1. Wireless Mesh Networks
Anatolij Zubow
Signal Encoding Techniques

2. Contents Signal Encoding Criteria Digital Data, Analog Signal Other
Amplitude-Shift Keying
Frequency-Shift Keying
Phase-Shift Keying
Performance
Minimum-Shift Keying
Quadrature Amplitude Modulation
Other
Analog Data, Analog Signal
Analog Data, Digital Signal 2

3. Encoding and Modulation Techniques
Digital Encoding
Actual form of x(t) depends on encoding technique
Analog Encoding (modulation)
Basis is continuous constant-frequency signal (= carrier signal)
Modulation
Process of encoding source data onto a carrier signal with frequency fC
3 frequency domain params: amplitude, frequency, and phase 3

4. Reasons for Choosing Encoding Techniques
Digital data, digital signal
Equipment less complex and expensive than digital-to-analog modulation equipment
Analog data, digital signal
Permits use of modern digital transmission and switching equipment
Digital data, analog signal
Some transmission media will only propagate analog signals
E.g., optical fiber and unguided media (wireless)
Analog data, analog signal
Analog data in electrical form can be transmitted easily and cheaply
Done with voice transmission over voice-grade lines 4

5. Signal Encoding Criteria
Digital signal  sequence of discrete, discontinues voltage pulses  each pulse is a signal element  encoding each data bit into signal elements (simplest case is 1:1 mapping)
Analog signal  a signal elements is pulse of constant frequency, phase, and amplitude
1:1, 1:many, many:1 correspondence between data elements and signal elements 5

6. Signal Encoding Criteria
What determines how successful a receiver will be in interpreting an incoming signal?
Signal-to-noise ratio
Data rate
Bandwidth
An increase in data rate increases bit error rate
An increase in SNR decreases bit error rate
An increase in bandwidth allows an increase in data rate 6

7. Factors Used to Compare Encoding Schemes
Mapping of data bits to signal elements
Signal spectrum
With lack of high-frequency components, less bandwidth required
Transfer function of a channel is worse near band edges
Clocking
Ease of determining beginning and end of each bit position
Separate clock channel or synchronization based on transmitted signal
Signal interference and noise immunity
Performance in the presence of noise (BER)
Cost and complexity
The higher the signal rate to achieve a given data rate, the greater the cost 7

8. Basic Encoding Techniques
Digital data to analog signal
Appliance
Transmission of digital data through public telephone network (modem)
Cellular networks (radio)
Amplitude-shift keying (ASK)
Amplitude difference of carrier frequency
Frequency-shift keying (FSK)
Frequency difference near carrier frequency
Phase-shift keying (PSK)
Phase of carrier signal shifted 8

9. Modulation of Analog Signals for Digital Data9

10. Amplitude-Shift Keying
One binary digit represented by presence of carrier, at constant amplitude
Other binary digit represented by absence of carrier
where the carrier signal is A cos(2πfct)
Notes:
Susceptible to sudden gain changes
Inefficient modulation technique
On voice-grade lines (up to 1200 bps)
Used to transmit digital data over
optical fiber 10

11. Binary Frequency-Shift Keying (BFSK)
Two binary digits represented by two different frequencies near the carrier frequency
where f1 and f2 are offset from carrier frequency fc by equal but opposite amounts 11

12. Binary Frequency-Shift Keying (BFSK)
Less susceptible to error than ASK
On voice-grade lines, used up to 1200bps
Used for high-frequency (3 to 30 MHz) radio transmission
Can be used at higher frequencies on LANs that use coaxial cable
Appliance: BFSK for full-duplex operation over voice-grade line
Example: Full-Duplex FSK transmission on a voice-grade line 12

13. Multiple Frequency-Shift Keying (MFSK)
More than two frequencies are used
Each signaling element represents more than 1 bit
More bandwidth efficient but more susceptible to error
f i = f c + (2i – 1 – M)f d
f c = the carrier frequency
f d = the difference frequency
M = number of different signal elements = 2 L
L = number of bits per signal element 13

14. Multiple Frequency-Shift Keying (MFSK)
To match data rate of input bit stream, each output signal element is held for:
Ts=LT seconds
where T is the bit period (data rate = 1/T)
So, one signal element encodes L bits
Total bandwidth required
2Mfd
Minimum frequency separation required
2fd=1/Ts
Therefore, modulator requires a bandwidth of
Wd=2L/LT=M/Ts
Max data rate depends on frequency deviation = 2Lfd 14

15. Multiple Frequency-Shift Keying (MFSK)
Example:
fc=250 kHz, fd=25 kHz, and M=8 (L=3 bits)
Determine the frequency assignment for each of the possible 3-bit data combinations.
MFSK Frequency Use (M = 4)
Input stream of 20 bits is encoded 2 bits at a time 15

