Radiocommunication Channel and Digital Modulation: Basicswireless.ictp.it/school_2005/lectures/struzak/R_Chnnl_Digit_Modula... · PTP, PMP, Mesh • A point-to-point (PTP) link is

ICTP-ITU/BDT-URSI School on Radio-Based Computer Networking for Research and Training in Developing Countries The Abdus Salam International Centre for Theoretical Physics ICTP, Trieste (Italy), 7th February - 4th March 2005

Radiocommunication Channel and Digital Modulation: Basics

Prof. Dr. R. [email protected]

Note: These are preliminary notes, intended only for distribution to participants. Beware of misprints!

Outline

• Radiocommunication channel• Modulation • Spreading spectrum • Nonlinearities & intermodulation• Summary

Property of R. Struzak 2

Microwave radio link



Wireless Local Loop


BSS

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.


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)


Station 1TX RX

TXRX

Frequency Channel 2

Station 2

FrequencyChannel 1

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


Radio Link model

Envi

ronm

ent

T-antenna

Propagation medium

R-antenna

Noise

Original message/ data

Reconstructed message/ data

EM waves:time-distance-direction-polarization

Receiver Time seriesProcessing/De-coding

TransmitterCoding/ProcessingTime series


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.

Radio wave

Transmittingantenna

RF cable (signal attenuation)

Original signal

Transmitter (signal processing)

Electrical current EM wave

Focus of the school


Receiving station

Radio wave

Receivingantenna

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 environmentElectrical signal is represented by a function of time.


Modern radio: details

BASEBAND PROCESSING& PC INTERFACEDAC

CRYSTALREFERENCE

FILTER

SYNTHETIZER

ADC

FILTER

IFFILTER

SYNTHETIZER

RF FILTER RF FILTER

ANTENNA

RF A

MP

LIFI

CA

TIO

NR

F U

P/ D

OW

NC

ON

VE

RS

ION

IF G

AIN

& S

ELE

CTI

VIT

Y

SWITCH

TRANSMITTER COMMON PART RECEIVER

MO

DU

LATI

ON

& D

EM

OD

ULA

TIO

N


• Modern radio = combination of radio and computer hardware & software– Software-defined

radio• Systems with

most functions defined 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

From

oth

er s

ourc

es

To o

ther

des

tinat

ions


Outline



Modulation• = process of translation

the message from baseband signal to bandpass (modulated carrier) signal at frequencies that are very high compared to the baseband frequencies.

• Demodulation is the reverse process – Note: An information-bearing

signal is non-deterministic, i.e. it changes in an unpredictable manner.

Modulator/Signal Processing

Carrier Generator

m(t)

s(t)

f(t)

s'(t)

Demodulator/Signal Processing

m'(t)

RADIO ENVIRONMENT

TRANSMITTER RECEIVER


Communication Channel

Original messagem(t)

Transmitters(t) = U(m, f) m(t) = message (information, data)

s(t) = signal carrying the messagef = f(a,b,c,…, t) (carrier function)a,b,c, … = modulation parametersU, V, W = operatorsξ = noise, fading, perturbationsx(t) = perturbed signal at the receiver inputy(t) = reproduced message

Task: make y ≈ m (within an acceptable error)

Transport mediumx(t) = V(s, ξ)

Receivery(t) = W(x)

Reproduced (received) message

y = W{V[ξ,U(m,f)]}Property of R. Struzak 16

Modulation Process( )1 2 3

1 2 3

, , ,... , (= carrier), , ,... (= modulation parameters)

(= time)

n

n

f f a a a a ta a a at

=

• Modulation implies varying one or more characteristics (modulation parameters a1, a2, … an) of a carrier f in accordance with the information-bearing(modulating) baseband signal

• Each of the parameters a, b, c... carrying information can be modulated independently, increasing communication capacity at a cost of complexity.


