LRC Mobile Radio Networks Link Level: the Radio Channel

Transcription

1 LRC Mobile Radio Networks Link Level: the Radio Channel Roberto Verdone Office Hours: Monday 4 6 pm (upon prior agreement via ) Slides are provided as supporting tool, they are not a textbook! A.Y Credits: 6

2 Outline 1. Fundamentals of Radio Propagation / 1 2. Radio Channel Characterisation 3. Large Scale phenomena 4. Small Scale phenomena a) Wideband characterisation b) Narrowband characterisation 5. The Narrowband Mobile Radio Channel 6. Link Performance in the Presence of Fading 7. Area Coverage Probability 8. Exercises 9. Fundamentals of Radio Propagation / 2 The scope of this lecture block is to introduce the basics of radio channel characterisation that will be useful to follow the link level analysis performed in this course.

3 1. Fundamentals of Radio Propagation / 1

4 Fundamentals of Radio Propagation / 1 peak transmit power d peak receive power T Pt radio space Pr R transmit antenna system receive antenna system gain G t efficiency η ta gain G r efficiency η ra radio or propagation channel

5 Fundamentals of Radio Propagation / 1 Radio à Waves

6 Fundamentals of Radio Propagation / 1 Radio à Waves Radio Communication is* the transmission, emission, reception of signs, signals, writings, images, sounds or information of whatever nature, making use of electromagnetic waves x λ E y H d z * MIN. SV. EC DIP. COM. IT. Piano Naz. di ripartiz. delle frequenze Glossario

7 Fundamentals of Radio Propagation / 1 Radio à Waves Faraday Maxwell Hertz Lodge Guglielmo Marconi: 1895 first wideband reception at Villa Griffone (Pontecchio Marconi) 1897 first ship-to-shore communications over a distance of 12 Kms 1901 first transoceanic transmission

8 Fundamentals of Radio Propagation / 1 Radio à Waves Phase speed in clear sky c = m/s = f λ Power density in free space p(d) = 0.5 E m 2 / 377 = Pt Gt η ta / 4 π d 2 W/m 2 Received power is Pr = p(d) Gr η ra / 4 π / λ 2 W Waves tend to interact with objects of size equal to or larger than λ Efficient antennas have size close to λ Antenna gains depend on directivity VLF LF MF HF VHF UHF SHF EHF f [ MHz ] 0,03 0, millimetre waves λ [ m ] Mobile Radio Networks

9 Fundamentals of Radio Propagation / 1 Radio à Waves 3 > f [ MHz ] λ [ m ] > 100 Ground Waves 3 < f [ MHz ] < < λ [ m ] < 100 Sky Waves 30 < f [ MHz ] 10 > λ [ m ] Space Waves Ground waves Sky waves Space waves Near-optical propagation VLF LF MF HF VHF UHF SHF EHF f [ MHz ] 0,03 0, millimetre waves λ [ m ] Mobile Radio Networks

10 Fundamentals of Radio Propagation / 1 Radio à Frequency Spectrum

11 Fundamentals of Radio Propagation / 1 Radio à Frequency Spectrum VLF LF MF HF VHF UHF SHF EHF f [ MHz ] 0,03 0, λ [ m ] Frequency band assignments to services are: 1) Requested by industry alliances, standardisation bodies 2) Negotiated within and recommended by ITU-R 3) Regulated on a Country basis by National Authorities 4) Released to operators / users based on National rules (context, etc.)

12 Fundamentals of Radio Propagation / 1 Radio à Frequency Spectrum ISM Bands: Licence - Exempt in Most Countries VLF LF MF HF VHF UHF SHF EHF f [ MHz ] 0,03 0, λ [ m ] MHz RFid MHz RFid MHz Proprietary Radios MHz Proprietary Radios, LoRa, GHz Proprietary Radios, Bluetooth, WiFi, Zigbee, GHz WiFi,

13 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel

14 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel d T Pt Pr R If radio space is uniform, isotropic, perfect dielectric, without obstacles, Pr = Pt Gt Gr η ta η ra / Aio Aio = ( 4 π d / λ ) 2 [Friis, 1945] Otherwise Aio replaced by Ai = c * d β * x where c is constant, x is r.v.

