April 26, 2005 Week 14 1

EE521 Analog and Digital CommunicationsJames K. Beard, Ph. D.jkbeard@temple.eduTuesday, March 29, 2005http://astro.temple.edu/~jkbeard/

Week 14 2April 26, 2005

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Week 14 3April 26, 2005

Essentials Text: Bernard Sklar, Digital Communications, Second

Edition SystemView Office

E&A 349 MWF 10:30 AM to 11:30 AM Hours during Finals Week TBA

Term Projects Due TODAY, April 26 Final Exam

Tuesday, May 10, 6:00 PM to 8:00 PM Here in this classroom Posted within 3 days; you get your grade from Blackboard

Week 14 4April 26, 2005

Today’s Topics Term Project Review EE551 in the Fall Evaluation

Starts promptly at 9:00 PM Takes 15-20 minutes I will leave the room Need a student volunteer

Hand out and collect forms Deliver to office here at Ft. Washington Main Office

Week 14 5April 26, 2005

Term Project Generate a frequency sweep

Start frequency: End frequency:

Add noise to obtain a noise floor Digitize to 16 bits (later relaxed to 8 bits) Modulate using FSK, BPSK or QPSK Convert from baseband to a carrier frequency Model a fading channel with up to 12 paths. Demodulate and detect Analyze BER

Week 14 6April 26, 2005

Modulation Problems with FSK

16 bits requires 16 X 7+ kHz or 120+ kBPS It’s a lot of bandwidth I.F. forced higher than the 450 kHz first mentioned SystemView sample rate forced to high rates

The MFSK token in the Communications library performs quantization The bit stream isn’t available directly The BER token requires that the bit stream be generated

separately The MFSK input must be at the SystemView sample rate

Output will be at the inpuput sample rate Sampled data must be re-sampled or held

Week 14 7April 26, 2005

Getting the Bit Stream with MFSK Go from input to characters

Go from characters to bit stream

Scale and shift characters for MFSK modulator

Week 14 8April 26, 2005

Modulation Problems with MPSK No high-level token for MPSK

Use two or four bit symbolsUse Quad Mod, sine function or PM to get

PSKUse PSK Demod to get back characters

Gray code required to achieve theoretical BER

Character rate 8 to 16 times sample rateSame bandwidth problems as MFSK

Week 14 9April 26, 2005

Other Operations Convert from baseband to a carrier frequency

Not required for channel models Channel models take complex input Carrier frequency is a parameter

Modulation to carrier best demodulated to baseband for the channel model token Simplifies the SystemView sample rate issue Prepares the data for demodulation at the output Can be done by modulating to a complex I.F. at

baseband

Week 14 10April 26, 2005

The Channel Models

Data formats are complex in, complex out The channel models include phase

Multiple paths are summed coherently Result is a log normal, Rayleigh, or other fading

channel Model is meaningful for complex data

Generate I.F. centered at zero or use quadrature demodulator for input to channel modles

Week 14 11April 26, 2005

BER Measurement Inject noise before the channel model

Sample the noise output before summing You generate an accurate Eb/N0 easily there Use a variance in the noise generator that gives a base

(minimum) Eb/N0 Use an amplifier in dB with linked gain to control the

Eb/N0

Use of Global Parameter Links, the BER token, and multiple iterations for BER curves explained in Appendix A of the Comms library documentation

Week 14 12April 26, 2005

Coding/Decoding Not specified in the term project scope Omitting coding

Avoided timing and synchronization issues on the decoder

Left us with basically a modulation and channel modeling project

Coding Offers an insight on the effect of FEC on the BER

curve Isn’t the whole picture without interleaving Context will be part of next Fall’s EE551

April 26, 2005 Week 14 13

EE521 Analog and Digital CommunicationsReview Topicsjkbeard@temple.edu

Week 14 14April 26, 2005

Complex Signals Base property is distinction of signal at negative

frequencies from signal at positive frequencies Use in communications systems

Signal generation steps Digital character generation Character generation Complex FSK, MPSK, GMSK, etc. generation Real signal synthesis at I.F. for upconvert

Demodulation steps Complex demodulation used for coherent pilot PLL Complex demodulation of PSK, MSK, etc.

Week 14 15April 26, 2005

Principles of Complex Signals

Multiplication

Multiplication between a complex number and the complex conjugate of another

1 2 1 1 2 2

1 2 1 2 1 2 2 1

z z x j y x j y

x x y y j x y x y

*1 2 1 1 2 2

1 2 1 2 1 2 2 1

1 2 1 2

z z x j y x j y

x x y y j x y x y

z z j z z

Week 14 16April 26, 2005

Power and Energy of Complex Signals Power

Energy

2

*

2

1lim

T

x TT

P x t x t dtT

*xE x t x t dt

Week 14 17April 26, 2005

Sampling and Aliasing

Sampling a tone at ft at a rate of fs results in aliasing to frequencies fk

The aliasing order k is any integer – zero, positive or negative

The base ambiguity region of a sampled signal on the next slide

k t sf f k f

Week 14 18April 26, 2005

Ambiguity Range for Complex Signals

02sf

2sf 4

sf4sf

Week 14 19April 26, 2005

Sampling a Real Signal

This is what we must do with a real R.F. signal

The negative frequency image is always there even with a quadrature demodulator (why?)

Study of the figure revealsNyquist’s sampling limitWhy we want to alias to ± fs/4

Week 14 20April 26, 2005

Three Types of Error Correcting Codes Convolutional codes

Most often used Provide spectrum usage within 2 dB of the Shannon limit with

Viterbi decoding Block codes

Good for simple codes such as Hamming codes Simple to understand and use Provide a basis for understanding other codes

Recursive codes Used in Turbo Codes; achieve almost the Shannon limit May be the codes of the future Usage is complicated because output does not terminated

Week 14 21April 26, 2005

Decoding Simple Block Codes

Works with correct-one, detect-two codes Find the syndrome for single-bit errors Match with the syndrome of the received

message Invert that bit in the received message to form

the corrected message Check the syndrome for zero Invert the coding to find the decoded message

April 26, 2005 Week 14 22

EE551Signal Processing and Communication TheoryFall, 2005CRN 088905Thursday evenings in Ft. WashingtonJames K Beard

Week 14 23April 26, 2005

EE551 Format and Topics Base topics from Sklar

Review of EE521 topics Ch. 7 and Ch. 8, Channel Coding: Part 2, Part 3 Ch. 9, Modulation and Coding Trade-Offs Ch. 5, Communications Link Analysis Ch. 10, Synchronization Ch. 11, Multiplexing and Multiple Access Ch. 12, Spread-Spectrum Techniques Ch. 14, Encryption and Decryption Ch. 15, Fading Channels

Others TBD Term Project in SystemView Seminar format

Round-table on specified topics every week You will present your term project

Week 14 24April 26, 2005

FINAL IS MAY 10FINAL IS MAY 10

Week 14 25April 26, 2005

Your Grade for EE521

Based on Quizzes Term project Final exam

Do well on the Final Examination First exam was fair Second exam was good Nobody helped themselves with the Quiz 2 Backup A good Final Exam grade is paramount

Week 14 26April 26, 2005

Final Exam Procedure

Show up here at 6:00 PM SHARP on May 10 Your exam will be waiting Rules

No talking Questions

Submitted to me on paper Responses on whiteboard for all

I will pick up exams promptly at 8:00 PM Check off your problems – don’t miss any If you get done early, check and re-check your work