1. ECEN5533 Modern Commo Theory Lesson #18. 22 February 2016 Dr
ECEN5533 Modern Commo Theory Lesson # February 2016 Dr. George Scheets
Read 3.1
Problems
Design Problem #1 due 26 February
Quiz #2 on 7 March
Exam #1 final results Hi = 97, Low = 77, ave = 85.75, σ = 8.30 A > 88, B > 75

2. ECEN5533 Modern Commo Theory Lesson #19. 24 February 2016 Dr
ECEN5533 Modern Commo Theory Lesson # February 2016 Dr. George Scheets
Read 3.2
Problems 2.18, 2.19, 3.1
Design Problem #1 due 26 February
Quiz #2 on 7 March

3. ECEN5533 Modern Commo Theory Lesson #20. 26 February 2016 Dr
ECEN5533 Modern Commo Theory Lesson # February 2016 Dr. George Scheets
Problems 3.2, 5, & 6
Design Problem #1 due 26 February
Quiz #2 on 7 March

4. Binary Matched Filter Detector
Integrate
over T
Decide
1 or 0
r(t) + n(t)
s1(t) - so(t) ^
x(t)
Decide 1 or 0 Box has:
Sampler: Samples once per bit, at end of bit interval
Comparator: Compares sample voltage to a threshold
Hold: Holds voltage for one symbol interval.

5. Binary Matched Filter Detector
Analog Or
Digital
Filter
h(t) = x(T-t)
Decide
1 or 0
r(t) + n(t) ^
x(t)
Alternatively, could just have a filter matched to the pulse.
The output over time of this filter and the previous differ,
except at the sample time T, they're the same.

6. Symbol Detection
Matched Filter P(BE) < Single Sample Detector P(BE)
Single Sample Detector P(BE) independent of Bit Rate
If system remains wideband (square pulse in & out)
Sampling done at baseband
Matched Filter P(BE) gets worse as Bit Rate ↑
Eventually → Single Sample Detector P(BE)
Multiply r(t) by s1(t) - s0(t) prior to integration
RF system? s1(t) – s0(t) is a sinusoid Integrator sees product of two sinusoids Get a difference frequency term = baseband pulses Get a double frequency term, filtered out by integrator

7. Intersymbol Interference
Given a chunk of bandwidth
There is a maximum tolerable symbol rate
Nyquist showed
Rs symbols/second can be moved in Rs/2 Hertz
Using sinc pulses instead of square pulses
Real World
Closer to Rs symbols/second in Rs Hertz
EX) V.34 Modems (33.6 Kbps) 3429 symbols/second in about 3500 Hertz

8. ISI due to Brick-Wall Filtering
4.5 z k z2 k
4.5 20 40 60 80
100
120
140 k

9. ISI due to Brick-Wall Filtering
4.5 z k z2 k
Equalizer can undo some of this.
4.5 20 40 60 80
100
120
140 k

10. M-Ary Signaling
One of M possible symbols is transmitted every T seconds.
M is usually a power of 2
Log2M bits/symbol
M = 256? Each symbol can represent 8 bits

11. M-Ary Signaling Bandwidth required
Function of symbols/second
Function of symbol shape
The more rapidly changing is the symbol, the more bandwidth it requires.
An M-Ary signal with the same symbol rate and similar symbol shape as a Binary signal uses essentially the same bandwidth.
More bits can be shoved down available bandwidth

12. Digital Example: Binary Signaling
Serial Bit Stream (a.k.a. Random Binary Square Wave)
One of two possible pulses is transmitted every T seconds.
time +1
volts -1 T
If T = seconds, then this
1 MBaud waveform moves 1 Mbps.
(Baud = symbols per second)

13. Example:M-Ary Signal Same BW as previous binary signal.
One of M possible symbols is transmitted every T seconds. EX) 4-Ary signaling. Note each symbol can represent 2 bits.
volts
+1.34
If T = seconds, then
this 1 MBaud signal moves
2 Mbps.
+.45
-.45
time
Same BW as
previous binary signal.
-1.34 T

14. M-Ary Signaling No Free Lunch For equal-power signals
As M increases, signals get closer together...
... and receiver detection errors increase

