Analysis and Modelling of Multi-ChannelMillimetric Wave Propagation Measurements In A

Tropical Littoral Environment

Hedley J. Hansen∗‡, Manik Attygalle∗, Alex Vanderklugt∗, Alex Baldock∗, Keith Mason∗,Andrew S. Kulessa†, Jorg. M Hacker†, Stephen J. Salamon‡ and Martin Veasey §

∗Defence Science Technology Group, Edinburgh, S. Australia 5111,Email: hedley.hansen@dst.defence.gov.au

†Airborne Reasearch Australia, PO Box 335, Salisbury South, SA 5106Email: andy.kulessa@airborneresearch.org.au

‡Adelaide University, S Australia 5005, Email: stephen.salamon@adelaide.edu.au§MET Office,Exeter, UK , Email: martin.veasey@metoffice.gov.uk

Abstract—Anomalous propagation of microwave and millime-tric radiation in the surface boundary layer makes assessmentof radio wave systems difficult and subject to significant errordue the variability of meteorological parameters. The valida-tion of models relies on trials that involve ships moving withsensors recording meteorological parameters, on paths wherecoordinating radio link and radar experiments are operating. TheTropical Air-Sea Propagation Study (TAPS) held near LucindaNorth Queensland was such a study. This paper presents ananalysis of microwave and millimetric wave (9, 17 and 35GHz) transmit-receive link measurements recorded during TAPSfor the period when BPSK modulated waveforms were beingtransmitted to ranges well beyond the radar horizon. The radiowave propagation measurements described are used to investigatethe suitability of using Fourier-Split-Step 2-D parabolic equationmethods for modelling microwave and millimetric propagation insea surface environments. The limitations of these methods usedfor predicting wave propagation are demonstrated.

Keywords—microwave millimetric wave propagation, atmosp-heric effects, sea surface, parabolic equation modelling, pheno-menology.

I. INTRODUCTION

Modelling the effects of ducting of radio waves at the seasurface requires sophisticated propagation prediction methods.[1]. During the last two decades a large number of waveproblems have been successfully modelled using the ParabolicEquation Method (PEM). This applies a 2-D paraxial approx-imation to the wave equation. This approximation has theadvantage of being able to be solved numerically and providessolutions for complex propagation environments when ray-based [2] or normal-mode based techniques are unreliableor too resource intensive [3]. The PEM uses meteorologicalparameters as inputs, allows complex boundary conditions tobe applied and different antenna patterns to be included. Dueto these attributes, it provides the Atmospheric PropagationModel (APM) solution for addressing microwave radar andcommunication performance assessment problems in the com-plex sea surface zone [4].

The validity of PEM approaches has been verified atBeyond-Line-of-Site (BLOS) ranges in case studies reported

in the literature [1]. At low altitudes from the sea surface,the validity of the 2-D paraxial assumption becomes unclear,especially when the substantial scattering diffraction and depo-larization leads to 3-D multipath effects typical of an urban en-vironment. The paraxial approximation only considers forwardscattering waves and therefore the validity of surface waveradar detection performance assessments will vary dependingon the strength of surface backscattering or clutter present.As emerging compact RF systems are continually moving tohigher frequencies, from the traditional radar bands into themillimetric wave bands, sea surface roughness effectively be-comes more significant enhancing surface backscatter effects.Equally important is that PEMs rely on real-time troposphericenvironmental modelling inputs, for constructing refractivityprofiles, and this is challenging in the sea surface tropospherewhere the refractive index gradients effects due to turbulenceresult in ducting refractivity profiles.

This paper presents an analysis of microwave and millime-tric wave (with frequencies of 9, 17 and 35 GHz) transmit-receive link measurements. Atmospheric propagation measu-rements of height distributed radio wave transmissions throughlittoral and marine surface boundary layer environments wererecorded as part of the Tropical Air-sea Propagation Study(TAPS) 2013 trials in northern Queensland during Nov-Dec2013. [5]. The results show that long random sequence BPSKmodulated signals were received at ranges well beyond theradar horizon. The path loss analysis of the microwave andmillimetric wave data links suggest a ducting environment andsurface layer evaporative ducting is considered as responsiblefor the observed anomalous propagation measured.

