Air Ground Channel Characterization for Unmanned Aircraft ...download.xuebalib.com/m1kQA8K0gwP.pdf26 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 1, JANUARY 2017 Air–Ground

26 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 1, JANUARY 2017

Air–Ground Channel Characterization for UnmannedAircraft Systems—Part I: Methods, Measurements,

and Models for Over-Water SettingsDavid W. Matolak, Senior Member, IEEE, and Ruoyu Sun, Member, IEEE

Abstract—The use of unmanned aerial systems (UASs), whichare also known as unmanned aerial vehicles, and by the term“drones” in the popular press, is growing rapidly. To ensure safety,UAS control and nonpayload communication (CNPC) links mustoperate very reliably in a variety of conditions. This requiresan accurate quantitative characterization of the air–ground (AG)channel, and this channel characterization is the focus of this pa-per. After providing motivation and background, we describe ourmethods and modeling approach, followed by a description of oursimultaneous dual-band (L-band ∼970 MHz, C-band ∼5 GHz)measurement campaign and the over-water (OW) measurementsites. Example results for path loss and root-mean-square delayspread are provided, as well as the results for channel stationaritydistance (SD), used in calculating small-scale Rician K-factor andcorrelations between the two receiver antennas that we employedin each frequency band. Two distinct SD measures—the powerdelay profile (PDP) correlation coefficient and the spatial auto-correlation matrix collinearity—were used and found to be ofthe same order. Path-loss exponents are near that of free space,but significant two-ray cancelation effects for these OW settingswarrant more accurate models, which we provide. Delay spreadsin the OW channels are also dominated by the two-ray componentsand are hence typically very small (∼10 ns) but can exceed 350 ns.A third intermittent multipath component (MPC) is also presenta nonnegligible fraction of time; hence, we provide statisticalwideband AG channel models to represent this. Future papers inthis series will report results for the AG channel with ground sitesin other types of environments.

Index Terms—Air–ground (AG) channel, delay spread, pathloss, unmanned aircraft systems (UAS).

I. INTRODUCTION

IN recent years, the use of unmanned aircraft systems (UAS)has grown rapidly. These vehicles, also known as unmanned

Manuscript received March 25, 2015; revised September 25, 2015; acceptedJanuary 31, 2016. Date of publication February 15, 2016; date of currentversion January 13, 2017. This work was supported by National Aeronau-tics and Space Administration (NASA) Glenn Research Center under GrantNNX12AR56G. The review of this paper was coordinated by Prof. T. Kuerner.

D. W. Matolak is with the Department of Electrical Engineering, Universityof South Carolina, Columbia, SC 29208 USA (e-mail: [email protected]).

R. Sun was with the University of South Carolina, Columbia, SC 29208USA. He is now with National Institute of Standards and Technology, Boulder,CO 80305 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2016.2530306

aerial vehicles, and by the misnomer “drones”1 in the popularpress, are being used worldwide for an ever-growing numberof applications. Example applications include cargo transport,public safety, search and rescue, agriculture, scientific andindustrial surveys, extension of range for existing terrestrialsystems, and of course, military use [1]. According to a recentreport by the U.S. Department of Transportation [2], the numberof UAS in the USA alone will increase from several hundredin 2015 to over 230 000 in 2035. The majority of these UASsare expected to be small and “micro” UASs, but even a smallfraction of this number of “medium” and “large” UASs meansa substantial increase. Due to this rapid growth, numerous orga-nizations are working to ensure the safe and reliable integrationof UASs into the airspace worldwide. The Radio TechnicalCommission for Aeronautics (RTCA) [3] is the U.S. standardsbody responsible for civil aviation. The RTCA provides inputsto the International Civil Aviation Organization (ICAO) [4],and ICAO in turn provides inputs to the International Telecom-munications Union (ITU) [5] for aeronautical communicationsrequirements and best practices.

One concern regarding UAS operation, which is also sharedby the public, is safety.2 Hence, one of the charges of theRTCA special committee 228 (SC-228) is the developmentof requirements for highly reliable UAS control and nonpay-load communications (CNPC). Another is the development ofrequirements for “detect and avoid” functions. For develop-ment of minimum operational performance standards (MOPS),SC-228 has employed estimates of required data rates from [1]and from current civil aviation messaging statistics. Estimatednumbers of UAS distributed in portions of the airspace havealso been used to determine the air–ground (AG) cell radius, asthe envisioned UAS AG communication network will consistof spatially distributed ground sites (GSs), each controlling

1Although the term “drone” is unfortunately now well-established for UAS[it is the third entry in Merriam-Webster’s online dictionary (http://www.merriam-webster.com/dictionary/drone)], its original meaning was a male hon-eybee that mated with the queen bee, but otherwise did no work. This definitionevolved into the synonym “parasite.” Given the uses that we cite here for UAS,one can argue that UAS are the exact opposite of drones, doing much work thatis often dangerous or tedious for humans.

2News of UASs appears in the popular press daily, e.g., the recent crash onthe White House lawn, http://www.cnn.com/videos/politics/2015/01/26/lead-dnt-starr-drone-at-white-house.cnn

0018-9545 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

MATOLAK AND SUN: AIR–GROUND CHANNEL CHARACTERIZATION FOR UNMANNED AIRCRAFT SYSTEMS I 27

their local airspace, analogous to terrestrial cellular systems,and analogous to the current air traffic control system. Thecurrent value for the maximum UAS link range (∼cell radius)is approximately 129 km.

Spectrum for UAS has been tentatively Granted in two bands:the L-band (approximately 1–2 GHz), and a portion of C-band(5.03–5.091 GHz). Unfortunately, the L-band is heavily usedby other systems, both aviation and otherwise; thus, the “clean”available L-band spectrum currently considered for UAS is only17 MHz, from 960 to 977 MHz. Any UAS CNPC system willhave to coexist with all the other systems that operate in theL-band.

It is well known that the channel over which any communica-tion system operates can substantially degrade performance [6].Thus, to optimize CNPC performance, a good set of modelsfor the AG channel is critical. This is the primary topic ofthis paper. Historically, the AG channel has been treated aseither a free-space channel or a two-ray channel [7] that addsa reflection from the Earth surface to the direct or line of sight(LOS) component. This is particularly inadequate for UASoperations, which may be at low altitudes and near groundclutter such as buildings and trees. Most traditional AG channelmodels are also narrowband, and this too is inadequate for UASCNPC systems that are expected to carry compressed videoand other signaling information. Since UAS are not requiredto accommodate passenger or pilot comfort in their flight paths,UAS flight dynamics can also differ from those of conventionalpassenger aircraft. We refer readers to [8] for a comprehensiveliterature review of the AG channel to 2012; some specific ref-erences pertinent to the over-water (OW) channels we addressin this paper are cited subsequently. Here, we note only a fewpertinent references.

One of the earliest AG channel references is [9], in whichthe authors determined over-ocean link ranges at very highfrequency (VHF) for a range of aircraft altitudes; beyond-the-horizon propagation was found possible for some small fractionof time due to atmospheric effects. Another early reference is[10], in which the authors employed geometry to devise a flatfading model, consisting of a LOS component plus multipathreflections modeled as having complex Gaussian quadraturecomponents.

The work in [11] described a narrowband L-band AG channelat 900 MHz, illustrating two-ray behavior for measurements inthe central and western USA, with ground antenna heights of5–12 m and a range of aircraft altitudes. The work in [12] is oneof the first studies on wideband AG channel modeling, here atVHF, with a 5-MHz signal bandwidth. The authors presentedtypical two-ray results, and estimated Rician K-factors from∼2–20 dB, with average K = 16 dB. Delay spread results wereprovided for flight tests at two specific airports: mean and max-imum RMS delay spreads (RMS-DSs) were ∼4 and ∼7 μs,respectively.

More recent work includes some in the 2-GHz band in [13],for the aeronautical telemetry channel, with a high-gain narrowbeam tracking GS antenna, and [14] for campus area channels.Finally, on this summary review, the recent paper [15] provideddelay spreads and multiple-input–multiple-output (MIMO)channel parameters for a very low altitude small UAS channel

in the 900-MHz band. Again, see [8] for more on the AGchannel literature.

Given the above, it was recognized that accurate widebandAG channel models in the L-band and C-band, which are vitalfor CNPC system design and evaluation, are missing. We areworking for NASA on a project for UAS integration in thenational airspace system, and the AG channel characterizationis one portion of that project.

