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EE 433EE 433Wireless and Cellular CommunicationsWireless and Cellular Communications

Course IntroductionCourse IntroductionFall Fall 20152015

Dr. C. R. AndersonDr. C. R. Anderson

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Homework/Absence PoliciesHomework/Absence Policies

Assignments approximately weekly, as posted on the EE433 website.

We have 5-6 “Labs” scheduled throughout the semester. Labs will be graded using a new “Interview Grading” technique pioneered at CU Boulder.

Homework is due in class. Late homework will only be accepted for a valid excuse. If you know ahead of time that you are going to be out for an excused absence, you must coordinate with me prior to the missed class.

Homework Grading: Organized, legible, self contained, and in the prescribed format. Solutions will be graded in class and collected by the instructor.

Travel: Travel is an extremely vital and important component of Dr. Anderson’s research program, and this semester is no exception. Currently, plans are on the books to remote-teach EE433 from Sept. 21-30; other instructors may fill in other travel dates as necessary.

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Notes on My Teaching StyleNotes on My Teaching Style

I intentionally present the material in a slightly different manner than the textbook. The reason is that if I teach exactly like the book, you gain nothing from reading the book.

I believe in emphasizing the fundamentals and understanding the material over simply memorizing equations. As a result, you may find a quiz or two with (gasp!) no numbers or (double gasp!) an essay question.

Test and quiz grading: I’m fairly lenient if you can demonstrate that you understand the underlying concept. I’m also a stickler for things like significant figures, units, etc. because accuracy and precision are primary aspects of all forms of engineering.

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Sampling TheoremSampling Theorem

A/D Conversion Process

1. Bandlimit the signal to a maximum bandwidth of interest.

2. Sample the signal with (Discrete Time, Continuous Amplitude)

3. Quantize the signal into one of amplitudes.

4. Represent (code) the amplitudes as an N-bit binary word.

Sampling Theorem

If a signal is bandlimited such that then

is completely determined by its samples ,

provided that the sampling frequency .

( ) 0S f for f B= ≥

( )s t ( )0s nT

2s

f B≥

2s

f B≥

2N

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Communication signals can be represented in a couple

of different ways:

1. Quadrature Notation

where x(t) and y(t) are real-valued baseband signals called the in-phase and quadrature components of s(t)

2. Magnitude and Phase

where is the magnitude of s(t),

and is the phase of s(t).

Complex Representation of SignalsComplex Representation of Signals

( ) ( )s t x t f t y t f tc c( ) ( ) cos ( ) sin= −2 2π π

( )( )s t a t f t tc( ) ( ) cos= +2π θ

a t x t y t( ) ( ) ( )= +2 2

θ( ) tan( )

( )t

y t

x t=

−1

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Basics of ModulationBasics of Modulation

cos(2 )c

A f tπ φ+

A sinusoidal signal can be modulated in three different ways…

Amplitude FrequencyPhase

Angle Modulation

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Amplitude modulation (AM)Amplitude modulation (AM)

Amplitude modulated signal sAM

Carrier signal vc

(carrier frequency fc = 5-kHz)

××××

Information signal m(t)

The AM signal (sAM) is the product of the carrier and the information signal

( ) ( )1 cos 2am c c

s A m t f tπ= +

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Frequency ModulationFrequency Modulation

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10-3

-1

-0.5

0

0.5

1

Time (msec)

Vo

ltag

e (

V)

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10-3

-1

-0.5

0

0.5

1

Time (msec)

Vo

ltag

e (

V)

input signal (±1-V, 1-kHz square wave)

FM signal (fc = 10-kHz, fd = 4-kHz)

f = 10-kHz

f = 14-kHz

f = 6-kHz

f = 14-kHz

f = 6-kHz

f = 14-kHz

( ) ( )( )FM cos 2 ( )c c fs t A f k m t tπ= +

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Frequency Shift KeyingFrequency Shift Keying

( ) ( )( )FSK cos 2 ( )c c f ms t A f m s t tπ= +

( ) ( )FSK cos 2c is t A f tπ=

Or another way of thinking of it:

01 11 00 11 01 00 11

Example of 4-FSK waveform in time domain

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Spectrum and Performance of FSKSpectrum and Performance of FSK

Spectrum of 4-FSK Signal

0

be

EP Q

N

=

2-FSK Coherent Demod:

2-FSK Incoherent Demod:

M-FSK Incoherent Demod:

M-FSK Coherent Demod:

021

2

bE

N

eP e

−

=

021

2

SE

N

e

MP e

−−≈

0

Se

EP M Q

N

= ⋅

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Performance of FSKPerformance of FSK

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Phase Shift KeyingPhase Shift Keying

( ) ( )PSK cos 2c c is t A f tπ θ= +

0 1 1 0 1 0 1

Example of 2-PSK waveform in the time domain

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Spectrum and Performance of PSKSpectrum and Performance of PSK

Bandwidth: 2b

RBW

N=

Prob. Error BPSK:0

2 b

e

EP Q

N

=

Prob. Error MPSK:0

22 sinb

e

NEP Q

N M

π ≈

2 bR

N

Spectrum of PSK Signal

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Performance of PSKPerformance of PSK

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Superheterodyne ReceiverSuperheterodyne Receiver

RF Section IF Section Baseband

RF – Radio FrequencyIF – Intermediate FrequencyBaseband – Original Message

Definition: Heterodyning is the process of translating a signal from a high-frequency carrier to a lower intermediate frequency.

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Image Frequency ProblemImage Frequency Problem

LowSide

Injection

HighSide

Injection

In both cases we have TWO frequencies that are downconverted to the EXACT SAME IF frequency.