Bandpass-2011

7/27/2019 Bandpass-2011

http://slidepdf.com/reader/full/bandpass-2011 1/40

Digital Communications

Digital Bandpass Transmission

References for Transparencies:

Bruce Carlson - Mc Graw Hill,

Comlab.hut.fin,

Lectured by Assoc. Prof. Dr. Thuong Le-Tien

November, 2011

7/27/2019 Bandpass-2011


Digital Bandpass Transmission

CW detection techniques

– Coherent

– Non-coherent

– Differentially coherent

Examples of coherent and non-coherent detection error rate

analysis (OOK)

A method for ‘analyzing’ PSK error rates

Effect of synchronization and envelope distortion (PSK)

Comparison: Error rate describing

– reception sensitivity

– bandwidth efficiency2( / )

e b T f r B1 0( / )

e b f E N

7/27/2019 Bandpass-2011


Bandpass TransmissionLink (without Encryption)

Information:

- analog:BW &

dynamic range

- digital:bit rate

Information:

- analog:BW &

dynamic range

- digital:bit rate

Maximization of information

transferred

Maximization of information

transferred

Transmitted power;

bandpass/basebandsignal BW

Transmitted power;

bandpass/baseband

signal BW

Message protection &

channel adaptation;

convolution, block

coding

Message protection &

channel adaptation;

convolution, block

coding

M-PSK/FSK/ASK...,

depends on channel

BW & characteristics

M-PSK/FSK/ASK...,

depends on channel

BW & characteristics wireline/wireless

constant/variable

linear/nonlinear

wireline/wireless

constant/variable

linear/nonlinear

Noise

Noise

Interference

Interference

Channel

Channel

Modulator

Modulator

Channel

Encoder

Channel

Encoder

Source

encoder

Source

encoder

Channel

decoder

Channel

decoder

Sourcedecoder

Sourcedecoder

Demodulator

Demodulator

Information

sink

Information

sink

Information

source

Information

sourceMessage

Message

estimate

Received signal

(may contain errors)Transmitted

signal

Interleaving

Interleaving

Fights against burst

errors

Fights against burst

errors

Deinterleaving

Deinterleaving

7/27/2019 Bandpass-2011


CW Binary Waveforms(Digital Modulation, type-2)

ASK

FSK

PSK

DSB

7/27/2019 Bandpass-2011


ASK power spectrum

7/27/2019 Bandpass-2011


Binary QAM

(a) transmitter (b) signal constellation

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Digital frequency modulation (a) FSK (b)continuous-phase FSK

Power spectrum

of binary FSK

with f d=rb/2

This freq. equals the freq

shift away from f c when ak =+/-1

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Illustration of MSK.

(a)phase path(b) i and q waveforms

7/27/2019 Bandpass-2011


Carrier Wave Communications

Carrier wave modulation is used to transmit messages over adistance by radio waves (air , copper or coaxial cable), by optical

signals (fiber), or by sound waves (air, water, ground)

CW transmission allocates bandwidth around the applied

carrier that depends on

– message bandwidth and bit rate

– number of encoded levels (word length)

– source and channel encoding methods

Examples of transmission bandwidths for certain CW

techniques: MPSK, M-ASK

Binary FSK (f d =r b / 2)

MSK (CPFSK f d =r b / 4 ), QAM:

2/ / log ( 2 )

T b b

nr r n r M M

T br / 2

T br

FSK: Frequency shift keying

CPFSK: Continuous phase FSK

7/27/2019 Bandpass-2011


CW Detection Types Number of allocated signaling levels determines constellation

diagram (=lowpass equivalent of the applied digital modulation

format )

At the receiver, detection can be

– coherent (carrier phase information used for detection)

– noncoherent (no carrier phase used for detection)

– differentially coherent (‘local oscillator’ synthesized from

received bits)

CW systems characterized by bit or symbol error rate (number

of decoded errors(symbols)/total number of bits(symbols))

7/27/2019 Bandpass-2011


Coherent Detection by Correlator and Matched Filter Receiver

Coherent detection utilizes carrier phase information and requires in-phase replica of the carrier at the receiver (explicitly or implicitly)

It is easy to show that these two techniques have the same

performance:

( ) s t

( ) ( )h t s t

0( ) ( ) ( )v t s t y d

0

( ) ( ) ( )

( ) ( )

v t s t y t

s t y d

( )t

( ) y t

( )t ( )v T

( )v T

7/27/2019 Bandpass-2011


Optimum binary detection (a) parallel matched filters

(b) correlation detector

7/27/2019 Bandpass-2011


Correlation receiver for OOK or BPSK

7/27/2019 Bandpass-2011


Non-coherent Detection

2-ASK

2-FSK

Base on filtering signal energy on allocated spectra and using

envelope detectors

Has performance degradation of about 1-3 dB when compared

to coherent detection (depending on E b /N 0 )