For modeling the AG channel, we can—and have—employed some geometry-based (GB) techniques, but have yetto develop a comprehensive set of statistical GB models for allGS environments; this is a task for future work. Even if wehad such models, the model accuracy must be compared withmeasurements for validation in any case; hence, our approachwas to first gather the measured data that would allow empiricalmodeling and subsequent validation of GB models.

Specific contributions of this paper include the following, allfor the OW AG setting:

• measurement-based models for path loss in the L-bandand C-band;

• measurement-based models for AG channel multipathcomponent (MPC) statistics for C-band;

• estimation of AG channel stationarity distance (SD) (bytwo distinct methods);

• quantification of correlations among spatially andfrequency-separated signals;

• quantification of Rician K-factors.The second part in this planned series of papers will address

the hilly/mountainous terrain GS environment AG channel, andsubsequent parts will address the suburb/near-urban case, andairframe shadowing. Our prior published AG channel workreported only example results.

The remainder of this paper is organized as follows. InSection II, we describe our modeling methods and review avail-able analytical models, AG channel environment classifications,our modeling approach (specifically for the OW AG channels),and the overall AG channel measurement campaign. Section IIIdescribes the measurement system and OW measurement sites,and Section IV provides examples of the OW measurement re-sults, including results for path loss, delay spread, correlationsamong signals, and Rician K-factors. In Section V, we providemodels for path loss and wideband statistical models for theOW AG channel. Section VI is the conclusion.

II. METHODS

A. Available Analytical Models

As noted, the nondispersive free-space model and the two-ray model have classically been applied to the AG channel.The maximum excess delay possible for the two-ray modelis τ2,max = 2hG/c, with c being the speed of light and hG

being the GS antenna height. For the most likely ground-station(GS) antenna heights (hG < 30 m) τ2,max ≤ 200 ns, and thisexcess delay occurs only when the aircraft is directly over theGS, with smaller delays for other aircraft positions. Althoughthe two-ray model is attractive for its simplicity, it is clearlyinaccurate for settings where obstacles anywhere near the GS


can induce MPCs. For longer link distances, earth curvaturemust also be accounted for, and as shown in the Appendix,the curved-earth two-ray (CE2R) model is appropriate for this.Earth surface roughness, atmospheric refraction, and sphericalearth divergence are also not accounted for in the classical two-ray model; we incorporate these as well.

Classical rough terrain propagation models, such as theLongley–Rice, Terrain Integrated Rough Earth Model [7], andthe model by Okumura et al. [16], predict only median attenu-ations and cannot estimate MPCs. These models also require afairly large amount of input data.

A large amount of required input data is also characteristic ofray-tracing methods. These GB (“high frequency”) models canprovide fairly accurate results when compared with measure-ments, at least for specular MPCs. They must be augmentedto incorporate diffuse components, which increases their com-plexity. As with the rough-terrain models, they are inherentlysite specific, unless “randomized,” yielding the so-called GBstochastic channel models (GBSCMs) such as the model in[17], as well as the WINNER [18] and COST 2100 models [19].

Another body of knowledge germane to the AG channelis that on the land mobile satellite channel. This channelcan be largely analogous to the AG channel (discounting anyionospheric or other high-altitude atmospheric effects). Themobile satellite channel has traditionally been a narrowbandchannel, with little work on wideband effects. Much of thework also pertains to limited ranges of elevation angles. A goodreview of this channel appears in [20].

B. AG Channel Classes

As with terrestrial cellular channels, classification of thevarious types of AG channels presents ambiguities and overlaps[21]. We began with classification first by type of terrain. Thisincludes flat, hilly, mountainous, and over water. For each ofthese terrain types, a further division by GS environment is use-ful. Representative environments include desert, rural (plains),forest, suburb, and near urban. Note that these classificationsare not always disjoint and are not necessarily exhaustive.Given the constraints imposed by a practical AG channel mea-surement campaign, we have addressed a representative subsetof these channel classes. The channel classification problem canbe complex (see [22] for a discussion for the cellular channel).

C. Modeling Approach

From our collected measurement data, AG channel modelsare being developed for each setting. These models will be pa-rameterized via as many features as practical (e.g., GS setting,elevation angle, etc.). A complete model can be in the form ofthe time-varying channel impulse response (CIR) or, its Fouriertransform, the time-varying transfer function (channel transferfunction). One desirable attribute of these models is that theycan be employable in computer simulations, and for this, wecould use the several model types [21], including stored CIRsobtained from measurements; deterministic high-frequency ap-proximations, such as ray-tracing or ray-launching; stochasticmodels traditionally in the form of tapped-delay lines (TDLs),

Fig. 1. Channel model development procedure [23].

which must be augmented to account for statistical nonsta-tionarity; and combinations of the above, e.g., GBSCMs [17],which employ limited ray-tracing with stochastically distrib-uted objects, the distributions of which can (should) be obtainedfrom measurements.

Our current approach for the AG channel models is to employa combination model. A diagram of our general modelingapproach appears in Fig. 1. As with nearly all modeling, our AGchannel modeling procedure is a combination of analysis andmeasurements. In the analytical part, we specify measurementsetting according to several characteristics (e.g., rural hilly, overfreshwater, etc.), specify estimated ground electrical parameters(conductivity and permittivity), and use these along with carrierfrequency and GB information to estimate two components ofthe CIR: the LOS and surface-reflected component. The GB in-formation includes the GS and aircraft coordinates and antennaheights. Aircraft and GS antenna patterns are also used. Themeasurement part derives from power delay profiles (PDPs)collected as samples (vectors of (power, phase) versus delay)over time during the flight tests. In addition, measured wereGPS coordinates and other typical aviation data such as altime-ter readings. The measured PDPs contain the LOS and groundreflection components, additional MPCs from other structuresnear the GS, and possibly reflections from the aircraft itself.

D. Measurement Campaign

Channel measurements are time-consuming and expensive.These characteristics are more significant in the AG case thanin terrestrial measurements since not only must one conductmeasurements without interference to “normal conditions,”coordination with air traffic control is required for all but thelowest altitude flights or in the most remote locations. This hasimpacts on flight routes and the times of day during which testflights can be conducted. Permission to transmit our signals inthe frequency bands of interest also had to be obtained priorto any flight tests. Actual test planning included selection offlight test locations, specification of flight paths (“trajectories”or “tracks”), careful calibration of test equipment, explicitdefinition of test procedures (including voice communication


Fig. 2. NASA Glenn Research Center’s-3B Viking aircraft [28].

among test team members), coordination with air traffic controland local airport authorities, etc.

For our measurements, we used NASA Glenn ResearchCenter’s S-3B Viking aircraft, shown in Fig. 2. This is a pilotedaircraft, with seating for two pilots and two research engineers.The remaining space within the cabin is for test equipment.In addition to the channel measurement equipment, which wedescribe in Section III, the S-3B contained the usual suite ofaircraft technologies including GPS receivers, inertial naviga-tion systems, an Inmarsat satellite communication transceiver,and VHF radios for communication with air traffic control. Aspectrum analyzer was also employed to ensure no in-bandinterference was present during our testing. Being a pilotedaircraft, arbitrary flight dynamics were not possible, but sometest flights did include banking turns that will enable us todevelop models for airframe shadowing effects (NASA’s goalin this project—in line with RTCA—was to first characterizethe AG channel for medium–large aircraft).

Worth noting is that, in most of our tests, electronic noisefrom some of the other aircraft systems was found in thedata recorded by the channel measurement system [24]. Thisnoise was found to be approximately Gaussian distributed indecibels (hence a lognormally distributed noise voltage) withmean several decibels above that of the internal channel mea-surement system noise floor. This noise was easily removedusing a thresholding algorithm in postprocessing, but it didreduce measurement dynamic range by approximately 4 dB.The false-alarm probability (of mistaking a noise spike for anMPC) was set to 0.001, via the algorithm in [25]. Subsequentlyprocessing PDPs in the time domain enabled us to identify andremove the rare noise spikes that remained after thresholding.To be specific, all recorded PDPs employed a threshold 25 dBdown from the largest component, the aforementioned absolutethreshold to remove aircraft electronic noise, and processingover time to remove any remaining (rare) isolated noise spikes.

