ece 463: digital communications lab

ECE 463: Digital Communications Lab.

Lecture 4: Modulation Part IHaitham Hassanieh

Previous Lecture:ü Pulse Shaping Filtersü Matched Filtersü Symbol Timing Recoveryü Eye Diagrams

This Lecture:q Channel Distortionq Non-Coherent vs. Coherent Modulation

Digital Communication System

TX RX

1011010110011001 1011010110011001

Bits-to-SymbolsMapper

Bits

LPF BPF

PA

PLL

Mixer

Pulse Shaping

DACModulation (Encoding)

Symbols-to-Bits Mapper

Bits

ChannelEqualization

& Sync.

Demodulation(Decoding)

LPFBPFLNA

PLL

Mixer

ADC MatchedFilter

Symbol Timing

Recovery

Frame Sync.

Digital Communication System

TX RX

1011010110011001 1011010110011001

Bits-to-SymbolsMapper

Bits

Modulation (Encoding)


Bits


Frame Sync.

The Channel

TX RX

1011010110011001 1011010110011001

ChannelBits-to-SymbolsMapper

Bits



Bits


Frame Sync.

! " # " = ! " + &(")

Channel adds noise (AWGN)!

The Channel

TX RX

1011010110011001 1011010110011001


Bits



Bits


Frame Sync.

! " # " = ! " − & + ((")

Channel delays the signal!

The Channel

TX RX

1011010110011001 1011010110011001


Bits



Bits


Frame Sync.

! " # " = %! " − ( + *(")

Channel attenuates the signal (Pathloss)

-./ = 01/0./23456 3 -1/ ℎ ∝ 2

6

The Channel

TX RX

1011010110011001 1011010110011001


Bits



Bits


Frame Sync.

! "

Channel rotates the signal (Adds Phase)

ℎ ∝ %& '

()

* " = ,! " − / + 1(")

The Channel

TX RX

1011010110011001 1011010110011001


Bits



Bits


Frame Sync.

! " # " = %! " − ( + *(")

ℎ ∝ /0 1

23

×1526789: ℎ ! " − ( 1526789 :5; ×126789: ℎ ! " − ( 126789;! "

→ = = 2?@A( = 2? B/0B = 2? 0/ → ℎ ∝ /

0 1267C/E

The Channel

+1−1 $

%

Consider BPSK Modulation.0 → −11 → +1

( ) ℎ×( )

+1−1 $

%

+, )

The Channel

−3 +3+1−1

−3

+3

+1

−1%

&Consider QAM Modulation

Demodulating correctly requires COHERENCE!i.e., Need to estimate & correct for the channel ℎ

CHANNEL EQUALIZATIONNext Lecture

Modulation

Coherent Non-CoherentSignal at RX must be

phase coherent with TX signal to be able to decode correctly.

Need to correct for channel as well as timing

and frequency offsets.

No need for phase coherence at the

receiver to decode.

“No” need for channel equalization

Simpler Receiver Architecture

Based on the type of receiver

ModulationBased on how the bits are encoded

ASKAmplitude

Shift Keying

Bits:


ASKAmplitude

Shift Keying


ASK FSKAmplitude

Shift KeyingFrequency

Shift Keying

Bits:


ASK FSKAmplitude


Shift Keying


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

Bits:


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

BPSK


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

4-PSK


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

8-PSK


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

M-PSK

Phase is integer multiple of: !"#Bits per symbol: log!'


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

4-QAM

QAM

Phase & Amplitude

Modulation(APSK)


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

16-QAM


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

64-QAM


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

256-QAM


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

M-QAM

IQ gird: !× !Bits per symbol: log&!


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

OOK, ASK CFSK, MSK, GMSK BPSK, QPSK, CPM PAM, M-QAM


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)

PPMPulse PositionModulation


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)


Bits:


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)



ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)


Bits:

PWMPulse WidthModulation


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)




ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)



DQPSKDifferential

QPSK

DQAMDifferential

QAM

Encode bits as difference between consecutive symbols

DBPSK: Differential Binary Phase Shit KeyingBPSK Modulation

0 → −11 → +1

& '

( ' = ℎ& '

DBPSK Modulation0 → & ' + 1 = −&(')1 → & ' + 1 = +&(')

./ = 001& ' < 0

./ = 101& ' > 0

→ Real ( ' = Real ℎ & 'Without knowing ℎ, it is not possible to decode correctly.

./ = 001& ' &∗ ' + 1 < 0

./ = 101& ' &∗ ' + 1 > 0

( ' = ℎ& '→ ( ' (∗ ' + 1= ℎ& ' ℎ∗&∗ ' + 1

DBPSK: Differential Binary Phase Shit KeyingBPSK Modulation

0 → −11 → +1

& '

( ' = ℎ& '

DBPSK Modulation0 → & ' + 1 = −&(')1 → & ' + 1 = +&(')

./ = 001& ' < 0./ = 101& ' > 0

→ Real ( ' = Real ℎ & '

Without knowing ℎ, it is not possible to decode correctly.

./ = 001& ' &∗ ' + 1 < 0./ = 101& ' &∗ ' + 1 > 0

( ' = ℎ& '→ ( ' (∗ ' + 1= ℎ 9& ' &∗ ' + 1

Without knowing ℎ, it is possible to decode correctly.


ASK FSKAmplitude


Shift Keying

PSKPhase

Shift Keying

QAM

Phase & Amplitude

Modulation(APSK)



DQPSKDifferential

QPSK

DQAMDifferential

QAM

OOK, ASK CFSK, MSK, GMSK BPSK, QPSK, CPM PAM, M-QAM

DBPSK, DQPSK, DQAM

Definitions & Variables

• !: Wavelength• #: Distance between transmitter and receiver• $: Channel Phase• %&: Carrier Frequency• ': Speed of light• ( = ℜ+ , - &0 = ℑ2 , -• 3: Number of constellation points in

modulation

• 45: Decoded bit

• ,(-): Transmitted Baseband Signal• 8 - : Additive Gaussian Noise• 9(-): Received Signal• :: Propagation delay in the signal• ℎ: Channel Coefficient.• <=>: Received Power• <?>: Transmitted Power• @=>: Receiver Antenna Gain • @?>: Transmitter Antenna Gain

ece 463: digital communications lab

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