basics of wireless communication · transmitter output has an impulse at the carrier frequency for...

M.H. Perrott

High Speed Communication Circuits and SystemsLecture 19

Basics of Wireless Communication

Michael H. PerrottApril 16, 2004

Copyright © 2004 by Michael H. PerrottAll rights reserved.

1

M.H. PerrottM.H. Perrott

Amplitude Modulation (Transmitter)

Vary the amplitude of a sine wave at carrier frequency foaccording to a baseband modulation signal

DC component of baseband modulation signal influences transmit signal and receiver possibilities- DC value greater than signal amplitude shown above

Allows simple envelope detector for receiver Creates spurious tone at carrier frequency (wasted power)

2cos(2πfot)

y(t)

Transmitter Output

x(t)0

2


Impact of Zero DC Value

Envelope of modulated sine wave no longer corresponds directly to the baseband signal- Envelope instead follows the absolute value of the

baseband waveform- Envelope detector can no longer be used for receiver

The good news: less transmit power required for same transmitter SNR (compared to nonzero DC value)

2cos(2πfot)

y(t)

Transmitter Output

x(t)

0

3


Accompanying Receiver (Coherent Detection)

Works regardless of DC value of baseband signal Requires receiver local oscillator to be accurately

aligned in phase and frequency to carrier sine wave

2cos(2πfot)

y(t)

2cos(2πfot)

z(t)Lowpass

r(t)

Transmitter Output

Receiver Output

x(t)

y(t)

0

4


Impact of Phase Misalignment in Receiver Local Oscillator

Worst case is when receiver LO and carrier frequency are phase shifted 90 degrees with respect to each other- Desired baseband signal is not recovered

2cos(2πfot)

y(t)

z(t)Lowpass

r(t)

Transmitter Output

Receiver Output

x(t)

y(t)

0

2sin(2πfot)

5


Frequency Domain View of AM Transmitter

Baseband signal is assumed to have a nonzero DC component in above diagram- Causes impulse to appear at DC in baseband signal- Transmitter output has an impulse at the carrier frequency

For coherent detection, does not provide key information about information in baseband signal, and therefore is a waste of power

2cos(2πfot)

y(t)

Transmitter Output

x(t)

f-fo fo0

1 1

f

X(f)

0

avg(x(t))

f-fo fo0

Y(f)

6


Impact of Having Zero DC Value for Baseband Signal

Impulse in DC portion of baseband signal is now gone- Transmitter output now is now free from having an

impulse at the carrier frequency (for ideal implementation)

2cos(2πfot)

y(t)

Transmitter Output

x(t)

f-fo fo0

1 1

f

X(f)

0

avg(x(t)) =0

f-fo fo0

Y(f)

7


2cos(2πfot)

y(t)

Transmitter Output

x(t)

f-fo fo0

1 1

f

X(f)

0

f-fo fo0

Y(f)

2cos(2πfot)

z(t)Lowpass

r(t)

Receiver Output

y(t)

f-fo fo0

1 1

f-fo fo0

Z(f)

2fo-2fo

Lowpass

Frequency Domain View of AM Receiver (Coherent)

8


Impact of 90 Degree Phase Misalignment

2cos(2πfot)

y(t)

Transmitter Output

x(t)

f-fo fo0

1 1

f

X(f)

0

f-fo fo0

Y(f)

2sin(2πfot)

z(t)Lowpass

r(t)

Receiver Output = 0

y(t)

f-fo fo0

Z(f)

2fo-2fo

Lowpass

f-f1

f10

j

-j

9


Quadrature Modulation

Takes advantage of coherent receiver’s sensitivity to phase alignment with transmitter local oscillator- We essentially have two orthogonal transmission

channels (I and Q) available to us- Transmit two independent baseband signals (I and Q) onto two sine waves in quadrature at transmitter

