22. Amplitude-Shift Keying (ASK) Modulation - Engineering

Introduction
Amplitude-Shift Keying (ASK) Modulation on Mac
22. Amplitude-Shift Keying (ASK) Modulation
The transmission of digital signals is increasing at a rapid rate. Low-frequency analogue
signals are often converted to digital format (PAM) before transmission. The source
signals are generally referred to as baseband signals. Of course, we can send analogue
and digital signals directly over a medium. From electro-magnetic theory, for efficient
radiation of electrical energy from an antenna it must be at least in the order of magnitude of
a wavelength in size; c = fλ, where c is the velocity of light, f is the signal frequency
and λ is the wavelength. For a 1kHz audio signal, the wavelength is 300 km. An
antenna of this size is not practical for efficient transmission. The low-frequency signal is
often frequency-translated to a higher frequency range for efficient transmission. The
process is called modulation. The use of a higher frequency range reduces antenna size.
In the modulation process, the baseband signals constitute the modulating signal and the
high-frequency carrier signal is a sinusiodal waveform. There are three basic ways of
modulating a sine wave carrier. For binary digital modulation, they are called binary
amplitude-shift keying (BASK), binary frequency-shift keying (BFSK) and binary phaseshift
keying (BPSK). Modulation also leads to the possibility of frequency multiplexing.
In a frequency-multiplexed system, individual signals are transmitted over adjacent, nonoverlapping
frequency bands. They are therefore transmitted in parallel and simultaneously
in time. If we operate at higher carrier frequencies, more bandwidth is available for
frequency-multiplexing more signals.
Binary Amplitude-Shift Keying (BASK)
A binary amplitude-shift keying (BASK) signal can be defined by
s(t) = A m(t) cos 2πf c t, 0 < t < T (22.1)
where A is a constant, m(t) = 1 or 0, fc is the carrier frequency, and T is the bit
duration. It has a power P = A2 /2, so that A = 2P . Thus equation (22.1) can be
written as
s(t) = 2P cos 2πfct, 0 < t < T
= PT
2
cos 2πfct, T
0 < t < T
= E
2
cos 2πfct, T
0 < t < T (22.2)
22.1

Amplitude-Shift Keying (ASK) Modulation on Mac
where E = PT is the energy contained in a bit duration. If we take
φ1 (t) = 2
T cos 2πfct as the orthonormal basis function, the applicable signal space or
constellation diagram of the BASK signals is shown in Figure 22.1.
Figure 22.1 BASK signal constellation diagram.
Figure 22.2 shows the BASK signal sequence generated by the binary sequence
0 1 0 1 0 0 1. The amplitude of a carrier is switched or keyed by the binary signal m(t).
This is sometimes called on-off keying (OOK).
Figure 22.2 (a) Binary modulating signal and (b) BASK signal.
The Fourier transform of the BASK signal s(t) is
S(f) = A
∞
∫ [m(t) e
2 −∞
j 2πfct ] e-j2πft dt +
A
∞
2
∫ [m(t) e
−∞
-j 2πfct ] e-j2πft dt
S(f) =
A
2 M(f - fc ) +
A
2 M(f + fc ) (22.3)
The effect of multiplication by the carrier signal Acos 2πf c t is simply to shift the
spectrum of the modulating signal m(t) to f c . Figure 22.3 shows the amplitude
spectrum of the BASK signals when m(t) is a periodic pulse train.
Figure 22.3 (a) Modulating signal, (b) spectrum of (a), and (c) spectrum of BASK
signals.
Since we define the bandwidth as the range occupied by the baseband signal m(t) from 0
Hz to the first zero-crossing point, we have B Hz of bandwidth for the baseband signal
and 2B Hz for the BASK signal. Figure 22.4 shows the modulator and a possible
implementation of the coherent demodulator for BASK signals.
Figure 22.4 (a) BASK modulator and (b) coherent demodulator.
M-ary Amplitude-Shift Keying (M-ASK)
An M-ary amplitude-shift keying (M-ASK) signal can be defined by
s(t) = A ⎧ i cos 2πfct, 0≤t
≤T
⎨
⎩0,
elsewhere
22.2
(22.4)

