chapter5-2_mobile basics

8/12/2019 chapter5-2_Mobile Basics

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Mathematical analysis of Nyquist criterion

heff (t) = (t) p(t) hc(t) hr(t)

p(t) = pulse shape of the symbolhc(t) = channel impulse responsehr(t) = receiver impulse response

heff (t) should have fast decay with a small magnitude near

the sample values for n 0 for a ideal channel, hc(t) = (t), it should be possible torealize or closely approximate shaping filters at bothreceiver and transmitter to produce the desired Heff (f)


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Example :

heff (t) = sin (t/Ts)(t/Ts)

satisfies equation (1) but the filter is not causal (not buildable)

Alternative filter

heff (t) = sin (t/Ts) . z(t)(t/Ts)

also satisfies the Nyquist criterion (1)


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Raised Cosine roll-off filter

Most popular pulse shaping filter used in mobilecommunications

hRC (t) = sin (t/Ts)(t/Ts) [ cos (t/Ts) / {1 (4t/2Ts)2]

As the value of a (rolloff factor) increases, the bandwidth

of the filter also increases


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As the value of a (rolloff factor) increases, the time

sidelobe levels decrease.

Implementation of raised-cosine filter

Use identical [HRC (f)]1/2filters at transmitter and receiver

Symbol rate possible through the raised cosine roll offfilter

Rs= 1/Ts = 2B/ (1 + )


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Where B is the absolute filter bandwidth

Geometric representation of Digital Modulation Signals

Modulation signal set S = {S1(t), S2(t),..... SM(t)}

Binary M=2 M>2 M-ary

No. Of bits of information possible = log2M bits/symbol


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Types of Digital Modulation

Linear Nonlinear Spread spectrum

Amplitude oftransmitted signals(t) varies linearlywith message signal

m(t)

Amplitude ofcarrier isconstant

Transmissionbandwidth >>minimumrequired signal

bandwidth

Bandwidth efficient useful foraccommodatingmore users in a

limited spectrum QPSK (quadrature

PSK) OQPSK (Offset PSK)

Higher bandwidthbut highimmunity againstrandom FM noise

FSK GMSK (Gaussian

min. Shift keying) MFSK

Inefficient forsingle user, butefficient formulti-users


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/4 QPSK

Linear modulation

Quadrature Phase shift keying (QPSK)

TS = symbol duration = 2 TB

ES = Energy per symbol = 2 EB

Constellation diagram Q (Quadrature)

(Es)1/2

I(in phase)


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Properties of QPSK

BPSK

BW = 2 RB = 2 / TB

QPSK

BW = RB = 1 / TB

Quadrature Phases = 0, /2, , 3/2

Average probability of bit error is additive white Gaussiannoise


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Pe,QPSK= Q[2 EB / N0]

Non-linear or envelope modulation

Binary Frequency shift keying

The frequency of a constant amplitude carrier signal is

switched between 2 values ( 1 and 0)

SFSK=Vh(t)= (2Eb/Tb )1/2 cos [2fc +2f ]t, 0 t Tb (1)

SFSK=Vl(t) = (2Eb/Tb )1/2 cos [2fc - 2f ]t, 0 t Tb (0)


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Properties of QPSK

Transmission BandwidthBT = 2f + 2B, B = Bandwidth digital baseband signal

If a raised cosine pulse-shaping filter is usedBT = 2f + (1 + )R

Probability of errorPe,FSK= Q[(EB / N0)

1/2]


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Spread Spectrum Modulation techniques

Spread spectrum techniques employ a transmissionbandwidth >> minimum required signal bandwidth

The system is inefficient for a single user, but is efficientfor many users

Many users use the same bandwidth without significantly

interfering with one another


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Principle of spread spectrum technique

Spread spectrum signals are pseudo random, andspreading waveform is controlled by a PN (pseudo noise) sequence or code

Spread spectrum signals are demodulated at the receiverby cross correlation (matching) with the correct PNsequence


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Advantages of spread spectrum techniques

PN codes are approximately orthogonal, and the receivercan separate each user based on their codes

Resistance to multipath fading, because of largebandwidths and narrow time widths


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PN Sequences

Pseudo Noise or Pseudo random sequence in a binarysequence that resembles the autocorrelation of a randombinary sequence

PN sequence generated by using sequential logic circuits

Very low cross correlation between any two sequences

Very low correlation between shifted versions of thesequence


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Frequency Hopped Spread spectrum (FH-SS)

A frequency hopping signal periodically changes thecarrier frequency in a pseudo-random fashion. The set of

possible carrier frequencies is called a hopset.

Bandwidth of channel used in hopset Instantaneous

bandwidth B Bandwidth of spectrum over which the hopping occurs

total hopping bandwidth Wss

Time duration between hops hopping period Ts Data is sent by hopping the transmitter carrier to

seemingly random channels, small bursts of data are sentusing conventional narrow band modulation before T/Rhops again.


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Frequency Hopping Modulator

Frequency hopping

Data signal

Oscillator

Modulator

Frequency

Synchronizer

PN code

generatorCode


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Frequency hopping demodulator

Frequency

hopping Data

signal

Hit => Two users using the same frequency band at thesame time

Properties of FH-SS

WidebandFilter

Frequency

synthesizer

PN codegenerator

B P filter Demodulation

Synchronizationsystem


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Fast frequency hoppingMore than one frequency hop during each transmittedsymbol =>Hopping rate >= symbol rate

Slow frequency hoppingHopping rate < symbol rate

Probability of error for BPSKPe= 0.5exp(-Eb/ 2N0)(1 ph ) + 0.5 phph = probability of hit = 1 (1 1/M)

k-1 (k-1) / M

M possible hopping channels exists (slots)

If there are K 1 interfering users

Processing gain = Wss / B


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Modulation performance in fading and multipath

channels

Slow, flat fading channels

s(t) r(t)

r(t) = (t) e-j(t) s(t) + n(t)(t) = gain of the channel(t) = phase shift of the channel

n(t) = additive gaussian noise

Average signal to noise ratio at receiver= (EB / N0)

2, EB / N0 = bit energy to noise ratio

Slow flat fading

channel


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Probability of error in slow flat fading channels

Probability of error

Pe=

0Pe (X) p(X) dX

Pe (X) = Probability of error for an arbitrary modulation at aspecific value of signal to noise ratio

p(X) = pdf of X due to fading channel

= (1 / )exp(-x / ) , x>=0 (for Rayleigh channel__

= 2Eb / N0


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Comparison of Pe (X) and Pe for different systems

Coherent Binary PSK Pe (x) = Q[(2EB / N0)1/2]

Pe = 0.5 [1 / (1+)]

Coherent binary FSkPe (x) = Q[(EB / N0)1/2]

Pe = 0.5 [1 / (2+)]

Differential Binary PSKPe (x) = 0.5exp[(-EB / N0)]

Pe = [0.5 / (1+)]

Non-coherent orthogonal binary FSKPe (x) = 0.5exp[(-EB / 2N0)]

Pe = [1 / (2+)]


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Coherent GMSKPe (x) = Q{(2Eb)}Pe = 0.5 {1 [/(+ 1)]

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=0.68, BT= 0.25, = 0.68=0.85, BT= , = 0.85BT= Bandwidth bit duration product for GMSK

chapter5-2_mobile basics

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