II. EXPERIMENT

This section describes data sets that form the basis ofthis investigation. TAPS13 was a coordinated internationalprogram [5], whose purpose was to make atmospheric and RFpropagation measurements for validating meso-scale refractiveindex structure predictions and various propagation models inthe marine tropical environment.

Fig. 1. Path of MV Ferguson 05 Dec 2013 0730-1200LT

A. Multi-element RF Transceiver Network

The millimetric wave propagation experiment comprisedheight-distributed multi transmit-receive radio link channels.There were seven transmissions, viz., X band (9 GHz), Kuband (17 GHz), W band (94 GHz) and four Ka band (35GHz) complex wave modulated sources. There were sevendownconverter receiver elements, four tuned for receiving theKa band transmissions and single receivers, one each forreceiving the X, Ku and W band transmissions. The verticallydistributed transmission sources were located, as shown in themap in Fig. 1, at Lucinda, near Townsville and the verticallydistributed receive elements were mounted on the MarineVessel (MV) Cape Ferguson, as shown in Fig.2 . For eachday of the 26 Nov-05 Dec 2013 trial period, the vessel movedseaward (eastward) from a point 5 km from the Lucindatransmit site to a position 80 km offshore.

The transmission of BPSK signals occurred on 05 Dec2013 over a four-and-a-half-hour period from 730 to 1230Local Time (LT). The experimental arrangement is summarisedin Table I. The heights of transmitters 1 to 4 are shown as 11m, 8 m, 5 m and 3.5 m from sea level respectively. Thesevalues represent the midpoints of a variation of -0.8 to +0.8m due to an incoming tide of 1.6 m over the time window ofthe case study.

1) Shore-based MIMO Transceiver Setup: The four-phasecoherent and synchronised waveforms were generated by two,2- channel Anritsu MG3710A Arbitrary Waveform Generators(AWG) that formed the transmit part of the 4x4 MIMO confi-guration. The synchronisations between the four transmissionswere achieved as per the setup shown in Fig. 3.

The outputs were nominally at 1.58 GHz IF frequency andthe four branches were up-converted to 35 GHz and directedto four transmit antennas at the different heights indicatedin Table I. All antennas were horizontally polarised. Threeadditional up-converted transmissions at 9, 17 and 94 GHzwere also set up at the height of 8 m. The three sources ofthese up-converted signals were provided by splitting the firstchannel into four parts as shown in Fig. 3.

The generated pulsed BPSK signal had a pulse-width of 5ms, the bandwidth was 10 MHz allowing 50000 chips withinthe 5 ms time period. The signal was sampled for 15 msevery 15 s. Four independent codes were generated for thefour channels using a uniformly distributed random numbergenerator.

2) Ship-based Receiver Elements: On-board the MV CapeFerguson receiver site, the four transmissions of 35 GHzfrequency were detected by four receiver elements mounted at

Fig. 2. Receiver element configuration on MV Ferguson 05 Dec 2013. Thestern of the ship is shown.

TABLE I. KA BAND LINKS: TRANSMITTER AND RECEIVER DETAILS

Transmitter Height (m) Receiver Height (m) Polarisation

1 11 1 11.5 H

2 8 2 8.5 H

3 5 3 3.5 H

4 3.5 4 8.5 V

Fig. 3. MIMO Transceiver

different heights as shown in Fig. 2 and summarised in TableI. There were three additional receiver elements located on theMV Cape Ferguson. For the period of this case study, the 9GHz and 17 GHz pair of receiver elements were on the 2nddeck at a height of 6 m and the 94 GHz receiver was on the 3rddeck at a height of 8.5 m. These receiver elements providedseven down-converted IF signals that were input into an eightchannel ADC card. The seven channels used were sampledsimultaneously at 125 MHz. The four 35 GHz and 94 GHztransmissions were down converted to a nominal frequencyof 31.25 MHz. The 9 and 17 GHz link signals were down-converted to a 526 MHz nominal frequency, which createdan alias frequency that folded down to 26 MHz. The datacapture was carried out for 15 ms every 15 seconds and savedin separate binary files. These files were time stamped usingGPS. This setup allowed for multi element time coordinatedsignal measurements.