The GS was deployed using a transportable tower system ona trailer (see Fig. 3). This GS had a dedicated 7-kW diesel gen-erator for power, a pneumatically extendable tower (∼4–20 m),and a weatherproof cabinet for test equipment, which includedthe channel measurement system transmitters, mast control,GPS receiver, and associated electronics.

Fig. 3. NASA Glenn Research Center’s transportable tower and GS system.

As noted, the cost and complexity of conducting AG channelmeasurements places limits on the number and types of GSlocations at which we could conduct tests. Our final list ofmeasurement sites is detailed in Table I. In total, the mea-surement campaign collected nearly 316 million PDPs in theseven different GS settings. We believe that this is the mostcomprehensive AG channel measurement campaign undertakento date.

III. MEASUREMENTS

A. Channel Measurement System

The AG channel measurement system was custom designed tooperate in the two frequency bands allocated for UAS: in L-bandfrom 960–977 MHz and in C-band from 5030–5091 MHz.Measurements were made simultaneously in the two bandsusing a single-input/multiple-output (SIMO) channel sounderthat transmitted a direct-sequence spread-spectrum (DS-SS)signal in each band. The C-band chip rate was 50 MHz, andthe L-band chip rate was 5 MHz. The DS-SS sequences arem-sequences of length 1023. The sounder was developed byBerkeley Varitronics Systems, Inc. [26]. Reception was by twoantennas in each band connected to the four individual stepped-correlator receivers (Rx’s); for all tests thus far, the receiverswere on the aircraft and the transmitters at the GS. The four Rxantennas were located on the bottom of the S-3B fuselage, ina rectangular pattern, with the same-band antennas located onopposite corners of the rectangle of size approximately 1.32 by1.4 m. Ground-site antenna gains are 6 dB for C-band, 5 dB forL-band, with elevation/azimuth beamwidths of approximately35◦/180◦ for C-band and 60◦/120◦ for L-band. The aircraftmonopole “blade” antennas are nearly omnidirectional in az-imuth, with a gain of 5 dB. All antennas are vertically polarized.Detailed antenna patterns were reported in [27].

The channel sounder gathers PDPs (and phase), which enableus to estimate several channel characteristics: propagation pathloss, dispersion (delay spread), Doppler effects, small-scalefading characteristics, and correlations among the signals re-ceived on different antennas and in different bands. The soundertransmitter output power in both bands was 10 W. A 7-dB-gainhigh-power amplifier and a 30-dB low-noise amplifier (LNA)are employed in C-band, and the L-band receivers use 15.5-dB-gain LNAs. For a minimum received signal-to-noise ratio of10 dB, the C-band maximum range is approximately 30 km,


TABLE IAG CHANNEL FLIGHT TEST ENVIRONMENT SUMMARY (AMSL = ABOVE MEAN SEA LEVEL)

TABLE IICHANNEL SOUNDER SPECIFICATIONS

whereas the L-band range is nearly 200 km. Earth-curvature-restricted flight ranges to approximately 40 km at the flightaltitudes used in most of our tests. Table II lists some of thechannel sounder specifications.

Sounding signals are filtered using root-raised cosine re-sponses (rolloff ∼0.3) for spectral containment. Thus, the50-MHz signal has delay resolution approximately 20 ns, and the5-MHz signal has delay resolution approximately 200 ns. Labo-ratory testing showed that our minimum measurable RMS-DS,in a single-path test, was approximately 10 ns. Due to finiteclock precision, the sounder exhibits a slow sample clock driftthat yields a nearly periodic power variation of a few dB, partlydue to truncation of some of the smaller valued samples becauseof our two thresholds (25 dB below the largest componentand the absolute noise threshold, as noted earlier). The slowclock drift is essentially deterministic and is easily removed inpostprocessing. More detail on sounder characteristics appearsin [23].

B. Over-Water Measurement Sites

Flight test measurements were made over both seawater andfreshwater. The over-sea tests were conducted over the PacificOcean near Oxnard, CA, in June 2013 and the over-freshwatertests were conducted over Lake Erie, near Cleveland, OH, USA,in October 2013 (see Table I). For all these tests, the GS antennaheights were 20 m.

Fig. 4 shows a Google Maps view of the 12 flight tracks (FTs)flown near Oxnard, CA, USA. Both straight and oval-shapedflight patterns were flown to allow variation of the aircraft atti-tude and antenna orientation. The maximum range was approx-imately 25 km, and the flight altitude was relatively constant atapproximately 800 m (±5 m) above sea level. Flight velocitywas also approximately constant at 90 m/s. This yielded eleva-tion angles from approximately 2◦–40◦. A view of the GS fromthe ocean is shown in Fig. 5. In addition, recorded during allflights were aircraft pitch and roll angles, and aircraft heading(not reported here, for brevity).


Fig. 4. Twelve over-sea FTs in Google Maps view.

Fig. 5. View of GS in the parking lot near Oxnard, from ocean (modifiedfrom [27]).

Fig. 6. Example over-freshwater FTs in Google Maps view.

In Fig. 6, we show the Google Maps view for two of the sixFTs for the over-freshwater flights above Lake Erie. For theseflights, the aircraft velocity was approximately 75 m/s, and

Fig. 7. View from GS looking northeast toward downtown Cleveland.

the altitude was approximately 580 m (±13 m, approximately)above the Lake Erie water level (on average 174 m abovesea level), with elevation angle ranging from approximately1.4◦–48◦. Fig. 7 shows a photo from the GS, looking approx-imately northeast toward downtown Cleveland.

IV. EXAMPLE RESULTS

Given the very large amount of measurement data, we cannotshow detailed results for all measurement conditions. Thus,here, we provide representative example measurement resultsfor path loss, delay dispersion, and correlations among varioussignal components. In Section V, we develop models for thechannel parameters from our aggregate data. Worth noting isthat, in these generally open LOS settings, the LOS signalcomponent exhibits a clear and predictable Doppler shift. Giventhe relatively few and intermittent MPCs observed in the OWsettings, we did not attempt to characterize any very short-termDoppler spreads. Preliminary results for the over-sea settingappeared in [28] and [29], and for the over-freshwater setting in[30]. To connect with terms in common current use, these OWAG channels can be termed sparse and 3-D multipath channels.

A. Path Loss

Radio propagation in OW environments has been studied formany years for both communications and radar applications.Although the ocean and many lakes typically offer a very opensetting, meteorological conditions can yield atypical propaga-tion effects on signals from VHF through EHF. This includesincreased attenuation from hydrometeors and atmosphericgases. These effects are largely negligible at frequencies belowabout 10 GHz3 [7]. No precipitation occurred during our flighttesting; therefore, we neglect these effects in our models. Sucheffects can be estimated using conventional techniques [31].

3For example, for a 30-km path, very heavy rainfall (100 mm/h) can produceup to 12 dB of attenuation at 5 GHz (0.4 dB/km) [28] if the rain is uniformlyheavy throughout the entire signal path, which is very unlikely. For L-band, rainattenuation is negligible, i.e., approximately 0.3 dB (0.01 dB/km) for a 30-kmlink uniformly filled with heavy rain.


Fig. 8. Path loss versus link range for over-sea measurements. (a) C-band.(b) L-band.

An effect opposite to that of extra attenuation signal—powerenhancement over that for free space—can result from thepropagation condition known as ducting [31]–[33]. Ducts act asleaky waveguides that can reduce signal attenuation below free-space path-loss values, and ducts occur during “anomalous”conditions—depending on air and sea surface temperatures, hu-midity, wind speed, etc. —where the index of refraction’s vari-ation deviates from its usual exponential decrease with altitude[31]. Although surface ducting probabilities are near 0.2 forthe Pacific Ocean near Oxnard [32], based upon our measuredpath losses, and on the fact that coupling into ducts is generallymost effective when both antennas (Tx and Rx) are within theduct [33], [34]—not the case for our GS and aircraft—we areconfident that no ducting occurred during our flight tests. Forvery low-altitude UAS flights or extremely high GS antennas,where Tx and Rx antenna heights are similar, evaporation orsurface ducts could enhance propagation.

In Fig. 8, we show path loss versus distance for both C-bandand L-band (all four receivers), e.g., straight FT over the ocean.In this unobstructed LOS case, path loss generally follows thefree-space curve, indicated on the figures. The two-ray “lobing”effect is apparent at the larger values of distance (> 10 km), andthis is more prominent for the L-band data since the sea is ef-fectively smoother at the longer L-band wavelength. The CE2R

Fig. 9. Path loss versus link range for over-freshwater measurements.(a) C-band. (b) L-band.

