Probabilistic Link Properties. Octav Chipara

Transcription

1 Probabilistic Link Properties Octav Chipara

2 Signal propagation Propagation in free space always like light (straight line) Receiving power proportional to 1/d² in vacuum much more in real environments (d = distance between sender and receiver) Receiving power additionally influenced by fading (frequency dependent) shadowing reflection at large obstacles refraction depending on the density of a medium scattering at small obstacles diffraction at edges shadowing reflection refraction scattering diffraction 2

3 Physical impairments: Fading (1) power long term fading short term fading t 3

4 Physical impairments: Fading (2) Strength of the signal decreases with distance between transmitter and receiver: path loss usually assumed inversely proportional to distance to the power of 2.5 to 5 Channel characteristics change over time and location Slow fading: slow changes in the average power received distance, obstacles Fast fading: quick changes in the power received signal paths change different delay variations of different signal parts different phases of signal parts 4

5 Physical Impairments: Noise Unwanted signals added to the message signal Many potential sources of noise natural phenomena such as lightning radio equipment, spark plugs in passing cars, wiring in thermostats, etc. Modeled in the aggregate as a random signal in which power is distributed uniformly across all frequencies (white noise) Signal-to-noise ratio (SNR) often used as a metric in the assessment of channel quality 5

6 Physical Impairments: Interference Signals at roughly the same frequencies may interfere with one another Example: IEEE b and Bluetooth devices, microwave ovens, some cordless phones CDMA systems (many of today s mobile wireless systems) are typically interference-constrained Signal to interference and noise ratio (SINR) is metric used in assessment of channel quality SNIR s,r = RSS s,r Noise+ Interference 6

7 Multipath propagation Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction LOS pulses multipath pulses signal at sender signal at receiver Time dispersion: signal is dispersed over time interference with neighbor symbols, Inter Symbol Interf. (ISI) The signal reaches a receiver directly and phase shifted distorted signal depending on the phases of the different parts 7

8 Signal propagation: Real world example sender transmission detection distance 8

9 Parametric propagation models Free space propagation model PL(d) =PL(d o ) d0 d 2 when not in free-space, the path loss exponent (2) is higher Log-normal propagation model PL(d) =PL(d o ) + 10nlog 10 d0 d + X X - Gaussian RV with mean zero, it accounts for shadowing n - path loss exponent, depends on environment (e.g., 3--6 indoors) d0 - reference distance in far field PL - path loss 9

10 Radio signal propagation Model signal strength (and its variation) at a distance useful for localization applications, coverage, etc networks with mobile users Model signal strength (and its variations) at a fixed distance useful for networking protocols (routing, ARQ, etc) fixed networks 10

11 Log-normal path model PL(d) =PL(d o ) + 10nlog 10 d0 d + X 11

12 Non-isotropic connectivity *Zhou et. al

13 Non-isotropic connectivity (2) 13

14 Attenuation over distance *Cerpa et. al

15 Impact of antenna height 15

16 Transitional region (aka grey region) 16

17 Transitional region Analytical Channel Model 1 Analytical PRR vs Distance P r (dbm) PRR connected region transitional region disconnected region distance (m) distance (m) 17

18 Transitional region Analytical Method to Determine Regions in Wireless Links 1 Analytical PRR vs Distance Beginning of Transitional Region End of Transitional Region P r (dbm) µ 2σ µ µ+2σ P n + γ U PRR connected region transitional region disconnected region 110 noise floor (P n ) P n + γ L distance (m) distance (m) Length of the transitional region increases with increases in shadowing => impact of multi-path decreases in path loss coefficient 18

19 Prevalence of good, bad, and intermediary links % of Links Mirage University Lake 19% 14% 5% Reception Ratio 0% 10% Packet Reception Rate 90% 100% Complementary CDF Packet Loss In Door Out Door Habitiat Poor No Link Intermediate Good Perfect Figure 1. Terminology used to describe links based A significant fraction of links fall within the transitional region these links are important for protocols but hard to utilize 19

20 Link symmetry Links are often asymmetric protocols that assume path symmetry will not work well (e.g., path reversal) 20

21 Temporal variability Observation: errors in packet transmissions tend to be clustered i.e., they are not independent Gillbert-Elliot channel: a simple channel model 21

22 logarithmic scale) Temporal properties of links P as a function of 1/RR. 1 CP vs Tau Conditional Probability good 1->1 medium 1->1 bad 1->1 good 0->0 medium 0->0 bad 0-> Autocorrelation Time Shift (seconds) (b) CP as a function of τ 22

23 Temporal properties of links Good and bad links are temporally stable Intermediary links have significant fluctuations 23

24 Next class Low-power MACs 24