1. Baseband Demodulation/ Detection
CHAPTER 3
Baseband
Demodulation/ Detection
School of Computer and Communication Engineering, Amir Razif B. Jamil Abdullah
EKT 431: Digital Communications

2. Last time we talked about:
Transforming the information source to a form compatible with a digital system
Sampling
Aliasing
Quantization
Uniform and non-uniform
Baseband modulation
Binary pulse modulation
M-ary pulse modulation
M-PAM (M-ary Pulse amplitude modulation)‏

3. Formatting and Transmission of Baseband Signal
Digital info.
Bit stream
(Data bits)‏
Pulse waveforms
(baseband signals)‏
Textual
info.
Format
source
Pulse
modulate
Sample
Quantize
Encode
Analog
info.
Sampling at rate
(sampling time=Ts)‏
Encoding each q. value to
bits
(Data bit duration Tb=Ts/l)‏
Quantizing each sampled
value to one of the
L levels in quantizer.
Mapping every data bits to a
symbol out of M symbols and transmitting
a baseband waveform with duration T
Information (data) rate:
Symbol rate :
For real time transmission:

4. Example of M-ary PAM
Assuming real time transmission and equal energy per transmission data bit for binary-PAM and 4-ary PAM:
4-ary: T=2Tb and Binary: T=Tb
Dariusz Kacprzak
Dariusz Kacprzak
Binary PAM
(rectangular pulse)‏
4-ary PAM
(rectangular pulse)‏ 3B A.
‘1’
‘11’ B T T
‘01’ T
‘10’
‘00’ T T
‘0’ T -B
-A.
-3B

5. Example of M-ary PAM … Dariusz Kacprzak Dariusz Kacprzak
Ts Ts
V V
0 Tb 2Tb 3Tb 4Tb 5Tb 6Tb
Dariusz Kacprzak
Dariusz Kacprzak
Rb=1/Tb=3/Ts
R=1/T=1/Tb=3/Ts
0 T T 3T 4T 5T 6T
Rb=1/Tb=3/Ts
R=1/T=1/2Tb=3/2Ts=1.5/Ts
T T T

6. Today we are going to talk about:
Receiver structure
Demodulation (and sampling)‏
Detection
Another source of error:
Inter-symbol interference (ISI)
Nyquist theorem
The techniques to reduce ISI
Pulse shaping
Equalization
Dariusz Kacprzak
Dariusz Kacprzak

7. Today we are going to talk about:

8. Introduction
The baseband pulse received at receiver not in ideal pulse shape, need to recover the pulse shape. Filtering & channel caused ISI.
The goal of the demodulator receiving signal
~ is to recover a baseband pulse with the best SNR and free of any ISI.
Equalization consists of sophisticated set of signal processing techniques. It is used to compensate for channel-induced interference.

9. Signals and Noise Two primary causes of error-performance degradation
(1) Effect of filtering at transmitter, channel and receiver
(2) Electrical noise interference produce by galaxy, atmospheric noise, switching transients, intermodulation noise, interference noise from other sources.
Noise and interference can be reduce the intensity or eliminate. But the thermal motion of electrons cannot be eliminated.

10. Demodulation and Detection
recovery of waveform to an undistorted baseband pulse.
Detection
the decision making process of selecting a digital of the waveform.
If error-correcting coding is not present
the detector output consists of estimates of message symbols (or bits), mi (hard decision).
If error-correcting coding is present
the detector output consists of estimates of channel symbols (coded bits) ui, which can take the form of hard or soft decisions.
Frequency down-conversion block;
performs frequency translation for bandpass signals operating at some radio frequency (RF)

11. Demodulation and Detection
Format
Pulse
modulate
Bandpass
modulate
M-ary modulation
Major sources of errors:
Thermal noise (AWGN)‏
disturbs the signal in an additive fashion (Additive)
has flat spectral density for all frequencies of interest (White)‏
is modeled by Gaussian random process (Gaussian Noise)
Inter-Symbol Interference (ISI)‏
Due to the filtering effect of transmitter, channel and receiver, symbols are “smeared”.
channel
transmitted symbol
estimated symbol
Format
Detect
Demod.
& sample

