CS 294-7: Digital Modulation
Prof. Randy H. Katz
CS Division
University of California, Berkeley
Berkeley, CA 94720-1776
© 1996
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Analog Modulation: AM Radio
Amplitude Modulation (AM)
Speech Amplitude
Signal
Time Time
Replica of
Speech Signal Carrier frequency
Carrier amplitude where
speech signal is zero
Time
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Analog Modulation: FM Radio
Frequency Modulation (FM) Noise has a greater effect
on amplitude than frequency
Speech
Signal
Sufficient to detect zero
Time
crossings to reconstruct
the signal
Signal goes
negative
Easy to eliminate amplitude
distortion
Amplitude
Carrier Amplitude
Constant envelope, i.e., envelope
Time of carrier wave does not change
with changes in modulated signal
Highest Lowest This means that more efficient
Frequency Frequency amplifiers can be used, reducing
power demands
3
Detection of FM Signal
Received
Noise translates into Signal
amplitude changes, and
sometimes frequency Limiter
changes
Detection based on
Differentiator
zero crossings: the
limiter
Rectifier
Alternative schemes
to translate limited signal
into bit streams Pulse
Generator
Slicer
Low Pass Thresholds
Filter
Slicer
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Digital Modulation Techniques
• Carrier wave s:
– s(t) = A(t) * cos[ (t)]
– Function of time varying amplitude A and time varying
angle
• Angle rewritten as:
– (t) = 0 + (t)
– 0 radian frequency, phase (t)
• s(t) = A(t) cos[ 0t + (t)]
– radians per second
– relationship between radians per second and hertz
» ƒ
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Digital Modulation Techniques
• Demodulation
– Process of removing the carrier signal
• Detection
– Process of symbol decision
– Coherent detection
» Receiver users the carrier phase to detect signal
» Cross correlate with replica signals at receiver
» Match within threshold to make decision
– Noncoherent detection
» Does not exploit phase reference information
» Less complex receiver, but worse performance
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Digital Modulation Techniques
Coherent Noncoherent
Phase shift keying (PSK) FSK
Frequency shift keying (FSK) ASK
Amplitude shift keying (ASK) Differential PSK (DPSK)
Continuous phase modulation (CPM) CPM
Hybrids Hybrids
Coherent (aka synchronous) detection: process received signal with
a local carrier of same frequency and phase
Noncoherent (aka envelope) detection: requires no reference wave
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Metrics for Digital Modulation
• Power Efficiency
– Ability of a modulation technique to preserve the fidelity of
the digital message at low power levels
– Designer can increase noise immunity by increasing signal
power
– Power efficiency is a measure of how much signal power
should be increased to achieve a particular BER for a given
modulation scheme
– Signal energy per bit / noise power spectral density: Eb / N0
• Bandwidth Efficiency
– Ability to accomodate data within a limited bandwidth
– Tradeoff between data rate and pulse width
– Thruput data rate per hertz: R/B bps per Hz
• Shannon Limit: Channel capacity / bandwidth
– C/B = log2(1 + S/N)
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Digital Modulation Techniques
• Modify carrier’s amplitude and/or phase (and frequency)
• Constellation: Vector notation/polar coordinates
Quadrature component (carrier shifted 90°)
Q = M sin
M = magnitude
Densely packed = phase
M
implies bandwidth
efficient
Bit error prob related I = M cos
to distances between In-phase component
closest points
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Considerations in Choice of
Modulation Scheme
• High spectral efficiency
• High power efficiency
• Robust to multipath effects
• Low cost and ease of implementation
• Low carrier-to-cochannel interference ratio
• Low out-of-band radiation
