coding no. 1 seattle pacific university modulation kevin bolding electrical engineering seattle...
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Coding No. 1Seattle Pacific University
Modulation
Kevin BoldingElectrical Engineering
Seattle Pacific University
Coding No. 2Seattle Pacific University
Digital Transmission of Analog Data
Sampling
Quantizing
Coding
Modulation
Transmission
Convert to discrete samples (time domain)
Convert to discrete levels (amplitude)
Optionally re-map to a different logical code (may expand)
Map to a physical code at desired frequency band
Amplify and transmit
Analog signal
Digitaldata
Coding No. 3Seattle Pacific University
Sampling
• Sampling theorem:
• If sample rate >= 2x max frequency (f)
• And samples have infinite precision (analog)
Can reproduce signal exactly after filtering out frequencies >f
01234
6789
101112131415
5
Pulse-Amplitude Modulation – PAMSamples have analog (infinite precision) values
• Undersampling
• If sample rate is < 2f then it is possible to map multiple waveforms to the data (aliasing)
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 4Seattle Pacific University
Pulse Code Modulation• PCM:
• Approximate analog samples with a discrete sample
• n bit sample 2n levels 0123456789
101112131415
7 8 10 13 13 12 10 7 2 1 1 1 2 5 7 8• Errors
• Not analog, so quantizing error is present
• Each additional bit halves the quantizing error (in volts)
• SNR is Power ratio (proportional to V2)
• Each extra bit used increases SNR by factor of 4 (6 dB)
• N bits Signal/quantization error = 4n or 6n dB
Sampling
Quantizing
Coding
Modulation
Transmission
For n-bit quantization, the SNR =6.02(n) + 1.76 dB
Coding No. 5Seattle Pacific University
Coding• Coding is the substitution of one digital code for
another digital code
• Incoming bit stream is assumed to be unencoded – raw bits (‘0’ means ‘0’ and ‘1’ means ‘1’)
• Substitute code may alter or add to the bit stream in a way that can be inverted
Sampling
Quantizing
Coding
Modulation
Transmission
• Purposes of coding• Encryption• Redundancy to help with error detection and
correction• Coding is addressed separately (later)
Coding No. 6Seattle Pacific University
Modulation• Modulation: Alteration of one wave (carrier) to carry
information provided by another (signal)
• Amplitude Modulation
• Frequency Modulation
• Phase Modulation
Sampling
Quantizing
Coding
Modulation
Transmission
• If the Modulating signal is a digital signal, we have a wider variety of choices • Vary amplitude, phase, or frequency
• ASK, PSK, FSK• Send more than one bit per symbol• Vary more than one aspect at the same time
• QAM – varies both amplitude and phase• For digital data transmission, the Bit Error Rate is the measure
of performance
Coding No. 7Seattle Pacific University
Bit Error Rate
• Digital signal quality is measured by the Bit Error Rate
• Number of errors per bit transmitted, usually assuming uniform, non-correlated noise
• For example, BER of 10-6 means an average of one error per million data bits transmitted
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 8Seattle Pacific University
Bit Errors From Noise
Sampling
Quantizing
Coding
Modulation
Transmission-3
-2
-1
0
1
2
3
Threshold
Errors from noise
• If the SNR is too low, errors occur• If the noise causes the signal to cross the threshold, the bit will be
read in error
Coding No. 9Seattle Pacific University
Bit Errors from Bandwidth Limited ISI• If the bandwidth is too low so pulses spread out
• Sequential pulses start to overlap and interfere with each other• Inter-symbol Interference (ISI)
Sampling
Quantizing
Coding
Modulation
Transmission
Threshold
Pulse-spreading
-1.5
-1
-0.5
0
0.5
1
1.5
Coding No. 10Seattle Pacific University
Bit Errors from Delay ISI• Multiple paths (due to reflections) have different lengths
• Each path has a different delay• Reflections overlap and spread out• Inter-symbol Interference (ISI)
Image source: http://www.complextoreal.com/chapters/isi.pdf
Coding No. 11Seattle Pacific University
Energy ratio E/N0 as a Measure of Quality of Signal