Examples:

7/27/2019 Bandpass-2011


Differentially coherent PSK (DPSK)

This methods circumvents usage of coherent local oscillator and

can achieve almost the same performance as PSK:

After the multiplier the signal is

and the decision variable after the LPF is

2

1

2

1

1

( ) 2 ( ) 2 cos( )

cos ( )

cos( )

cos 2 2 ( )

C C b C c k

C b k

C k k

C k k

x t x t T A t a

t T a

A a a

t a a

2

1

2

1

,( )

,

C k k

k

C k k

a a z t

a a

7/27/2019 Bandpass-2011


Differential Encoding and Decoding

Differential encoding and decoding:

Decoding is obtained by the simple rule:

that is realized by the circuit shown

right.

Note that no local oscillator is required

How would you construct the encoder?

1

1

start, say with 1

if 1,set

if 0,set

k

k k k

k k k

a

m a a

m a a

1k k k d a a

mk

ak

A B Y

0 0 1

0 1 0

1 0 0

1 1 1

XOR

7/27/2019 Bandpass-2011


Timing and Synchronization Performance of coherent detection is greatly dependent on how

successful local carrier recovery is Consider the bandpass signal s(t) with a rectangular pulses

pTb(t), that is applied to the matched filter h(t):

Therefore, due to phase mismatch

at the receiver, the error rate is

degraded to

( ) ( )cos( )

( ) ( ) ( )cos( )

C Tb C

b C Tb C

s t A p t t

h t Ks T t A p t t

( ) s t ( )h t

( )t

( ) ( ) ( ) cosb

C

b

t T z t s t h t KE t

T

2

0

2

( )

/ 2

bT

C b

s t dt

A T

210 cosb

e

E E p Q

( ) cosk

t KE

k t

2 2

1 0 0 0 1

2

1

0 10

0 0 0 0

1

( ) ( ) ( ) 2 ( ) ( )( )b b b bT T T T

E E E

s s d d s d s s d s

7/27/2019 Bandpass-2011


Example Assume data rate is 2 kbaud/s and carrier is 100 kHz for an

BPSK system. Hence the symbol duration and carrier period are

therefore the symbol duration is in radians

Assume carrier phase error is 0.3 % of the symbol duration.

Then the resulting carrier phase error is

and the error rate for instance for is

that should be compared to the error rate without any phase

errors or

Hence, phase synchronization is a very important point to

remember in coherent detection

1/ 2kbaud/s = 0.5msS

T 1/ 10C C

T f s

10 2314.2rad

0.5ms x

s x

o0.003 0.94 rad 54 x

8 9dB 2

( 16cos 54) 10e p Q

5( 16) 3 10

e p Q

(or carrier cycles)

7/27/2019 Bandpass-2011


Received signal consist of bandpass filtered signal and noise,

that is sampled at the decision time instants t k

yielding decision

variable:

Quadrature presentation of the signaling waveform is

Assuming that the BPF has the impulse response h(t), signal

component at the sampling instants is then expressed by

( )k m

Y y t z n

( 1)

0

( ) ( ) ( ) ( )

( ) ( )

b

b

b

m m b m k

m b

bk

k T

kT

T

t t z s t kT h t s h t d

s h d

kT

T

( ( ) x( ) ( ) )

A

x y t y t d

0,1m

( ) ( )cos( ) ( )sin( )m C k i C k q C

s t A I p t t Q p t t

Coherent Detection: Example: Optimum Binary Detection

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Express energy / bit embedded in signaling waveforms by

Therefore, for coherent CW we have the SNR and error rate

2

1 0

2

0 0 1

2

1

0 10

0 0

1

0 0

( ) ( )

( ) 2 ( ) ( )

( )b b

b b

T T

T T

E

E E

s s d d

s d s s d

s

Note that the signaling waveform

correlation greatly influences the SNR! 1 0/ 2

e p Q z z

2

max / 2/ 2

b bo

o

E E SNR N

N

1010011001

2/

2

01

2

2

2

2

4 2

E E Q

E E E Q P

E E E z z b

e

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Coherent M -ary PSK receiver

Decision thresholds

for M -ary PSK

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Error rate for M-PSK

In general,PSK error rate can be expressed by

where d is the distance between constellation points (or a=d/2 is

the distance from constellation point to the decision region

border) and is the average number of constellation points in

the closed neighborhood. Therefore

Note that for matched filter reception

2e n n

d a p n Q n Q

nn

qn

decision region

000

001

011111

101

100

110

010

d

2 sin( / 2)2 2 2 sin( / )