B. Coordinated Atmospheric Effects Instrumentation

Meteorological instrumentation was deployed at LucindaJetty, a 6 km platform used for loading sugar cane ontocargo ships. As a site for weather station instrumentation,it was ideal because it represents a coastal sea environment.Table II provides details of the instrumentation operated. Bulksea temperature and meteorological parameters (temperature,relative humidity and pressure), and, fast response data (windspeed, anemometer and the Licor7500-A) enabled estimates

TABLE II. WEATHER STATION INSTRUMENTATION

Instrument Measures

LICOR Li 7500A IRGA H2O in mmol/m-3

Gill Windmaster 3D Wind u,v,w in ms-1sonic temp in 0C at 20 Hz

Vaisala HMP 155 Relative Humidity (RH) inAir temp in0C at 20 s

Vaisala PTB330 pressure in hPa at 20 s

Sea Thermometer Sea surface Temperature in C at 20 s

GPS Time UT

to be made of refractive profiles near the sea surface layer.Refractive index profiling is obtained via momentum heat,humidity flux determinations which, in turn, deliver the scalingparameters enabling heat moisture and refractivity profiles forthe sea surface layer to be calculated. This profiling relieson flux estimates, derived from the bulk measurements (usingMonin Obukov Similarity Theory in the unstable sea surfacelayer atmosphere situation where turbulence dominates) andfrom the fast response measurements. The fast response dataprovides the flux estimates more directly, via a covariancemethod.

III. ANALYSIS

A. RF Network Measurements

The captured data was post processed using Matlab. Fig.4 shows the Signal-to-Noise Ratios (SNRs) recorded on theMV Ferguson receiver network with the X, Ku, W bandelements and with the associated Ka-band receiver elementwith a similar H (horizontal) antenna orientation. The X andKu band receiver elements were located at height h= 6 mwhilst the Ka-band element was at h= 8.5 m on the marinevessel. The processing gain associated with pulse compressionof these signals was 47 dB. The yellow dashed curve showsthe vessel’s distance from the transmit site in km. The differentperiods of signal fade exhibited in X (purple) Ku (green) andW band (brown) receptions are in accordance with enhancedatmospheric absorption expected at these frequencies. The W-band signal dropped out early at a range of ≈20 km whilst theX-band signal was detected to a range of >70 km.

The Path Loss (PL) parameters calculated from the signallevels presented in Fig. 4 are shown in Fig. 5, as a function ofLocal Time LT (top) and MV Ferguson range (bottom) fromthe Lucinda site. The top panel indicates that signal dropoutsoccurred at 0730, 0900, 1000 and 1100 LT when transmit andreceive antennas were unaligned. The MV was drifting at thesetimes because radiosondes were being launched [5].

There were four Ka-band transmissions. This study is con-cerned with the source that shared a common Local Oscillator(LO) with the X, Ku and W transmitters at height h= 8 m. Forthis source, Fig. 6 shows the PL parameters associated withthe signals measured with the receiver elements summarisedin Table I. The three links of similar antenna orientation (H)are shown. For the period between 0730 and 0900 LT whenthe MV Ferguson was at ranges <20 km from the transmittersite, PLs were lowest for the radio channel linked to the mastreceiver at h= 11.5 m (black). For the period after 1030 LT,when the MV Ferguson was moving to ranges beyond 30km,PLs were lowest for the radio channel linked to the lower

Fig. 4. SNR associated with X, Ku and Ka Band links. The Ka-band sensoris at a located at height=8.5m. The X and Ku band sensor is at height of 6m.

Fig. 5. Path Loss Parameters for X, Ku and Ka band Links

Fig. 6. Distributed Path Loss Parameters for Ka band Links

deck receiver at h=3.5 m (blue). This shows that for thisset of observations, the height of the receiver above the seasurface was not critical for signal reception at beyond-line-of-site ranges and at times, signal reception was best from thesensor located at the lowest height.

B. Meteorological Measurements

A montage of meteorological parameters recorded at Lu-cinda jetty for the 05 December 2013 period is shown inFig. 7. The top three panels show the specific humidity, windspeed and wind direction measurements that are significant forcharacterising the state of the sea surface environment. Thebottom panel shows the location of MV Ferguson platform atthe time of these measurements.

