Page 1. Radio Wave Propagation. Introduction

Transcription

1 Page Intrductin Radi was first pstulated in 873 by Maxwell wh fund mathematically that a wave that was bth electric and magnetic, and travelled at the speed f light shuld exist. This was demnstrated in 888 by Hertz Used fr practical cause in 895 by Marcni. Radi is an electrmagnetic phenmenn and radiates as phtns. It belngs t the family f radiatin that includes X rays, light and infrared waves. Table. belw details the different categries f radiatin. Frequency range Name/Abbreviatin Main Uses Less than 300 Hz Extremely lw (ELF) Submarine 300 Hz 3 khz Infra lw (ILF) Vice band 3 khz 30 khz Very lw (VLF) Audi band 30 khz 300 khz Lw (LF) Bradcast/ lng range 300 khz 3 MHz Medium (MF) Bradcast/lng range/shrtwave 3 MHz 30 MHz High (HF) Shrtwave band 30 MHz 300 MHz Very high (VHF) Mbile radi/paging/vhf TV 300 MHz 3 GHz Ultra high (UHF) Mbile radi/micrwave/tv 3 GHz 30 GHz Super high (SHF) Micrwave/Satellite 30 GHz 300 GHz Extremely high (EHF) Micrwave 300 GHz 3000 GHz Tremendusly high (THF) Experimental Basic Prpagatin Mdel All practical radi systems can be reduced t the basic scheme shwn in Fig.. It fllws frm the Fig. that there are three main independent electrnics and electrmagnetic design tasks related t radi wave cmmunicatin systems. The first task is the specificatin f the electrnic equipment that cntrls all peratins within the transmitter, including the transmitting antenna peratin. The radi prpagatin channel plays a separate independent rle. Its main utput characteristics depend n the cnditins f the radi wave prpagatin in the varius peratinal envirnments. The third task cncerns the same peratins and signals, but fr the receiver, with its wn peculiarities. Fr bth kinds f antennas, the transmitting and receiving, an imprtant issue is the influence f different kinds f bstacles lcated arund the antennas and the envirnmental cnditins. University f Lags, 009

2 Page Nise and Signal Nise Perfrmance All radi systems are limited in range by nise. When the intrusin f nise is such that an acceptable signal can n lnger be btained, then the system is said t be nise limited. Medium and shrt wave bradcast perate in a very nisy envirnment, whilst VHF and UHF perate in quieter envirnment and mst f the nise experienced is generated in the RF preamp f the receiver itself. Regardless f hw well the receiver is designed, there is a theretical nise pwer level, at a given temperature, cannt be imprved upn. This is Due t thermal nise which is prprtinal t perating temperature: antennas and amps will generate thermal nise cntinuusly Nise is typically separated int additive (r white nise) and multiplicative nise. Additive nise arise frm: Nise in the receiver antenna Nise within the electrnic equipment that cmmunicates with antenna Backgrund and ambient nise (galvanic, atmspheric, man-made etc Multiplicative nise arises frm: Multireflectins frm grund surfaces, walls and hills Multiscaterring frm rugh surfaces such as the sea, rugh terrain, building and trees Multidiffractin frm edges f walls, building rftps, and hilltps Additive nise is mainly due t the randm mtin f electrns within the varius cmpnents f equipment. The nise pwer inside the transmitter-receiver channel at a given system bandwidth B w is given by: N F = k B T 0 B w [] where k B = WsK is Bltzmannʼs cnstant, T 0 = 90K(7 C). [] can be written taking int accunt the nise factr, F, f the receiver: F = + T e T 0 [] where T e is the effective nise temperature at the receiver. N F = k B T 0 B w F [3] T perceive a relatively nise free signal, the incming signal must exceed the nise level by a respectable margin knwn as the Signal t Nise Rati (SNR). Fr cellular radi systems, SNR typically is db fr marginal receptin and 30 db fr gd quality receptin Prpagatin Radi waves prpagate at the speed f light. They reach the receiver in a multipath situatin in which the varius waves arrive with different radi paths and time delays. At the receiver, such waves are cmbined t give an scillating resultant signal, the variatins f which depends n the distributin f phases amngst the incming cmpnent waves. University f Lags, 009

