Tele3113 wk10tue

29 Sept 2009

TELE3113 Analogue and Digital Communications –Digital Band-pass Modulation

Wei [email protected]

School of Electrical Engineering and TelecommunicationsThe University of New South Wales

Passband Communication• In baseband date transmission, a sequence of bits is represented in

the form of discrete pulse modulated wave (PAM, PPM, PWM) or digital baseband modulated wave (PCM, DM, DPCM) that are transmitted over a low-pass channel (e.g., a coaxial cable).

• For a bandpass channel, e.g., wireless radio, microwave, satellite, optical fibre, we have to resort to the use of a modulation strategy configured around a carrier signal.

• Passband signals are generated by modulating a baseband signal onto a carrier.

• The frequency band of the transmitted signals over the channel is centred at the carrier frequency.

Passband Communication• Passband Analog communication

– A baseband analog signal is modulated onto a carrier using AM, FM, PM techniques.

• Passband Digital communication– A baseband digital signal is modulated onto a carrier using

digital signalling techniques such as • ASK (Amplitude shift keying), • PSK (Phase shift keying), • FSK. (frequency shift keying),

Passband Digital Signalling• In digital signalling, the binary digital information is first encoded

using a particular coding scheme, e.g. Polar NRZ, Unipolar RZ, Manchester, etc.

• The code is then impressed on a carrier by using a conventional modulation technique.

• For digital signalling, modulation is the switching (keying) of a carrier waveform parameter (amplitude, phase or frequency) between preset levels, whose values are discrete.

• This impresses the code, and therefore the information, on the carrier.

Two types of digital signallingDigital signalling can be1. Binary (ASK, BPSK, FSK)

The digital information is transmitted a bit at a time

2. Multilevel (QAM, Quardrature PSK, M-ary PSK)Several bits are grouped together too form symbols, and then symbols are modulated and then transmitted as one unit.

The primary performance issues in digital transmission: • Optimal transmitter and receiver design, • Minimising average probability of symbol error, • spectral properties, bandwidth occupied by a modulation scheme• An important property of any modulation scheme is its spectral

characteristic. This determines the bandwidth required for transmission.

Binary Digital SignallingAmplitude-Shift Keying (On-Off Keying)• Switching the amplitude of the carrier signal

between two discrete levels. • e.g. switching (keying) a carrier sinusoid "on" and

"off" with a unipolar binary signal• The ASK signal is represented by

• m(t) is the unipolar baseband data signal.• Ac is the amplitude of carrier.• ωc is the angular frequency of the carrier.

s t A m t tc c( ) ( ) cos( )= ω

• The spectrum of ASK signal, S(f), can be found from the Fourier transform

•

• Note: the bandwidth required to transmit the ASK s(t) is twice the bandwidth of the modulating signal m(t).

i.e. BT=2B

( ))ff(M)ff(M2A

=

dtee )t(m 2A

=

dte)tcos( )t(m A)f(S

ccc

t)ff(2jt)ff(2jc

ft2jcc

cc

++−

+∫

∫=

+−−−∞

∞−

−∞

∞−ππ

πω

ASK & OOK

Detection of ASK• ASK can be generated and detected in the same fashion as AM.• ASK may be detected by coherent or noncoherent approaches.

Frequency-Shift Keying (FSK)

• Switching the frequency of the carrier signal between discrete levels.

• In FSK, each discrete level of a code is represented by a specific frequency.

• e.g. A binary code with two levels is represented by two discrete frequencies.

Frequency-Shift Keying (FSK)

• In the time domain, the FSK signal is represented by

m(t) is the baseband data signal.Ac is the amplitude of the carrier.Df is the frequency deviation [rad./volt/sec].

⎥⎦

⎤⎢⎣

⎡+ω= ∫

∞−

dttmDtAtst

fcc )(cos)(

FSK

Detection of FSK

• FSK can be detected by either coherent or incoherent detection

Binary Phase-Shift Keying (BPSK)

• Switching the phase of the carrier signal between two discrete levels. Usually the two levels differ by 180º.