Transmitter Outputf

-fo fo0

1 1

f0

f-f1

f10

j

-j

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

10


Accompanying Receiver

Demodulate using two sine waves in quadrature at receiver- Must align receiver LO signals in frequency and phase to

transmitter LO signals Proper alignment allows I and Q signals to be recovered as

shown

Transmitter Outputf

-fo fo0

1 1

f0

Receiver Output

f-f1

f10

j

-j

2cos(2πf1t)

2sin(2πf1t)

y(t)

Lowpassir(t)

Lowpassqr(t)

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

f-fo fo0

1 1

f-f1

f10

j

-j

f0

Ir(f)

Qr(f)

f0

2

2

11


Impact of 90 Degree Phase Misalignment

I and Q channels are swapped at receiver if its LO signal is 90 degrees out of phase with transmitter- However, no information is lost!- Can use baseband signal processing to extract I/Q

signals despite phase offset between transmitter and receiver

Transmitter Outputf

-fo fo0

1 1

f0

Receiver Output

f-f1

f10

j

-j

2cos(2πf1t)

2sin(2πf1t)y(t)

ir(t)

qr(t)

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

f-fo fo0

1 1

f-f1

f10

j

-j

f0

Ir(f)

Qr(f)

f0

2

2

12


Simplified View

For discussion to follow, assume that - Transmitter and receiver phases are aligned- Lowpass filters in receiver are ideal- Transmit and receive I/Q signals are the same except for

scale factor In reality- RF channel adds distortion, causes fading- Signal processing in baseband DSP used to correct

problems

f0

Receiver Output

2cos(2πf1t)2sin(2πf1t)

Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

1

1

f0

Ir(f)

Qr(f)

f0

2

2


Baseband Input

13


Analog Modulation

I/Q signals take on a continuous range of values (as viewed in the time domain)

Used for AM/FM radios, television (non-HDTV), and the first cell phones

Newer systems typically employ digital modulation instead

Receiver Output


Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)


t

t

t

t

Baseband Input

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Digital Modulation

I/Q signals take on discrete values at discrete time instants corresponding to digital data- Receiver samples I/Q channels

Uses decision boundaries to evaluate value of data at each time instant

I/Q signals may be binary or multi-bit- Multi-bit shown above

Receiver Output


Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)


t

t

t

Baseband Input

tDecisionBoundaries Sample

Times

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Advantages of Digital Modulation

Allows information to be “packetized”- Can compress information in time and efficiently send

as packets through network- In contrast, analog modulation requires “circuit-

switched” connections that are continuously available Inefficient use of radio channel if there is “dead time” in

information flow Allows error correction to be achieved- Less sensitivity to radio channel imperfections

Enables compression of information- More efficient use of channel

Supports a wide variety of information content- Voice, text and email messages, video can all be

represented as digital bit streams

16


Constellation Diagram

We can view I/Q values at sample instants on a two-dimensional coordinate system

Decision boundaries mark up regions corresponding to different data values

Gray coding used to minimize number of bit errors that occur if wrong decision is made due to noise

DecisionBoundaries I

Q

DecisionBoundaries

00 01 11 10

00

01

11

10

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Impact of Noise on Constellation Diagram

Sampled data values no longer land in exact same location across all sample instants

Decision boundaries remain fixed Significant noise causes bit errors to be made


Q

DecisionBoundaries

00 01 11 10

00

01

11

10

18


Transition Behavior Between Constellation Points

Constellation diagrams provide us with a snapshot of I/Q signals at sample instants

Transition behavior between sample points depends on modulation scheme and transmit filter


Q

DecisionBoundaries

00 01 11 10

00

01

11

10

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Choosing an Appropriate Transmit Filter

Transmit filter, p(t), convolved with data symbols that are viewed as impulses- Example so far: p(t) is a square pulse

Output spectrum of transmitter corresponds to square of transmit filter (assuming data has white spectrum)- Want good spectral efficiency (i.e. narrow spectrum)

tt

Td

t

|P(f)|2

f

data(t) p(t) x(t)