12. Example: Impact of the channel

13. Receiver Structure
Typical demodulation and detection function of a digital receiver
Step 1 – waveform to sample transformation
Step 2 – decision making
Demodulate & Sample
Detect
Threshold
comparison
Frequency
down-conversion
Receiving
filter
Equalizing
filter
Compensation for channel induced ISI
For bandpass signals
Received waveform
Baseband pulse
(possibly distored)‏
Baseband pulse
Sample
(test statistic)‏

14. Receiver Tasks Demodulation and sampling:
Waveform recovery and preparing the received signal for detection:
Improving the signal power to the noise power (SNR) using matched filter
Reducing ISI using equalizer
Sampling the recovered waveform
Detection:
Estimate the transmitted symbol based on the received sample

15. Baseband and bandpass
Bandpass model of detection process is equivalent to baseband model because:
The received bandpass waveform is first transformed to a baseband waveform.
Equivalence theorem:
Performing bandpass linear signal processing followed by heterodyning the signal to the baseband, yields the same results as heterodyning the bandpass signal to the baseband , followed by a baseband linear signal processing.

16. Steps in Designing the Receiver
Find optimum solution for receiver design with the following goals:
Maximize SNR
Minimize ISI
Steps in design:
Model the received signal
Find separate solutions for each of the goals.
First, we focus on designing a receiver which maximizes the SNR.

17. Frequency down conversion block
Cont’d…
Receiving Filter;
or the modulator which perform waveform recovery in preparation of step-detection.
Filtering at transmitter and channel typically caused the received pulse sequence to suffer from ISI and not ready for sampling and detection.
The goal of the receiving filter is to recover a baseband pulse width the best possible SNR, free of ISI.
To accomplish this use matched filter or correlator.
Frequency down conversion block
perform frequency translation for bandpass signal operating at some radio frequency.
Receiving filter
to recover a baseband pulse with the best possible SNR and free of ISI
Optimal equalizing filter
is only needed for those systems where channel induced ISI can distort the signals.

18. Inter-nce (ISI)
Find optimum solution for receiver design with the following goals:
Maximize SNR
Minimize ISI
Transmitter
~ the information symbols characterized as impulse or voltage levels, modulate pulses that are then filtered to comply with some bandwidth constraint.
Baseband system
~ the channel has distributed reactance that distorts the pulses.
Bandpass system
~characterized by fading channels that behave like undesirable filters manifesting signal distortion.
Equalizing filter
~ configured to compensate for the distortion caused by transmitter & channel.
Figure 3.15 Page 136

19. Inter-Symbol Interference
Equalizing filter or receiving/equalizing filter~ configure to compensate distortion caused by transmitter & channel.
Baseband system model
Equivalent model
Lump filtering effect into~
Ht(f) –transmitting filter
Hc(f) –filtering within the channel
Hr(f) –equalizing filter
Tx filter
Channel
Rx. filter
Detector
Equivalent system
Detector
filtered noise

20. Cont’d…ISI
ISI in the detection process due to the filtering effects of the system channel induced distortion.
Overall equivalent system transfer function
creates echoes and hence time dispersion
causes ISI at sampling time

21. Nyquist Bandwidth constraint
The theoretical minimum required system bandwidth to detect Rs [symbols/s] without ISI is Rs/2 [Hz]. Happen when the H[f] is rectangular.
Single side bandwidth 1/2Timpulse response h(t) =sinc(t/T)
Equivalently, a system with bandwidth W=1/2T=Rs/2 [Hz] can support a maximum transmission rate of 2W=1/T=Rs [symbols/s] without ISI.
Ideal Nyquist filter
Ideal Nyquist pulse

22. Cont’d…Nyquist Bandwidth constrain
Bandwidth efficiency, R/W [bits/s/Hz]:
An important measure in DCs representing data throughput per hertz of bandwidth.
Showing how efficiently the bandwidth resources are used by signaling techniques.

