Coding No. 1 Seattle Pacific University Modulation Kevin Bolding Electrical Engineering Seattle Pacific University.

Coding No. 1Seattle Pacific University

Modulation

Kevin BoldingElectrical Engineering

Seattle 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


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


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• 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)


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


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


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


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


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


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


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


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


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


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


-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


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


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


Offset QPSK Modular Circuit

~

X

X

+

/2

ODD

EVEN

Sampling

Quantizing

Coding

Modulation

Transmission


OQPSK Signal Space

01 11

00 10

+135 o +45 o

-135 o -45 o

Sampling

Quantizing

Coding

Modulation

Transmission


/4 QPSK

~

X

X

+

/2

/4

ODD

EVEN

Every othersymbol

Sampling

Quantizing

Coding

Modulation

Transmission


/4-QPSK Signal Space Diagram

(0, 1)A (0, 0)A

(1, 1)A (1, 0)A

(0, 0)B

(0, 1)B

(1, 1)B

(1, 0)BSampling

Quantizing

Coding

Modulation

Transmission

Coding No. 1 Seattle Pacific University Modulation Kevin Bolding Electrical Engineering Seattle Pacific University.

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