1. TELE3113 Analogue and Digital
Communications –
Digital Band-pass Modulation
Wei Zhang
w.zhang@unsw.edu.au
School of Electrical Engineering and Telecommunications
The University of New South Wales
29 Sept 2009
2. 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.
3. 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),
4. 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.
5. Two types of digital signalling
Digital signalling can be
1. 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.
6. Binary Digital Signalling
Amplitude-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
s ( t ) = Ac m( t ) cos( ω c t )
• m(t) is the unipolar baseband data signal.
• Ac is the amplitude of carrier.
• ωc is the angular frequency of the carrier.
7. • The spectrum of ASK signal, S(f), can be
found from the Fourier transform
∞
• S ( f ) = ∫ A m( t ) cos( ω t )e − j 2πft dt
c c
−∞
∞ A
= ∫ c
m( t ) e − j 2π ( f − f c )t + e − j 2π ( f + f c )t dt
−∞ 2
Ac
= (M ( f − f c ) + M ( f + f c ))
2
• Note: the bandwidth required to transmit
the ASK s(t) is twice the bandwidth of the
modulating signal m(t).
i.e. BT=2B
9. Detection of ASK
• ASK can be generated and detected in the same fashion as AM.
• ASK may be detected by coherent or noncoherent approaches.
10. 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.
11. Frequency-Shift Keying (FSK)
• In the time domain, the FSK signal is
represented by
⎡ t
⎤
s (t ) = Ac cos ⎢ωc t + D f ∫ m(t )dt ⎥
⎣ −∞ ⎦
m(t) is the baseband data signal.
Ac is the amplitude of the carrier.
Df is the frequency deviation [rad./volt/sec].
13. Detection of FSK
• FSK can be detected by either coherent or
incoherent detection
14. 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
[
s ( t ) = Ac cos ω c t + D p m( t ) ]
m(t) is the baseband data signal.
Ac is the amplitude of the carrier.
Dp = is the peak phase deviation [rad./volt].
15. 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
( ) ( )
s ( t ) = Ac cos D p m( t ) cos( ω c t ) − Ac sin D p m( t ) sin( ω c t )
= Ac cos( D ) cos( ω t ) − A
p c c ( )
sin D p m( t ) sin( ω c t )
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.
16. 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
s ( t ) = − Ac m( t ) sin( ω c t )
• The transmitted signal phase is switched
between two values, 0, 1800
18. Detection of BPSK
• Coherent (Synchronous) detection must
be used
multiplier
BPSK signal baseband digital signal
LPF
cos ( ω c t)
19. 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
21. 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
22. 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
23. Differential Phase-Shift Keying
(DPSK)
• Differential Coding
– In differential coding, an input binary data
sequence {dn} is encoded into differential data
{en} determined by
en = d n ⊕ en −1
where ⊕ is a modulo 2 adder or exclusive OR
gate (XOR) operation
24. 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
25. Differential Phase-Shift Keying
(DPSK)
• At the receiver side, the encoded data {en} is
~
decoded to produce the data {d n } by
~ ~ ~
d n = en ⊕ en −1
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
28. Generation of DPSK
logic network phase-shift keying
DPSK signal
baseband binary data
carrier
one bit delay
29. Detection of DPSK
multiplier
DPSK signal baseband 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 +1 = -1 × -1
1 = 1 ⊕ 0 -1 = -1 × +1
1 = 0 ⊕ 1 -1 = +1 × -1
0 = 0 ⊕ 0 +1 = +1 × +1
