1. CS434/534: Topics in Networked (Networking) Systems Wireless Foundation: Modulation and Demodulation Yang (Richard) Yang Computer Science Department Yale University 208A Watson

2. Outline Admin and recap Wireless background Frequency domain
Basic concepts of modulation
Amplitude modulation
Amplitude demodulation

3. Admin PS1 deferred to Tuesday
Feel free to stop by Chris Leet office at any time to discuss PS1

4. Recap: Fourier Series of Periodic Function
A periodic function g(t) with period T on [a, a+T] can be decomposed as:
For periodic function with period 1 on [0, 1]

5. Signals at undesirable frequencies
Basic Question: Why Not Send Digital Signal in Wireless Communications?
Signals at undesirable frequencies
suppose digital frame repeat every T seconds, then according to Fourier series decomposition, signal decomposes into frequencies at 1/T, 2/T, 3/T, …
let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, … 1
digital signal t

6. Frequencies are Assigned and Regulated
Europe
USA
Japan
Cellular
Phones
GSM
450 -
457, 479
486/460
467,489
496, 890
915/935
960,
1710
1785/1805
1880
UMTS
(FDD) 1920
1980, 2110
2190
(TDD) 1900
1920, 2020
2025
AMPS ,
TDMA
CDMA
824
849,
869
894
1850
1910,
1930
1990
PDC
810
826,
940
956,
1429
1465,
1477
1513
Cordless
CT1+
885
887, 930
932
CT2
864
868
DECT
1900
PACS
1910, 1930 UB
1910
PHS
1895
1918
JCT
254
380
Wireless
LANs
IEEE
2400
2483
HIPERLAN 2
5150
5350, 5470
5725
902
928 I
EEE
5350, 5725
5825
2471
2497
5250
Others RF
Control
27, 128, 418, 433,
315, 915
426, 868
$22 billion: Amount operators paid the U.S. government over the past ten years for spectrum. Source Burton Group.
US operator:

7. Spectrum and Bandwidth: Shannon Channel Capacity
The maximum number of bits that can be transmitted per second by a physical channel is:
where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise

8. Why Not Send Digital Signal in Wireless Communications?
Transmitter
voice
Antenna: size ~ wavelength
20-20KHz
At 3 KHz,
Antenna too large!
Use modulation to transfer to higher frequency

9. Recap: Discrete Domain Analysis
FFT: Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1
Interpretation: consider x0, x1, …, xN-1 as sampled values of a periodical function defined on [0, 1]
Xk is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec
Draw on blackboard [Nfft, Nfft, …] = Ns (defined for 1 sec)

10. FFT Analysis vs Sample RateX1 X2
XNfft/2
Nfft=Nsample
1Hz
2Hz
Nfft/2 Hz
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
The freq. analysis resolution:

11. Frequency Domain Analysis Examples Using GNURadio
spectrum_1_realsin_rawfft
1K real cosine wave
1024 FFT
32000 sample rate
Prediction:
Where is the peak of FFT?
Commands
./plot/raw2numf signal.dat signal.show
./plot/raw2numfc fft.dat fft.show
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

12. Frequency Domain Analysis Examples Using GNURadio
spectrum_2_realsin_plus.grc
Two signal sources ( )
Audio sink
Scope Sink
FFT Sink (1024 FFT)
Prediction:
What is a good sample rate to see the result?
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

13. Frequency Domain Analysis Examples Using GNURadio
spectrum_2_realsin_multiply
Multiplication of previous signal by another sine wave
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

14. Advantage of I/Q representation
Advantages of I/Q representation
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

15. I/Q Multiplication Also Called Quadrature Mixing
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
spectrum of complex signal x(t)
spectrum of complex signal x(t)ej2f0t
spectrum of complex signal x(t)e-j2f0t

16. Outline Recap Wireless background Frequency domain
Modulation and demodulation

17. Basic Concepts of Modulation
The information source
Typically a low frequency signal
Referred to as baseband signal
Carrier
A higher frequency sinusoid
Example cos(2π10000t)
Modulated signal
Some parameter of the carrier is varied in accordance with the baseband signal