where
Amplitude-Shift Keying (ASK) Modulation on Mac
A i = A[2i - (M - 1)] (22.5)
for i = 0, 1, ..., M - 1 and M > 4. Here, A is a constant, fc is the carrier frequency,
and T is the symbol duration. The signal has a power Pi = Ai 2 /2, so that Ai = 2Pi .
Thus equation (22.4) can be written as
s(t) = 2Pi cos 2πfct, 0 < t < T
= Pi T
2
cos 2πfct, T
0 < t < T
= Ei 2
cos 2πfct, T
0 < t < T (22.6)
where E i = P i T is the energy of s(t) contained in a symbol duration for i = 0, 1, ...,
M - 1. Figure 22.5 shows the signal constellation diagrams of M-ASK and 4-ASK
signals.
Figure 22.5 (a) M-ASK and (b) 4-ASK signal constellation diagrams.
Figure 22.6 shows the 4-ASK signal sequence generated by the binary sequence
00 01 10 11.
Figure 22.6 4-ASK modulation: (a) binary sequence, (b) 4-ary signal, and (b) 4-ASK
signal.
Figure 22.7 shows the modulator and a possible implementation of the coherent
demodulator for M-ASK signals.
References
Figure 22.7 (a) M-ASK modulator and (b) coherent demodulator.
[1] M. Schwartz, Information Transmission, Modulation, and Noise, 4/e, McGraw
Hill, 1990.
[2] P. Z. Peebles, Jr., Digital Communication Systems, Prentice Hall, 1987.
22.3

s
0
0
s 1
E
Amplitude-Shift Keying (ASK) Modulation on Mac
φ
1
( t )
= 2
T cos 2 π f c t
Figure 22.1 BASK signal constellation diagram.
Binary
0 1 0 1 0 0 1
sequence
m(t )
BASK
signal
A
1
0
0
-A
s (t )
(a)
(b)
T
Time
Time
Figure 22.2 (a) Binary modulating signal and (b) BASK signal.
22.4

3
T
m ( t )
1
0 1 0 1
0
T
2T 3T
(a)
1
2T
2B
1
c
c T
-
-f
1
c
T
+
-f -f
t
3
c
T
+ -f
S ( f )
Amplitude-Shift Keying (ASK) Modulation on Mac
-3
T
Envelope
-2
T
-1
T
Envelope
M( f )
0
B =
1
T
(b)
1
2T
2
T
1
2T
3
T
0
(c)
...
2B
fc
f 1
c
T
f
+ f 3
c
T
+
f 1
c
T
-
f 3
c
T
-
...
Figure 22.3 (a) Modulating signal, (b) spectrum of (a), and (c) spectrum of BASK
signals.
m (t )
x
Acos 2π fct 0.5 A m (t ) cos 4 π fct +
0.5A
m (t )
s ( t ) s (t ) x
f t
cos 2π c
(a) (b)
Figure 22.4 (a) BASK modulator and (b) coherent demodulator.
22.5
~ 0.5A
m (t )
f

s
... i ...
0 E
i
(a)
φ (
1
t )
Amplitude-Shift Keying (ASK) Modulation on Mac
= 2
T cos 2 π f c t
s 0 s 1
0
s 3
s 2
Figure 22.5 (a) M-ASK and (b) 4-ASK signal constellation diagrams.
Binary
sequence
4-ary
signal
4-ASK
signal
0
m (t )
3
1
0
-1
-3
s (t )
A
0
-A
-3 A
1
3 A
0 0 0 1 1 0 1 1
(a)
(b)
T T
(c)
(b)
Time
Time
Time
φ (
1
t )
Figure 22.6 4-ASK modulation: (a) binary sequence, (b) 4-ary signal, and (b) 4-ASK
signal.
22.6

s (t )
Binary
sequence
Serial
to
parallel
converter
log 2 M bits
:
(a)
(b)
Amplitude-Shift Keying (ASK) Modulation on Mac
D/A
converter
m (t )
x
Acos 2π fct s (t )
0.5 A m ( t ) cos 4π fct +
0.5 A m( t )
x ~ 0.5A
m ( t )
:
m (t )
A/D
converter
Binary
sequence
cos 2π fct Comparator
Figure 22.7 (a) M-ASK modulator and (b) coherent demodulator.
22.7