23. Nyquist Pulses (filters)
Pulses (filters) which results in no ISI at the sampling time.
Nyquist filter:
Its transfer function in frequency domain is obtained by convolving a rectangular function with any real even- symmetric frequency function
Nyquist pulse:
Its shape can be represented by a sinc(t/T) function multiply by another time function.
Example of Nyquist filters: Raised-Cosine filter

24. Pulse shaping to reduce ISI
Goals and trade-off in pulse-shaping
Compress bandwidth of data impulse to small bandwidth greater than Nyquist minimum.
Reduce ISI; right sampling.
Efficient bandwidth utilization
Robustness to timing error (small side lobes)

25. Pulse Shaping to reduce ISI
System operate with small bandwidth
Pulse that spread in time will degrade the system’s error performance due to increase ISI.
Reduce the required system bandwidth.
Compress the bandwidth of the data impulse to some reasonably small bandwidth greater than the Nyquist minimum
Pulse shaping with Nyquist filter
Zero ISI is only when the sampling is performed at exactly the correct sampling time when the tails of pulses are large.
Due to effect of the received pulses can overlap one another
tail of pulse can smear into adjacent symbol intervals, thereby interfering with the detection process and degrading the error performance ISI.
The effects of filtering & channel induced distortion leads to ISI

26. The Raised-Cosine Filter
One frequently used H(f) transfer function belonging to the Nyquist class (zero ISI at the sampling time)
W~ absolute bandwidth
W0=1/2T~ minimum Nyquist bandwidth for rectangular spectrum
W-W0~ excess bandwidth
r =(W-W0)/W0~ Roll off factor where

27. Cont’d…Raise Cosine Filter Raise cosine characteristics
Roll off value; r. r=0 roll off is Nyquist minimum bandwidth case.
Example of Nyquist filters: Raised-Cosine filter
Relationship of bandwidth and symbol transmission rate
Relationship of DBS bandwidth WDBS and symbol transmission rate Rs 1
0.5

28. Cont’d…Raise Cosine Filter Pulse shaping filter;
Larger filter roll-off, the shorter the pulse tail (small amplitude)  less sensitive to timing errors & small degradation due to ISI, small excess bandwidth.
Longer pulse tail  larger pulse amplitude & greater sensitivity to timing error.
Nyquist filter
is one whose frequency transfer function can be represented by a rectangular function convolved with any real even-symmetric frequency function
Nyquist pulse
is one whose shape can be represented by a sinc (t/T) function multiplied by another time function
Most popular of Nyquist filter
(1) Raised-cosine filter
(2) Root-raised cosine filter

29. Example of Pulse Shaping
Square-root Raised-Cosine (SRRC) pulse shaping
Amp. [V]
Baseband tr. Waveform
Third pulse
t/T
First pulse
Second pulse
Data symbol

30. Example of Pulse Shaping …
Raised Cosine pulse at the output of matched filter
Amp. [V]
Baseband received waveform at
the matched filter output
(zero ISI)
t/T

31. Eye Pattern
Eye pattern: Display on an oscilloscope which sweeps the system response to a baseband signal at the rate 1/T (T symbol duration)
Eye pattern of binary antipodal signalling.
Optimum sampling time corresponds to maximum eye opening yield greatest protection against noise.
Eye closed~ ISI is increasing Eye open~ ISI is decreasing.
Distortion
due to ISI (DA)
Noise margin (MN)
amplitude scale
Sensitivity to
timing error (ST)
Timing jitter (JT)
time scale