15 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel Spatial Filtering d Pt Pr T R Pr = Pt Gt Gr η ta η ra / Ai Receiver Power [dbm] d -β β > 2 d -2 Transmission Range Receiver Sensitivity R R distance

16 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel Spatial Filtering d Pt Pr T R β = 2 β > 2 R d R

17 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel Channel Gain Fluctuations d T Pt Pr R Receiver Power outage events Receiver Sensitivity Outage Probability: probability that received power is less than receiver sensitivity time

18 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel Channel Gain Fluctuations d T Pt Pr R d R d

19 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel Device Location d T R R distance R d pdf 2d/R 2 random uniform distribution over circle time R distance

20 Fundamentals of Radio Propagation / 1 Radio à Unpredictable Channel d T Pt radio space Pr R Pr = k d -β ξ Reliability requires: Countermeasures to user mobility Countermeasures to channel fluctuations

21 2. Radio Channel Characterisation

22 Radio Channel Characterisation s t (t) s r (t) Real World Pt Fp(f) Pr Analysis measurements or computation Comprehension Synthesis Model deterministic or statistical We do not need models that describe carefully the real world! We need models that are useful for the sake of link performance analysis

23 Radio Channel Characterisation s t (t) s r (t) Pt Pr Fp(f) Assumptions on the radio channel: Linear Multiple sources generate received signal given by sum Far Field Planar waves at the receiver antenna (d >> λ) Time-Variant Fp(f) changes with time à Fp(f, t) Quasi-Static Fp(f, t) varies slowly with respect to channel propagation delays (WSSUS Wide Sense Stationary Uncorrelated Scattering)

24 Radio Channel Characterisation 1. Narrowband: Carrier transmitted P r = P t G = P t F p (f, t) 2 Channel Impulse Response (CIR): F h(t, τ) F p (f, t) 2. Wideband: Impulse transmitted Power Delay Profile (PDP): P h (τ) = Int t [ h(t, τ) 2 ] PDP [W/s] P r = Int [ P h (τ) ] Delay (τ)

25 Radio Channel Characterisation On Wide Sense Stationarity s t (t) CIR Time (t) t 1 t 2 t 3 t 4 t 1 t 2 t 3 t 4 Tcoh (s) Delay (τ) Time (t)

26 Radio Channel Characterisation Time (t) On Wide Sense Stationarity CIR Delay (τ) t 1 t 2 t 3 t 4 Tcoh (s)

27 Radio Channel Characterisation The main phenomena characterising the mobile channel can be categorised as: 1. Large Scale if observed only changing significantly the Tx-Rx relation 2. Small Scale if observed with small changes of the Tx-Rx relation d R D << d (few λ) d R Large Scale Small Scale

28 3. Large Scale Phenomena

29 Large Scale: Shadowing Obstacles Tx Humans, vehicles, hills, trees, Rx Narrowband characterisation x

30 Large Scale Obstacles Tx Humans, vehicles, hills, trees, Rx Shadowing effect: isotropic attenuation is the product of several terms: Aim = A1 * A2 * * An Aim [db] = A1 [db] + A2 [db] + + An [db] If n is large, and central limit theorem assumptions hold, then Aim [db] is Gaussian distributed. Standard deviation from 4 to 12 depending on environment

31 Large Scale Shadowing is usually log-normally distributed, for both mobile/stationary applications Autocorrelation function is R(d) = R 0 exp [ - d/d 0 ] [Gudmunson s Model] d 0 = metres Large scale fluctuations Received power [dbm] Link Reciprocal High frequency coherence Low spatial coherence distance

32 4. Small Scale Phenomena

33 Small Scale: Fading Tx Rx Multiple Paths Narrowband characterisation Wideband characterisation Transmitted Energy time Received Energy delay

34 Small Scale: Wideband Characterisation Power Delay Profile: P h (τ) = Int t [ h(t, τ) 2 ] Mean Delay: PDP T m = Int τ [ τ P h (τ) ] / P r delay (Root Mean Square) Delay Spread: σ τ = [(( Int τ τ 2 P h (τ) ) / P r ) T m 2 ]

35 Small Scale: Wideband Characterisation To be compared to symbol time.

36 Small Scale: Wideband Characterisation Tx Rx τ σ τ = τ / 2 Fp(f, t) 2 fc notch frequency Math. derivation 1 / τ

37 Small Scale: Wideband Characterisation Tx Rx t τ σ τ = τ / 2 Fp(f, t) 2 fc Pr t time frequency

38 Small Scale: Wideband Characterisation Tx Rx τ σ τ = τ / 2 Fp(f, t) 2 fc Bc frequency 1 / τ

39 Small Scale: Wideband Characterisation Tx Rx τ σ τ = τ / 2 BLER [log], one path only BLER [log], two paths Bc 1 / τ or larger Error Floor SNR [db] Bc << 1 / τ SNR [db]