• The carrier is generated in the transmitter • It may be a continuous (e.g. sinusoidal) current of

radio frequency, a sequence of short pulses, or noise– Systems using pulse sequences are also called

carrierless 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


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 mutual interference 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)




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). This generates three distinct modulation types: the amplitude modulation (AM), the frequency modulation (FM) and the phase modulation (PM)

• Each of these may be continuous, when the instantaneous amplitude, frequency and phase of the sinusoid are continuous functions of time, or may be pulsed, when the variations occur instantaneously


• Amplitude modulation (AM)– A = A(t) – ω = const – ϕ = const

• Frequency modulation (FM)– A = const– ω = ω(t) – ϕ = const

• Phase modulation (PM)– A = const– ω = const – ϕ = ϕ(t)

• Polarization modulation – Not used in radio

communications(used in some optical communications)

Carrier: A sin[ωt +ϕ] + polarztn.; A, ω, ϕ, polarztn. = const


Amplitude Shift Keying (ASK)


1 10

Baseband Data

0 0ASK

modulated signal

Acos(ωt) Acos(ωt)

• Pulse shaping can be employed to remove spectral spreading• ASK demonstrates poor performance, as it is heavily affected by noise,

fading, and interference

Frequency Shift Keying (FSK)


1 10 0

Baseband Data

BFSK modulated

signalf0 f0f1 f1

where f0 =Acos(ωc-∆ω)t and f1 =Acos(ωc+∆ω)t

• Example: The ITU-T V.21 modem standard uses FSK • FSK can be expanded to a M-ary scheme, employing multiple

frequencies as different states

Phase Shift Keying (PSK)


1 10 0

s0 s0s1 s1

Baseband Data

BPSK modulated

signal

where s0 =Acos(ωct) and s1 =Acos(ωct + π) • Major drawback – rapid amplitude change between symbols due to phase

discontinuity, 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

PSK graphic representationThe two signals

s0 =Acos(ωt) s1 =Acos(ωt + π) can be represented by two vectors (or points) in the signal plane [Re(s), Im(s)]

• Noise & interference can change positions of the points and modify decision: 0 or 1

A-A

Im(s)

Re(s)

Decision: s = s0 Decision: s = s1

10


Differential Modulation

• In the transmitter, each symbol is modulated relative to the previous symbol and modulating signal, for instance in BPSK 0 = no change,

1 = +1800

• In the receiver, the current symbol is demodulated using the previous symbol as a reference. The previous symbol serves as an estimate of the channel. A no-change condition causes the modulated signal to remain at the same 0 or 1 state of the previous symbol.


• 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: a corrupted symbol, and a corrupted reference (the previous symbol)


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 processing methods (e.g., pulse-position modulation)

– Used for sensing, short-range radar, and telecommunication applications

– Employ short pulses (duration of ~1 to 10 ns), occupying the bandwidth of more than 1.5 GHz (or more than 25% of the center frequency)


• In pulse-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 the pulse train is varied

• In pulse-time modulation (PTM) generic class, the time of occurrence of some characteristic of the pulsed carrier is varied, eg. Duration (PDM) or position (PPM)


• In pulse-position modulation (PPM), the temporal positions of individual pulses are varied in relation to the reference positions, in accordance the modulating signal


• Noise (random processes), and pseudo-random processes can also be used as ‘carriers’– Example: spread-spectrum systems – In some systems, the carrier and modulation format

change 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


Demodulation & Detection

• Demodulation– Is process of removing the carrier signal to

obtain the original signal waveform• Detection – extracts the symbols from the

waveform– Coherent detection– Non-coherent detection


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 same frequency 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.


• 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)


Non-Coherent Detection

• Requires no reference wave; does not exploit phase reference information (envelope detection)

• Applicable to– Differential Phase Shift Keying (DPSK)– Frequency Shift Keying (FSK)– Amplitude Shift Keying (ASK)

• Non coherent detection is less complex than coherent detection (easier to implement), but has worse performance.


