Antennas and Propagation. Chapter 6a: Propagation Definitions, Path-based Modeling

Transcription

1 Antennas and Propagation a: Propagation Definitions, Path-based Modeling

2 Introduction Propagation How signals from antennas interact with environment Goal: model channel connecting TX and RX Antennas and Propagation Slide 2

3 Free-Space Propagation Friis Range Equation Have seen before: Power varies as 1/r 2 with distance Obstacles excess loss relative to free space loss Simple model Here, γ is the loss exponent Free space: γ = 2 General channels: γ > 2 (3 to 6 are reasonable values) Model supported by empirical measurements Note: In propagation chapter, we will assume isotropic (point) sources. We can always do pattern multiplication after analysis if needed. Antennas and Propagation Slide 3

4 Free-Space Propagation (2) How do we get normalizing constant c? Assume we know receive power to be P R,ref at reference distance r ref For same transmit power, we now have Note: in db, we have power variation Means 10γ db of loss for every 10x distance Antennas and Propagation Slide 4

5 Free-Space Propagation (3) Simple power laws assume far-field condition Antennas are in far-field of each other Have a problem for r 0, since PR for a fixed reference power A common first-order correction If the antennas are touching P R = P T Far from the transmitter, the 1 will be negligible Antennas and Propagation Slide 5

6 Path-Based Models Fields radiated by antennas Outgoing spherical waves Far from source look planar (in a small area) Spherical wave fronts Look approximately planar far from source Direction of Propagation Always outward relative to source Antennas and Propagation Slide 6

7 Path-Based Models (2) Option 1 Model spherical waves from 1. Source, 2. reflections, 3. reflections of reflections, etc. Superimpose waves Can become very complicated Option 2 Only worry about waves traveling in certain directions Those connecting TX to RX Allows us to use a plane-wave, ray, or path representation Much simpler! Antennas and Propagation Slide 7

8 Definition Ray Portion of a spherical wave that travels in a specific direction In free space Ray propagates with complex envelope (amplitude) Complete Spherical Wave How many outgoing rays? Infinite! Relatively few directions matter for most channels Antennas and Propagation Slide 8

9 Definition: Path Path Set of connected rays linking transmit to receive Paths can arise from several different propagation mechanisms Antennas and Propagation Slide 9

10 Path Models Line-of-Sight (LOS) Unobstructed path from transmitter (TX) to receiver (RX) Quasi-Line-of-Sight Direct path when it is obstructed Antennas and Propagation Slide 10

11 Path Models (2) Shadow/Shadowing Like with visible light Region of relatively low field strength Behind an obstruction (e.g. 10dB drop) Antennas and Propagation Slide 11

12 Path Models (3) Path Set of connected rays linking TX to RX LOS path just has one ray segment Different types of reflections have 2 or more ray segments Antennas and Propagation Slide 12

13 Path Models (4) Specular Reflections When a plane wave encounters a planar surface Reflected and transmitted plane waves are created Described by Fresnel reflection and transmission Antennas and Propagation Slide 13

14 Path Models (5) Multipath Existence of multiple transmission paths Add coherently at receiver Results in rapid and deep fluctuating RX power level (20 db or more) Different from shadowing (sensitive to movement on the λ scale) Antennas and Propagation Slide 14

15 Path Models (6) Specular Transmission Wave transmitted through homogeneous obstacle Antennas and Propagation Slide 15

16 Path Models (7) Diffuse Scattering Wave encounters 1. Rough surface 2. Random medium Continuum of paths are created More difficult to deal-with than specular paths Antennas and Propagation Slide 16

17 Path Models (8) Diffraction Caused by edges or holes A new effective source is created at edge or hole Spherical waves emanate Antennas and Propagation Slide 17

18 Path Models (9) Path Loss Signal attenuation along a given path. Also can refer to total attenuation in signal level from TX to RX Numbers like 70 db to > 100dB typical for wireless Free-space Path Loss 1/r 2 spreading we saw before Antennas and Propagation Slide 18

19 Ranges of Interaction Near-Field Scatterer Must be modeled together with antenna Local Scattering Near TX or RX Distant Scattering Far from both TX/RX Antennas and Propagation Slide 19

20 Specular Paths Direct Path Source emits spherical waves Assume we only care about fields at receiver Plane wave in direction k due to direct path Antennas and Propagation Slide 20

21 Specular Paths Direct Path Source emits spherical waves Assume we only care about fields at receiver Plane wave in direction k due to direct path Antennas and Propagation Slide 21

22 Specular Paths Planar Surface Can be replaced with image By following wave-fronts, just have a plane wave Antennas and Propagation Slide 22