1/Td

Sdata(f)

f 00

*

f1/Td0

Sx(f)

Td

20


Highest Spectral Efficiency with Brick-wall Lowpass

Use a sinc function for transmit filter- Corresponds to ideal lowpass in frequency domain

Issues- Nonrealizable in practice- Sampling offset causes significant intersymbol interference

tt

Td

t

|P(f)|2

f

data(t) p(t) x(t)

1/(2Td)

Sdata(f)

f 00

*

f1/(2Td)0

Sx(f)

Td0-Td

21


Requirement for Transmit Filter to Avoid ISI

Time samples of transmit filter (spaced Td apart) must be nonzero at only one sample time instant- Sinc function satisfies this criterion if we have no offset

in the sample times Intersymbol interference (ISI) occurs otherwise Example: look at result of convolving p(t) with 4

impulses- With zero sampling offset, x(kTd) correspond to

associated impulse areas

t

p(t)

t

Td

data(t)

Td

* t

x(t)

Td

22


Derive Nyquist Condition for Avoiding ISI (Step 1)

Consider multiplying p(t) by impulse train with period Td- Resulting signal must be a single impulse in order to avoid ISI (same argument as in previous slide)

t

p(t)

t

Td

data(t)

Td

* t

x(t)

Td

t

p(t)

t

Td

impulse train

Td

t

p(kTd)

Td

23


Derive Nyquist Condition for Avoiding ISI (Step 2)

In frequency domain, the Fourier transform of sampled p(t) must be flat to avoid ISI- We see this in two ways for above example

Fourier transform of an impulse is flat Convolution of P(f) with impulse train in frequency is flat

*

t

p(t)

t

Td

impulse train

Td

t

p(kTd)

Td

f

P(f)

f

impulse train

f

1/Td1/Td

1/Td

0

F{p(kTd)}

24


A More Practical Transmit Filter

Transition band in frequency set by “rolloff” factor,

Rolloff factor = 0: P(f) becomes a brick-wall filter Rolloff factor = 1: P(f) looks nearly like a triangle Rolloff factor = 0.5: shown above

t

p(t)

0 Td-Td

P(f)

0 1/Td-1/Tdf

2Td

1+α2Td

1-α

Raised-cosine filter is quite popular in many applications

25


Raised-Cosine Filter Satisfies Nyquist Condition

In time- p(kTd) = 0 for all k not equal to 0 In frequency- Fourier transform of p(kTd) is flat- Alternatively: Addition of shifted P(f) centered about k/Td

leads to flat Fourier transform (as shown above)

t

p(t)

0 Td-Td

P(f)

0 1/Td-1/Tdf

Nyquist ConditionObserved in Frequency

Nyquist ConditionObserved in Time

26


Spectral Efficiency With Raised-Cosine Filter

More efficient than when p(t) is a square pulse Less efficient than brick-wall lowpass- But implementation is much more practical

Note: Raised-cosine P(f) often “split” between transmitter and receiver

tt

Td

t

|P(f)|2

f

data(t) p(t) x(t)

1/(2Td)

Sdata(f)

f 00

*

f1/(2Td)0

Sx(f)

Td0-Td

27


Receiver Filter: ISI Versus Noise Performance

Conflicting requirements for receiver lowpass- Low bandwidth desirable to remove receiver noise and

to reject high frequency components of mixer output- High bandwidth desirable to minimize ISI at receiver

output


Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)


BasebandInput

f

f

It(t)

Qt(t)

Ir(t)

Qr(t)

ReceiverOutput

Raised-CosineFilter

28


Split Raised-Cosine Filter Between Transmitter/Receiver

We know that passing data through raised-cosine filter does not cause additional ISI to be produced- Implement P(f) as cascade of two filters corresponding

to square root of P(f)

Place one in transmitter, the other in receiver Use additional lowpass filtering in receiver to further

reduce high frequency noise and mixer products

f


ir(t)

qr(t)

it(t)

qt(t)


