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

Chapter 6: Baseband Data Transmission EE456 – Digital Communications Professor Ha Nguyen September 2015 EE456 – Digital Communications 1

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. EE456 – Digital Communications 2

Chapter 6: Baseband Data Transmission Baseband Signaling Schemes Binary Dat a 0 0 0 1 0 1 1 1 1 Clock T b V (a) NRZ Code 0 Time V (b) NRZ - L 0 − V EE456 – Digital Communications 3

Chapter 6: Baseband Data Transmission V (c) RZ Code 0 V (d) RZ - L 0 − V V (e) Bi - Phase 0 EE456 – Digital Communications 4

Chapter 6: Baseband Data Transmission V (f) Bi - Phase - L 0 − V V (g) Miller Code 0 V (h) Miller - L 0 − V EE456 – Digital Communications 5

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 (f) Bi - Phase - L 0 − V V (g) Miller Code 0 V (h) Miller - L 0 − V EE456 – Digital Communications 6

Chapter 6: Baseband Data Transmission NRZ-L Code s 1 t s 2 t ( ) ( ) φ 1 t ( ) ☎ ✆ ✝ ✞ ✟ ☎ ☎ ✟ ✠ ✝ ☎ V T T 1 b b T 0 � 0 � b − T V 0 ✡ b ✁ ✂ ✄ ☛ ☞ ✌ ⇐ Choose 0 Choose 1 T T ✑ s 1 t s 2 t ( ) ( ) φ 1 t ( ) − E E 0 NRZ - L NRZ - L ✍ ✎ ✏ �� � P [ error ] NRZ-L = Q 2 E NRZ-L /N 0 . EE456 – Digital Communications 7

Chapter 6: Baseband Data Transmission RZ-L Code φ 1 t φ 2 t ( ) ( ) s 2 t s 1 t ( ) ( ) T 1 b V ✖ ✚ ✙ ✛ ✗✖ ✖ ✗ ✘ ✙ ✖ T T T 2 b b b T T T 2 0 ✤ 0 b b ✤ b 0 ✕ 0 ✕ − − T T 1 1 b b − V − V ✜ ✢ ✣ ✒ ✓ ✔ φ 2 t ( ) E s 2 t ( ) RZ - L Choose 0 �� � T P [ error ] RZ-L = Q E RZ-L /N 0 . Choose 1 T s 1 t ( ) 0 φ 1 t ( ) E RZ - L ✥ ✦ ✧ EE456 – Digital Communications 8

Chapter 6: Baseband Data Transmission Bi-Phase-Level (Bi φ -L) Code s 1 t s 2 t φ 1 t ( ) ( ) ( ) ✬ ✭ ✮ ✯ ✰ ✬ ✬ ✰ ✱ ✮ ✬ V V T 1 b T T b b 0 T 0 ✫ ✫ 0 ✲ b − V − V − T 1 b ★ ✩ ✪ ✳ ✴ ✵ ⇐ Choose 0 Choose 1 T T ✹ s 1 t s 2 t ( ) ( ) φ 1 t ( ) − E E 0 Bi φ Bi φ - L - L ✶ ✷ ✸ �� � P [ error ] Bi φ -L = Q 2 E Bi φ -L /N 0 . EE456 – Digital Communications 9

Chapter 6: Baseband Data Transmission Miller-Level (M-L) s 1 t s 2 t ( ) ( ) ✻ ✿ ✾ ❀ ✼ ✻ ✻ ✼ ✽ ✾ ✻ V V T b T 0 0 ✺ ✺ b − V s 3 t s 4 t ( ) ( ) ✻ ✿ ✾ ❀ ✼ ✻ ✻ ✼ ✽ ✾ ✻ V T b 0 ✺ 0 T ✺ b − V − V ❁ ❂ ❃ φ φ 2 t 1 t ( ) ( ) T T 1 1 b b T b 0 0 T ❄ ❄ b − T 1 b ❅ ❆ ❇ EE456 – Digital Communications 10

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! ❈ ❉ ❊ ❊ ❋ ● ❍ ■ φ 2 t ( ) s 2 t ( ) s 3 t s 1 t ❲ ( ) ( ) ❫ ❱ ❪ ❯ ❭ ❚ ❬ φ 1 t ❙ ❩ ( ) 0 ❙ ❩ ❘ ❨ ◗ ❳ s 4 t ( ) ❏ ❑ ▲ ▲ ▼ ◆ ❖ P ❴ ❵ ❛ EE456 – Digital Communications 11

