10/2/07 van Alphen & Katz 1 Digital Modulation Techniques - Overview - Digital Modulation Basics Vocabulary/Notation Basic Phase Modulation: BPSK, QPSK, MPSK, DPSK Basic Frequency Modulation: FSK Performance Measures & Fundamental Limits QPSK Variations (π/4 QPSK, OQPSK, MSK, DQPSK) QAM & OFDM Pulse Shaping Conclusions 10/2/07 van Alphen & Katz 2 Basic M-ary Digital Communication System A/D A/D Collect k bits; Collect k bits; bits bits → symbols symbols Modulate; Modulate; symbols symbols → waveforms waveforms Demodulate; Demodulate; waveform waveform → symbols symbols bits bits ← symbols symbols D/A D/A (analog) (analog) information information (analog) (analog) information information channel channel 10/2/07 van Alphen & Katz 3 M-ary Communication System: Symbol –Level Considerations Transmits one of M possible waveforms Each symbol corresponds to a message m i , i = 1, 2, …, M can represents k bits of information, where M = 2 k is associated with a waveform s i (t), of duration T seconds T = T s is called the symbol time or symbol duration To send message m i : transmit waveform s i (t), 0 < t ≤ T receiver guesses which of M possible messages was sent 10/2/07 van Alphen & Katz 4 Simplified QPSK Example Say we use Quaternary Phase Shift Keying (QPSK) as our modulation. We need M = 4 waveforms, with 4 different phase angles: cos(2πf 0 t) sin(2πf 0 t) 00 01 11 10 Bits-to-Waveforms (Gray-coded)
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10/2/07 van Alphen & Katz 1
Digital Modulation Techniques- Overview -
Digital Modulation Basics Vocabulary/Notation Basic Phase Modulation: BPSK, QPSK, MPSK, DPSK Basic Frequency Modulation: FSK Performance Measures & Fundamental Limits
Note that the mapping between bits andwaveforms is done using a Gray Code:Noise that pushes the received point past asingle decision boundary causes only asingle bit error.
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QPSK Example for Digital Image
Vector Value 5 7 4 …Binary-Coded 101 111 100Tx Bit Sequence for M = 4:(re-grouping) 10 11 11 10 …
Consider a vector, v, taken from a digital color image with 8quantization levels (3 bits) for R, G and B:
[5 7 4 … 4 0 3 5 … 6 2 1 0 … 5]
red green blue
(Grouping k = log2(M) = log2(4) = 2 bits per symbol)
Communications Efficiency: Eb/N0 required to Attain aParticular Bit Error Probability
Bandwidth/Communications Efficiency Plane: Plots Rb/W vs.Eb/N0 for particular modulation techniques, assuming aparticular pulse shaping. Goal: to be as near as possible tothe theoretical limit
Note: Separate plots are usually done for each required biterror probability
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The Bandwidth/Communications EfficiencyPlane
0
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-5 0 5 10 15 20 25 30 35
Rb/W,bps/Hz
Eb/N0, dB
ShannonBoundary: Rb = C
Rb < C Region:Modulation/CodingTechniques Exist w/P(E) 0
Rb > C Region: NoModulation/CodingTechniques w/P(E) 0
MSK: applies sinusoidal weight to OQPSK (constant envelope)- same BER as QPSK & OQPSK (MF detector in AWGN)- same bandwidth efficiency (bps/Hz) as QPSK & OQPSK- spectrum has wider mainlobe than QPSK & OQPSK, but faster drop-off of sidelobes (proportional to ω-4 vs. ω-2)
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QPSK Variations, cont.
QPSK π/4-QPSK OQPSK MSK - reduction of phasetransitions to obtain lesssidelobe regrowth andtherefore less ISI
MPSK GMSK, BT=.25 GMSK, BT = .3 GMSK, BT = .5 Ideal 0 dB .7 dB .3 dB .2 dB Practical1
Special Case of MSK: GMSK (Gaussian Pulse Shape, time-bandwidth product BT)• further narrows the spectrum, at the cost of re-introducing ISI (increasing BER)• smaller BT product more compact spectrum, but larger ISI