DSP for Software Radio

Waveform Processing – Single Carrier Systems

Dr. Jamil Ahmad

2

Digital Modulation Techniques

Contents System Review The Fundamentals Digital Modulation Waveforms Bandwidth and Power Efficient

Waveforms

3

System Review

Source Encode

Source Encode

EncryptionEncryption

ChannelEncoderChannelEncoder

ModulatorModulator

ChannelChannel

D/A Conversion

D/A Conversion

DecryptionDecryption

Source Decoder

Source Decoder

ChannelDecoderChannelDecoder

DemodulatorDemodulator

AnalogInputsignal

AnalogOutputsignal

DigitalOutput

DirectDigitalInput

DSP/RFFront-End

DSP/RFFront-End

A/D Conversion

A/D Conversion

Multiple Access

Multiplex

Waveform Processing

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The Fundamentals

Why Modulate? Antenna Length Multiple Access Shannon’s Capacity Theorem Bandwidth and Power

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The Fundamentals- Modulation Principles Almost all communication systems transmit

data using a sinusoidal carrier waveform. Electromagnetic signals propagate well. Choice of carrier frequency allows placement of

signal in arbitrary part of spectrum. Modulation is implemented in practice by:

Processing digital information at baseband. Pulse shaping and filtering of digital waveform. Baseband signal is mixed with signal from oscillator

to bring up to RF. Radio frequency (RF) signal is filtered amplified and

coupled with antenna.

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What is Modulation? Modulation shifts the spectrum of a baseband

signal to that it becomes a bandpass signal. A bandpass signal has non-negligible

spectrum only about some carrier frequency fc >> 0

Note: the bandwidth of a bandpass signal is the range of positive frequencies for which the spectrum is non-negligible.

Unless otherwise specified, the bandwidth of a bandpass signal is twice the bandwidth of the baseband signal used to create it.

BW=B BW=2B

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Digital Modulation Techniques The Definition

Bits into Symbols and waveform Basic Types

Amplitude Modulation (ASK) Frequency Modulation (FSK) Phase Modulation (PSK)

)cos( tA c

Amplitude Frequency Phase

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Digital Modulation

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Waveform Processing

Generic Modulation Waveform Generator

I/Q-Comp. Mapping

SymbolConverter

Differential/Grey Encoder

PulseShaping

SamplingConverter

Input Bits

ModulatedSignal

Bit Rate Symbol Rate Sampling Rate

Minimum Rate ?

)(

sc Fnfje /2

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Digital Modulation

Classification

Linear Modulation Techniques

Non-Linear Modulation Techniques

-Digital Phase Modulations (PSK)-Digital Amplitude and Phase Modulations (QAM)

-Continuous Phase Modulations (CPM)

- FSK- GMSK

Other Classifications:-Constant/Non-Constant Envelope-Bandwidth/Power Efficient Types

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Linear Modulation

I/Q Complex Mapping Two independent real baseband signals (I and

Q, Inphase and quadrature) are transmitted by modulating them into cosine and sine waveforms of the carrier frequency- Increased bandwidth Efficiency.

For I- and Q-components, Nyquist pulse shaping principle (Overlapping pulses with zero-intersymbol interference, 0-ISI) is utilized in order to achieve high spectral efficiency.

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Linear Modulation

Signal Representation

11,0,)()( 2

MkemTtgeAts tfj

m

jk

ck

Digital ModulationNyquist PulsesCarrier FrequencyM-ary Symbol Alphabet

1

0

)(2,2 M

j

jmmk nabb

M

M-ary Symbols Binary Bit Stream

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Digital Modulation

Complex I/Q ModulationTaking Real Part of s(t)

)2sin()()2cos()(

)2cos()()(

tftQtftI

tfmTtgAts

cc

mkck

Where

mkk

mkk

mTtgAtQ

mTtgAtI

)(sin)(

)(cos)(

In-phase Channel

Quadrature-Phase Channel

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Digital I/Q Modulation

Simplified Traditional Diagram

NyquistFilter

NyquistFilter

I(t)Re[]

Im[] Q(t)

)sin(

)cos(

kk

kk

jA

A

a(n)

)2cos( tfc

)2sin( tfc

s(t)

Constellation Mapping

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Digital Modulation Complex Symbol Constellation Diagram

BPSK

,02

0)(

1,0,)(cos)(

kM

tQ

kmTtgtI

k

mk

BPSK, M=2

Re

Im

Mapping Rule

bit phase0 -> 01 ->

16

Complex Constellation

QPSK M=4

4/,4/3,4/3,4/44

2

)(sin)(

3,2,1,0,)(cos)(

k

mTtgtQ

kmTtgtI

k

mk

mk

QPSK, M=4

Bandwidth Efficiency = log2M = 2 bits/s/Hz

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Complex Constellation

16-QAM M=16

1.0

3.0

-1.0

-3.0

k

k

mkk

mkk

A

mTtgAtQ

kmTtgAtI

)(sin)(

15,2,1,0,)(cos)(

Bandwidth Efficiency = log2M = 4 bits/s/Hz

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QPSK Modulation

Phase Maping in QPSK Grey Encoding Differential Encoding

Bits Phase (Grey)