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 and S 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 of information. With a signal set of size M, it is possible to transmit up to log2M bits per signal.


• Any element of set S can be represented as a point in a vector space whose coordinates are basis signals φj(t) such that

( ) ( )

( )

( ) ( )

2

1

0, ; (= are orthogonal)

1; ( normalization)

Then

i j

i

N

i ij jj

t t dt i j

E t dt

s t s t

φ φ

φ

φ

∞

−∞

∞

−∞

=

= ≠

⎡ ⎤= = =⎣ ⎦

=

∫

∫

∑Property of R. Struzak 39

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 bb

BPSK

E ES s t f t s t f t t TT T

E T

t f t t TT

S E

π π

φ π

⎧ ⎫⎡ ⎤ ⎡ ⎤⎪ ⎪= = = − ≤ ≤⎢ ⎥ ⎢ ⎥⎨ ⎬⎢ ⎥ ⎢ ⎥⎪ ⎪⎣ ⎦ ⎣ ⎦⎩ ⎭

= =

= ≤ ≤

= ( ) ( ){ }1 1,b bt E tφ φ⎡ ⎤ ⎡ ⎤−⎣ ⎦ ⎣ ⎦ -√Eb √Eb

Q

I

Constellation diagram


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 the complex envelope

– The distance between signals on a constellation diagram relates to how different the modulation waveforms are and how easily a receiver can differentiate between them.


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 but twice the bandwidth efficiency

• Large envelope variations occur due to abrupt phase transitions, thus requiring linear amplification


QPSK Constellation Diagram

Carrier phases {0, π/2, π, 3π/2}

Q

Carrier phases {π/4, 3π/4, 5π/4, 7π/4}

I

Q

I

• Quadrature Phase Shift Keying has twice the bandwidth efficiency of BPSK since 2 bits are transmitted in a single modulation symbol


Types of QPSK

I

Q


• Conventional QPSK has transitions through zero (i.e. 1800 phase transition). Highly linear amplifiers required.

• In Offset QPSK, the phase transitions are limited to 900, the transitions on the I and Q channels are staggered.

• In π/4 QPSK the set of constellation points are toggled each symbol, so transitions through zero cannot occur. This scheme produces the lowest envelope variations.

• All QPSK schemes require linear power amplifiers

I

QQ

I

Conventional QPSK Offset QPSK π/4 QPSK

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 per symbol. (Often referred to as linear as they require linear amplification. More bandwidth-efficient, but more susceptible to noise.)

• For M=4, 16QAM has the largest distance between points, but requires very linear amplification. 16PSK has less stringent linearity requirements, but has less spacing between constellation points, and is therefore more affected by noise.

• Simulation: http://www.educatorscorner.com/index.cgi?CONTENT_ID=2478Property of R. Struzak 45

Decision region


DistortionsDecision region

Perfect channel White noise Phase jitter


Eye Diagram• Eye pattern is an oscilloscope

display in which digital datasignal from a receiver is repetitively superimposed on itself many times

– (sampled and applied to the vertical input, while the data rate is used to trigger the horizontal sweep).

• It is so called because the pattern looks like a series of eyes between a pair of rails.

Time (symbols)

Mag

nitu

de

•If the “eye” is not open at the sample point, errors will occur due to signal corruption


GMSK• Gaussian Minimum Shift Keying (GMSK) is a form of

continuous-phase FSK in which the phase change is changed between symbols to provide a constant envelope. Consequently it is a popular alternative to QPSK

• The RF bandwidth is controlled by the Gaussian low-pass filter bandwidth. The degree of filtering is expressed by multiplying the filter 3dB bandwidth (B) by the bit period of the transmission (T), i.e. by BT

• GMSK allows efficient class C non-linear amplifiers to be used


Outline



Modulation Spectra• The Nyquist bandwidth is the

minimum bandwidth that can carry a given volume of information

• The spectrum occupied by a signal is usually larger and spill over adjacent channels causing interference

