Microsoft PowerPoint - Ch14_4A. Bruce Carlson Paul B. Crilly
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• Digital CW modulation • Coherent binary systems • Noncoherent binary systems • Quadrature-carrier and M-ary systems • Orthogonal frequency division multiplexing • Trellis-coded modulation
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• Coherent Detection – All the simulation have used coherent matched received
signal detection • As good as it can get
• Non-coherent Detection – Usually easier to implement with less requirements,
BUT it does not perform as well.
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– the symbol representation can be described as
– The optimal detector is a matched filter
– This generates a detection statistic for each transmitted symbol with optimal output energy.
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Detection Threshold
• Once the optimal symbol output power is known, the detection threshold can be set based on probability.
– For binary, equally probable symbols
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012 1 zzVopt
Figure 14.2-2
Conditional PDFs
An Alternate Form
• Instead of one filter per symbol, for binary we can combine the optimal filter for detection (based on superposition) as
• Whichever form is used: the optimal detector physically performs a correlation of the incoming waveform with the transmitted symbols
• Therefore, they are called correlation detectors! 9
ththth optoptopt 21
tTsKtTsKth bbopt 01
Bandpass binary receiver
• Using superposition of the “parallel matched filters”, the BPF is the difference of the two filters.
• This results in an optimal binary detector
thththBPF 01
Correlation receiver for OOK or BPSK
• Since both optimal filters consist of cosine waveforms, mix and integrate instead of filter an optimally sample. – Note that the integrator can be a rectangular window
filter that is optimally sampled. (Provides functionality near synchronization as well.)
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• Evaluating the expected value
• OOK
• PSK
• FSK
Generalized Probability of Error
• Using the optimal BPF filter and sampling for each symbol, the relationship will be based on:
• The BER is then based on
• Therefore picking arbitrary symbols is possible, but the symbol correlation coefficient will drive the BER performance.
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• There are multiple “orthogonal” tone separations. • The correlation coefficient can go negative! The minimum occurs at
approximately sinc(1.22) = -0.166 (which does improve performance)

0 10 22exp22exp
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• Synchronous coherent receiver can be very difficult to design.
• Can noncoherent systems be more easily designed without giving up significant BER performance? – YES! – For a 1-2 dB Eb/No performance loss.
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Figure 14.3-2
Noncoherent OOK receiver
• Using an envelope detector – the noise pdf for a zero symbol becomes Rician and is
non-longer Gaussian. – The noise pdf for a one symbol remains Gaussian
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Figure 14.3-3
2 c
opt AV
Figure 14.3-5
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• Qualitative comments – Using envelope detectors on each symbol output, the
Rician error distribution effects the z detection statistic.



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(a) coherent BPSK (b) DPSK (c) coherent OOK or FSK (d) noncoherent FSK (e) noncoherent OOK: Figure 14.3-4
Binary error probability curves
Detection for M-ary Systems
• Determine the detection statistic for all symbols • Select the maximum statistic • Decode the binary values from the selected
symbol
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• Applicable for complex constellations: – M-QAM – M-PSK
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Figure 14.4-1
Figure 14.4-2
Carrier synchronization for quad-carrier receiver
• Carrier synchronization is a challenge and can be why non-coherent detection is required!