Modelling of the microwave and millimetric wave propaga-tion relies on meteorological inputs for generating refractiveindex fields. Profiling the refractive index fields relating toevaporative duct formation in the sea surface layer is modelledaccording to Monin-Obukov similarity theory which assumesduct formation is driven by turbulent mixing, dependent onthe presence of sea surface gustiness. Duct formation is also

Fig. 7. Meteorological parameters recorded at Lucinda Jetty

associated with increasing specific humidity levels as moistureladen air extends upward from the sea surface. A developingevaporative duct forming during the recording period whenthe MV Ferguson was beyond 20 km from the transmittersite is consistent with the presence of increasing wind speeddisplayed after 0900 LT. By 1500 LT, the evaporative duct waswell established [5].

During the period of study, coordinated airborne measure-ments of temperature, pressure, humidity and hence refracti-vity were carried out by VH-OBS, an Eco-Dimona aircraftequipped for in situ meteorological measurements. These me-asurements confirm the onset of a sea-breeze commencingaround 0900 LT and the depth of the surface layer increasingduring the period of study in accordance with evaporativeducts forming. The aircraft measurements showed the marineboundary layer also supported a higher altitude elevated ductresulting from the early phase of the sea breeze circulationduring the period of study then surface layer ducts, laterin mid-afternoon. These latter features had an insignificantbearing on propagation. The sole ducting mechanism thataffected the signal transmissions was the evaporation ductwhich strengthened during the course of the day.

The environmental changes at 0900 LT are significant be-cause the RF link reception, as indicated by the superimposedX and Ku PL range characteristics shown in Fig. 5, alsosimultaneously exhibited changes in signal reception. Prior to0900 LT, Fig. 5 indicates signal reception for the Ku link waspoorer than the X-band link. After 0900 LT, signal receptionwas similar for both links as shown by the similar PL valuesuntil 1100 LT.

IV. MODELLING

Using the flattened Earth coordinate system, troposphericradio wave propagation has been approximated by the outgoingwave part of the parabolic equation

∂u

∂x= ik

(1 −

√1

k2∂2

∂z2+m(x, z)

2

)u (1)

where k is the wave number, m(x, z) = n(x, z)(1+z/a0),a0 is Earth radius, n is the refractive index and

u (x, z) = eik·x[ka0sin (z/a0) ez/2a0

]1/2Eφ (2)

for horizontal polarizations where E is the azimuthal field [6]-[7].

Equation 1 reduces to

∂u (x, z)

∂x=i

k

∂u (x, z)2

∂z2+ik

2(n (x, z)

2 − 1)u (x, z) (3)

whose solution has been implemented using the Fourier SplitStep method (FSS). It provides a 2-D narrow angle forwardscatter scalar form for computing the field and path loss ateach step along the path. The solution for u emerges at rangex+ dx provided the refractive index is constant over dx. Theinverse Fourier Transform (FT) is then applied to the solutionof the desired u(x+ dx, z) to give

u (x+ ∆x, z) = ei·n(x,z)·xF−1[e−ikp2∆x

2k Fu (x, z)] (4)

where Fu(x, z) is the FT of u(x, z), F−1 denotes the inverseFT and p is the wave number, the transform variable pair withz. The first exponent in Equation 4 denotes what is termed theenvironmental propagator and the second term, the free spacepropagator. This equation therefore decouples environmentalfrom diffraction effects. Reported results with FSS and otherparabolic equations solutions link Propagation Factor (PF) andPath Loss (PL), the major parameters used for radar coverageand communication link budget assessment to u(x, z) by

PL = 20 log(4πr

λ) − PF (5)

andPF = 20 log u (x, z) + 10 log λ (6)

where λ is the free space wavelength, r is the distance betweencorresponding points and the first term in Equation 4 is the freespace loss [1].

The FSS implementation has emerged as the preferredtechnique for assessment tools predicting the performance ofradar and communication systems. This case study providesan opportunity for testing implementations of the FSS methodwhere challenges are presented in satisfying boundary condi-tions in sea surface environments.

