EE456 Digital Communications Professor Ha Nguyen September 2015 - - PowerPoint PPT Presentation

SLIDE 1

Chapter 6: Baseband Data Transmission

EE456 – Digital Communications

Professor Ha Nguyen September 2015

EE456 – Digital Communications 1

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Chapter 6: Baseband Data Transmission

Introduction to Baseband Data Transmission

Bits are mapped into two voltage levels for direct transmission without any frequency translation. Various baseband signaling techniques (line codes) were developed to satisfy typical criteria:

1

Signal interference and noise immunity

2

Signal spectrum

3

Signal synchronization capability

4

Error detection capability

5

Cost and complexity of transmitter and receiver implementations

Four baseband signaling schemes to be considered: nonreturn-to-zero-level (NRZ-L), return-to-zero (RZ), bi-phase-level or Manchester, and delay modulation or Miller.

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Chapter 6: Baseband Data Transmission

Baseband Signaling Schemes

1 1 1 1 1 a Binary Dat V V V −

b

T Time Clock Code NRZ (a) L

• NRZ

(b)

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Chapter 6: Baseband Data Transmission

V V V − V Code RZ (c) L

• RZ

(d) Phase

• Bi

(e)

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Chapter 6: Baseband Data Transmission

V V − V V V − L

• Phase
• Bi

(f) Code Miller (g) L

• Miller

(h)

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Chapter 6: Baseband Data Transmission

Miller Code

Has at least one transition every two bit interval and there is never more than two transitions every two bit interval. Bit “1” is encoded by a transition in the middle of the bit interval. Depending on the previous bit this transition may be either upward or downward. Bit “0” is encoded by a transition at the beginning of the bit interval if the previous bit is “0”. If the previous bit is “1”, then there is no transition. V V − V V V − L

• Phase
• Bi

(f) Code Miller (g) L

• Miller

(h)

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Chapter 6: Baseband Data Transmission

NRZ-L Code

✁ ✂ ✄

• )

(

1 t

s

b

T V −

☎ ✆ ✝ ✞ ✟ ☎

• )

(

2 t

s V

b

T

☎ ✟ ✠ ✝ ☎ ✡

) (

1 t

φ

b

T 1

b

T

☛ ☞ ✌

) (

1 t

φ ) (

1 t

s ) (

2 t

s

✍ ✎ ✏

L

• NRZ

E

L

• NRZ

E −

T T

1 Choose Choose

✑

⇐

P [error]NRZ-L = Q

• 2ENRZ-L/N0
• .

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Chapter 6: Baseband Data Transmission

RZ-L Code

✒ ✓ ✔

V −

✕

V

b

T ) (

2 t

s

✖ ✗ ✘ ✙ ✖

) (

1 t

s

✕

V −

b

T

✖ ✚ ✙ ✛ ✗✖

2

b

T

✜ ✢ ✣

) (

1 t

φ

✤

b

T

b

T 1 −

✤

b

T 1

b

T

b

T 1 − ) (

2 t

φ 2

b

T

) (

1 t

φ ) (

1 t

s ) (

2 t

s ) (

2 t

φ

L

• RZ

E

L

• RZ

E

T

1 Choose

T

Choose

✥ ✦ ✧

P [error]RZ-L = Q

• ERZ-L/N0
• .

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Chapter 6: Baseband Data Transmission

Bi-Phase-Level (Biφ-L) Code

★ ✩ ✪

) (

1 t

s

✫

V −

b

T

✬ ✭ ✮ ✯ ✰ ✬

V V −

✫

V

b

T ) (

2 t

s

✬ ✰ ✱ ✮ ✬ ✲

b

T 1

b

T

b

T 1 − ) (

1 t

φ

✳ ✴ ✵

) (

1 t

φ ) (

1 t

s ) (

2 t

s

✶ ✷ ✸

T T

1 Choose Choose

✹

⇐

L

• Biφ

E

L

• Biφ

E −

P [error]Biφ-L = Q

• 2EBiφ-L/N0
• .

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Chapter 6: Baseband Data Transmission

Miller-Level (M-L)

V −

✺

V

b

T ) (

2 t

s

✻ ✼ ✽ ✾ ✻ ✺

) (

1 t

s

b

T

✻ ✿ ✾ ❀ ✼ ✻

V V −

✺

) (

4 t

s

b

T

✺

) (

3 t

s V −

b

T

✻ ✼ ✽ ✾ ✻ ✻ ✿ ✾ ❀ ✼ ✻

V

❁ ❂ ❃ ❄

) (

1 t

φ

b

T 1

b

T

b

T 1 −

❄

) (

2 t

φ

b

T

b

T 1

❅ ❆ ❇

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Chapter 6: Baseband Data Transmission

Applying the principle of minimum-distance rule in each bit (or symbol) duration is sensible, but not necessarily optimum for Miller-L signalling!