Chapter 6: Baseband Data Transmission Performance of the symbol-by-symbol minimum-distance receiver for Miller-L φ 2 t r ( ) 2 s 2 t r ( ) ˆ 2 0 E . 5 M - L s 1 t s 3 t ( ) ( ) φ 1 t 0 ( ) 45 0 r E 1 M - L s 4 t ( ) r ˆ 1 �� 2 � �� P [ error ] M-L = 1 − 1 − Q E M-L /N 0 �� � − Q 2 �� � �� � = 2 Q E M-L /N 0 E M-L /N 0 ≈ 2 Q E M-L /N 0 EE456 – Digital Communications 12

Chapter 6: Baseband Data Transmission Performance Comparison −1 10 −2 10 M−L RZ−L −3 10 P [error] NRZ−L and Bi φ −L −4 10 −5 10 −6 10 0 2 4 6 8 10 12 14 E b / N 0 (dB) E NRZ-L = E RZ-L = E Bi φ -L = E M-L = V 2 Tb ≡ Eb (joules/bit) .  �  � 2 Eb � �  , P [ error ] NRZ-L = P [ error ] Bi φ -L = Q  N 0     � � � Eb � � � Eb �  , P [ error ] M-L ≈ 2 Q �  . P [ error ] RZ-L = Q   N 0 N 0 EE456 – Digital Communications 13

Chapter 6: Baseband Data Transmission Spectrum Let P 2 = P and P 1 = 1 − P .  � � 2 ∞ S RZ-L ( f ) � sin( πfT b / 2)  (1 − P ) + P 1 � f − n �  . = P δ E πfT b / 2 T b T b n = −∞ (1 − 2 P ) 2 δ ( f ) + 4 P (1 − P )sin 2 ( πfT b ) S NRZ-L ( f ) 1 = . ( πfT b ) 2 E T b � 2 � 2 + 4 P (1 − P )sin 4 ( πfT b / 2) S Bi φ -L ( f ) ∞ 1 � f − n � (1 − 2 P ) 2 � = δ . ( πfT b / 2) 2 E T b nπ T b n = −∞ n � =0 S M-L ( f ) 1 = 2 θ 2 (17 + 8 cos 8 θ ) (23 − 2 cos θ − 22 cos 2 θ − 12 cos 3 θ + 5 cos 4 θ E +12 cos 5 θ + 2 cos 6 θ − 8 cos 7 θ + 2 cos 8 θ ) , where θ = πfT b , P = 0 . 5 . EE456 – Digital Communications 14

Chapter 6: Baseband Data Transmission 2.5 Miller-L 2 Normalized PSD, P s ( f ) /E 1.5 Impulses at f = 0 and f = 1 /T b NRZ-L 1 Bi φ -L 0.5 RZ-L 0 0 0.5 1 1.5 2 Normalized frequency, fT b EE456 – Digital Communications 15

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 φ 1 ( t ) and φ 2 ( t ) are � r (1) = − 0 . 2 , r (1) � � r (2) = +0 . 2 , r (2) � = − 0 . 4 , = − 0 . 8 , 1 2 1 2 � � � � r (3) = − 0 . 61 , r (3) r (4) = − 1 . 1 , r (4) = +0 . 5 , = +0 . 1 . 1 2 1 2 Transmitted signal Distance squared 0 → T b T b → 2 T b 2 T b → 3 T b 3 T b → 4 T b s 1 ( t ) 1.6 1.28 2.8421 4.42 s 2 ( t ) 2.0 3.28 0.6221 2.02 s 3 ( t ) 0.8 2.08 0.4021 0.02 s 4 ( t ) 0.4 0.08 2.6221 2.42 The decision by the symbol-by-symbol minimum-distance rule would be { s 4 ( t ) , s 4 ( t ) , s 3 ( t ) , s 3 ( 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 2 n possible transmit sequences. The receiver computes the distances (or squared distances) from the received waveform to all 2 n possible transmitted waveforms (over 0 ≤ t ≤ nT b ) and decide on the transmitted sequence based on the minimum distance! EE456 – Digital Communications 16

Chapter 6: Baseband Data Transmission 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 t / T b 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 2 n 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

Chapter 6: Baseband Data Transmission Performance Comparison of Symbol-by-Symbol vs. Sequence Demodulation 0 10 −1 10 −2 10 P [error] −3 10 −4 10 −5 10 Symbol−by−symbol demodulation (analytical result) Sequence demodulation (simulation result) −6 10 0 2 4 6 8 10 12 14 E b / N 0 (dB) 2 dB gain at the error probability of 10 − 2 and 0.5 dB at 10 − 6 . EE456 – Digital Communications 18