Wireless data networks Physical Layer Martin Heusse X L A TEX E
Attenuation / Propagation • Ethernet (twisted pair), attenuation < 10dB for 100m • Fiber: typically 1dB/km • Radio waves in the air: 10 − 2 dB/km But—the signal is not guided: the energy is projected on a surface that grows with the distance ( λ ) 2 P r = P t G t G r 4 π d (Friis transmission equation) P r , t received / transmitted power; G r , t rec./trans. antenna gain; d : distance, λ : wavelength ( G r λ is the effective area of the receiver) PHY. 2
Consequences • ✓ d = 1 km → − 80 dB ✓ d = 10 m → − 40 dB ✓ d = 1 m → − 30 dB • I’m deaf when I’m talking • Relatively high gain input amplification PHY. 3
Real world propagation • Reflections • Diffraction • Absorption Loss at 5GHz ✓ Wood house siding: 8̃dB ✓ Concrete wall: 22dB • Scattering • Doppler (People movement) PHY. 4
Fresnel zone • Elliptically shaped surface of revolution where the reflected/diffracted path length is different by a multiple of 180° from the direct path n = 3 n = 2 n = 1 d 1 d 2 a r 1 b Transmitter Receiver Propagation path (can be curved) Figure 2.19 Fresnel zones around a propagation path shown in 2 dimensions. • Surface such that: d 1 + d 2 + n λ /2 = a + b √ n λ d 1 d 2 • r n ≈ d 1 + d 2 PHY. 5
Two ray ground d h t d 1 d 2 h r ( λ 2 ) 2 � ( ) e − j δφ � d • P r = P t G t G r � 1 − � � 4 π d d 1 + d 2 � ( ) d e − j δφ | 2 ≈ δφ 2 • If d 1 + d 2 ≈ d then | 1 − d 1 + d 2 λ 2 h t h r and (…) δφ = 2 π λ ( d 1 + d 2 − d ) ≈ 2 π d • Then: ( h t h r ) 2 P r = P t G t G r d 4 (No more proportional to λ …) PHY. 6
Antennas • Current → charge displacement → Electrical field… Current in a two-wire transmission line _ + • Corpuscular version: electrons emit photons when shaken! PHY. 7
Antennas (cont.) • Eletrical field lines λ /2 • Dipole antenna PHY. 8
Antennas (cont.) Figure 4.11 Three-dimensional pattern of a λ / 2 dipole. ( SOURCE: C. A. Balanis, “Antenna Theory: A Review” Proc. IEEE , Vol. 80, No 1. Jan. 1992. 1992 IEEE). Do not point it toward the intended receiver! • Marconi antenna λ /4 Same thing, using the reflection on a ground plane. PHY. 9
Antennas (cont.) θ θ 0 ° Relative power 30 ° 30 ° (dB down) 10 − − 60 ° 20 60 ° 30 + + 30 20 10 90 ° 90 ° 120 ° 120 ° − − 150 ° 150 ° 180 ° Two-dimensional amplitude patterns for a thin dipole of l = 1 . 25 λ (Copied from Balanis) PHY. 10
Other antennas • Horn July 11, 1962, first transmission from the US to france of a TV signal, bounced back by the Telstar satellite. The satellites were low orbiting so that required a tracking antenna. No positioning system on the satellite: they were spheres and no parabolic antenna!! Antenna weight: 280 tons! 6.69 GHz uplink, 4.12 GHz downlink. The radome is inflated. Still the biggest radomes ever built, and still there in Plemeur-Bodou! Reflector Driven element Directors • Yagi PHY. 11
Other antennas (cont.) + • Parabola All points equidistant from a fixed line and a fixed point PHY. 12
Modulation techniques • ASK • FSK • PSK (BPSK, QPSK) • QAM PHY. 13
Signal shaping • PSK exemple: abrupt transitions on symbol boundaries 1.0 0.5 f (x) 0.0 −0.5 −1.0 0 1 2 3 4 5 t → Infinite spectrum! () ★ Signal shaping ✓ Ex.: raised cosine spectrum. ✓ The impulse response of a raised cosine is 0 at every nT (no interference at sampling instant) PHY. 14
Example: QAM modulation R bps Shaping Shaping sin(2 π f c t) cos(2 π f c t) + PHY. 15
What is fading? • Additive white Gaussian noise (AWGN) ✓ Thermal noise, electronics, propagation • Rayleigh fading: multiple indirect paths; no dominant (LOS) path ✓ The signal enveloppe follows a Rayleigh distribution ★ Rician: there is a dominant path; parameter K = power ( LOSpat ) powerotherpaths PHY. 16
What is fading? (cont.) PHY. 17
Spread spectrum • Use as much of the channel as possible Make E b b / N 0 as large as possible • Helps in presence of narrow band interferences • Spread the transmitted power over a wider freq. range (ISM bands…) PHY. 18
FHSS • • PHY. 19
DSSS • XOR each bit of data with a predefined sequence (or code) • Same operation at the receiver ( x ⊗ c ⊗ c = x ) • Used by 802.11b • Related to CDMA PHY. 20
OFDM Orthogonal Frequency Division Multiplexing • Many narrow band symbols sent in parallel ( → gain and phase is constant in each sub-channel) • Good spectrum utilization • Limited complexity at both the emitter and receiver • Works great with severe channel conditions • But: ✓ Sensitive to Doppler shift ✓ Requires linear amplifiers, high peak to average power ratio (the power peaks when the sine waves add to each other) PHY. 21
OFDM Orthogonal Frequency Division Multiplexing (cont.) 1 sin(x+pi)/(x+pi) sin(x)/x 0.8 sin(x-pi)/(x-pi) 0 0.6 0.4 0.2 0 -0.2 -0.4 -10 -5 0 5 10 PHY. 22
OFDM Orthogonal Frequency Division Multiplexing (cont.) R bps T Serial to parallel T IFFT T Parallel to serial DAC f c PHY. 23
OFDM Orthogonal Frequency Division Multiplexing (cont.) • Applications ✓ (A)DSL (250 sub-carriers split between uplink and downlink) ◮ Symbol duration: 231.88 µ s ↔ sub-carrier spacing: 4.3125 kHz ✓ 802.11a, g (48 sub-carriers) ✓ DVB-T (up to 8192 sub-carriers), DAB ✓ WiMAX ✓ LTE PHY. 24
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