BasebandInput

f

f

It(t)

Qt(t)

Ir(t)

Qr(t)

f

f f

ReceiverOutput

Raised-CosineFilter

Raised-CosineFilter

AdditionalLowpassFiltering

29

M.H. Perrott

Multiple Access Techniques

30


The Issue of Multiple Access

Want to allow communication between many different users

Freespace spectrum is a shared resource- Must be partitioned between users

Can partition in either time, frequency, or through “orthogonal coding” (or nearly orthogonal coding) of data signals

31


Frequency-Division Multiple Access (FDMA)

Place users into different frequency channels Two different methods of dealing with transmit/receive of

a given user- Frequency-division duplexing- Time-division duplexing

f

Channel1

Channel2

ChannelN

32


Frequency-Division Duplexing

Separate frequency channels into transmit and receive bands

Allows simultaneous transmission and reception- Isolation of receiver from transmitter achieved with duplexer- Cannot communicate directly between users, only between

handsets and base station Advantage: isolates users Disadvantage: deplexer has high insertion loss (i.e.

attenuates signals passing through it)

Transmitter RXTX

f

Duplexer Antenna

RX

TX

Receiver TransmitBand

ReceiveBand

33


Time-Division Duplexing

Use any desired frequency channel for transmitter and receiver

Send transmit and receive signals at different times Allows communication directly between users (not

necessarily desirable) Advantage: switch has low insertion loss relative to

duplexer Disadvantage: receiver more sensitive to transmitted

signals from other users

TransmitterSwitch Antenna

RX

TX

Receiver

switchcontrol

34


Time-Division Multiple Access (TDMA)

Place users into different time slots- A given time slot repeats according to time frame period

Often combined with FDMA- Allows many users to occupy the same frequency

channel

t

Time Slot1

Time Slot2

Time SlotN

Time Slot1

Time SlotN

�Time Frame

35


Channel Partitioning Using (Nearly) “Orthogonal Coding”

Consider two correlation cases- Two independent random Bernoulli sequences

Result is a random Bernoulli sequence- Same Bernoulli sequence

Result is 1 or -1, depending on relative polarity

y(t)x(t)

c(t)

1-11

-11

-1

y(t)x(t)

c(t)

1-11

-11

-1

y(t)x(t)

c(t)

1-11

-11

-1

y(t)x(t)

c(t)

1-11

-11

-1

A

-A

B

-B

B

B B

B

Uncorrelated Signals Correlated Signals

36


Code-Division Multiple Access (CDMA)

Assign a unique code sequence to each transmitter Data values are encoded in transmitter output stream by

varying the polarity of the transmitter code sequence- Each pulse in data sequence has period Td

Individual pulses represent binary data values- Each pulse in code sequence has period Tc

Individual pulses are called “chips”

y1(t)x1(t)

PN1(t)

y2(t)x2(t)

PN2(t)

y(t)

SeparateTransmitters

Transmit SignalsCombine

in FreespaceTd

Tc

37


Receiver Selects Desired Transmitter Through Its Code

Receiver correlates its input with desired transmitter code- Data from desired transmitter restored- Data from other transmitter(s) remains randomized

y1(t)x1(t)

PN1(t)

y2(t)x2(t)

PN2(t)

x(t) y(t)

SeparateTransmitters

Transmit SignalsCombine

in Freespace

Receiver(Desired Channel = 1)

PN1(t)

Lowpassr(t)

38


Frequency Domain View of Chip Vs Data Sequences

Data and chip sequences operate on different time scales- Associated spectra have different width and height

tt

Tc

t

data(t) p(t) x(t)

Sdata(f)

f0

*1

-1Tc

1

-1

1

Sx(f)|P(f)|2

f1/Tc0

Tc

Td

1/Tdf1/Tc0

Tc

Td

1/Td

ttTd

t

data(t) p(t) x(t)