A. Modelling PL Measurements

As a precursor to presenting the modelling outputs ofdifferent FSS implementations, it is pertinent to show, using atypical FSS process, how sensitive calculated PL values are tothe Lucinda meteorological inputs measured over the courseof four-and-a-half-hour period of this study. This is shown forthe X-band link in Fig. 8. This presents on-the-fly generationof slices of PL values at height h=6 m as meteorologicalmeasurements from Lucinda jetty were fed into a perfectreflecting surface implementation of the FSS method. Thedifferent coloured sets of curves are associated with one-hourintervals of the 05 Dec recording period. The colour sequencein time is red, blue, yellow and black. This shows that overthe recording period, the PL parameter of the link decreasedindicated improving wave reception in the sea surface zone.During the period of the red set of values, the wind speedand specific humidity changes at 0900 LT described earlieroccurred. The wide range of PL values shown indicates thatapplying an evaporative duct model when wind speeds are toolow, delivers incorrect modelling results.

Sets of PL values were therefore modelled for each linkof the network as follows. Fig. 9 shows the modelled X-band 9 GHz path loss versus range characteristic from a

Parabolic Equation (PE) modelled simulation of the radiolink used in this study. The refractive index profile input isdisplayed in Fig.10 by the blue curve that was calculated usingthe meteorological bulk measurements recorded at Lucindaat 1200 LT (the red curve shows the corresponding profiledetermined using the fast response measurements). The MVFerguson was 70 km from the transmit site at 1200 LT andthe X-band receiver element was located at a height of 6m above the sea surface. The calculated PL value comparedwith measurement was therefore the value at this distance andheight shown in Fig. 9

Performing this process for the full set of MV Ferguson’slocations during the measurement period, allowed sets ofsequential refractivity profiles to deliver sets of predicted PLparameters for all links.

Different implementations of the FSS using these environ-mental inputs predict the PL parameters for the links shownin Fig.11. Table III provides modelling details. The modelledPL parameters for X, Ku, and Ka band links are displayed,with scatter plots of their corresponding measurements, in thetop, middle and bottom panels respectively. The AdvancedRefractive Effects Prediction System (AREPS) tools used theFSS PEM technique for propagation modelling, and AREPSresults are shown for comparison [4]. Modelling predictionsfrom Flinders University are also shown which account for theincoming tide (see FC-ASK in Table 3), and use a refractivitymodel based on fast response measurement inputs [8].

The predictions shown are all solutions to Equation 2.Therefore the inconsistencies between different PL predictionsdemonstrate the sensitivity of calculated outputs to environ-mental weather inputs parameters. Accordingly, the differentcolours shown in Fig.11 group the predicted PL values intothe different weather input parameters used. The bulk measu-rements delivered the predicted PLs shown in blue. Those thatthe fast response measurements delivered are shown in red. Theenvironmental inputs, sourced from AREPS libraries, deliveredPL values shown in magenta. The ”Marsden Grid” inputsare from the meteorological climatology database pertinent tothe Northern Australian Coral Sea region. The ”std atmos”estimate uses the sample standard atmosphere profile provided.The PL predictions, shown in cyan, are the PL predictionvalues obtained treating the sea as a perfect reflecting surface.

The top and middle panels show the different estimates(e.g., AREPS4.1-Bulk and HJH-DMT Bulk, and, FC-ASK-FFand HJH-DMT-FF ) obtained from solving Equation 3 usingthe same environmental inputs. This inconsistency is underexamination and it relates to different implementations usingtheir own scaling and analytical corrections in accounting forsea surface effects.

The PL calculations estimated from AREPS’s databaselibraries failed to predict the performance of the experimentalsystem delivering the PL measurements. This demonstratesthe limitations presented by using such inputs for modellingpropagation performance for specific periods of study such asthis. Measured PLs are lower than those values predicted usingAREP’s standard atmosphere input which is as expected as theperiod of study provided an evaporative ducting environment.The estimates for the X-band link show predicted PLs fromMarsden grid inputs overestimate performance by ≈ 10-20dB.

Fig. 8. Path Loss outputs from Lucinda Measurements for the 0730-1200LT period on 05 Dec 2013

Fig. 9. Modelled Path Loss range characteristic at 12 noon 05 Dec 2013

The X and K-band Links predictions, assuming the seasurface to be a Perfect Conducting(PC-HJH) surface (the cyancurves), agree with measurement, except for the period where45<range<50 km just discussed.