23 Specular Paths Planar Surface Can be replaced with image By following wave-fronts, just have a plane wave Just considering propagation along path Antennas and Propagation Slide 23

24 Specular Paths Planar Surface Can be replaced with image By following wave-fronts, just have a plane wave Just considering propagation along path Representation much simpler! Antennas and Propagation Slide 24

25 Specular Path Computation Note: waves keep expanding outward as we have multiple reflections (Different from diffraction) Antennas and Propagation Slide 25

26 Diffraction Properties Edge, corner, hole Creates a new effective source One incoming ray leads to infinite outgoing rays Antennas and Propagation Slide 26

27 Diffraction Computation σ is diffraction coefficient Depends on 1. type of edge 2. directions of incoming and outgoing waves Exact expressions for σ only available for knife edge Expression for wedges, but approximate Antennas and Propagation Slide 27

28 Example 1: Channel Power Measurement Measurement of Channel Power P R /P T Scenario Indoor (hallway) environment. Single frequency. LOS/NLOS Transmit Receive Antennas and Propagation Slide 28

29 Raw Measurement Indoor: Movement Path 1 Antennas and Propagation Slide 29

30 Shadowing: Outdoor to Indoor Antennas and Propagation Slide 30

31 Shadowing: Building Corner Antennas and Propagation Slide 31

32 Example 2: 2D FDTD Simulations Show 2D FDTD movie Antennas and Propagation Slide 32

33 Modeling of System/Channel In physical world Infinite bandwidth time-domain signals present and interact Have real input/output relationship In practice Only interested in signals in a small fractional bandwidth Complex baseband representation more convenient Antennas and Propagation Slide 33

34 Complex Baseband All band-pass signals written in form True (band pass) time-domain signal Slowly varying complex envelope Center frequency/ or carrier Antennas and Propagation Slide 34

35 Complex Baseband Model Goal: Show that complex baseband and time-domain models equivalent Write our complex baseband signal as Antennas and Propagation Slide 35

36 Complex Baseband Model (2) Spectrum of baseband TX signal Up-Converted Spectrum (* sym) Up-conversion Same information in baseband channel spectrum Effect of antenna/channel in h(t) Antennas and Propagation Slide 36

37 Complex Baseband Model (2) Same information in baseband channel spectrum Effect of antenna/channel in h(t) Antennas and Propagation Slide 37

38 Complex Baseband Model (3) Output of channel For convenience let Antennas and Propagation Slide 38

39 Complex Baseband Model (4) Region of support for H b (ω) should be limited Can only have it go as low as -ω 0. Otherwise definition does not makes sense Normally, we have W/2 < ω 0 (otherwise up-conv. aliases) z(t) Because no overlap, second term is 0 Antennas and Propagation Slide 39

40 Complex Baseband Model (5) Finally, what happens at receiver Antennas and Propagation Slide 40

41 Channel Response How to compute H b (ω)? Connects source signal x to receive signal y Equivalent circuit model Which signals correspond to input/output? Complete Model of Transmit, Receive, Antennas, Channel Complete model Transmit electronics Antennas and propagation channel Receive electronics Goal: Compute complete input/output relationship Antennas and Propagation Slide 41

42 Multiple Sources and Loads Represent source and load with diagonal matrices What does this mean? When is this not be the case? Antennas and Propagation Slide 42

43 Propagation Channel Represented with paths using the function For this analysis, assume we know this function Later will show how to model it Antennas and Propagation Slide 43

44 Transmit: Input current First, compute currents delivered to antennas Antennas and Propagation Slide 44

45 Transmit: Radiated field Given the currents Radiated field (single polarization) Multiple polarizations Antennas and Propagation Slide 45

46 Receive: Incident Field General polarimetric relationship Double directional channel response Relates receive incident fields to transmit far-fields Antennas and Propagation Slide 46

47 Receive: Induced voltages Single polarization: open-circuit voltage on ith antenna For multiple polarizations What is the physical interpretation of these integrals? Antennas and Propagation Slide 47

48 Receive: Load Voltages Have open-circuit voltages, but we measure loaded voltages Antennas and Propagation Slide 48

49 Connecting it all together! Antennas and Propagation Slide 49

50 Complete Model Channel without coupling Consider Channel operates directly on signals Antennas and Propagation Slide 50

51 Multiple-Input Multiple-Output (MIMO) Wireless system with multiple TX and RX antennas: Typical signal processing representation. Still valid in case of coupled antennas? Yes, but need to use Note: for coupled antennas, can be a huge difference between H and H nc! Antennas and Propagation Slide 51

52 Next Time Details of modeling H(ω) Antennas and Propagation Slide 52