• Constant or near constant envelope
– Constant: only phase is modulated
– Non-constant: phase and amplitude modulated
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Binary Modulation Schemes
• Amplitude Shift Keying (ASK)
– Transmission on/off to represent 1/0
– Note use of term “keying,” like a telegraph key
• Frequency Shift Keying (FSK)
– 1/0 represented by two different frequencies slightly
offset from carrier frequency
Data
High Frequency
Low Frequency
FSK Waveform
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Phase Shift Keying
• Binary Phase Shift Keying (BPSK)
– Use alternative sine wave phase to encode bits
– Simple to implement, inefficient use of bandwidth
– Very robust, used extensively in satellite communications
Data
Q
Carrier
Carrier + π
I
0 state 1 state
BPSK Phases separated by 180˚
Waveform
(π radians)
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Phase Shift Keying
• Quadrature Phase Shift Keying (QPSK)
– Multilevel modulation technique: 2 bits per symbol
– More spectrally efficient, more complex receiver
Q
01 state 11 state
Output waveform is
I sum of modulated ±
Cosine and ±Sine wave
00 state 10 state
Phase of carrier:
π/4, 3π/4, 5π/4, 7π/4
2x bandwidth efficiency of BPSK
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Quadrature Phase Shift Keying
10 11
3π π
4 4
-Cos + Sin Cos + Sin
-Cos - Sin Cos - Sin
Cosine Carrier Wave
5π 7π
4 4
00 01
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Minimum Shift Keying
• Special form of (continuous phase) frequency shift keying
– Minimum spacing that allows two frequencies states to be orthogonal
– Spectrally efficient, easily generated
Minimum Shift Keying (MSK)
1.5 cycles Q
Amplitude
Time I
1 cycle 1 cycle
Phase continuity at the bit transitions
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Generating Minimum Shift Keying
Data
Odd, Even Bits
stretched to 2 bit Odd Bits
times Even Bits
High
Bit Value MSK Output Frequency
Odd Even Freq Sense
1 1 Hi +
-1 1 Lo –
Low
1 -1 Lo + Frequency
-1 -1 Hi –
MSK
Notice smooth Waveform
phase transitions!
Hi Lo Lo Lo Lo Hi Lo Hi Hi
+ – – – – + – – –
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Gaussian Minimum Shift
Keying (GMSK)
• MSK + premodulation Gaussian low pass filter
• Increases spectral efficiency with sharper cutoff,
excellent power efficiency due to constant envelope
MSK
Waveform
+90°
GMSK
No sudden shifts in phase Waveform
-90°
• Used extensively in second generation digital
cellular and cordless telephone applications
– GSM digital cellular: 1.35 bps/Hz
– DECT cordless telephone: 0.67 bps/Hz
– RAM Mobile Data 17
π/4-Shifted QPSK
• Variation on QPSK
– Restricted carrier phase transition to +/- π/4 and +/- 3π/4
– Signaling elements selected in turn from two QPSK constellations,
each shifted by π/4
– Maximum phase change is ±135˚ vs. 180˚ for QPSK, thus maintaining
constant envelope (i.e., amplitude of QPSK signal not constant for
short interval during 180˚ phase changes)
• Popular in Second Generation Systems
– North American Digital Cellular (IS-54): 1.62 bps/Hz Q
– Japanese Digital Cellular System: 1.68 bps/Hz
– European TETRA System: 1.44 bps/Hz
– Japanese Personal Handy Phone (PHP) I
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π/4-Shifted QPSK
• Advantages:
– Two bits per symbol, twice as efficient as GMSK
– Phase transitions avoid center of diagram, remove some design
constraints on amplifier
– Always a phase change between symbols, leading to self clocking
… 00 00 01 …
00
Phase 01 00 00 10
Data Change 10
00 45°
01 135°
10 -45°
01
11 10
11 -135° 01 11
11
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Quadrature Amplitude
Modulation
• Quadrature Amplitude Modulation (QAM)
– Amplitude modulation on both quadrature carriers
– 2n discrete levels, n = 2 same as QPSK
• Extensive use in digital microwave radio links
Q
16 Level QAM
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