Wireless Mesh Networks Anatolij Zubow (zubow@informatik.hu-berlin.de) Signal Encoding Techniques

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

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

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

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

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

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

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

Modulation of Analog Signals for Digital Data 9

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

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

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

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

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

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

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

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

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

QPSK and OQPSK Modulators Example of QPSK and OQPSK Waveforms 19

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

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

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

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

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

Performance in Presence of Noise 25

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

QAM Modulator 27

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

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

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

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