00011011

-3/43/4-/4/4

Phase(Diff. Change)

0/2/2

11

10

01

00

00

01

1011

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QPSK Digital Modulator Architecture

SymbolConverter

Differential/Grey Encoder

Digital

Modulator

PulseShaping

SamplingConverter

Input Bits

ModulatedSignal

Baseband Processor

00 001 110 211 3

Binary-M-ary

0 123

-3/43/4-/4/4

b(n) nkcos

ksin

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QPSK Modulator

Differential Encoder

0 123

0/2/2

b(n) nkcos

ksinT

nnn 1

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Pulse Shaping

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-4

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

T (n+1)TnT

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Digital Modulation Techniques

Role of Pulse Shaping Issues with QPSK Design Example

Input Bit Rate = 1MbpsPulse Shaping = 0.3B = ?

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Digital Modulations

OQPSK Same Signal Constellation as QPSK Phase Variations Restricted to Only

90o Less Co-Channel Interference

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Digital Modulations

OQPSK)2sin()()2cos()()( tftQtftIts cc

1

0

1

0

( ) cos ( )

( ) sin ( )2

K

kk

K

kk

I t A g t kT

TQ t A g t kT

SymbolConverter

Grey Encoder

QPSK

Modulator

SamplingConvert

Input Bits

ModulatedSignal

Insert T/2 Delay

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Digital Modulations

MSK Continuous Phase Frequency Modulation Technique

1,4

2cos)(

kk

kc bxt

T

bfts

Carrier SymbolPeriod

InputSymbols

Continuous Phase

2)(

2 11

kkkk bb

kxx

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Digital Modulation

MSK Phase Modulation

tftQtftIts cc 2sin)(2cos)()(

T

txbtQ

T

txtI

kk

k

2sincos)(

2coscos)(

Where

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Digital Modulations

Comparison 1 0 0 1 0 0 001 1

I(t) forQPSK/OQPSK

Q(t) forQPSK

Q(t) forOQPSK

I(t) forMSK

Q(t) forMSK

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Digital Modulation

Spectrum Comparison

QPSK/OQPSK

BPSKMSK

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Digital Modulations

GMSK Gaussian Filtered MSK Used in GSM and DECT More Compact Spectrum than MSK Some ISI Member of CPM Schemes

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Digital Modulations

GMSK ),(2cos(

2)( ttf

T

Ets c

i

ii iTtqht )(2),( Where

,...2,1,0),1(,...,2,1 iMi

For GMSK2/1

2

h

M

t

dgtq )()(

)2/(

2ln

2erf)2/(

2ln

2erf

2

1)( Tt

BTt

B

Ttg bb

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Digital Modulations

GMSK

222

2ln

2

2ln

2)(

tB

b

b

eBth

Filter Impulse Response

GaussianLPF

FM Modulatorh=0.5

(t) s(t)

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Digital Modulations

/4-QPSK Better Bandwidth Efficiency than

GMSK Better Spectral Efficiency than

QPSK/OQPSK Both Absolute and Differential Phase

Encoding Used in IS-54 and PHS

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Digital Modulations

/4-QPSK Gray Encoding

0 123

-3/4 3/4-/4/4

b(n) nncos

nsin/4

Gray Encoder

t=2nT

t=(2n+1) T

/4-QPSK Modulator

In Bits Modulated Signal

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/4-QPSK

Differential Encoding

0 123

/43/4-/4-3/4

b(n) nncos

nsin/4

Differential Encoder

t=2nT

t=(2n+1)T

/4-QPSK Modulator

T

nnn 1

0

1 2

3

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Digital Modulations

M-PSK

1,...,1,0,2

MaaM kkk

M=8

M=16

)2sin()()2cos()()( tftQtftIts cc

1

0

1

0

)(sin)(

)(cos)(

K

kk

K

kk

kTtAtQ

kTtAtI

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Digital Modulation Techniques

Issues with MPSK Less Amplitude fluctuations Allows Differential Encoding Frequency/Phase Sync Problems with

Higher Order MPSK Degraded BER Performance for higher

Order as Non-Optimal Euclidean Distance Between Constellation Points.

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Digital Modulation Techniques

M-QAM Better BER Performance for higher M

than equivalent M-PSK Bandwidth Efficient - Allows Power-

Bandwidth Tradeoffs Requires Linear/Linearised PAs Generally not Suitable for Wireless

Applications Used in DVB ETSI Standard

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Digital Modulation Techniques

M-QAM

)2sin()()2cos()()( tftQtftIts cc

1

0

1

0

)(sin)(

)(cos)(

K

kkk

K

kkk

kTtAtQ

kTtAtI

M=16

Square Constellation Requires Absolute GrayEncoding

39

Digital Modulation Techniques

M-QAM for Wireless Application Star Constellation Non-Optimal ED Allows Differential

Encoding Viewed as 2 8-PSK

Signals