15. Digital Example: Binary Signaling
This is a _ watt signal.
Sampled voltage values are 2 volts apart. 1
time +1
volts -1 T
If T = seconds, then this
1 MBaud waveform moves 1 Mbps.
(Baud = symbols per second)

16. Example: 4-Ary Signal 1 This is also a _ watt signal.
Some sample voltages are 0.89 volts apart.
In the presence of noise, will have more errors here. 1
volts
+1.34
If T = seconds, then
this 1 MBaud signal moves
2 Mbps.
+.45
-.45
time
-1.34 T

17. Where is this used?
M-Ary signaling used in narrow bandwidth environments...
... preferably with a high SNR
Example: Dial-up phone modems
... sometimes with a not so high SNR
Digital Cell Phones

18. Digital Example: Binary Signaling
Serial Bit Stream (a.k.a. Random Binary Square Wave)
One of two possible pulses is transmitted every T seconds.
time +1
volts -1 T
If T = seconds, then this
1 MBaud waveform moves 1 Mbps.
(Baud = symbols per second)

19. PDF for Noisy Binary Signal
fR'(r')
area under
each bell
shaped curve
= 1/2 -1 +1
r' volts
Threshold is where PDF's cross (0 volts)

20. Example:M-Ary Signal
One of M possible symbols is transmitted every T seconds. EX) 4-Ary signaling. Note each symbol can represent 2 bits.
volts
+1.34
If T = seconds, then
this 1 MBaud signal moves
2 Mbps.
+.45
-.45
time
-1.34 T

21. PDF for Noisy 4-ary Signal
area under
each bell
shaped curve
= 1/4
fR'(r')
Gray
Code
is best.
-1.34
-0.45
+0.45
+1.34
r' volts
Threshold is where PDF's cross (-0.89, 0, volts)
Six tails are on wrong side of thresholds.
Area of tails = P(Symbol Error)

22. Equalization Seeks to reverse effects of channel filtering H(f)
Ideally Hequalizer(f) = 1/H(f)
Result will be flat spectrum
Not always practical if parts of |H(f)| have small magnitude
Adaptive Filters frequently used

23. System with Multipath h(t) = 0.9δ(t) – 0.4δ(t - 0.13)
H(f) = e -jω0.13

24. Required Equalizer Filter |Heq(f)| = 1/|H(f)| Heq(f) = 1 / (. 9 -
Required Equalizer Filter |Heq(f)| = 1/|H(f)| Heq(f) = 1 / ( e -jω0.13 )

25. Heq(f) = 1 / (. 9 -. 4e -jω0. 13 ) Heq3(f) = 1. 111 + 0. 4938e-jω0. 13
Heq(f) = 1 / ( e -jω0.13 ) Heq3(f) = e-jω e -jω
Impulse Response of a 3 tap FIR Equalizing filter.
h(t) = 1.111δ(t) δ(t – 0.13) δ(t – 0.26)

26. Tapped Delay Line Equalizer a.k.a. FIR Filter or Moving Average Filter
Input
Output
1.111
|H(f)*Heq3(f)| Σ
0.4938
Delay
0.13 sec
0.2194
Delay
0.26 sec
Ideally |H(f)Heq(f)| = 1
Was 0.5 < |H(f)| < 1.3
Now 0.9 < |H(f)Heq3(f)| < 1.1

27. Time Domain (3 Tap Equalizer)
System Input
System Output
Multipath
Equalizer Output

28. Tapped Delay Line Equalizer 8 Taps
Input
Output
1.111 Σ
0.4938
Delay
0.13 sec
Delay
0.91 sec

29. Time Domain (8 Tap Equalizer)
System Input
Multipath Output
Equalizer Output

30. Rough Rule of Thumb Want antenna aperture > 1/4 wavelength
To get relatively efficient EM radiation
Wavelength λ = (speed of EM wave) (frequency of EM wave)
Baseband pulses → Huge Antenna

31. Radio Waves

32. Phasor Representations
Phasor comparison of AM, FM, and PM
Geometrical Representation of Signals & Noise
Useful for M-Ary symbol packing
If symbol rate & shape are unchanged, bandwidth required is a function of the number of dimensions (axes)