40 Small Scale: Wideband Characterisation Tx Rx τ σ τ = τ / 2 BLER [log], one path only BLER [log], two paths Bc 1 / τ or larger Error Floor SNR [db] Bc << 1 / τ SNR [db] Bc > 1 / τ (with rake receiver)

41 Small Scale: Wideband Characterisation τ / T << 1 Signal strength (random) attenuation τ / T ~ 1 or larger signal distortion τ represents delay spread of the channel impulse response

42 Small Scale: Narrowband (Mobile) Characterisation Tx Rx Speed v

43 Small Scale: Narrowband (Mobile) Characterisation d 0 = metres Large Scale fluctuations Received power [dbm] Small Scale fluctuations Rayleigh/Rice/ distributed envelope wavelengths (λ / 2 under typical urban conditions) distance

44 Small Scale: Narrowband (Mobile) Characterisation Received power [dbm] Small Scale fluctuations Non Link Reciprocal (for long ranges) Low frequency coherence Low spatial coherence distance

45 Small Scale: Narrowband (Mobile) Characterisation time = distance / speed s Pedestrian User Large Scale fluctuations Received power [dbm] s Small Scale fluctuations Speed: 1 m/s 2G, 3G, 4G frequency bands time

46 Small Scale: Narrowband (Mobile) Characterisation time = distance / speed 1-10 s Vehicular User (Urban) Large Scale fluctuations Received power [dbm] s Small Scale fluctuations Speed: 10 m/s 2G, 3G, 4G frequency bands time

47 Small Scale: Narrowband (Mobile) Characterisation time = distance / speed s High Speed Train Large Scale fluctuations Received power [dbm] s Small Scale fluctuations Speed: 80 m/s 2G, 3G, 4G frequency bands time

48 Small Scale: Doppler Effect Spectrum Transmitted Carrier fo Frequency Tx Rx Speed v Spectrum fo fo + Δf Doppler shift Frequency Received Carrier Δf is proportional to v/λ

49 Small Scale: Doppler Spectrum Spectrum Transmitted Carrier fo Frequency Tx Rx Speed v Spectrum fo - Δf fo fo + Δf Frequency Received Carrier Δf is proportional to v/λ

50 Small Scale: Doppler Spectrum Spectrum fo - Δf fo fo + Δf Frequency BLER [log], no Doppler BLER [log], with Doppler Bc v / λ Bc >> v / λ Error Floor SNR [db] SNR [db]

51 Small Scale: Narrowband (Stationary) Characterisation Do not use previous model for v tending to zero; the speed of obstacles has to be considered The Doppler spectrum might change (typically bell-shaped) The fluctuation rate depends on speed of scatterers The statistics of channel fluctuations might change

52 Small Scale: Narrowband Characterisation Channel fluctuations are fast or slow depending on the user speed. In any case, one has to define what Fast or Slow means with respect to the figures considered e.g. The quality of human oriented communications: it is known that human perception is not sensitive to fluctuations faster than a few Hertz, Hence, link quality has to be averaged over fast fluctuations where fast means with a frequency larger than a few Hertz (for instance, fading for pedestrian or vehicular speeds in the GSM frequency band)

53 Radio Channel Characterisation in a nutshell The main phenomena characterising the mobile channel can be categorised as: Large Scale Small Scale shadowing due to obstacles along the entire path fading due to multipath caused by reflections, diffractions, over objects in the vicinity of receiver (scatterers) Channel characterisation can be Narrowband Single carrier is transmitted: link budget is the issue flat or time selective fading (small scale) shadowing (large scale) Wideband Short pulse is transmitted: multipath delay is the issue frequency selective fading (small scale) We focus mainly on link budget related issues (i.e. narrowband characterisation)

54 Radio Channel Characterisation in a nutshell Frequency bands from 400 MHz to 4 GHz Fading Shadowing Coherence Time T coh ms 1 10 s Coherence Band B coh MHz MHz Coherence Space S coh m m

55 Inquiry Based Session Does 2G (Bc = 200 KHz, fc = 1800 MHz) suffer from frequency selective fading? Does WiFi (Bc = 22 MHz, fc = 2.4 GHz) suffer from frequency selective fading? Does 2G (Bc = 200 KHz, fc = 1800 MHz) suffer from time selective fading?