3 Page 3 The signal amplitude variatins are knwn as fading. Fading is basically a spatial phenmenn, but signal variatins are experienced as tempral variatins by a receiver and/r transmitter mving thrugh the multipath field r due t mving scatters in essence we are talking abut space and time dmain variatins f electrmagnetic fields in land envirnments. There is als the randm fading in the frequency dmain, as experienced by mbile cmms systems: this therwise knwn as the Dppler effects and refers t the cmplicated interference picture f the received signal caused by receiver/transmitter mvements. In built up areas, the urban prpagatin channel is apprximately statinary in time, but the spatial variatins f signal level have a triple nature: Path Lss defined as an verall decrease in the signal strength with distance between tw terminals the transmitter and receiver when the signal is expressed in db. The physical prcesses, which cause this phenmenn are the spreading f electrmagnetic wave radiated utwards in space by the transmitter antenna and the bstructing effects f any natural and man-made bject surrunding this antenna. The spatial and tempral variatins f the signal path lss are large and slw. Shadw (r Slw) Fading: This is a large scale (in the space dmain) and lng term (in the time dmain) fading. It is caused by diffractin frm buildingsʼ crners ad their rftps, r frm hillʼs tp lcated alng the radi link surrunding the terminal antennas. The spatial scale f the large-scale variatins is f the rder f the bstructinsʼʼ dimensins. Fast Fading: Small scale fading in the space dmain and shrt term (r fast) signal variatins in the time dmain, which are caused by the mutual interference f the wave cmpnents f the multi ray field. The characteristic scale f such waves in the space dmain is changed frm half wavelength t three wavelength Path Lss, Slw Fading and Fast Fading Path lss determines the effectiveness f the prpagatin channel in varius kinds f envirnments. It defines variatins f the signal amplitude r field intensity alng the prpagatin path frm pint t pint within the cmmunicatin channel. Letʼs assume that the signal wave amplitude at the pint r alng the prpagatin path is r the signal wave intensity is J ( r ) = A ( r ). In the prcess f prpagatin alng the A r University f Lags, 009

4 Page 4 path, at any next pint r, the signal wave amplitude is A r = A. J r r r the intensity Path lss is defined as the lgarithmic difference between the amplitude r the intensity at the pints r and r alng the prpagatin path in the medium. L = 0 lg A r A r [4] Slw Fading: Slw spatial signal variatins tend t nrmal r Gaussian distributins, the average signal pwer variatins, as a result f their averaging within sme individual small area, tend t the lg-nrmal distributin with the standard deviatin that depends n the relief f the terrain and n the type f built up area. Fast Fading: bserved ver distances f abut half r ne wavelength. Tw main situatins can be discussed: Subscribersʼ antennas are statinary with respect t the base statin: this situatin is referred t as static multipath situatin. Narrwband signals travel alng different paths f varying lengths due t multiple reflectins and scattering Subscribersʼ antennas are in mtin relative t the base statin: this situatin is referred t as dynamic multipath situatin. The spatial variatins f resultant signal at the receiver can be seen as tempral variatins at the receiver as it mves thrugh the multipath field Signal fading ccurs in the time dmain Dppler effects Radi Survey is the prcess f measuring the prpagated radi field strength ver an area f interest. It is an essential part f cellular radi site selectin prcess. It is a design aid and als a maintenance tl. As a design aid, it helps determine the ptential cverage f a prpsed base statin site. As a maintenance tl, it cnfirms the cntinual satisfactry cverage. A radi survey is usually perfrmed using a field strength-measuring receiver lcated in a vehicle. Smetimes the reciprcal path that is the path frm the mbile t base statin is measured instead. Bth measurements are mathematically equivalent except in satellite mbile links It is imprtant t nte that field strength is a statistical variable parameter and thus the measurement methd needs t allw fr this Three factrs cntribute t the field strength value measured Path Lss (free space) Lg Nrmal Fading Rayleigh (r Multipath) Fading University f Lags, 009

5 Page 5 Path Lss Predictin Mdels in Varius Outdr Cmm Links Free Space Path Lss If we cnsider a nn-istrpic antenna placed in free space as a transmitter f P T watts and with a directivity gain G T, then at an arbitrary large distance frm the surce (i.e. r > r F ), the radiated pwer is unifrmly distributed ver the surface area f a sphere f radius r. If P R is the pwer f the receiver antenna, lcated at a distance r frm the transmitting antenna and has a directivity gain G R, then the path lss is defined as (refer t [4]): L = 0 lg P T P R [5] L = lg f MHz + 0 lg r km db [6] [6] is derived by inserting the expressin fr Friis frmula in [5]. Path Lss ver a Flat Terrain This represents the simplest case f radi wave prpagatin ver terrain where the grund surface is assumed flat. This assumptin is valid fr radi links between subscribers up t 0 5 km apart. The main prcess is a reflectin frm the flat terrain, which is described by the reflectin cefficient. Reflectin Cefficients The expressins fr the cmplex cefficients f reflectins ( Γ) fr wave with vertical and hrizntal plarizatins is given belw respectively: Γ V = Γ V e jϕ V = ε r sinψ ε r cs ψ ε r sinψ + ε r cs ψ [7] Γ H = Γ H e jϕ H = sinψ ε r cs ψ sinψ + ε r cs ψ [8] where ψ is the grazing angle defined as π θ, θ 0 0 is the angle f wave incidence. The knwledge f reflectin ceff amplitude and phase variatins is a very imprtant factr in the predictin f path lss fr different situatins in the land prpagatin channels. Grund prperties are determined by the cnductivity and abslute dielectric permittivity f the subsil medium Nte: The Fresnel reflectin ceff, Γ, accunts fr the electrical prperties f the earth surface. Since the earth is a lssy medium, the value f the reflectin ceff depends n the cmplex relative permittivity f the surface, the grazing angle and wave plarisatin University f Lags, 009