• The spectrum occupied by a signal can be reduced by application of filters

• Technical standards and RR impose limits on spectral masks

Nyquist MinimumBandwidth

Frequency

Rel

ativ

e M

agni

tude

(dB

) AdjacentChannel


Capacity of communication system

C = B*log2{1 + [S/(No*B)]}

Bandwidth, Hz

Noise density, W/HzReceived signal power, W

Capacity, bit/s

The capacity to transfer error-free information is enhanced with increased bandwidth B, even though the signal-to-noise ratio is decreased because of the increased bandwidth.


SS communications basics

Originalinformation

Propagation effects Transmission

Reconstructedinformation

Original signal Spread signal

Spread signal+ Reconstr. signal

Spreading

De-spreading

Unwanted signals + Noise


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 a synchronous 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 controlled impulse response. Signal detection at R by identical filter & correlation computation)


SS communication techniques

• FH: frequency hoping (frequency synthesizer controlled by pseudo-random sequence of numbers)

• DS: direct sequence (pseudo-random sequence of pulses used for spreading)

• 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)


Multiple-access techniques

• FDMA: frequency-division multiple access• TDMA: time-division multiple access• CDMA: code-division multiple access• Other (e.g. OFDM)


FDMA

FrequencyTime

Power densityFDMA

Freq

uenc

y


TimeFrequency channel

Bm

Bc

Transmission is organizedin frequency channels. Each link is assigned a separate channel.

Example: Telephony Bm = 3-9 kHz

TDMA

Time

Power densityTDMA

Frequency


Freq

uenc

y

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 417µs)

FH SS (CDMA)


Freq

uenc

y

CDMA

Time

Power density

Frequency

Time-frequency slot

BmBc

Transmission is organized in time-frequency “slots”. Each link is assigned a sequence of the slots, according to a specific code.

Time

DS SS: transmitter

Modulator X Antenna

[A(t), ϕ(t)]Information

[g1(t)]

Modulated signalS1(t) = A(t) cos(ω0t + ϕ(t))band Bm Hz

Spread signal g1(t)S1(t)band Bc HzBc >> Bm

Carriercos(ω0t)

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 if i = j and gi(t) gj(t) = 0 if i ≠ j


DS SS-receiver

Spreading function

[g1(t)]

Correlator &

bandpassfilter

Xantenna

To d

emod

ulat

or

Linearcombinationg1(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)


SS-receiver’s InputUnwanted 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(ω)*Bc]


Bc = Input correlator bandwidthI(ω) = Average spectral power density of unwanted signals in BcS = Power of the wanted signal

SS-correlator/ filter output

Bm

Bc


(S/ I)out = S/ [I(ω)*Bm]Bc = Input correlator bandwidth Bm = Output filter bandwidthI(ω) = 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 bandwidthas g1(t) g1(t)S1(t) = S1(t) with g1(t) g1(t) = 1

Uncorrelated (unwanted) signalsspread & rejected by correlator + noiseg1(t) S’(t); g1(t) N(t); g1(t) gj(t)Sj(t) = 0

as gi(t) gj(t) = 0 for i ≠ j

Signal-to-interference ratio

Spreading = reducing spectral power density

SS Processing Gain =

= [(S/ I)in/ (S/ I)out ] = ~Bc/ Bm

Example: GPS signalRF bandwidth Bc ~ 2MHz Filter bandwidth Bm ~ 100 Hz

Processing gain ~20’000 (+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)Property of R. Struzak 64

Outline



• Sources of undesired nonlinear effects:– Receiver RF input/ mixing stage– Transmitter output stages – Vicinity of the equipment (usually of the

transmitter)


• 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)


• Non-ideal wideband memory-less linear devices are often treated by expressing the output (Y) of the system as a power series of the total input signal X:Y a a X a X a X a Xn

n= + + + + + +0 1 22

33 ... ...