) (

1 t

φ ) (

1 t

s ) (

2 t

s ) (

2 t

φ ) (

3 t

s ) (

4 t

s

❈ ❉ ❊ ❊ ❋

• ❍

■ ❏ ❑ ▲ ▲ ▼ ◆ ❖ P ◗ ❘ ❙ ❙ ❚ ❯ ❱ ❲ ❳ ❨ ❩ ❩ ❬ ❭ ❪ ❫ ❴ ❵ ❛

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Chapter 6: Baseband Data Transmission

Performance of the symbol-by-symbol minimum-distance receiver for Miller-L

) (

1 t

φ ) (

1 t

s ) (

2 t

s ) (

2 t

φ ) (

3 t

s ) (

4 t

s

L

• M

E

1

r

2

r

1

ˆ r

2

ˆ r

L

• M

5 . 0 E 45

P [error]M-L = 1 −

• 1 − Q
• EM-L/N0

2 = 2Q

• EM-L/N0
• − Q2

EM-L/N0

• ≈ 2Q
• EM-L/N0
• EE456 – Digital Communications

12

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Chapter 6: Baseband Data Transmission

Performance Comparison

2 4 6 8 10 12 14 10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

Eb/N0 (dB) P[error] NRZ−L and Biφ−L RZ−L M−L ENRZ-L = ERZ-L = EBiφ-L = EM-L = V 2Tb ≡ Eb (joules/bit). P [error]NRZ-L = P [error]Biφ-L = Q  

• 2Eb

N0   , P [error]RZ-L = Q  

• Eb

N0   , P [error]M-L ≈ 2Q  

• Eb

N0   . EE456 – Digital Communications 13

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Chapter 6: Baseband Data Transmission

Spectrum

Let P2 = P and P1 = 1 − P . SRZ-L(f) E = P sin(πfTb/2) πfTb/2 2  (1 − P ) + P 1 Tb

∞

• n=−∞

δ

• f − n

Tb   . SNRZ-L(f) E = 1 Tb (1 − 2P )2δ(f) + 4P (1 − P )sin2(πfTb) (πfTb)2 . SBiφ-L(f) E = 1 Tb (1 − 2P )2

∞

• n=−∞

n=0

2 nπ 2 δ

• f − n

Tb

• + 4P (1 − P )sin4(πfTb/2)

(πfTb/2)2 . SM-L(f) E = 1 2θ2(17 + 8 cos 8θ) (23 − 2 cos θ − 22 cos 2θ − 12 cos 3θ + 5 cos 4θ +12 cos 5θ + 2 cos 6θ − 8 cos 7θ + 2 cos 8θ), where θ = πfTb, P = 0.5.

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Chapter 6: Baseband Data Transmission

0.5 1 1.5 2 0.5 1 1.5 2 2.5 Normalized frequency, fTb Normalized PSD, Ps(f)/E NRZ-L Impulses at f = 0 and f = 1/Tb Miller-L RZ-L Biφ-L

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Chapter 6: Baseband Data Transmission

Optimum Sequence Demodulation for Miller Signaling

The symbol-by-symbol (i.e., bit-by-bit) minimum-distance rule is not optimum for Miller modulation since it does not exploit memory in the scheme. To see this, consider the following example. Assuming that the four Miller signals have unit energy and the projections of the received signals on to φ1(t) and φ2(t) are

• r(1)

1

= −0.2, r(1)

2

= −0.4

• ,
• r(2)

1

= +0.2, r(2)

2

= −0.8

• ,
• r(3)

1

= −0.61, r(3)

2

= +0.5

• ,
• r(4)

1

= −1.1, r(4)

2

= +0.1

• .

Transmitted signal Distance squared 0 → Tb Tb → 2Tb 2Tb → 3Tb 3Tb → 4Tb s1(t) 1.6 1.28 2.8421 4.42 s2(t) 2.0 3.28 0.6221 2.02 s3(t) 0.8 2.08 0.4021 0.02 s4(t) 0.4 0.08 2.6221 2.42 The decision by the symbol-by-symbol minimum-distance rule would be {s4(t), s4(t), s3(t), s3(t)}. However, this is not a valid transmitted sequence! The optimum receiver for Miller modulation is the sequence minimum-distance rule, which works as follows. Consider a sequence of n bits. Then there are 2n possible transmit sequences. The receiver computes the distances (or squared distances) from the received waveform to all 2n possible transmitted waveforms (over 0 ≤ t ≤ nTb) and decide on the transmitted sequence based on the minimum distance!

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Chapter 6: Baseband Data Transmission 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 1 1.5 2 2.5 3 3.5 4 t/Tb While the concept of sequence min-distance is very simple. The challenge is the computational complexity in finding the closest sequence to the received signal out of 2n possible sequences - Find for yourself what is this number if n is merely 100 bits! Thanks to Dr. Andrew Viterbi, there is a clever way, known as the Viterbi Algorithm, that can find the closest sequence very quickly!!! For those interested, please read the textbook. EE456 – Digital Communications 17

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Chapter 6: Baseband Data Transmission

Performance Comparison of Symbol-by-Symbol vs. Sequence Demodulation

2 4 6 8 10 12 14 10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 Eb/N0 (dB) P[error] Symbol−by−symbol demodulation (analytical result) Sequence demodulation (simulation result)

2 dB gain at the error probability of 10−2 and 0.5 dB at 10−6.

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