• One approach to generating a coherent carrier is:
Coherent M-ary PSK receiver
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Figure 14.4-3
-20 -15 -10 -5 0 5 10 15 20 -20
-15
-10
-5
0
5
10
15
Real
Figure 14.4-4
-20 -15 -10 -5 0 5 10 15 20 -20
-15
-10
-5
0
5
10
15
Real
PSK signal constellations
• MPSK Symbols are typically “Gray-code” encoded prior to transmission – In the Gray-code, adjacent symbols are only different
by 1 bit value! 28
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(a) M=4 (b) M=8 Figure 14.5-1
MPSK Eb/N0 Examples
-8 -6 -4 -2 0 2 4 6 8 -8
-6
-4
-2
0
2
4
6
Real
Im ag
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10
-8
-6
-4
-2
0
2
4
6
8
Real
-20 -15 -10 -5 0 5 10 15 20 -20
-15
-10
-5
0
5
10
15
Real
10-4
10-3
10-2
10-1
Es/No (dB)
S E
10-4
10-3
10-2
10-1
Eb/No (dB) B
10-6
10-5
10-4
10-3
10-2
10-1
Es/N0 (dB)
S E
R
M=2 Sim M=2 Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=16 Sim M=16 Bound
-5 0 5 10 15 20 10-7
10-6
10-5
10-4
10-3
10-2
10-1
Eb/N0 (dB)
B E
R
M=2 Sim M=2 Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=16 Sim M=16 Bound
Simulated Performance MFSK
• MFSK_Ber and MFSK_PP_Plot
0 2 4 6 8 10 12 14 16 10-7
10-6
10-5
10-4
10-3
10-2
10-1
Es/N0 (dB)
S E
R
M=2 Sim M=2 Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=16 Sim M=16 Bound
-5 0 5 10 15 10-7
10-6
10-5
10-4
10-3
10-2
10-1
Eb/N0 (dB)
B E
R
M=2 Sim M=2 Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=16 Sim M=16 Bound
Notes: Additional required bandwidth as M increases. Also MFSK symbols are all orthogonal!
Comparing MPSK and MFSK
• MPSK – More Eb/N0 required for higher M for symbol error rate – 2- and 4-PSK have the same BER
• Otherwise higher BER for higher M
• MFSK – More Eb/N0 required for higher M for symbol error rate,
BUT it does not increase as fast as MPSK – Less Eb/N0 required for higher M for BER!
– How could this be? • The symbols are all orthogonal!
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(a) transmitter (b) receiver (c) square signal constellation and thresholds with M=16
Figure 14.4-8
410beP
Based on the same BER
M-QAM advantage
What if question?
• Could you take the MFSK or MPSK simulations and use them to develop a M-QAM simulation? – Define constellation – Modulate symbols – I,Q correlators – Map I,Q results to constellation – Determine symbol errors and bit errors
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OFDM LTE Advanced and most recent WiFi
• Multiplexing in both phase and frequency domains – Without the costly hardware of conventional FDM – Can be implemented using IFFT/FFT hardware – Modern DSP ICs and Software Defined Radio Concepts!
• OFDM form of Multicarrier (MC) modulation
• Carriers are mutually orthogonal
• We parse up a given message into separate components to OFDM them onto a channel
a symbol is transmitted at a lower rate increased immunity to multipath (very important for Cellular) may not have to employ complex equalization processing
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Applications • IEEE 802.11 (Wi-Fi) and IEEE-802.16 (WiMax) • LTE Advanced • Modems, DSLs
• OFDM system of parsing symbols onto separate frequencies and phases can be extended to multiple access (MA) applications.
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• Combination of coding and modulation • Uses systematic convolutional coding • Lower bit error rate in exchange for increased
complexity • Maximize Euclidean distance (not necessarily
Hamming) between constellation points to minimize errors
• Does not reduce overall message rate • Coding gain achieved by incorporating more bits
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Digital Communications
Basic forms
• Amplitude Shift Keying (M-ASK) • Phase Shift Keying (M-PSK) • Frequency Shift Keying (M-FSK)
– Continuous Phase FSK (CP-FSK) – Gaussian Minimum Shift Keying
(GMSK) • Quadrature Amplitude Modulation
– Include error correction with the modulation. Reed-Solomon codes and Viterbi decode.
• Orthogonal Frequency Division Modulation (OFDM)
• Direct Sequence Spread Spectrum (DSSS) – Code Division Multiple Access
(CDMA) • Frequency Hopping (FH)
– fast or slow rates
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