Characterization and Simulation of HF Propagation in a realistic disturbed and horizontally inhomogeneous Ionosphere

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1 Characterizatio ad Simulatio of HF Propagatio i a realistic disturbed ad horizotally ihomogeeous Ioosphere Vadim E. Gherm ad Nikolay N.Zerov Departmet of Radiophysics Uiversity of St.Petersburg St.Petersburg Russia Hal J. Strageways School of Electroic ad Electrical Egieerig Uiversity of Leeds Leeds U.K.

2 Widebad HF simulator Curret developmets i HF (3 30 MHz) broadcastig ad commuicatios e.g DRM ad the eed for higher speed data liks require the characterisatio of the HF chael for digital sigals ad at wider badwidths (10 khz 1 MHz) tha previously employed. Deficiecies of existig arrow bad simulators Narrow bad HF simulators e.g. the Watterso model are available but are ot adequate to characterise the widebad HF chael. The Watterso model is limited by:- a fixed (i.e. o dispersio) delay for each ioospheric mode (e.g. 1 hop E 1 hop F hop F) oly a Gaussia distributio for the Doppler spread oly the low agle ( ad ot the high agle) ray path chaels havig time ad frequecy statioarity

3 Deficiecies of existig wide bad simulators Although most of the these restrictios are overcome i the more recet Mastragelo et al. widebad simulator model (based o the work of Vogler ad Hoffmeyer) this model also has various disadvatages. It is empirically based ad cosequetly requires a large umber of iput parameters for each propagatio mode. These caot be directly determied from the parameters of the trasmissio path ad model ioosphere. The empirical models are based o a limited amout of data for a udisturbed ioosphere ad it is rather questioable whether extrapolatio to disturbed ioosphere coditios is valid.

4 Deficiecies of existig wide bad simulators cotiued It is ot clear what is the basis for the delay profile modellig which is the mai differece from the Watterso model. The model assumes that the fadig observed at itervals ( taps ) alog the delay profile of a propagatioal mode is idepedet of fadig at other taps but there is o supportig evidece for this. There is also implicitly the assumptio that fadig of amplitude ad phase are idepedet. Doppler shift ad Doppler spread should ot be idepedetly chose variables for differet propagatioal modes e.g. IF1 1F F.

5 New widebad HF simulator Thus a ew widebad HF simulator has bee costructed for commuicatio/data liks ivolvig multipath ioospheric reflected paths e.g. 1E F etc for both o- ad e- modes. It is based o a detailed physical (rather tha empirical) model icludig both backgroud ad stochastic ioospheric compoets. It also icludes the effect of the Earth s magetic field both o propagatio ad the shape of the time-varyig irregularities. A oise model which icludes Gaussia ad impulsive oise ad iterferers is icluded.

6 Methodology I our simulator the chael simulatio for the multipath HF ioospheric sky wave radom chael is based o the most geeral theory of HF wave propagatio i the real fluctuatig ioosphere. The complex phase method (or modified Rytov s approximatio) is employed. This accouts for the mai effects of HF propagatio i the disturbed ioosphere:- Ray bedig due to the ihomogeeous backgroud ioosphere Scatterig by radom ioospheric irregularities icludig diffractio by localised ihomogeeities The Earth s magetic field is take ito accout through the aisotropic spatial spectrum of the ioospheric turbulece The propagatio paths are determied usig a Nelder-Mead homig-i algorithm together with a 3D ray-tracig model which takes ito accout the effect of the geomagetic field o the refractive idex ad also permits horizotal gradiets of electro desity to be icluded.

7 Simulatio of radom time series ad statistical momets of the HF field A radom realisatio of a pulsed sigal propagated through the fluctuatig ioosphere ca be represeted as the followig Fourier itegral i the frequecy domai + ( τ ) ( ω ) ( ω ) ( ω ) iω τ E r t = P T r t R r t e dω (1) E is the field at the poit of observatio r represeted by the sum of propagatig ioospheric modes; P is the spectrum of the trasmitted pulse; T is the trasfer fuctio of the -th mode i the backgroud ioosphere; R are the radom fuctios (also called phasors) which accout for the effects of the ioospheric electro desity fluctuatios o each mode.

8 Employig (1) the statistical momets (e.g. scatterig fuctio) of the received sigal E ca be obtaied ad its radom time series represetatio geerated. To this ed: i) trasfer fuctios T of each mode propagatig i the backgroud ioosphere should be costructed; ii) statistical properties of radom fuctios R (phasors) should be described.

9 To determie trasfer fuctios T the Joes 3D raytracig code was further exteded to eable solutio of the homig-i problem ad amplitude calculatios. This eables determiatio of T for ay give model of the 3D backgroud ioosphere.

10 Solvig the statistical problem for phasors R is the core poit of the problem. It is cosidered i the approximatio of the complex phase method. The method is the extesio of the classic Rytov s approximatio to the case of the 3D ihomogeeous aisotropic backgroud medium ad the poit source field. It works i terms of complex phases ψ ψ R = e ψ = χ + is ()

11 Complex phases are represeted by the appropriate itegrals writte i ray-cetred co-ordiates where the referece rays are costructed for a arbitrary 3D backgroud ioosphere. For each ray-cetred co-ordiate system defied by a give referece ray the appropriate complex phase is writte i the Fresel approximatio for forward scatterig. Ioosphere Earth

12 ψ 1 ( s 00) 0 exp ik = 4π ( s q1 q ) ( s) + ( s q q ) det B ( s) [( ) ( ) ( ) ] g g g b + b q + b + b q + b + b q q. 11 k 11 1 dsdq 1 dq ε 0 h s ^ (3) 1 ^ + ^ B ^ ^ ^ 0 + B B C = s c ^ B = B+ ik = B ^ g The elemets of matrices are defied from equatios q ( s00) 1 30 i qk ^ B ( s) B ^ g ^ g ^ g ^ g B ^ 0 + B B = C l s ( s00) l ( s00) q i q k (4)