18. Types of Modulation Analog modulation Digital modulation
Amplitude modulation (AM)
Frequency modulation (FM)
Double and signal sideband: DSB, SSB
Digital modulation
Amplitude shift keying (ASK)
Frequency shift keying: FSK
Phase shift keying: BPSK, QPSK, MSK
Quadrature amplitude modulation (QAM)

19. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Basic concepts
Amplitude modulation

20. Example: Amplitude Modulation (AM)
Block diagram
Time domain
Frequency domain

21. Example: am_modulation Example
Setting
Audio source (sample 32K)
Signal source (300K, sample 800K)
Multiply
Two Scopes
FFT Sink

22. Example AM Frequency Domain
Note: There is always the negative freq. in the freq. domain.

23. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Basic concepts
Amplitude modulation
Amplitude demodulation

24. Problem: How to Demodulate AM Signal?

25. Design Option 1 Step 1: Multiply signal by e-j2πfct
Implication: Need to do complex multiple multiplication

26. Design Option 1 (After Step 1)
-2fc

27. Design Option 1 (Step 2)
Apply a Low Pass Filter to remove the extra frequencies at -2fc
-2fc

28. Design Option 2: Quadrature Sampling

29. Quadrature Sampling: Upper Path (cos)

30. Quadrature Sampling: Upper Path (cos)

31. Quadrature Sampling: Upper Path (cos)

32. Quadrature Sampling: Lower Path (sin)

33. Quadrature Sampling: Lower Path (sin)

34. Quadrature Sampling: Lower Path (sin)

35. Quarature Sampling: Putting Together
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

36. Summary: Demod of AM
Design option 1: multiply modulated signal by e-jfct, and then LPF
Design option 2: quadrature sampling

37. Remaining Hole: How to Design LPF
Frequency domain view
freq B -B
freq B -B

38. Design Option 1 compute freq zeroing out outband freq
compute lower-pass time signal
freq B -B
This is essentially how image compression works.
Problem(s) of Design Option 1?

39. Design Option 2: Impulse Response Filters
GNU software radio implements filtering using
Finite Impulse Response (FIR) filters
Infinite Impulse Response (IIR) Filters
FIR filters are more commonly used
FIR/IIR is essentially online, streaming algorithms
They are used in networks/communications/vision/robotics…

40. FIR Filter
An N-th order FIR filter h is defined by an array of N+1 numbers:
They are often stored backward (flipped)
Assume input data stream is x0, x1, …, … hN h2 h1 h0

41. xn-3 xn-2 xn-1 xn xn+1 * * * * h3 h2 h1 h0 FIR Filter compute y[n]:
3rd-Order Filter h3 h2 h1 h0
compute y[n]:

42. FIR Filter
xn-3
xn-2
xn-1 xn
xn+1 * * * * h3 h2 h1 h0
compute y[n+1]

43. FIR Filter
is also called convolution between x (as a vector) and h (as a vector), denoted as

44. Key Question Using h to Implement LPF
How to determine h?
Approach:
Understand the effects of y=g*h in the frequency domain

45. Backup Slides

46. GNURadio: Design Objective
A software development toolkit that provides signal processing blocks to implement software-defined radio systems.

47. GNURadio Hardware Arch
Hardware Frontend
Host Computer
RF Frontend
(Daugtherboard)
ADC/DAC and
Digital Frontend
(USRP)
GNU Radio
Software

48. Basic Software Concepts
Block
Flow graph

49. Basic Software Concepts
gr_basic_block (name, in/out signature, msg queue)
gr_block (Leaf block; key functions forecast/general_work)
Example:
gr_hier_block2 (container block; key functions: connect/disconnect/lock/unlock)
gr_top_block (flow graph; start/stop/wait)

50. Software/Execution Model
Software model
Python
Application management (e.g., GUI)
Flow graph construction
Non-streaming code (e.g., MAC-layer)
C++
Signal processing blocks
Certain routines also coded in assembly
Execution model
Python thread for each top_block
Python Application development Flow graph construction
C++ Signal processing blocks
Discussion: benefits/issues of the hybrid software structure?

51. Summary: GNURadio
Interesting/key software design techniques you learned from GNURadio?