For the X-band link the AREPS 4.1-Bulk PL estimates are≈10dB lower than those delivered by the HJH-PC solution.This suggests that AREPS has overestimated system perfor-mance. The X and Ku-band AREPS 4.1-Bulk solutions usedthe trial period’s Lucinda bulk weather parameter measure-ments as inputs. Comparing the X and Ku band estimates showthe frequency dependence of link performance delivered by theassessment tool. At 40 km range the calculated PL estimateis 140 dB compared to 160 dB for the Ku band link, whichis consistent with expected atmospheric absorption affectingKu-band waves more than X-band waves.

Sea surface roughness effects have been addressed byincorporating sea surface impedance into the FSS implementa-tion by using the Discrete Mixed Fourier Transform (DMFT)[7]. The differences displayed in the X-band PL estimatesfrom this solution (HJH-DMT-Bulk) with the perfect reflectingsurface solution (HJH-PC-Bulk) is in agreement with findingsreported [1].

Comparing the PL calculations estimated from the HJH-DMT-Bulk and HJH-DMT-ff implementations for the X-bandlink shows the sensitivity of link PL performance estimationto different evaporative modelling processes.

For the Ka-band link channel, no modelling results withAREPS are provided because the assessment tool does notprovide propagation results for radio waves exhibiting fre-quencies greater than 18 GHz. The HJH-FC-ff and HJH PLestimates account for higher frequency atmospheric absorptionby including height dependent imaginary terms in the refractiveindex.

Fig. 10. Bulk (blue) and Fast Response (Red) weather station measurementgenerated modified Refractive Index profiles. The blue profile provided thepathloss characteristic shown in Fig.9.

Fig. 11. Modelled Path Loss with measurement for (top) 9GHz (middle) 17GHz and (bottom) 35 GHz links

TABLE III. MODELLING DETAILS

Colour Name FSS Solution Solution Details

blue Bulk AREPS4.1-BULK Discrete Mixed Tansform (DMT)+AREPS Evap. Duct Model

Lucinda HJH-DMT-Bulk DST DMTEvap.Duct model

red-Fast Response HJH-DMT-ff DST DMT+ Evap. Duct ModelLucinda FC-ASK Flinders Finite Conductivity

Evap. Duct Model

magenta AREPS4.1-NWP AREP’s Marsden Grid inputAREPs4.1-stdatmos AREPS sample Evap duct model

-Cyan PC-HJH DST-Perfect ConnductivityEvap.Duct model-Bulk

V. DISCUSSION

The analysis presented in this study has provided theopportunity to compare different implementations of the FSSPEM over a period when BLOS ducting of microwave andmillimetric radiation was occurring. The climatology measu-rements provided indicate that wind driven turbulence in thesea surface zone support evaporative duct formation.

The different implementations of the PEM modellingapproach can deliver reliable information provided there isconsideration of the constraints and assumptions that havebeen adopted for delivering their solutions. The differences

in prediction that are shown demonstrate the sensitivity ofPL calculations to boundary conditions, the environmentalinputs, and the modelling approaches adopted for generatingthe refractive index fields close to the sea surface.

The FSS PEM approaches used here, have adopted un-realistic assumptions about the sea surface environment. FirstMonin-Obukov Similarity Theory has been considered the onlyprocess responsible for supporting ducted propagation and yetit is known that surface evaporation and turbulence is not theonly refracting mechanism present that can redirect rays nearthe sea surface. Second, in order for meteorological inputsfrom a single location site such as Lucinda Jetty to providecalculated PLs for the links, FSS implementations assumethat the atmosphere between Transmit and Receive site ishomogeneous.

This study has extrapolated implementations of the PEMto millimetric Ka band radio wave transmissions. This ca-pability is not provided by existing assessment tools. Roughsea scattering effects become more significant for propagatingmillimetric waves. The sea surface zones present complexenvironments where out-of-plane scattering, multipath andlateral propagation effects are supported. This case study hastherefore presented an observation set reflecting the limitationsof applying 2-D modelling solutions to 3-D environmentalscenarios.

ACKNOWLEDGMENT

The authors thank DST Group for supporting the TAPS13Trial. HJH acknowledges RF Technologies Group, CEWD,DST Group for providing technical support.

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