1. ارتباطات داده (883-40) انتقال باندپایه
دانشکده مهندسی کامپیوتر
ارتباطات داده (883-40) انتقال باندپایه
نیمسال دوّم 93-92
افشین همّت یار

2. Baseband Pulse Transmission
Introduction
Matched Filter
Error Rate Due to Noise
Inter-Symbol Interference
Nyquist’s Criterion of Distortionless Baseband Binary Transmission
Correlative-Level Coding
Baseband M-ary PAM Transmission
Digital Subscriber Lines
Optimum Linear Receiver
Adaptive Equalization

3. Introduction significant low-frequency content.
Digital data: broad spectrum with a
significant low-frequency content.
Baseband transmission of digital data requires low- pass
channel with a large enough bandwidth
Typically the channel is despersive. Its frequency
response deviates from that of an ideal low-pass filter.
Inter-Symbol Interference: effect of adjacent pulses on
each other
ISI >> major source of bit errors
Pulse shaping >> reducing ISI
Channel noise >> another source of bit errors
Detection of a pulse signal of known waveform immersed
in additive white noise >> matched filter

4. Matched Filter (1) Filter input: Filter output:
Linear receiver:
Filter input:
Filter output:
Peak pulse signal to noise ratio:

5. Matched Filter (2)
Filter output Sampled output PSD of noise Average power of output noise Peak pulse signal to noise ratio

6. Matched Filter (3)
Problem: for a given G(f), which H(f) makes the η maximum? Schwarz’s inequality : for two complex functions φ1(x) and φ2(x) in the real x, satisfying the conditions and we may write equality holds if, and only if

7. Matched Filter (3)
for our problem:   

8. Matched Filter (4)
Property: The peak pulse signal-to-noise ratio of a matched filter depends only on the ratio of the signal energy to the power spectral density of the white noise at the filter input. 
Independent of g(t) waveform

9. Matched Filter (5)

10. Error Due to Noise (1) Two possible kinds of error:
Error of the first kind: Symbol 1 is chosen
when a 0 was actually transmitted
Error of the second kind: Symbol 0 is chosen
when a 1 was actually transmitted.

11. Error Due to Noise (2)

12. Error Due to Noise (3)
Complementary Error Function:
Upper band:

13. Error Due to Noise (4)   
Transmitted signal energy per bit: 

14. Inter-symbol Interference (1)
{bk}: Incoming binary sequence consists of symbols 1 and 0, each with duration Tb
{ak}: Sequence of PAM short pulses 

15. Inter-symbol Interference (2)
ISI Noise

16. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (1)
Normalization
Ignoring noise

17. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (2)
The frequency function P(f) eliminates intersymbol interference for samples taken at intervals Tb provided that it satisfies:
Note: P(f) refers to the overall system, incorporating the transmit filter, the channel, and the receive filter.
Ideal Nyquist Channel:

18. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (3)
P(f) has abrupt transitions which is physically unrealizable.
p(t) has low rate of decay and there is practically no margin
for timing error.

19. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (4)

22. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (5)
Raised Cosine Spectrum:

23. Nyquist’s Criterion for Distortionless Baseband Binary Transmission (6)
Full-Cosine Rolloff (α=1):
Useful in timing extraction form the received signal
Required double the ideal Nyquist channel
α= (minimum)
α=1

24. Correlative-Level Coding (1)
Duobinary
Signaling
Scheme
Decision Feedback:

25. Correlative-Level Coding (2)
Precoding (for Avoiding Error Propagation):

26. Correlative-Level Coding (3)
Example:
Binary Sequence {bk}
Precoded sequence {dk}
Two-level Sequence {ak}
Duobinary coder output {ck}
Binary sequence
obtained by decision rule

27. Correlative-Level Coding (4)
Modified Duobinary Signaling

28. Correlative-Level Coding (5)
Generalized form of Correlative-level Coding
(Partial Response Signaling) w4 w3 w2 w1 w0 N
Type of class
Duobinary 1 2 I 3 II -1 4
III
Modified Duobinary IV 5 V

29. Correlative-Level Coding (6)
Useful Characteristics:
Binary data transmission over a physical baseband
channel can be accomplished at a rate close to Nyquist
rate, using realizable filters with gradual cutoff characteristics.
Different spectral shapes can be produced, appropriate for the
application at hand.
Price: A larger signal-to-noise ratio is required to yield the same average probability of symbol error, because of an increase in the number of signal levels used.