• E/N0 : Energy per bit / Noise power density
• Similar to SNR, but also accounts for the bandwidth used
• Normally expressed in dB
• Equal to SNR if transmitting 1bit/Hz
Sampling
Quantizing
Coding
Modulation
Transmission
• The “quality” of a modulated signal increases with:
• Increased Signal-to-Noise ratio (S/N)
• Increased bitRate-to-Bandwidth ratio (B/R)
• A combined metric can be formed by multiplying these• S/N * B/R = SB/NR = (S/R) / (N/B)
S/R = signal power / bits / time = (signal power)(time)/bits = Energy per bit = E or Eb
N/B = Noise power / Bandwidth = Noise power density = N0
Coding No. 12Seattle Pacific University
Energy ratio and BER• Higher E/N0 means more “resources” available to a signal
• Resources = SNR and bandwidth
• Real measure of quality is the BER
• For a given modulation scheme, we can plot the BER vs. E/N0
• We want BER to be low
• We expect BER to go down with increased E/N0
Error rate vs. E/N0 Ratio for Various Modulation Schemes
1E-12
1E-11
1E-10
1E-9
1E-8
1E-7
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
0 2 4 6 8 10 12
E/N0 (dB)
Pro
bab
ilit
y o
f E
rro
r
ASK
BPSK
DPSK
Worse
Better
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 13Seattle Pacific University
Binary Phase Shift Keying
Sampling
Quantizing
Coding
Modulation
Transmission
• Use PM techniques
• Use phase angles (usually 0 and )
0 1 0 1 1 1 0 1 0 0 0 1 0 1
(t)=, if s(t) = 1
0, if s(t) = 0
X LPFBPSK
Recovered Carrier
Data out
BPSK Recovery (Coherent)
• Coherent Recovery (BPSK):In-phase carrier availableat receiver.
• Incoherent Recovery (DPSK):Differential encoding allowsrecovery without carrier
Coding No. 14Seattle Pacific University
QPSK
• BPSK uses two phase angles, 0 and • Two possibilities for symbol One bit per symbol
• If we use more phase angles, we can send more data per symbol
• Quadrature (or Quaternary) PSK
• QPSK uses angles • Four possibilities for symbol Two bits per symbol
BPSK
QPSK
• Noise causing phase change within +/- will not cause error
• Noise causing phase change within +/- will not cause error
• Symbol error rate twice as high as BPSK, but sends twice as many bits/second Efficiency tie?
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 15Seattle Pacific University
Generating QPSK• Generate two signals in quadrature to each other ( out of
phase)
• Cosine and Sine work well
• Horizontal axis is the I-axis, Vertical is the Q-axis
• Represent bits: 0 -1, 1 +1
• Group consecutive bits together in pairs; first bit is value is I, second is Q
• Multiply coordinates by the I and Q carriers and add
I=-1,Q=1
I=-1,Q=1
I=-1,Q=-1
I=1,Q=1
I = In Phase Carrier (cosine)
Q = Quadrature Phase Carrier (sine)
X
Data
QPSK Generation
Splitter
X
+ QPSK
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 16Seattle Pacific University
-1.5
-1
-0.5
0
0.5
1
1.5
QPSK Waveform
I=1,Q=1 I=-1,Q=1 I=-1,Q=-1 I=1,Q=1 I=1,Q=-1
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 17Seattle Pacific University
Constant Envelope Modulation• Signal is sent by modulating the phase or
frequency of carrier• BPSK, QPSK are the most common
• No signal is modulated on the amplitude• Distortion of carrier amplitude does not affect the
signal• Can be linear or nonlinear in digital mobile
systemsSampling
Quantizing
Coding
Modulation
Transmission
Coding No. 18Seattle Pacific University
QPSK Signal Transition Diagram
01 11
00 10
+135 o +45 o
-135 o -45 o
Sampling
Quantizing
Coding
Modulation
Transmission
• Shows transitions possible from one state to the next
• In QPSK, all transitions are possible
• The diagonal transitions create a particularly abrupt change in phase• Create large sidelobes
outside of the primary band
Coding No. 19Seattle Pacific University
Offset QPSK Modular Circuit
~
X
X
+
/2
ODD
EVEN
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 20Seattle Pacific University
OQPSK Signal Space
01 11
00 10
+135 o +45 o
-135 o -45 o
Sampling
Quantizing
Coding
Modulation
Transmission
Coding No. 21Seattle Pacific University
/4 QPSK
~
X
X
+
/2
/4
ODD
EVEN
Every othersymbol
Sampling
Quantizing
Coding
Modulation
Transmission