16. Phase-Shift Keying (PSK)
Phase of the carrier signal is
shifted to represent data
Two-level PSK (BPSK)
Uses two phases to represent binary digits
With a bit stream as a discrete function d(t) (11; 0-1)
Differential PSK (DPSK)
Phase shift with reference to previous bit
Binary 0 – signal burst of same phase as previous signal burst
Binary 1 – signal burst of opposite phase to previous signal burst
Advantages of DPSK?
No need for an accurate local oscillator phase 16

17. Phase-Shift Keying (PSK)
Four-level PSK
Quadrature phase-shift keying (QPSK)
More efficient use of bandwidth
Each element represents more than one bit
Phase shifts separated by multiples of π/2 (90°) 17

18. Quadrature Modulation
In general a wireless channel is bandwidth limited
Is it possible to utilize a given bandwidth multiple times?
Quadrature modulation
Makes use of two modulators with different carriers (sine and cosine)
The binary data stream is split into the in-phase (I) and quadrature-phase (Q) components which are then separately modulated onto two orthogonal basis functions (here two sinusoids). 18

19. QPSK and OQPSK Modulators
Example of QPSK and OQPSK Waveforms 19

20. QPSK signal in the time domain
Example:
Short segment of a random binary data-stream
The odd-numbered bits have been assigned to the in-phase component and the even-numbered bits to the quadrature component
The total signal (=the sum of the two components) is shown at the bottom.
Jumps in phase can be seen as the PSK changes the phase on each component at the start of each bit-period.
The topmost waveform alone matches the description of BPSK 20

21. Phase-Shift Keying (PSK)
Multilevel PSK
Using multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achieved
D = modulation rate, baud
R = data rate, bps
M = number of different signal elements = 2L
L = number of bits per signal element
Example: 9600-bps (2400-baud) modem uses 12 phase angles, 4 of which have 2 amplitude values (= 16 different signal elements) 21

22. Performance Bandwidth of modulated signal (BT) ASK, PSK BT=(1+r)R
FSK BT=2Δf +(1+r)R
R = bit rate
0 < r < 1; related to how signal is filtered
Δf = f2-fc=fc-f1
MPSK
MFSK
L = number of bits encoded per signal element
M = number of different signal elements 22

23. Expression Eb/N0
Ratio of signal energy per bit to noise power density per Hertz
where S is the signal power and R the data rate
The bit error rate (BER) for digital data is a function of Eb/N0
Given a value for Eb/N0 to achieve a desired error rate, parameters of this formula can be selected
As bit rate R increases, transmitted signal power must increase to maintain required Eb/N0 23

24. Performance in Presence of Noise
Eb/N0 = signal energy per bit to noise power density per Hertz (= (S/R)/N0, R is the data rate) 24

25. Performance in Presence of Noise25

26. Quadrature Amplitude Modulation
QAM is a combination of ASK and PSK
Two different signals sent simultaneously on the same carrier frequency, by using two copies of the carrier frequency, one shifted by 90° with respect to the other
Each carrier is ASK modulated
The two independent signals are simultaneously transmitted over the same medium
At the receiver the two signals are demodulated and the results combined to produce the original binary input
E.g. four-level ASK: combined stream can be in one of 16 = 4 * 4 states (16-QAM) 26

27. QAM Modulator 27

28. Constellation Diagram
A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as QAM or PSK.
By representing a transmitted symbol as a complex number and modulating a cosine and sine carrier signal with the real and imaginary parts (respectively), the symbol can be sent with two carriers on the same frequency.
BPSK
QPSK
16-QAM 28

29. Coherent Reception
An estimate of the channel phase and attenuation is recovered.
It is then possible to reproduce the transmitted signal, and demodulate.
It is necessary to have an accurate version of the carrier, otherwise errors are introduced.
Carrier recovery methods include:
Pilot Tone (such as Transparent Tone in Band)
Less power in information bearing signal
High peak-to-mean power ratio
Pilot Symbol Assisted Modulation
Carrier Recovery (such as Costas loop)
The carrier is recovered from the information signal 29

30. Differential Reception
In the transmitter, each symbol is modulated relative to the previous symbol, for example in differential BPSK:
0 = no change; 1 = +180°
In the receiver, the current symbol is demodulated using the previous symbol as a reference.
The previous symbol acts as an estimate of the channel.
Differential reception is theoretical 3dB poorer than coherent.
This is because the differential system has two sources of error: a corrupted symbol, and a corrupted reference (the previous symbol).
Non-coherent reception is often easier to implement. 30

31. Resources
William Stallings, Wireless Communications and Networks, Prentice-Hall, 2005.
Andrea Goldsmith, Wireless Communications, Cambridge University Press, 2005. 31