• The BPSK signal is represented by

m(t) is the baseband data signal.Ac is the amplitude of the carrier.Dp = is the peak phase deviation [rad./volt].

[ ]s t A t D m tc c p( ) cos ( )= + ω

Binary Phase-Shift Keying (BPSK)ref Couch pg 343

• let m(t) a polar signal with peak values of ± 1 and rectangular pulse shape. Then

Since cosine is an even function.

– The first term is called the pilot carrier term which does not carry any useful information --- power wasted!

– The second term is the data term carrying the coded message.– The peak phase deviation Dp determines the ratio of the data to

the pilot term.

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

s t A D m t t A D m t t

A D t A D m t tc p c c p c

c p c c p c

( ) cos ( ) cos ( ) sin

cos cos ( ) sin

= −

−

sin

= sin

ω ω

ω ω

Optimal BPSK• To maximise the signalling power efficiency

(large proportion of power is to be carried by the data term), the pilot term must be minimised, i.e.

Dp = ∆θ = 90º = π/2

• Hence for the optimal BPSK, the signal becomes

• The transmitted signal phase is switched between two values, 0, 1800

( )s t A m t tc c( ) ( ) sin= − ω

BPSK

Detection of BPSK

• Coherent (Synchronous) detection must be used

BPSK signalmultiplier

baseband digital signalLPF

cos ( t)ωc

Detection of BPSK

• If a low-level pilot carrier component is transmitted a PLL can be used to recover carrier

• Otherwise a Costas loop may be used to synthesise the carrier reference from this BPSK-SC signal– 180º phase ambiguity must be resolved

• Can be accomplished by sending a known test signal

• or using differential coding

Figure 3-57 Ziemer Costas phase-locked loop.Note: m2(t) ambiguity for ±1

Costas phase-locked loop

• Note: m2(t) thus ambiguity for ±1• Hence loop is just as likely to phase lock

such that the demodulated output is proportional to – m(t) as it is to m(t)

• Thus we cannot be sure of the polarity of the output and binary 1’s could be read as binary 0’s

Differential Phase-Shift Keying (DPSK)

• Motivation of DPSK:– Remove the 180º phase ambiguity in

BPSK by using differential coding at the Tx and differential decoding at the Rx.

– When serial data is passed through many circuits along a communications channel the waveform is often unintentionally inverted• Often occurs during switching between

several data paths

Differential Phase-Shift Keying (DPSK)

• Differential Coding– In differential coding, an input binary data

sequence {dn} is encoded into differential data {en} determined by

where ⊕ is a modulo 2 adder or exclusive OR gate (XOR) operation

1−⊕= nnn ede

Differential Phase-Shift Keying (DPSK)

• Each digit in the encoded sequence is obtained by comparing the present input bit with the past encoded bit

• A binary 1 is encoded if the present input bit and the past encoded bit are of opposite state

• A binary 0 is encoded if the states are the same

Differential Phase-Shift Keying (DPSK)

• At the receiver side, the encoded data {en} is decoded to produce the data { } by

The tilde denotes data at the receiver.• Hence the encoded signal is decoded by

comparing the state of adjacent bits– If the present received encoded bit has the same

state as the past encoded bit a binary 0 is decoded– A binary 1 is decoded for opposite states

1~~~

−⊕= nnn eed nd~

General Differential Coding System

Example of Differential Coding

Generation of DPSK

DPSK signallogic network

baseband binary data

one bit delay

phase-shift keying

carrier

Detection of DPSKDPSK signal

multiplierbaseband data

LPF

one bit delay

When the baseband data is represented in polar code: e.g. 1 --- -1v and 0 --- +1v, the modulo 2 adder logic at the receiver side can be easily realised using a one-bit delay and a multiplier.

0 1 1 11 1 1 11 0 1 10 1 1

1 + - - 1 0 - - + 1 1 - + - 1 0 0 + + + 1

= ⊕ = ×= ⊕ = ×= ⊕ = ×= ⊕ = ×