6 Page 6 Line f Sight (LOS) Tw Ray Mdel First prpsed fr describing the prcess f radi wave prpagatin ver flat terrain. It is based n the superpsitin f a direct ray frm the surce and a ray reflected frm the flat grund surface (Fig. ) Starting frm the relatin between the field strength and pwer at the transmitter: E = 30G T G R P T r [9] The ttal field at the receiver is the sum f direct and received waves: E R = E T + r Γ e jkδr r [0] kδr = Δϕ is the phase difference between the reflected and direct waves which can be presented as: Δϕ = π λ r + h + h R T r + h R h T r [] We can simplify [] by making sme assumptins. Fr r ( h T ± h R ) and r h T ± h R with the assumptin that r r r, [] becmes, Δϕ = 4πh R h T λr [] If we assume that the antennas are mnidirectinal such that G R G T = and that the reflectin ceff, Γ ψ small), then we can write an expressin fr the abslute value f pwer at the receiver: fr the farthest ranges frm transmitter (when the grazing angle is λ P R = P T 4πr + cs Δϕ cs Δϕ + sin Δϕ [3] λ Δϕ = P T 4πr sin [4] [4] Implies that a maximum (received pwered) is btained when sin x, this distance is knwn as the critical range, r b : r b 4h R h T λ [5] University f Lags, 009

7 Page 7, Δr = h h T R r Δϕ Fr small incident angles, that is, when sin Δϕ large distances between antennas relative t antenna heights. We can nw write an apprximate expressin fr path lss:. This is valid fr L FT = 0 lg P T P R = 0 lg r 4 h R h T = 40 lg r 0 lg h m ( h Tm Rm ) [6] [6] is knwn as the path lss in the mdel f flat terrain. [6] can be rewritten in the frm shwn belw using [5]. L = L B + 0 lg r r b L B + 40 lg r r b r r b r > r b [7] Where L B is the path lss in free space at the distance that equals the critical range. Path Lss in Clutter Cnditins Nn Line f Sight (NLOS) cnditin Here we cnsider the situatin where bth transmit and receiver antenna are placed abve grund in NLOS cnditins. In this cnditin, diffractin phenmenn ccurs due t the presence f bstacles such as trees r hill. The diffractin phenmenn is based n Huygensʼ principle, furthermre each bstructin is replaced with a knife edge. Prpagatin ver a single knife-edge Assume we can mdel an bstacle as a simple knife-edge dented in the figure belw as OO ' - which lies between the transmitter and the receiver. The phase difference Δϕ between the direct ray frm the surce (at pint O) dented TOR and that diffracted frm pint Oʼ dented TOʼR can be btained frm the path difference and the phase difference assuming that the height f the bstacle is much smaller than the characteristics ranges between the antennas and the bstacles: Δd d + d d d h [8] University f Lags, 009

8 Page 8 Δϕ = kδd = π Δd [9] λ We can re-write [9] in terms f the Fresnel Kirchhff Diffractin parameter: Δϕ = π υ [0] where υ is the Fresnel Kirchhff Diffractin parameter. The effect f diffractin arund an bstacle is determined by quantifying the required clearance ver the bstacle. This is achieved analytically thrugh the applicatin f Fresnel zne ellipsids, these are drawn arund bth ends f the radi link, transmitter and receiver. The crss sectinal radius f any ellipsid f the n Fresnel zne at a distance d and d = d d can be presented as a functin f these parameters as shwn belw: r n h n = nλd d d + d [] Taking int accunt [8 0], [] the Fresnel (als called the diffractin parameter) can be written as: d υ n = h + d n λd d d = ( + d )nλd d λd d ( d + d ) = ( n) [] Nte: Cntributin t the ttal field at the receiving pint frm successive Fresnel znes tends t be in phase ppsitin and therefre interfere destructively rather cnstructively. Lsses f the wave energy ver a single knife-edge can be btained analytically by use f scalled Fresnel cmplex integrals based n Huygensʼ principle: E = E 0 + j exp j π t dt [3] The ttal field after diffractin frm bstructin can be presented in the fllwing frm: υ E = E ˆD exp( jδϕ ) [4] Where E 0 is the incident wave frm the transmitter lcated in free space, ˆD is the diffractin ceff r matrix, and Δϕ is the phase difference between the diffracted and direct waves. We can represent the Fresnel integral as shwn belw: University f Lags, 009