(see the Appendix) model fits the measured data better thanthe flat-earth two-ray model, particularly as distance increases.L-band path loss is a few decibels larger than the analyticalmodel values for distances from approximately 1–4 km dueto aircraft antenna gain effects at the higher elevation angles.Fig. 9 shows analogous results for the over-freshwater case,with comments directly analogous to those for the over-searesults.

B. RMS-DS

We report delay dispersion quantified by the RMS-DS. Thetime-varying (complex baseband) CIR can be expressed asfollows:

h(τ, t) =∑i

αi(t)e−jφi(t)δ [τ − τi(t)] (1)

where αi, φi, and τi denote the time-varying ith MPC’s am-plitude, phase, and delay, respectively. In processing, we alignCIRs so that the LOS component has zero delay. With this CIRdefinition, RMS-DS is as follows:

στ =

√∑L−1k=0 α

2kτ

2k∑L−1

k=0 α2k

− μ2τ (2)


Fig. 10. RMS-DS versus link range for over-sea measurements in C-band,straight FT.

where L denotes the number of MPCs, and the mean excessdelay is given by

μτ =

∑L−1k=0 α

2kτk∑L−1

k=0 α2k

. (3)

We report our RMS-DS results for C-band only because theL-band resolution of 200 ns is often not sufficient to identify allMPCs; in more dispersive environments, L-band delay spreadmay also be reported. In addition, MPCs present in C-band willalso generally be present at L-band at the same values of relativedelay, but with different amplitude characteristics due to thedifferent reflection (scattering, diffraction, etc.) conditions atthe different carrier frequency. It has also been observed for ter-restrial cellular settings that RMS-DS is a fairly weak functionof frequency [35], [36] for our bands.

We discuss channel statistical stationarity in more detail inSection V, but here, note that the OW AG channel is predom-inantly a two-ray channel with intermittent MPCs. We thuscharacterize the instantaneous RMS-DS [37] and its variationto illustrate the range of channel conditions encountered.

Fig. 10 shows RMS-DS versus distance for one of the straightFTs. Both the instantaneous RMS-DS and a moving-averagedversion (window length 1000 PDPs) are shown. The RMS-DSbegins near 50–70 ns at the short distance, then rapidly drops toan average value of approximately 10 ns (the sounder’s min-imum value; see Table II). This is in near-perfect agreementwith the result computed by the CE2R model (see Appendix A).Deviations from this deterministic result appear as “bumps” ortemporary increases in RMS-DS due to reflections from objectson the surface.

Fig. 11 shows one of these bumps, along with a sequence ofPDPs illustrating the temporary MPC at relative delay approxi-mately 600 ns (30Tc, with Tc = 20 ns the chip duration). TheseRMS-DS bumps occur for a small percentage of PDPs, and aremostly of the form shown in Fig. 11(a). With the LOS compo-nent and surface reflection denoted rays one and two, we termthese intermittent rays the third ray. In the over-sea case, the thirdray is present for approximately 2.5% of the time. In[38], a three-ray model is found suitable for over-sea measurements at 8 GHzusing an omnidirectional aircraft antenna and a directional GS

Fig. 11. RMS-DS “bump” near 2.27 km link range for over-sea measurementsin C-band, straight FT. (a) RMS-DS versus link range. (b) Sequence of PDPsshowing MPCs that cause RMS-DS “bump.”

Fig. 12. Decimated sequence of PDPs showing MPCs from near-shore obsta-cles for over-freshwater measurements at C-band.

antenna. In [39], a three- or four-ray model is found suitable for5-GHz over-sea measurements at altitudes comparable to ours(for a lower altitude, they found up to seven rays present, withrays beyond the fourth occurring less than 1.7% of the time). Thesource of these intermittent MPCs was reported to be the roughocean surface itself in [38]; Meng et al. [39] did not comment


TABLE IIISUMMARY OF RMS-DS STATISTICS FOR OW AG CHANNEL

on the potential MPC sources. Neither the work in [38] nor thatin [39] provide explicit models for the over-sea AG channel.From observations made by our crew at the GS and the aircraftpilots during the over-sea flight tests, the ocean near Oxnardwas populated by a number of boats and large ships, as well asseveral offshore drilling platforms. These obstacles, as well asthe sea surface itself, constitute the likely sources of the MPCs.

Without real-time knowledge of the locations of such obsta-cles, geometric modeling is difficult; hence, we characterize ourthird ray statistically in Section V.

In the over-freshwater case, our results were more compli-cated due to the proximity of downtown Cleveland (see Fig. 6).Specifically, even with the main beam of the GS antennas aimeddirectly out toward Lake Erie, some of the large buildings inCleveland’s city center were within the main beams, and thisgeometry provided reflections at relative delays up to 15 μs,with amplitudes up to 15 dB below that of the LOS component.This yielded RMS-DS values as large as 400 ns. These large-delay reflections are not an inherent characteristic of an OWchannel (illustrating the ambiguity of the channel classificationproblem). Thus, we truncated the over-freshwater PDPs to arelative delay of 1 μs. This allows only the nearest obstaclesalong the shoreline to create MPCs. The obstacles presentinclude various docked boats, a lighthouse, and several oiltanks. Fig. 12 shows example PDPs for the over-freshwatersetting. In Table III, we summarize the RMS-DS statistics forour OW AG channels.

C. Stationarity Distance

To estimate statistical channel parameters, it is necessaryto determine the region of space over which the channelstatistics can be assumed constant.4 We quantify this regionby the SD.5 Estimation of SD is a topic of current research,and we do not discuss this extensively here, but compare toa commonly used related criterion and estimate the OW AGchannel SD via two methods. The related criterion is basedon terrestrial propagation in non-LOS (NLOS) conditions, andwas devised in [40]. This criterion pertains to the distanceover which received amplitude values should be averaged to

4In general, a balance must be struck. It is desirable to have as long a datarecord as possible to obtain reliable statistics, yet the data record should not belong enough to span a period (or distance) over which the statistics change.

5Note strictly that the region should be a volume of space, but for our OWAG application, we evaluate the simpler linear distance to/from the GS.

estimate a local mean power value, thus averaging out small-scale fading. This rule yields a distance of 20λ–40λ, and thishas been extensively used for terrestrial cellular radio channels.In addition, underlying the derivation in [40] is the assumptionof Rayleigh amplitude statistics. The 20λ–40λ criterion is notstrictly an SD. Moreover, neither the NLOS nor Rayleighconditions apply in our OW settings; therefore, we wouldnot expect the 20λ–40λ value to pertain directly to our LOSAG channel in any case, yet it is a common value to whichwe can compare. Additional investigations will consider morethorough SD comparisons with related work.

The SD can be computed in several ways. For our wideband(50-MHz C-band) measurements, we have chosen to use twomethods. The first method [41] can be viewed as a widebandmethod, which computes a temporal correlation coefficient forthe temporally varying PDP. The second method [42] requiresmultiple receiving or transmitting antennas, but is a narrowbandmetric that estimates correlation among channel gains. Othermethods, such as the evolutionary spectrum [43] or the spectraldivergence [44] could also be used, but we reserve those forfuture work. We briefly review the two methods we have used,the temporal PDP correlation coefficient (TPCC) [41], and thespatial correlation collinearity [42].

For the TPCC, we begin with the CIR for the ith time instant,given by (1), and repeated here to make explicit the ith timeinstant, i.e.,

h(τ, ti) =

Li∑k=1

αk,ie−jφk,iδ(τ − τk,i) (4)

with parameter definitions as noted in (1), and Li the number ofMPCs in the ith PDP. The ith (instantaneous) PDP is then

P (τ, ti) =

Li∑k=1

(αk,i)2δ(τ − τk,i). (5)

Computation of the TPCC in [41] begins by averagingN PDPs of the form of (5). The averaged PDP is denotedPavg,N (τ, ti)

Pavg,N (τ, ti) =1N

i+N−1∑i

P (τ, ti). (6)

The averaging of the instantaneous PDPs is done to smoothsomewhat the effects of small-scale fading and remove anyequipment-related variation; therefore, N should be large


enough to do this, without being so large as to include PDPs thatare affected by larger scale effects or PDPs that are, in effect,outside the region of stationarity.6

From [41], using our average PDP Pavg,N (τ, ti), we computethe TPCC c(Δt, ti) as follows:

c(Δt, ti)

=

∫Pavg,N (τ, ti)Pavg,N (τ, ti +Δt)dτ

max{∫[Pavg,N (τ, ti)]

2 dτ,∫[Pavg,N (τ, ti +Δt)]2 dτ}

.

