Nonlinearities & intermodulation
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References Campbell AT. Untangling the Wireless Web
Radio Channel Issues, Lecture NotesE6951, comet.columbia.edu/~campbell
Proakis J.Digital Communications,McGraw & Hill Int.
Rappaport TS. Wireless Communications,Prentice Hall PTR
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Any question?
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Thank you for your attention
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Copyright 2005 Ryszard Struzak. This work is licensed under the
Creative Commons Attribution License
http://creativecommons.org/licenbses/by/1.0 These materials may be used freely for individual study, research, and
education in not-for-profit applications. Any other use (and/or displaying
the material in the WWW) requires the written authors permission
If you cite these materials, please credit the author. If you have
comments or suggestions, please send these directly to the author at
r.struzak@ieee.org.
Copyright note
Property of R. Struzak 83