2 2e

d A AQ Q Q M

2

2, log ( )

b b

A E nE M E

2

2n

7/27/2019 Bandpass-2011


M -ary QAM system (M-aray APK, Amplitude-Phase Keying)

(a) Quadrature-Carrier transmitter (b) Quadrature-Carrier receiver

(c) square signal constellation and thresholds with M =16

7/27/2019 Bandpass-2011


Quadrature-carrier receiver with correlation detector

Signal energy

The source information be grouped into dibits represented by Ik Qk

Each dibit corresponds to one symbol of 2 successive bits of source

7/27/2019 Bandpass-2011


PLL system for carrier synchronization for quad-carrier

receiver

The probabiblity of obtaining of a correct symbol is:

The transmission bandwidth for QPSK/QAM is BT=rb /2Whereas BPSK require BT=rb.

7/27/2019 Bandpass-2011


Error rate for M-QAM, example 16-QAM

2e n n

d a p n Q n Q

2 2 22 2

4 4 8 3 4 23

4 8 4

4 2 8 10 4 18 1016

nn

a a a a

2

2

0

23 3 3

10 10e

a A E p Q Q

symbol error rate

Constellation follows from 4-bit words and therefore

0 04

3 2 3 4

4 10 4 5b

bb

E E

E E p Q Q

N N

2

( ) / ,

log ,

e

b

p p E n

n M E nE

2

2

2 3

18

a

a

2 2

2

310a a

a

22a

2a

7/27/2019 Bandpass-2011


7/27/2019 Bandpass-2011


Envelope distortion and QPSK

QPSK is appealing format, however requires constant envelope

Passing constellation figure via (0,0) gives rise to envelope -> 0

Prevention:

– Gray coding

– Offset - QPSK

– Pi/4 QPSK

Apply two /4 offsetQPSK constellations by turns

7/27/2019 Bandpass-2011


Non-coherent DetectionExample: Non-coherent On-off Keying (OOK)

Bandpass filter is matched to the signaling waveform (not to

carrier phase), in addition f c >>f m, and therefore the energy for ‘1’is simply

Envelopes follow Rice and Rayleigh distributions for ‘1’ and ‘0’

respectively:

2

1( / 2)

b C T A

distribution for "1"

distribution for ”0”"

7/27/2019 Bandpass-2011


Non-coherent Binary Systems: Noisy Envelopes

AWGN plus carrier signal have the envelope whose probability

distribution function is

– For nonzero, constant carrier component Ac , Rician

distributed:

– For zero carrier component Rayleigh distributed:

For large SNR ( AC >> ) the Rician envelope simplifies to

Therefore in this case the received envelope is then essentially

Gaussian with the variance 2 and mean equals

2 2

02 2 2( ) exp , 0

2C C

A

x x A xA p x I x

2

2 2( ) exp , 0

2 A

x x x x

2

2 2( ) exp , 02 2

C A

C

x A x p x x A

( ) A C

p x A

7/27/2019 Bandpass-2011


Envelope Distributions with different

Carrier Component Strengths

Rayleigh distribution

Rice distribution

C A

7/27/2019 Bandpass-2011


Noncoherent OOK Error Rate

The optimum threshold is at the intersection of Rice andRayleigh distributions (areas are the same on both sides)

Usually high SNR is assumed and hence threshold is

approximately at the half way and the error rate is the average

of '0' and '1' reception probabilities

Therefore, error rate for non-coherent OOK equals

0 112e e e P P

where

2 2

0

1

0

/2

/2

( ) exp /8 exp / 2

( ) ( / 2 ) ( )

C

C

e An C b

e A C b

A

A

P p y dy A

P p y dy Q A Q

probability to detect "0" in error

probability to detect "1" in error

1 1exp( / 2) ( ) exp( / 2), 12 2e b b b b

P Q

7/27/2019 Bandpass-2011


Comparison Error Rate Comparison

a: Coherent BPSK

b: DPSK c:Coherent OOK

d: Noncoherent FSK

e: noncoherent OOK

a: Coherent BPSK

b: DPSK c:Coherent OOK

d: Noncoherent FSK

e: noncoherent OOK

7/27/2019 Bandpass-2011


Comparison of Quadrature Modulation Methods

Note that still the performance is good, envelope is not

constant. APK (or M-QASK) is used in cable modems

APK=MQASK

( pe=10-4)

M-APK: Amplitude Phase Shift Keying

7/27/2019 Bandpass-2011


Summary of binary modulation systems

Documents

Bandpass-2011