(7)

This metric quantifies how similar the average PDP at timeti is to the average PDP at time ti +Δt; naturally, this isalso a function of the starting time ti (or location, or rangeRi). The coefficient c(Δt, ti) is also not completely equivalentto the usual correlation coefficient definition since c(Δt, ti)cannot be negative, but it is normalized so that 0≤c(Δt, ti)≤1.The TPCC is easily translated to a spatial correlation viaknowledge of platform velocity: distance Δx = vΔt, with v =velocity. We compute (7) for a range of Δt, for each value ofti, and select as the SD the value of distance Δx such thatc(Δx, ti) > 0.9. The value 0.9 is conservative, i.e., with veryhigh probability, the channel is stationary during this time (overthis distance). For simplicity, we apply these computations toour straight FTs.

For the over-sea straight FT1, the aircraft flew straight towardthe GS. Average aircraft velocity was 92 m/s, and the PDPupdate rate was approximately 2900 Hz, for all four receivers.Link distances ranged from 3 to 24.1 km in C-band and from2.2 to 24.1 km in L-band.7

A selected plot of values of c(Δx,Ri) versus link distanceand Δx is shown in Fig. 13. The quasi-periodicity one canobserve is attributable to two-ray “oscillations.”8 The value ofΔx in Fig. 13 for which c(Δx,Ri) > 0.9 is approximately 5 m.To determine an SD, we can apply to all data in this environ-ment, we collected statistics of c(Δx,Ri) over all our over-ocean data (statistics were also used in [45]). These statisticsappear in Table IV. The SD is well approximated by a log-normal distribution (parameters in Table IV). For computationof all channel statistics, the median value of SD is employed:∼250λC in C-band (∼15 m). This is substantially larger thanthe 20λ–40λ value, and this is as expected in this LOS channel.

6Note that this selection involves some assumption regarding the veryparameter (SD) we are trying to estimate! Hence, we rely on engineeringjudgment, including knowledge of our equipment’s variation rate, to select N .Due to periodic variation of our C-band received power, caused by a slowrelative drift of the sampling clocks in the Tx and Rx, as previously noted,the averaging distance we selected [corresponding to N in (6)] is 200λ. Theaveraging distance has to be large enough to completely remove the samplingclock drift effect but small enough not to remove actual channel variations.Removing the drift prior to estimating TPCC yields essentially the same resultsas when drift was not removed but the 200λ averaging was applied. Removinglarge-scale path loss (linear fit) before computing TPCC also has a negligibleeffect in this environment.

7Different minimum link distances result from slightly different GS antennapatterns for the two bands

8The two-ray model indeed includes a multipath effect, but characterizingit as “small-scale” or “large-scale” can be subjective, and for given values ofantenna heights, carrier frequency, and surface electrical parameters, the “rateof channel variation” is strongly distance dependent.

Fig. 13. Contour of C-band PDP correlation coefficient c(Δx,R) versus linkrange R and Δx for segment of FT1.

TABLE IVC-BAND SD STATISTICS, OVER-SEA FT1

We have also found the 250λC value of SD to hold for the over-freshwater FTs.

The L-band OW PDPs have MPCs (including the mainsurface reflection) that are almost always unresolvable; hence,the coefficient c(Δx, ti) does not represent wideband effectsper se. Based upon the physical environment, we expect thatthe SD for L-band (with physically longer wavelength) willnot be smaller than the SD for C-band; hence, our conservativeestimate of ∼15 m should apply to the L-band as well.

For the second method of estimating SD, we compute thecorrelation matrix distance (CMD), which is also a normalizedmetric between 0 (highly correlated) and 1 (uncorrelated).Since this measure’s values are opposite to that of the TPCC andthe conventional correlation coefficient, we actually computethe complement of the CMD, known as the collinearity = 1 −CMD [46], whose value between 0 and 1 can be interpreted inthe same manner as the TPCC (0 for uncorrelated, 1 for fullycorrelated). Computations begin with the CIR of (1), which we


express as hmn(τ, ti) for the response between Tx antenna nand Rx antenna m. Using this, we compute the narrowbandcomplex channel gain at time ti, i.e.,

hmn(ti) =

Li∑k=1

αk,ie−jφk,i . (8)

We then vectorize the responses of (8) for the NT Tx anten-nas and NR Rx antennas, and compute an empirical correlationmatrix for either the Tx or Rx. For our 1 × 2 SIMO case(NT = 1, NR = 2), we have

h(ti) =

[h11(ti)

h21(ti)

](9)

then the correlation matrix (at the Rx) is

R(ti) =1N

i+N−1∑k=i

h(tk)hH(tk) (10)

where N is the number of responses used, analogous to thatfor the TPCC in (6), and the superscript H denotes Hermitiantranspose. Our metric is then

collinearity(i, j)= 1−dc(i, j)=tr {R(ti)R(tj)}

‖R(ti)‖F ‖R(ti)‖F

=tr {R(ti)R(tj)}√

tr [RH(ti)R(ti)] tr [RH(tj)R(tj)](11)

where tr denotes matrix trace, and ‖ · ‖F is the Frobenius norm.Fig. 14 shows a contour of collinearity(i, j) for the same FT1

as in Fig. 13 for the TPCC. The same threshold as for the TPCC,i.e., collinearity(i, j) > 0.9, is selected as the conservative SDvalue. Statistics are included in Table IV, which show thatthe collinearity-based SD is roughly half that of the TPCC-based SD. Based upon evaluation of our small-scale parameters(Rician K-factor and interantenna correlations) described ear-lier, we have found that results do not appreciably change whencomputed over either of the median values of SD (6.4 m forcollinearity or 14–15 m for TPCC); hence, we have selectedan SD of 15 m. For all channel parameters computed in thefollowing, estimation was done over this value of SD.

D. Rician K-Factor

For our OW channels with an LOS component, we alsoestimated the K-factor of the Rician fading distribution [6].This was done using a sliding window of width equal tothe SD. We employed three different methods to estimate theK-factor: a maximum likelihood (ML) fit KML, a second-moment method K2 [47], and a fourth-moment method K4

[48]. In all cases, we found essentially perfect agreement be-tween the ML and fourth-moment estimates, with occasionaldiscrepancy for the second-moment method. Aggregate plots ofK versus distance over all straight FTs for the over-sea settingappear in Fig. 15. A linear fit to K-factor (in decibels) versusrange R in kilometers is given as follows:

K(R) = K0 + nK(R−Rmin) + Y (12)

Fig. 14. Contour of C-band collinearity(1, 2) versus link range R and Δx forsegment of FT1.

where K0 is a constant value for the minimum distance Rmin

(2.2 km for C-band and 1 km for L-band), nK is the slope,and Y is a zero-mean Gaussian random variable with standarddeviation σY . Since the slopes are so small, a very good approx-imation can be obtained using K(R) ∼= K0 + Y . Aggregatestatistics for KML appear in Table V.

E. Interband and Spatial Correlation

Using our value of SD, we look at the correlation betweensignal components on the two different antennas in each band,and between components on antennas employing differentbands. The components in question are in general all receivedsignal components, on all four antennas, in both bands. In ourOW channels, we are primarily interested in the correlations ofthe main (LOS) components since the vast majority of receivedpower is contained within the LOS components. Preliminaryresults appeared in [24].

For the two C-band antennas for example, the amplitudecorrelation is computed by

ρAC1,AC2=

E [(AC1 − μAC1) (AC2 − μAC2

)]

σAC1σAC2

(13)

where E denotes expectation, the A’s in the numerator aresample amplitude vectors, and the μ’s are the means of the Avectors. Specifically, AC1 = (AC1,1, AC1,2, . . . , AC1,n) is thevector of LOS amplitude samples for C-band Rx1 with AC1,i

being the ith amplitude sample and analogously for C-bandRx2. Both vectors span only the SD, and the σ’s are the standarddeviations of the respective sample vectors.

To gain insight into what we might expect for the cross-correlation among the LOS signal components of the AGchannel, and to check measurement results, we have developedan analysis for the theoretical two-ray channel, specificallythe CE2R. We apply our analysis to the over-freshwater casehere. In this analysis, we select parameters close to those ofthe measurements: an altitude difference of 566.3 m between


Fig. 15. Rician K-factor versus link range for over-sea FT8. (a) C-band.(b) L-band.