9 Page 9 cs π t dt = υ cs π t dt = C υ υ sin π t dt = υ sin π t υ Therefre [3] can re re-written as: 0 0 [5] dt = S( υ) E = E 0 + j ± C( υ) j ± S( υ) [6] Since the main gal f diffractin thery is t btain the parameters ˆD and Δϕ by use f the Fresnel integrals, we can d this by cmparing [4] and [6]. S + ˆD = sin Δϕ + π ( ( ( ) S + Δϕ = tan C + π 4 [7] T btain an exact slutin by use f an integral equatin such as [4] is very cmplicated. Empirical and semi-empirical mdels, based n numerus experimental data, have been develped and are usually used t btain the diffractin lsses in NLOS cmmunicatin links. Fr knife-edge diffractin lsses, the Leeʼs apprximate mdel is used: 0 = L Γ = L Γ = L Γ L υ L υ L υ 3 L( υ) = L Γ 4 L( υ) = L Γ = 0 db υ db 0.8 < υ < 0 [ ] db 0 < υ < ( ) db <υ<.4 = 0 lg υ = 0 lg 0.5 exp 0.95υ = 0 lg υ = 0 lg 0.5 db υ >.4 υ [8] Fading (re-visited) Fading is due t shadwing, blckage and multipath. The term is applied t signal lss that changes fairly slwly relative t the signal bandwidth and the term scintillatin is used t describe rapid variatins in signal strength. These terms are usually applied t atmsphere phenmena, hwever. When mdelling a terrestrial mbile radi channel, the principal effects are usually due t terrain and terrain features. In this cntext it is custmary t talk abut fading in terms f large scale r small scale fading rather then scintillatin. Small scale fading is further characterised as fast r slw and as spectrally flat r frequency selective. University f Lags, 009

10 Page 0 Fading is rughly gruped int categries: large scale and small scale fading. Large scale fading is smetimes called slw fading r shadwing althugh the term slw fading has a mre precise meaning in the cntext f small scaling fading. Large scale adding is ften charaterised by a lg nrmal prbability density functin and is attributed t shadwing and the resulting diffractin and/r multipath. Changes in large scale fading are assciated with significant changes in the Tx/RX gemetry, such as when changing lcatin while driving. Small scale fading is assciated with very small changes in the TX/RX gemetry, n the rder f a wavelength. Small scale fading may be either fast r slw and is due t changes in multipath gemetry and/r Dppler shift frm changes in velcity r the channel Surface Rughness When determining if grund reflectins is likely t be significant, a means f quantifying the smthness (flatness) f the reflecting surface is required. The Rayleigh criterin prvides a metric f surface rughness. The Rayleigh rughness is derived based n the terrain variatin Δh that will prvide a 90 degree phase shift at the Rx between a reflectin at a terrain peak versus a reflectin frm a terrain valley at the same distance. The Rayleigh criterin is given as: H r = λ 8Sinθ [9] Frm the gemetry drawn n the bard, it can be determined that: Sinθ = h r + h t d [30] [9] can be re-written as: H r = λd 8 h r + h t [3] The surface is treated as smth when Δh << H R Mre n Diffractin and Hugyenʼs Principle Diffractin is the physical phenmena whereby an electrmagnetic wave can prpagate ver r arund bjects that bscure the line f sight. Diffractin has the effect f filling in shadws, s that sme amunt f electrmagnetic energy will be present in the shadwed regin. The easiest way t view the effect f diffractin is in terms f Huygenʼs principles, which states that each pint n a wavefrnt acts as the surce f a secndary wavelet and all these wavelets cmbine t prduce a new wavefrnt in the directin f prpagatin. Cmpensating fr diffractins frm a runded hilltp The diffractin frm a runded hilltp r surface is determined by cmputing the knife edge diffractin fr the equivalent height, h and then cmputing the excess diffractin lss, L exc due t the runded surface. University f Lags, 009

11 Page The first step is t determine the radius, r f the cylinder that circumscribes the actual diffractin pints n the bstacles. Then the extent f the diffractin surface, D s can be fund. The expressin fr the excess diffractin lss is given as: L exc =.7α πr λ [3] where α = υ λ d + d d d [33] r = D s d d α d + d [34] University f Lags, 009