13 The scatterig effects are described i the Fresel approximatio for forward scatterig. As a result the full-wave type solutio of the problem of HF propagatio i the 3D fluctuatig ioosphere is determied accoutig for ray bedig ad scatterig o local radom ihomogeeities icludig the cotributio of diffractio i the scatterig. The product of the complex phase method is the spaced time ad frequecy auto- ad cross-correlatio fuctios of χ ad S ad their frequecy ad time spectra ad fially statistical properties of phasor R

14 This is all further utilised to produce the statistical momets of the full field as well as radom time series for χ ad the full field. I the umerical simulatio the aisotropic iverse power law spatial spectrum of fluctuatios of the ioospheric electro desity is employed B C N ε σ ε 0 ( ) κ s = C [ 1 ε ( s ) ] ( s) N N N - ormalisatio coefficiet 0 σ 1 + -distributio of the dielectric permittivity of the backgroud ioosphere alog the referece ray -variace of the fractioal electro desity fluctuatios κ K tg tg + κ K S tr tr p (5) K tg =π/l tg ; K tr =π/l tr where l tg ad l tr are the outer scales of the turbulece tagetial ad trasverse to the geomagetic field directio respectively

15 ( ) ( ) ( ) ( ) ) (1 ω ω ω ω τ ω τ + = d e t R t T P t E i r r r Scatterig fuctio for the field E from (1) ( ) t Ω Ψ δ is the correlatio fuctio for expressed R ( ) ( ) ( ) [ ] { } t d d d t i i t t t T t T P P t F d g d s Ω + Ω Ω Ψ Ω + Ω Ω + Ω = δ ω δ τ τ δ δ δ δ δ π ω τ exp 1 * * i terms of correlatio fuctios of ad. χ S (6)

16 Two-mode scatterig fuctio

17 ( ) ( ) ( ) ( ) ω ω ω ω τ ω τ + = d e t R t T P t E i r r r Time ad frequecy radom walk of phasor R

18 Simulatios IRI ( Iteratioal Referece Ioosphere) iput parameters St.Petersburg July local time 14:00 R1 = 70 Oblique path East-West distace 900 km. Carrier frequecy 8.3 MHz. Parameters of electro desity fluctuatios: Aisotropic iverse power law spatial spectrum with the spectral idex p=3.7 Outer scales: 5 km - across ad 15 km alog the magetic field R.m.s. of the relative electro desity fluctuatios 1% froze drift velocity across the path of propagatio V = 0.5 km/sec Trasmitted sigal: Rectagular impulses pulse repetitio cycle s legth of a pulse: 0. msec for the badwidth of 10 khz 0.1 mseс for the badwidth of 0 khz 0.05 mseс for the badwidth of 40 khz

19 Badwidth 10 khz

20 Badwidth 10 khz

21 Badwidth 0 khz

22 Badwidth 0 khz

23 Badwidth 40 khz

24 Badwidth 40 khz

25 Iter-symbol Iterferece Iter-symbol iterferece ca be ivestigated by addig ay umber of pulses i fast time Fast time e e

26 Spatial Diversity I spatial diversity systems two or more spaced ateas are employed It is importat that the ateas are sufficietly far apart that the fadig is idepedet at each The most importat cotributio to the fadig is geerally that of the time-varyig irregularities The correlatio distace for mulipath HF commuicatios has bee determied usig the HF simulator assumig froze i drift of the irregularities. As a example cosider a North South path from 40 to 50 latitude with a East-West drift of the irregularities of 0.5 km/s E ad F layer reflected paths exist for both mageto-ioic modes but the correlatio of the F-mode falls off more rapidly with distace.

27 Correlatio at spaced ateas with fast time vs. distace apart of ateas Distace apart of ateas i E-W directio m ms

28 Coclusios The aalytic-umerical techique demostrated allows simulatio of the effects o the widebad ioospheric HF chaels for a wide rage of the followig parameters: (1) the trasmissio badwidth () the trasmissio frequecy (3) the variace of fractioal electro desity fluctuatios (4) the speed ad directio of the drift of the turbulece (5) the aisotropy ad outer scale of the irregularities (6) the backgroud ioosphere model (7) the orietatio of the propagatio path to the geomagetic meridia (8) the multi-mode effects. (9) the oise models.

29 Coclusios cotiued The simulator ca be used to test out ew modems for spread spectrum systems; both direct sequece ad frequecy hoppig. The simulator ca be used for the plaig of ew DRM broadcasts It ca also be used to ivestigate spatial diversity systems ad icreased chael capacity for fixed HF liks usig SIMO/MIMO by determiig the correlatio betwee spaced ateas takig ito accout the time-varyig irregularities ad multipath iterferece. The simulator ca also be used to idetify the correspodece betwee physical parameters (e.g. the variace ad aisotropy of the electro desity fluctuatios orietatio of the propagatio path to the magetic meridia bulk ioosphere motios) with observed chael parameters (e.g. Doppler spread ad shift time delay spread). This permits cotiued refiemet of the simulator. A hardware versio of the simulator could be costructed.

EL 675 UHF Propagation for Modern Wireless Systems. Henry L. Bertoni Polytechnic University

EL 675 UHF Propagation for Modern Wireless Systems. Henry L. Bertoni Polytechnic University EL 675 UHF Propagatio for Moder Wireless Systems Hery L. Bertoi Polytechic Uiversity otext for Discussig Wireless hael haracteristics Frequecies above ~ 300 MHz (λ < m) adio liks i ma-made eviromets At