*1

-1

1

-1

1

Td

39


Frequency Domain View of CDMA

CDMA transmitters broaden data spectra by encoding it onto chip sequences

CDMA receiver correlates with desired transmitter code- Spectra of desired channel reverts to its original width- Spectra of undesired channel remains broad

Can be “mostly” filtered out by lowpass

r(t)

Sy1(f)

f1/Tc0

Tc

Sx(f)

f1/Tc0

Tc

Td

1/Td

Sx1(f)

f0

Td

1/Td

Sy2(f)

f1/Tc0

Tc

Sx2(f)

f0

Td

1/Td

y1(t)x1(t)

PN1(t)

Transmitter 1

y2(t)x2(t)

PN2(t)

Transmitter 2y(t)

PN1(t)

Lowpass

Sx1(f)

40

M.H. Perrott

Constant Envelope Modulation

41


The Issue of Power Efficiency

Power amp dominates power consumption for many wireless systems- Linear power amps more power consuming than nonlinear ones

Constant-envelope modulation allows nonlinear power amp- Lower power consumption possible

Baseband to RFModulation

Power Amp

TransmitterOutput

BasebandInput

Variable-Envelope Modulation Constant-Envelope Modulation

42


Simplified Implementation for Constant-Envelope

Constant-envelope modulation limited to phase and frequency modulation methods

Can achieve both phase and frequency modulation with ideal VCO- Use as model for analysis purposes- Note: phase modulation nearly impossible with practical VCO

Baseband to RF Modulation Power Amp

TransmitterOutput

BasebandInput

Constant-Envelope Modulation

TransmitFilter

43


Example Constellation Diagram for Phase Modulation

I/Q signals must always combine such that amplitude remains constant- Limits constellation points to a circle in I/Q plane- Draw decision boundaries about different phase regions


Q

DecisionBoundaries

000001

011

110111

100

101

010

44


Transitioning Between Constellation Points

Constant-envelope requirement forces transitions to allows occur along circle that constellation points sit on- I/Q filtering cannot be done independently!- Significantly impacts output spectrum


Q

DecisionBoundaries

000001

011

110111

100

101

010

45


Recall unmodulated VCO model

Relationship between sine wave output and instantaneous phase

Impact of modulation- Same as examined with VCO/PLL modeling, but now we

consider out(t) as sum of modulation and noise components

Modeling The Impact of VCO Phase Modulation

Φmod(t)

Φtn(t)

Phase/Frequencymodulation Signal

f

PhaseNoise

fo

Sout(f)Overall

phase noise

Φout2cos(2πfot+Φout(t))

out(t)f

0

SΦmod(f)

SpuriousNoise

46


Relationship Between Sine Wave Output and its Phase

Key relationship (note we have dropped the factor of 2)

Using a familiar trigonometric identity

Approximation given |tn(t)| << 1

47


Relationship Between Output and Phase Spectra

Approximation from previous slide

Autocorrelation (assume modulation signal independent of noise)

Output spectral density (Fourier transform of autocorrelation)

- Where * represents convolution and

48


Impact of Phase Modulation on the Output Spectrum

Spectrum of output is distorted compared to Smod(f) Spurs converted to phase noise

Φmod(t)

Φtn(t)


f

PhaseNoise

fo

Sout(f)Overall

phase noise


out(t)f

0

SΦmod(f)

SpuriousNoise

Φmod(t)

Φtn(t)


ffo

Sout(f)Overall

phase noise


out(t)f

0

SΦmod(f)

49


I/Q Model for Phase Modulation

Applying trigonometric identity

Can view as I/Q modulation- I/Q components are coupled and related nonlinearly to mod(t)

f0

SΦmod(f)

cos(2πf2t)

sin(2πf2t)

y(t)

-fo fo0

cos(Φmod(t))

sin(Φmod(t))

f0

Sa(f)

Sy(f)

it(t)

qt(t)

f0

Sb(f)f

Φmod(t)

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basics of wireless communication · transmitter output has an impulse at the carrier frequency for...

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