TABLE VAGGREGATE ML OW RICIAN K-FACTOR STATISTICS

GS antenna and aircraft, relative freshwater surface permittivityεfw = 81 and conductivity σfw = 0.01 S/m [7], average windspeed for Lake Erie on October 22, 2013 of 4.98 m/s [49](applied to compute the water surface reflection coefficientaccording to the Miller–Brown surface roughness model [35]),and the atmospheric refractivity, accounted for via the modifiedearth radius approach (see the Appendix).

Fig. 16. Analytical correlation coefficient between LOS components on twoC-band antennas (Δd = 1.4 m) versus horizontal (great circle) link distance d,straight FT over freshwater (a) d = 1 m–30 km, (b) d = 1 m–5 km, and(c) empirical correlation for short link distances.

The horizontal distance along the Earth surface (great circlepath) between aircraft Rx1 and GS is denoted dk1, and for ouranalysis, this ranges from 388–30 000 m (since some approx-imations are employed, the CE2R model is valid only whenhorizontal distance exceeds 388 m). The horizontal distance forRx2 is dk1 +Δd, where Δd is the relative distance between thetwo intraband antennas (Δd ∼ 1.4 m). For this analytical flightpath, the elevation angle ranges from 1.3◦ to 76◦. Amplitudevalues required to compute (13) are obtained from receivedpower in a link budget equation using the CE2R path loss

Pr = Pt +GPA +GLNA +Gt +Gr − LC − PLCE2R (14)

where Pt is transmit power; GPA is the C-band power amplifiergain; GLNA is the LNA gain; Gt and Gr are the transmitterand receiver antenna gains, respectively; and PLCE2R the CE2Rpath loss. All parameter values except cable loss LC (7.5 dB inC-band and 4 dB in L-band) have been previously provided.

Fig. 16 shows the analytical correlation coefficient for theCE2R model versus distance, with computation over variousvector lengths [subscript n for the last element of vector ACi


TABLE VIOVER-SEA C-BAND CE2R ANALYTICAL AND EMPIRICAL CORRELATION

COEFFICIENT STATISTICS, SD = 15 m, AND Δd = 1.4 m

in (13)]. These vector lengths represent different hypotheticalvalues of SD: Our measurement-based value of 15 m plusvalues both smaller (5 m) and larger (150 m). All cases showvery interesting behavior in which due to two-ray effects, thecorrelation coefficient oscillates from +1 to −1. This is mostpronounced for short link distances, but for small values ofSD, oscillation between values of 0 and 1 appears at largerlink distances as well. When we add Rician fading to theCE2R, conclusions are the same, although with Rician fading,the actual correlations versus distance appear slightly “noisy,”hence, values vary slightly more. The use of different antennaseparations changes the specific values of the plots but not thegeneral shape and variation. The interesting conclusion is thatdue to two-ray effects, LOS component correlation betweentwo separated antennas is not always near unity as one’s in-tuition might conclude; two-ray effects are “offset” by the Δdbetween the two antennas. Empirical values of the correlationappear in Fig. 16(c), and intraband correlation statistics appearin Table VI.

Interband correlation coefficient values, for correlation be-tween the C-band and L-band LOS components, are gen-erally small. These interband correlations are well modeledas Gaussian with mean zero and standard deviation approxi-mately 0.3.

V. CHANNEL MODELS

A. Path Loss

Example path-loss results were provided in Section IV-A,where we noted that the free-space and CE2R (see Appendix)models could be used. We divided all data into large elevationangle (small distance) and small elevation angle (large distance)segments. While in the large elevation angle segment wherelink range is small, path loss is actually of lesser interest sincereceived signals are relatively strong. Our aircraft antenna gainsvary most at higher elevation angles corresponding to shortlink ranges. Therefore, we developed the two segment modelsand selected the 5◦ elevation angle threshold as it representsthe approximate transition where our aircraft antenna patternbegins to deviate from the manufacturer’s pattern. Path-lossmodels are provided in three forms, with increasing complexityand accuracy: a single log-distance model for the entire distancerange, a two-segment log-distance model, and a two-segmenttwo-ray model that incorporates small-scale fading. Modelparameters were obtained from least-squares fits to the data.

Single Log-distance Model

PL(R) =A0 + 10nA log

(R

Rmin

)+XA + ζFA

Rmin ≤R ≤ Rmax. (15)

Two-segment Log-distance Model

PL(R)

=

⎧⎨⎩A0,S+10nS log

(R

Rmin

)+XS+ζFS , θ>θt(R<Rt)

A0,L+10nL log(

RRt

)+XL+ζFL, θ<θt(R>Rt).

(16)

Two-Ray Model

PL(R)=

⎧⎪⎨⎪⎩

FE2R(R)−20 log [a(R)], ψ > ψmin

CE2R(R)+BL+ζFC,L

−20 log [a(R)], π/2 > ψ > ψmin.(17)

In these models, R is the link range; the A0’s are constantsat the minimum valid link distances; subscripts S and L in (16)denote short and long distance segments, respectively; the n’sare the path-loss exponents; threshold elevation angle θt is 5◦

(threshold range Rt); variable ζ = −1 for travel toward theGS and +1 for travel away from the GS; the F ′s’s are small(positive) adjustment factors for direction of travel9; the X’s arezero-mean Gaussian random variables with standard deviationσX ; BL is the average difference between the measured pathloss and the CE2R model10; grazing angle ψ is computed in thetwo-ray model with ψmin(mrad) = (2100/fMHz)

1/3 [50]; anda(R) is the Rician fading variable. An unfiltered (memoryless)Rician fading process represents the measured data well; thisphysically results from the rough surface scattering from thewater surfaces. The abbreviation FE2R denotes the flat-earthtwo-ray model [7] and CE2R denotes the curved-earth two-ray model. Model parameters appear in Table VII. In this table,we also provide, for the log-distance models, values we denoteXmax (dB), which quantify the maximum deviation betweenthe deterministic portions of the log-distance models and themeasurement data. These values generally represent the peaktwo-ray attenuation values and are of interest for link budgetcomputations in the OW AG channels.

B. Stochastic Tapped Delay Line Models

Given the sparsity of the OW AG channel, we need notemploy any deconvolution algorithm to identify MPCs. For theover-sea case, we found that the channel is well modeled bythe two-ray model plus an intermittent third MPC we term theintermittent third ray. For both OW AG channels, the CIR isgiven by

hOW(τ, t) = h(OW)2−ray,F (τ, t) + z3(t)α3(t)e

−jφ3(t)δ (τ − τ3(t))(18)

9Generally, the “nose” of the plane is slightly above horizontal—pitchis slightly positive–thus altering slightly the plane’s orientation for the twodirections of travel.

10This term is attributable to various factors, including small deviationsfrom a constant flight altitude, and imperfect estimates of the atmosphericrefractivity, electrical constants, and antenna gains. With values < 1.6 dB, theresulting path-loss models are fairly accurate.


TABLE VIIOW PATH-LOSS PARAMETERS

Fig. 17. TDL model for OW AG channels.

where the first term h(OW)2−ray,F (τ, t) is the FE2R or CE2R model

for frequency band F , z3(t) is a random process that controlsthe presence/absence of the third ray and hence z3 ∈ {0, 1},α3 is the intermittent third ray amplitude, φ3 is its phase, andτ3 denotes its delay. Fig. 17 shows the TDL model. With theintermittent nature of the third ray, we provide statistical mod-els for its probability of occurrence, duration (or “lifetime”)D3, relative delay, and relative amplitude, with the latter twoparameters relative to the LOS component values (delays areaccurate to within the 20 ns delay resolution). Statistics forthese parameters are easiest to express as functions of distance.Model users can translate to functions of time as needed byspecifying flight paths and velocities.

Fig. 18 shows the relative “on probability” for the intermit-tent third ray as a function of link distance, for both sea andfreshwater. An exponential (least-squares) fit to the data appearsin each plot of the following form:

p(R) = aebR (19)

Fig. 18. Intermittent third ray fractional “on probability” versus link range.(a) Over sea. (b) Over freshwater.

with parameters a and b given in the figure, and range R in (19)is in kilometers. The intermittent ray duration D3, as a functionof link distance, for both water types is shown in Fig. 19.Exponential fits of the exact same form as (19) are also shown.Parameters for the on probability and duration fits appear inTable VIII, which also includes the standard deviations of thefits (RMSE).

The intermittent third-ray phase is well modeled as uniformon [0, 2π). For the intermittent third ray relative amplitude, overall our OW data, we have found that this amplitude is very wellmodeled by a Gaussian distribution, with mean value μ3 dBbelow the LOS component amplitude, and standard deviationσ3 dB. For the over-sea case, μ3 = 22.6 and σ3 = 5.2, and forthe over-freshwater case, μ3 = 23.2 and σ3 = 3.9.

Finally, the intermittent third ray excess delays are shown inFig. 20. The excess delay values were divided into two sets forthe over-sea case: 1) 0.1 μs ≤ τ3 ≤ 1.1 μs; and 2) 6 μs ≤ τ3 ≤7 μs (not shown in Fig. 20 for clarity). The probabilities for thedelays lying in these two sets are 0.9923 and 0.0077. For theover freshwater case, excess delays lie between 0.1 and 0.9 μs.The delays are not easily fit by any standard distributions, butwe include exponential fit parameters of the form of (19) forthe over-sea subset of smallest delay values, (0.1 μs ≤ τ3 ≤1.1 μs), also in Table VIII. For the rare over-sea delay values


Fig. 19. Intermittent third ray duration versus link range. (a) Over sea. (b) Overfreshwater.

TABLE VIIIEXPONENTIAL FIT PARAMETERS FOR INTERMITTENT THIRD RAY ON

PROBABILITY, DURATION, AND “SHORT-DELAY” EXCESS DELAYS,VERSUS LINK DISTANCE, FOR FIGS. 18 AND 19

in set 2, delay values can be modeled as uniform over thedelay range 6 μs ≤ τ3 ≤ 7 μs. For the over-freshwater case,we also provide a set of exponential fit parameters of the form

Fig. 20. Excess delay of intermittent third ray versus link range for (a) over seaand (b) over freshwater.

of (19) for the delay values. As a simpler alternative for theover-freshwater third-ray excess delays, we have also found thatan exponential distribution, independent of distance, fits fairlywell. This distribution is

p(τ3) =1μexp [−(τ3 − 100)/μ] (20)

where μ = 17 ns.To implement the model as a function of link distance, we

provide the following algorithm description.

1) For a given value of link range, implement the FE2R in[7] or the CE2R provided in the Appendix.

2) From a distribution specified by Fig. 18 and Table VIII,generate random variable z3. If z3 = 0, third ray notpresent, then go to step 1 and increment/change linkdistance; if z3 = 1, go to step 3.

3) From a distribution specified by Fig. 19 and Table VIII,generate the third ray’s duration D3. (If needed, convertduration in meters to time or symbol units)

4) Draw Gaussian random variable with mean μ3, standarddeviation σ3, to set third ray relative amplitude. Selectthird ray phase from a uniform distribution on [0, 2π).


5) From distribution specified in Fig. 20 and parametersin Table VIII (or (20) for the simpler over-freshwateroption), set third ray relative delay τ3.

6) Increment/change distance as desired, update the two-raymodel values, and maintain third ray for duration D3.After D3 is reached, go to step 1 and continue.

VI. CONCLUSION

In this paper, we have introduced our work on the generationof empirical channel models for the AG channel, with the aimof providing detailed models for use in evaluation of UAScommunication systems. We provided a motivation for thiswork, described AG channel model alternatives, and noted theabsence of established wideband models for the two allocatedUAS bands. Our measurement campaign, which is designed togather data in a variety of ground site environments, was brieflydescribed, including a description of the measurement equip-ment and the measurement sites. Example OW measurementresults were provided for propagation path loss, RMS-DSs,SD computed by two methods, and Rician K-factors. Theseresults were used to develop path-loss models and widebandTDL third-ray dispersive channel models.

As expected in the open OW settings, propagation path lossfollows the free-space increase with distance, but significantdeviations (> 10 dB) from this linear decibel increase withlog(distance) arise from the strong water surface reflection.Hence, the two-ray model, particularly the curved-earth ver-sion, is more accurate than a free-space or log-distance path-loss model. To better agree with measured data, we augmentedthe two-ray path-loss model with Rician fading, with meanK-factors ∼12 dB for L-band and 27–30 dB for C-band. TheseK-factors were computed over a SD estimated at approximately15 m (correlation value ≥0.9), and the origin of the Ricianfading is scattering from the rough water surface. For widebandmodeling, we found that an intermittent third ray, added to thetwo ray model, suffices in both our over water environments.Statistics for the third ray were provided. RMS-DS values aretypically small (∼our minimum measurable value of 10 ns), butoccasionally reach as large as 360 ns because of the intermittentthird ray. Subsequent papers in this series will provide AGchannel models for hilly/mountainous, and suburb/near-urbanenvironments. Geometry-based models would incorporate asmuch environment data as obtainable, and both “fine tune”and validate with our measured results. Additional work on theeffects of different aircraft types and aircraft dynamics wouldalso be of interest.

APPENDIX

CURVED-EARTH TWO-RAY MODEL

The two-ray impulse response at time index k for frequencyband F and environment type (e) is given by

h̃(e)2−ray,F (τ, k) = α0,ke

−j2πR1,k/λδ(τ − τ0,k))

+ αs,ke−j2πR2,k/λΓk,FDkrF δ(τ − τs,k) (A1)

where the free-space LOS component amplitude is α0,k =c/(4πfcR1,k) and the free-space surface reflection amplitude is

Fig. 21. Geometry for curved-earth approximations, adapted from [51].

αs,k = c/(4πfcR2,k), with R1,k being the direct or LOS com-ponent range, and R2,k the length of the surface-reflected path.With c being the speed of light, the delays are τ0,k = R1,k/c,and τs,k = R2,k/c. Wavelength λ = c/fc, with fc being thecarrier frequency. We assume that the range R1,k is known(or is the independent variable for our impulse response), thusα0,k and τ0,k are known. The CE2R geometry is shown inFig. 21, adapted from [51] (we drop the primes (′) on R1

and R2 in Fig. 21 in our analysis). We normalize (A1) sothat the LOS component has amplitude α0 = 1 (and phase ofzero), and the relative surface reflection amplitude coefficientis then given by αs,n,k = R1,ke

−j2πΔRk/λ/R2,k, with ΔRk =R2,k −R1,k. Variable Γk,F is the surface reflection coefficient,which depends upon frequency, polarization, grazing angle ψ′

2,and the electrical constants of the surface; see, e.g., [7] forformulas for Γ and for the electrical constants. The CIR is then

h(e)2−ray,F (τ, k) = δ(τ − τ0,k)

+ αs,n,ke−j2πΔRk/λΓk,FDkrF δ(τ − τs,k). (A2)

Thus what remains to specify the CIR completely is thesurface roughness factor rF and divergence factor Dk, whichwe discuss subsequently, and the reflection path length R2,k (orΔRk), which enables us to compute τs,k and the grazing angleψ′2; this angle is required to compute the reflection coefficient

Γk for the appropriate surface type.The electrical11 constants of the earth (permittivity εr and

conductivity σ) have been tabulated for multiple conditionssuch as dry ground, wet ground, freshwater, seawater, etc., e.g.,[7]. Note that our model can also account for the antenna gainpatterns for the LOS and surface reflection. If we maintainthe unity amplitude for the LOS component, this amounts toanother scale factor on the relative surface reflection amplitude,

11We assume the surfaceis nonmagnetic, i.e., μ = μ0, which is the perme-ability of free-space.


i.e., we multiply αs,n,k by the relative antenna pattern factorαa, where αa = gSUR/gLOS is the (possibly complex) ratioof antenna (voltage) gain values for the two components, witheach component (numerator and denominator) the product ofthe transmitter and receiver antenna gains.

Without the surface roughness factor rF , the assumption isthat the earth’s surface is smooth (rF = 1). When the earthis not smooth, the reflection will not be specular, and whenrough enough, the physical propagation effect will not be re-flection but will actually be scattering, with the scattered signaldispersed into multiple components that propagate away fromthe surface in multiple directions. In this case, the energy thatpropagates to the receiver can be significantly less than thatestimated via αs,n,kΓk,FDk. Roughness is quantified relativeto the wavelength λ, and the most common criterion applied forthis is the Rayleigh criterion, expressed in terms of a roughnesscoefficient Cr as [7] Cr = 4πsg sin(Ψk)/λ, where the quantitysg is the standard deviation of the earth surface height about itsmean value. In this approximation, which assumes that surfaceheight can be modeled by a Gaussian distribution, the reflectiongets multiplied by the factor rF = exp(−C2

r /2) [52]. For awater surface, the Miller–Brown model [32] employs rF =exp(−C2

r /2)I0(−C2r /2), with I0 the modified Bessel function

of the first kind, order zero, and sg can be found from windspeed as sg = 0.0051u2, where u is the wind velocity in metersper second.

For the curved-earth case, the computation of the grazingangle ψ′

2 is difficult [50]. We thus resort to approximationsand here provide the complete analysis, for which only partsare given in [50] and [53, Sec. VI]. In Fig. 21, point A is theaircraft, point B is the GS antenna, and point C is the centerof the Earth. In [50], two approximations are provided, “forsmall angular distances for terminals near the surface of theEarth, and for very large distances between terminals such asthe case of an Earth terminal and a geostationary satellite.”The first approximation is germane to our UAS channel. Weuse the modified earth radius given by ka, where k = 1/[1 +(a/n0)dn/dh], with a being the Earth radius a ∼= 6378 km,n0 the index of refraction at the surface level, and dn/dhthe refractivity gradient with respect to altitude h. Typically,k = 4/3 is used, but one can use a more accurate value ifn0 and dn/dh are available (we used n0 = 1.000315 and thecommon exponential form for refractivity gradient (dn/dh) =315(−0.136) exp(−0.136h), with h in kilometers [31]). InFig. 21, aircraft height (assumed known) is h1, which we denoteas hA,k, and GS antenna height (also known) is h2, which weterm hG.

First we find angle qk = θ1,k + θ2,k via solving the followingequation (law of cosines), with range R1,k, and the antennaheights given as follows:

R21,k = (ka+ hA,k)

2 + (ka+ hG)2

− 2(ka+ hA,k)(ka+ hG) cos(qk). (A3)

Next, we find distance dk

dk = kaqk (A4)

and with the information to this point, we compute three“intermediate quantities” [50], [53]

mk =d2k

4ka(hA,k + hG)(A5)

ck =hA,k − hG

hA,k + hG(A6)

bk = 2√

mk+1

3mkcos

{π

3+

13arc cos

[3ck2

√3mk

(mk+1)3

]}.

(A7)

Then, we compute

d1,k =dk(1 + bk)

2(A8)

d2,k = dk − d1,k (A9)

θ1,k =d1,k(ka)

. (A10)

From this, we can compute grazing angle, and then thepath-length difference between the LOS and ground reflectedcomponents is

Ψk =hA,k + hG

dk

[1 −mk

(1 + b2k

)](A11)

ΔRk =2d1,kd2,kΨ2

k

dk. (A12)

We then find the path length of the ground reflection as follows:

R2,k = R1,k +ΔRk (A13)

which enables us to find the relative surface reflection phaseΔφs,k = 2πΔRk/λ. At this point, we can also find the surfacereflection coefficients Γk, normalized surface reflection ampli-tude αs,n,k, and surface component delay τs,k. What remainsis to find the elevation angle θe, and the reflection divergencefactor Dk (0 < Dk < 1). To find Dk, we require lengths �1,kand �2,k [50]; for this, we apply the law of cosines on thetriangle with vertices at points A,C, and the reflection point

l21,k = (ka+ hA,k)2 + (ka)2 − 2(ka)(ka+ hA,k) cos(θ1,k)

(A14)

where θ1,k is obtained from (A10). Then, the other segment ofthe ground reflection path is

l2,k = R2,k − l1,k (A15)

and we then obtain the divergence factor, i.e.,

Dk =

[1 +

2ka sin(Ψk)

l1,kl2,kl1,k + l2,k

]−1/2

. (A16)

The elevation angle is another useful parameter, found byadditional trigonometry. Referring to Fig. 21, we find

vk =π

2− qk (A17)


then using the law of sines obtain for the side pk, we have

pk =(ka+ hG) sin(qk)

sin(vk)(A18)

and then we apply the law of cosines to find the angle φk, i.e.,

(ka+ hG)2 = R2

1,k + (ka+ hA,k)2

− 2R1,k(ka+ hA,k) cos(φk) (A19)

then the law of sines again for angle φk, i.e.,

βk = sin−1

[R1,k sin(φk)

pk

](A20)

and finally the elevation angle is simply computed as follows:

θe,k = π − φk − βk. (A21)

This concludes the analysis for the curved-earth two-ray CIR in(A1) or (A2).

ACKNOWLEDGMENT

The authors would like to thank the NASA Glenn ResearchCenter engineers for their invaluable assistance in this work,in particularly for the collection and initial processing of theflight test data. We would like to specifically thank J. Griner,K. Schalkhauser, and R. Kerczewski. The authors would alsolike to thank the flight crew, J. Ishac, and S. Walker for his workon the flight track graphics.

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David W. Matolak (M’83–SM’00) received the B.S. degree from ThePennsylvania State University, State College, PA, USA, in 1983; the M.S.degree from the University of Massachusetts (UMass), Amherst, MA, USA,in 1987; and the Ph.D. degree from The University of Virginia, Charlottesville,VA, USA, in 1995, all in electrical engineering.

He was with the Rural Electrification Administration, Washington, DC,USA, where he worked on upgrading specialized rural telecommunicationsystems; for the UMass LAMMDA Laboratory, where he worked the full-waveanalysis, design, fabrication, and testing of planar microwave transmission linesand antennas; for the Microwave Radio Systems Development Department,AT&T Bell Laboratories, where he worked on the analytical and empirical char-acterization of nonlinearities and their effect on quadrature amplitude modula-tion transmission; for the Communication Systems Laboratory, The Universityof Virginia, where he focused on analysis of trellis coding and equalizationfor time-division multiple-access mobile radio systems; for Lockheed MartinTactical Communication Systems, where he was a Lead System Engineer onthe development of a wireless local loop synchronous code-division multiple-access communication system; for the MITRE Corporation, where he workedon the analysis and modeling of various digital radio communication systems;and for Lockheed Martin Global Telecommunications where he worked onmobile satellite communication system analysis and design. From September1999 to August 2012, he was with the School of Electrical Engineering andComputer Science, Ohio University, Athens, OH, USA. Since August 2012, hehas been with the Department of Electrical Engineering, University of SouthCarolina, Columbia, SC, USA.

Dr. Matolak has served on dozens of IEEE Conference Technical Programcommittees and was also the Chair of the Geo Mobile Radio StandardsGroup within the Satellite Communications Division of TelecommunicationsIndustries Association. He serves as an Editor for the IEEE TRANSACTIONS

ON VEHICULAR TECHNOLOGY. He is a member of Eta Kappa Nu and SigmaXi Societies, the American Association for the Advancement of Science, andthe International Union of Radio Science (URSI).

Ruoyu Sun (S’13–M’15) was born in Hohhot,China. He received the B.S. degree from TianjinUniversity, Tianjin, China, in 2004; the M.S. degreefrom Beijing Jiaotong University, Beijing, China, in2007; and the Ph.D. degree from the University ofSouth Carolina, Columbia, SC, USA, in 2015, all inelectrical engineering.

From 2007 to 2008, he was with T3G TechnologyCompany, Ltd., Beijing, as a System IntegrationTest Engineer, working on time-division synchro-nous code-division multiple-access (TD-SCDMA)

mobile protocol solutions. From 2008 to 2009, he was with Motorola Inc.,Beijing, as a Software Engineer, working on Global System for MobileCommunications/General Packet Radio Service base station controller/basetransceiver station system integration testing. From 2009 to 2010, he was withST-Ericsson Inc., Beijing, as a System Integration Test Engineer, working onTD-SCDMA high-speed uplink packet access mobile protocol solutions. Heis currently a Postdoctoral Researcher with the National Institute of Standardand Technology, Boulder, CO, USA, doing wireless channel measurementsand modeling for millimeter-wave systems. His research interests include radiopropagation channel measurements and modeling.

Dr. Sun has served on multiple IEEE Conference Technical Programcommittees.

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Air Ground Channel Characterization for Unmanned Aircraft ...download.xuebalib.com/m1kQA8K0gwP.pdf26 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 1, JANUARY 2017 Air–Ground