X(t) Y(t)

X(t) = A1sin(w1t) + A2sin(w2t) + …The coefficients a are presumed to be real and independent on X.


• 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. The approach presented here can easily be extended to the evaluation of the second-order and other nonlinearities of a receiver.

30 1 3Y a a X a X= + +


Blocking dynamic range (BDR)2 3

0 1 2 3 ...y a a x a x a x= + + + +

Noise Floor

Out

put p

ower

(dB

m)

Input power (dBm)

P1dB-inMDS

1dBP1dB-out

BDR (Blocking Dynamic Range)

MDS = MinimumDetectable Signal (Output Noise Floor)


IP1dB_b

• Two-signal Input Referred Blocking 1 dB Gain Compression Point – Refers to the condition when there are 2 single-

frequency input signals x(t) = [A1 cos(ω1t) + A2 cos(ω2t) and one of them (the blocker) is significantly stronger than the other, that is A2 >> A1.

( )20 1 3 2 1

3( ) cos 1 ...2

y t a a a A A tω⎛ ⎞= + + +⎜ ⎟⎝ ⎠


• If a3 < 0, the weaker signal A1cos(ω1t) experiences progressively less gain as the stronger signal A2cos(ω2t) gets stronger. The gain drops by 1 dB from its ideal value when the blocker amplitude reaches

11 _

3

0.0725IP dB b

aA

a=


• Assume a small signal test, i.e. A small enough such that

• The input level for which the output components at ω1 and ω2 have the same amplitude as those at (2ω1–ω2) and (2ω2–ω1) is the input referred third-order intercept point:

21 3

94

a a A

133

3

43IIP

aA

a=


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 on

the power of the original signals and on the degree of device nonlinearity

• Technical standards and RR impose limits on out-of-band (spurious) radiations


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 is the sum: {|C1| + |C2| + ... + |Cn|}


IIP3

• Two-signal Input-Referred Third-order Intercept Point

• A third-order intermodulation component (IM3) due to two sinusoidal input signals of equal amplitude (Acosω1t, Acosω2t) [ ] [ ]

[ ] ( ) ( )

30 1 1 2 3 1 2

2 3 30 1 3 1 2 2 3 1 2 3 2 1

( ) cos( ) cos( ) cos( ) cos( )

9 3 3cos( ) 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

ω ω ω ω

ω ω ω ω ω ω

= + + + + =

⎛ ⎞= + + + + − + −⎜ ⎟⎝ ⎠


Example: 3rd order intermodulation

• Two ‘real’ signals of frequencies F1 and F2 when applied to a nonlinearity, produce six ‘false signals’ (3-rd order intermodulation 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 interfere one with another, intermodulation products can interfere with one or another. Frequencies Fia, Fib, can be close to F1 or F2. More ‘real’ signals, more the number of ‘false signals’


F1 F2

2F1-F22F2-F1

2F22F1

2F1+F2 2F2+F1

3F1 3F2


• 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 can

only be extrapolated from small signal measurements as they 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


Summary

• Radiocommunication channel• Modulation • Spreading spectrum • Nonlinearities & intermodulation


References

• Campbell AT. Untangling the Wireless Web – Radio Channel Issues, Lecture Notes E6951, comet.columbia.edu/~campbell

• Proakis J. Digital Communications, McGraw & Hill Int.

• Rappaport TS. Wireless Communications, Prentice Hall PTR


Any question?

Thank you for your attention


• 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 author’s permission

• If you cite these materials, please credit the author. If you have comments or suggestions, please send these directly to the author at [email protected].

Copyright note


Documents

Radiocommunication Channel and Digital Modulation: Basicswireless.ictp.it/school_2005/lectures/struzak/R_Chnnl_Digit_Modula... · PTP, PMP, Mesh • A point-to-point (PTP) link is