32. Example of Eye Pattern: Binary-PAM, SRRQ pulse
Perfect channel (no noise and no ISI)

33. Example of Eye Pattern: Binary-PAM, SRRQ pulse …
AWGN (Eb/N0=20 dB) and no ISI

34. Example of eye pattern: Binary-PAM, SRRQ pulse …
AWGN (Eb/N0=10 dB) and no ISI

35. Example of eye pattern with ISI: Binary-PAM, SRRQ pulse
Non-ideal channel and no noise

36. Example of Eye Pattern with ISI: Binary-PAM, SRRQ pulse …
AWGN (Eb/N0=20 dB) and ISI

37. Example of eye pattern with ISI: Binary-PAM, SRRQ pulse …
AWGN (Eb/N0=10 dB) and ISI

38. Equalization Step 1 – waveform to sample transformation
Step 2 – decision making
Demodulate & Sample
Detect
Threshold
comparison
Frequency
down-conversion
Receiving
filter
Equalizing
filter
Compensation for channel induced ISI
For bandpass signals
Received waveform
Baseband pulse
(possibly distored)
Baseband pulse
Sample
(test statistic)

39. Non-constant amplitude
Equalization
Equalization~ signal processing or filtering techniques that is designed to eliminate or reduce ISI.
Equalization categories;
(1) Maximum likelihood sequence estimation (MLSE)
Making measurement of hc(t) & provide means of adjusting the receiver to the transmission environment.
Migittaing technichque of MLSE  adjusting itself so that better deal with the distorted sample; verterbi equalization.
(2) Equalization with filter
Use filter to compensate the distorted pulse.
Popular approach. Linear device (transversal equalizer) or nonlinear device (decision feedback equilizer)
Non-constant amplitude
Amplitude distortion
Non-linear phase
Phase distortion

40. Pulse Shaping and Equalization to remove ISI
Overal system transfer function
Transmmit & received filter chosen to match so that;
Square-Root Raised Cosine (SRRC) filter and Equalizer
No ISI at the sampling time
Taking care of ISI
caused by tr. filter
caused by channel

41. Equalization: Channel examples
Example of a frequency selective, slowly changing (slow fading) channel for a user at 35 km/h

42. Equalization: Channel examples …
Example of a frequency selective, fast changing (fast fading) channel for a user at 35 km/h

43. Equalizing filters … Baseband system model Equivalent model Tx filter
Channel
Equalizer
Rx. filter
Detector
Equivalent system
Equalizer
Detector
filtered noise

44. Equalization – cont’d Equalization using
MLSE (Maximum likelihood sequence estimation)
Filtering
Transversal filtering
Zero-forcing equalizer
Minimum mean square error (MSE) equalizer
Decision feedback
Using the past decisions to remove the ISI contributed by them
Adaptive equalizer

45. Equalization by Transversal Filtering
A weighted tap delayed line that reduces the effect of ISI by proper adjustment of the filter taps.
Coeff.
adjustment

46. Transversal equalizing filter …
Zero-forcing equalizer:
The filter taps are adjusted such that the equalizer output is forced to be zero at N sample points on each side:
Mean Square Error (MSE) equalizer:
The filter taps are adjusted such that the MSE of ISI and noise power at the equalizer output is minimized.
Adjust
Adjust

47. Example of Equalizer 2-PAM with SRRQ Non-ideal channel One-tap DFE
Matched filter outputs at the sampling time
ISI-no noise,
No equalizer
ISI-no noise,
DFE equalizer
ISI- noise
No equalizer
ISI- noise
DFE equalizer

48. Example 3.1: Equalization. Pg 331
The tab weight of an equalizing transversal filter are to be determined by transmitting a single pulse as a training signal. Let the equalizer be a three tap one . Given a received distorted set of pulse sample {x(k)}, with voltage values {0.0, 0.1, 1.0, -0.2, 0.1} Use a zero-forcing solution to find the tab weights that reduce the ISI so that the equalized pulse samples {z(k)} have no ISI. Using these weights, calculate the ISI values of the equalizing pulse at the sample times k=+ 2, + 3. What is the largest magnitude sample contributing to ISI and what is the sum of all the ISI magnitudes?
Solution: