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##### Physical layer basics

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**Physical layer basics**• transmit bit stream from sender to receiver • what does sender need to do? • what is transmitted into the air? • what happens in the air? • what does receiver need to do?**modulation**channel coding source coding At sender analog signal bit stream • source coding/compression • reduce redundancy • channel coding • add redundancy (why?) • modulation • from bit stream to wave form • from analog form (e.g., music) to another form**Modulation in wireless communication**• translate digital data to analog signal (baseband) • shifts center frequency of baseband signal up to the radio carrier • example carrier frequency • 802.11b/g: 2.4 GHz, 802.11a (5 GHz), GSM: 1.9 GHz • why? • Antenna size: on the order of signal’s wavelength • More bandwidth available at higher carrier frequency • Medium characteristics (path loss, shadowing, reflection, scattering, diffraction) depend on signal’s wavelength**analog**baseband signal digital data modulation modulation 101101001 radio carrier Modulation at sender**Modulation schemes**• Amplitude Shift Keying (ASK) • Frequency Shift Keying (FSK) • Phase Shift Keying (PSK)**Amplitude Shift Keying (ASK)**• Pros: simple • Cons: susceptible to noise • Example: optical system, infra-red 1 0 1 t**Frequency Shift Keying (FSK)**• Pros: less susceptible to noise • Cons: requires larger bandwidth 1 0 1 t 1 0 1**Phase Shift Keying (PSK)**• Pros: • Less susceptible to noise • Bandwidth efficient • Cons: • Receiver must synchronize in frequency and phase w/ transmitter t**Q**I 1 0 Q 11 10 I • QPSK (Quadrature Phase Shift Keying): • 2 bits coded as one symbol • needs less bandwidth compared to BPSK • symbol determines shift of sine wave • Often also transmission of relative, not absolute phase shift: DQPSK - Differential QPSK 00 01 A t 01 11 10 00 Variant of phase shift keying • BPSK (Binary Phase Shift Keying): • bit value 0: sine wave • bit value 1: inverted sine wave • very simple PSK • low spectral efficiency • robust, used in satellite systems**Example: 16-QAM (4 bits = 1 symbol)**Symbols 0011 and 0001 have the same phase φ,but different amplitude a. 0000 and 1000 have same amplitude but different phase Used in Modem Q 0010 0001 0011 0000 φ I a 1000 Quadrature Amplitude Modulation (QAM) • combines amplitude and phase shift keying • It is possible to code n bits using one symbol • 2n discrete levels • bit error rate increases with n**What is transmitted in air?**• radio wave (baseband modulated w/ carrier radio) • high-frequency, short wavelength • wave length * frequency = speed of light 3x108m/s • e.g., 802.11b, wavelength 0.1m**Frequency range (bandwidth)**• need a wide spectrum • e.g., 802.11b bandwidth 20 MHz • w/o noise: Nyquist’s result • w/ noise (e.g., thermal noise, background radiation) • Shannon’s channel capacity theorem: the maximum number of bits that can be transmitted per second by a physical channel is: • W: frequency range • S/N: signal noise ratio**Frequencies for communication**twisted pair coax cable optical transmission 1 Mm 300 Hz 10 km 30 kHz 100 m 3 MHz 1 m 300 MHz 10 mm 30 GHz 100 m 3 THz 1 m 300 THz visible light VLF LF MF HF VHF UHF SHF EHF infrared UV VLF = Very Low Frequency UHF = Ultra High Frequency LF = Low Frequency SHF = Super High Frequency MF = Medium Frequency EHF = Extra High Frequency HF = High Frequency UV = Ultraviolet Light VHF = Very High Frequency**Frequency regulation**• ITU-R holds auctions for new frequencies, manages frequency bands worldwide (WRC, World Radio Conferences)**What happens in the air?**• path loss: attenuation due to distance • fading (frequency dependent) • shadowing • reflection at large obstacles • refraction depending on the density of a medium • scattering at small obstacles • diffraction at edges refraction shadowing reflection scattering diffraction**Received**Signal Power (dB) path loss shadow fading Rayleigh fading log (distance) Typical picture**Detour: dB and Power conversion**• dB • Denote the difference between two power levels • (P2/P1)[dB] = 10 * log10 (P2/P1) • P2/P1 = 10^(A/10) • Example: P2 = 100 P1 • dBm and dBW • Denote the power level relative to 1 mW or 1 W • P[dBm] = 10*log10(P/1mW) • P[dB] = 10*log10(P/1W) • Example: P = 0.001 mW, P = 100 W**Path loss**• determine average received power • proportional to 1/dn • d: distance from sender to receiver • vacuum: n=2 • in practice: n larger than 2**Path loss models**• Free space model • Pr(d): receiver power, Pt: transmitter power • d: distance from transmitter to receiver • Gt: transmitter antenna gain • Gr: receiver antenna gain • lambda: wave length, L: constant • Two-ray ground reflection model • ht: height of transmitter, hr: height of receiver**Log-normal/shadow fading**• long-term variation or fading Gaussian r.v. Average received power**Multipath fading**• Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction LOS pulses multipath pulses LOS: Line Of Sight signal at sender signal at receiver**When transmitter and/or receiver moves?**• Short-term fading • quick changes in the power received • Doppler shift long term fading power t short term fading**signal**power interference spread signal power spread interference detection at receiver f f Spread spectrum technology • spread a narrow band signal into a broad band signal using a special code • Resilient to narrow band interference • Side effects: • coexistence of several signals without dynamic coordination • tap-proof**Effects of spreading and interference**dP/df dP/df user signal broadband interference narrowband interference i) ii) f f sender dP/df dP/df dP/df iii) iv) v) f f f receiver**tb**user data 0 1 XOR tc chipping sequence 0 1 1 0 1 0 1 0 1 1 0 1 0 1 = resulting signal 0 1 1 0 1 0 1 1 0 0 1 0 1 0 tb: bit period tc: chip period DSSS (Direct Sequence Spread Spectrum) • XOR the signal with pseudo-random number (chipping sequence) • generate a signal with a wider range of frequency: spread spectrum • spread factor: tb/tc • military applications use spread factor up to 10,000**spread**spectrum signal transmit signal user data X modulator chipping sequence radio carrier transmitter correlator lowpass filtered signal sampled sums products received signal data demodulator X integrator decision radio carrier chipping sequence receiver DSSS System**FHSS (Frequency Hopping Spread Spectrum)**• Discrete changes of carrier frequency • sequence of frequency changes determined via pseudo random number sequence • Two versions • Fast Hopping: several frequencies per user bit • Slow Hopping: several user bits per frequency • Advantages • frequency selective fading and interference limited to short period • simple implementation • uses only small portion of spectrum at any time**tb**user data 0 1 0 1 1 t f td f3 slow hopping (3 bits/hop) f2 f1 t td f f3 fast hopping (3 hops/bit) f2 f1 t tb: bit period td: dwell time FHSS: Example**Comparison between slow hopping and fast hopping**• Slow hopping • Pros: cheaper • Cons: less immune to narrowband interference • Fast hopping • Pros: more immune to narrowband interference • Cons: tight synchronization increased complexity**FHSS (Frequency Hopping Spread Spectrum)**spread transmit signal narrowband signal user data modulator modulator frequency synthesizer hopping sequence transmitter narrowband signal received signal data demodulator demodulator hopping sequence frequency synthesizer receiver**demodulation**At receiver analog signal bit stream source decoding channel decoding**analog**baseband signal digital data demodulation synchronization decision 101101001 radio carrier Demodulation at receiver**Signal interference and noise ratio**• Signal (S) • Noise (N) • Includes thermal noise and background radiation • Often modeled as additive white Gaussian noise • Interference (I) • Signals from other transmitting sources • SINR = S/(N+I) (sometimes also denoted as SNR)