56 5. The Narrowband Mobile Radio Channel

57 The Narrowband Mobile Radio Channel Received power [dbm] Prm(d) x distance Pr(x) = Prm(d) m 2 (x) r 2 (x) = Pra(x) r 2 (x) Pr(x) short term average power (over few carrier cycles) Pra(x) = Prm(d) m 2 (x) long term average power (over fading: few wavelenghts) Prm(d) median power (distance dependent component)

58 The Narrowband Mobile Radio Channel Pr(x) = Prm(d) m 2 (x) r 2 (x) Model Assumptions Shadowing: m 2 (x) is assumed to be log-normal distributed: Pra(x) [dbm] = Prm(d) [dbm] + s(x) [db] s(x) is Gaussian, zero mean, std dev. σ Fading: r(x) is assumed to be Rayleigh distributed (worst case), i.e. f(x) = r 2 (x) is negative exponentially distributed: pdf(f) = [1 / X] exp (- f / X) u(f) X = E[r(x) 2 ] =1 u(f) step function Median Power: Prm(d) = k d -β

59 6. Link Performance with Fading

60 Link Performance with Fading BLER [log] SNR [db] Human oriented applications: BLERa = Long term average BLER BLERa [log] BLERa = E [BLER(SNR)] = g(snra) Machine type applications: P out = Link Level Outage Probability P out = Prob [ BLER > BLER* ] = Prob [ SNR < SNR* ] = 1 exp(-snr*/snra) (Rayleigh) Pout [log] SNRa [db] SNRa [db]

61 7. Area Coverage Probability

62 Area Coverage Probability BLERa [log] R pdf(d) 2d/R 2 d R d SNRa [db] P cova = E d [P cov (d)] = Int_0^R [ P cov (d) 2d / R 2 ] P cov (d) = Prob [ BLERa(d) < BLERa* ] = Prob [ SNRa(d) > SNRa* ] = Prob [ Pra(d) > Pra* ] Pra(d) [dbm] = Prm(d) [dbm] + s P cov (d) = Prob [ s > (Pra* - Prm(d) [db]) ] = 0.5 erfc[(pra* - Prm(d) [db]) / σ 2 ] Math. derivation à P cov (R) = f (R, a) a = M sh [db] / σ M sh = Prm(R) / Pra*

63 Area Coverage Probability: compl. error function (erfc) erfc(x) = 2 π e t 2 dt x x E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04

64 Area Coverage Probability: compl. error function (erfc) x erfc(x) = 2 π e t 2 dt x E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-17

65 Area Coverage Probability a = M sh [db] / σ 1 Coverage probability at cell border P cov a

66 Area Coverage Probability a = M sh [db] / σ 1 Average coverage probability P cova a β = 2 β = 3 β = 4

67 Area Coverage Probability 1 β = 3, k = 0.01, P * ra = 101 dbm σ = 6 σ = 9 σ = 12 Average coverage probability Cell radius [km]

68 Area Coverage Probability 1 β = 4, k = 0.01, P * ra = 101 dbm σ = 6 σ = 9 σ = 12 Average coverage probability Cell radius [km]

69 8. Exercises

70 Exercise LRC#1 Assume that the median received power at a distance of one meter is -10 dbm. The propagation exponent is equal to 4. Compute the probability that the long term average power is less than -93 dbm at a distance of 100 m, with standard deviation of shadowing equal to 6. Exercise LRC#2 Assume that the long term average power in a link is equal to -67 dbm. Under Rayleigh fading conditions, what is the probability of having short term average power less than -80 dbm?

71 Exercise LRC#3 Determine the maximum radius of a GSM cell (frequency band: 1800 MHz) assuming standard deviation of shadowing equal to 6, isotropic loss at 1 m set as 40 db and propagation exponent equal to 3. Transmitted power is 10 W, transmit and receive antenna gains are 10 db and 0 db respectively. Neglect losses due to antenna connections. The receiver sensitivity is -101 dbm. The requirement on average coverage probability is 90%. Exercise LRC#4 For the same set of parameters as above, draw a diagram showing the maximum cell radius as a function of the propagation exponent, from 3 to 4.

72 9. Fundamentals of Radio Propagation / 2

73 Fundamentals of Radio Propagation / 2 Radio à Frequency Spectrum VLF LF MF HF VHF UHF SHF EHF f [ MHz ] 0,03 0, λ [ m ] Spectrum usage f [ MHz ] More than 90% is actually unutilised!

74 Fundamentals of Radio Propagation / 2 Radio à Frequency Spectrum Ultra Wide Band Spectrum usage [Ross, 60s] f [MHz] Cognitive Radio Spectrum usage [Mitola, 1991] f [MHz]

75 Waves

76 Radio Networks Link Level: the Radio Channel The End Portonuovo