30. Baseband M-ary PAM Transmission

31. Digital Subscriber Lines (1)
Twisted pairs for High data rate, Full duplex, Digital transmission capability
Time
Duplex Compression
Operation Multiplexing
Echo
Cancellation

32. Digital Subscriber Lines (2)
Simplified hybrid transformer
Squared magnitude response of twisted pairs:

33. Digital Subscriber Lines (3)

34. Digital Subscriber Lines (4)
Line Codes for Digital Subscriber Lines
The power spectral density of the transmitted signal should be zero at zero frequency, since no DC transmission through a hybrid transformer is possible.
The power spectral density of the transmitted signal should be low at high frequencies for the following reasons:
Transmission attenuation in a twisted pair is most severe at high frequencies.
Crosstalk between adjacent twisted pair increases dramatically at high frequencies because of increased capacitive coupling.
Manchester (large bandwidth  NEXT & ISI)
Modified Duobinary (moderate bandwidth, min ISI)
Bipolar(AMI) (slightly inferior to M.D.)
2B1Q(4PAM) (greatest baud reduction, best NEXT & ISI)

35. Digital Subscriber Lines (5)
Line Codes for Digital Subscriber Lines
Using the 2B1Q as the line code and VLSI implementation of a transceiver that incorporates adaptive equalizers and echo cancellers, it is possible to achieve a bit error rate of 10-7 with 12dB noise margin, when 1 percent worst-case NEXT is present, operating full duplex at 160 Kbps in the vast majority of twisted-pair is an accepted performance criterion for digital subscriber lines.
Noise margin is the amount of receiver noise (including
uncancelled echo) that can be tolerated without exceeding the 10-7 error rate.

36. Digital Subscriber Lines (6)
Asymmetric Digital Subscriber Lines
Data transmission downstream (toward the subscriber) at bit rates of up to 9 Mbps
Data transmission upstream (away form the subscriber) at bit rates of up to 1 Mbps
Plain Old Telephone Service (POTS)

37. Optimum Linear Receiver (1)
Channel noise acting alone  Matched filter
Intersymbol interference acting alone  Pulse-shaping filter
In real life, channel noise and ISI act together:
Zero forcing equalizer  ISI forced to zero, ignoring the effect of the channel noise  noise enhancement
Mean-square error criterion  reducing the effects of both channel noise and ISI
Performs as well as, or often better than zero-forcing.

38. Optimum Linear Receiver (2)
Mean-square error criterion

39. Optimum Linear Receiver (3)
( 1)

40. Optimum Linear Receiver (4)
( 2)
( 3) (4) (5)

41. Optimum Linear Receiver (5)
( 6)
1 … 
Minimum J 
 

42. Optimum Linear Receiver (6)
Power spectral density of the sequence [q(kTb)]:
C(f) of the optimum linear receiver is periodic with period 1/Tb.
Optimum linear receiver is cascade of two basic components:
A matched filter whose impulse response is q(-t),
where q(t) = g(t)*h(t).
A Transversal (tapped-delay-line) equalizer whose
frequency response is the inverse of the periodic
function Sq(f)+ (N0/2).
Esponse is the inverse of the periodic function Sq(f)+(N0/2).

43. Optimum Linear Receiver (7)
Cascade connection of matched filter and transversal equalizer

44. Adaptive Equalization
Esponse is the inverse of the periodic function Sq(f)+(N0/2).

45. Eye Diagram (1)
Esponse is the inverse of the periodic function Sq(f)+(N0/2).

46. Eye Diagram (2)
Esponse is the inverse of the periodic function Sq(f)+(N0/2).