MITSUBISHI-B Project:
Title:
Novel technique to estimate wave spectra using ocean HF radar for environmental
monitoring
Industrial Partner:
MITSUBISHI Electric Corp., Information Technology R&D Center.
Mitsubishi Electric is a world leader in the manufacture and sales of electrical and electronic
products and systems used in a broad range of fields and applications. As a global leader
among green companies, our technologies are being applied to contribute to and support
society and daily life around the world. The Information Technology R&D Center is actively
creating new businesses through basic research and development in the fields of informationtechnology, media intelligence, electro-optics microwaves, and communication technologies.
We are also seeking technologies that reinforce our position on the leading edge of progress,
with work to renew existing businesses through the fruits of our R&D in the field of IT.
Industry Mentors
Hiroshi Kameda, PhD, Information Technology R&D Center
Tetsutaro Yamada, PhD, Information Technology R&D Center
Ryuhei Takahashi, Information Technology R&D Center
Kei Suwa, Information Technology R&D Center
Introduction
Since ancient times, humans have lived in close contact with the ocean through fishingand maritime trade, and this relationship has expanded further in the 20th century as humanactivities have increased in quantity and quality. The direct benefits we derive from the ocean
include sea food, maritime transportation, water and mineral resources, and energy.
Especially in recent years, various oceanographic surveys and studies have revealed theexistence of unutilized energy and mineral resources in the oceans.
The observation of sea surface conditions is necessary to realize these goals. Observation
results are utilized for disaster prevention and mitigation through marine warnings, as well
as for providing information on sea conditions necessary to improve the efficiency and safetyof the marine transportation and fishery industries. They are also used to determine thelocation of oil spills, floating debris, and people in distress, and to design coastal structures1

such as breakwaters and harbors.
Sea surface observations by ocean HF radars include ocean current velocity observations,wave height observations, and tsunami observations. In this project, we focus on wave heightobservation. Wave height observations capture statistical characteristics such as temporaland spatial changes of the wave height. Since the wave height characteristics are inherently
inhomogeneous and change from moment to moment in each area of the sea, we divide awide area of the sea surface into grids and observe the wave height characteristics and theirtemporal variation for each grid. The wave height characteristics of each grid are captured
as wave spectra (also called directional spectra). The wave spectra represent the wave
height values for each direction and frequency component of the waves in the sea surfacegrid.
Ocean HF radar is a sensor that obtains wave spectra utilizing Bragg resonancephenomena of wave components to radar signals. Ocean environmental monitoring including
wave height observation by ocean HF radar has been conducted not only in Japan and theUnited States, but also in the Asia-Pacific region, China, and Europe[1][2][3][4][5].
Technical Background
1. Principle of Radar
The principle of object sensing by radar is to transmit radio waves toward an object andreceive the reflected waves to measure the object's range, velocity, and direction. The range
is determined immediately from the time difference between transmission and reception, i.e.,
the round-trip time of the radio wave. Velocity is radial velocity relative to the radar station,
which is determined by Doppler frequency analysis of the received signal. The direction isimmediately determined from the direction in which the radar antenna beam is pointed.
Fielded radars, including ocean HF radars, operate in complex radio propagation
environments and are required to detect and track desired signals while suppressing
unwanted signals. This requires complicated sensor processing systems that apply state-ofthe-art technology, but the basic principles remain the same as described in the previousparagraphs. In this project, it is sufficient to understand what is explained in the following
paragraphs in order to tackle the project theme.
Ocean HF radar is installed along the coastline. The radar transmits the radio waves to thewide area of sea surface and receives the reflected echoes from the sea surface. The
received signals are measured in grids separated by direction and range, as shown in Figure
1. The width of the direction and range separations is determined by the radar's azimuth andrange resolutions, which in this project are approximately 7.5 deg and 1500 m, respectively.
After repeating this measurement for several seconds, a Doppler spectrum is obtained from2the received signal for each grid.

Figure 1 Radar Range-Direction Grids
2. Doppler Spectra of Sea Echoes
The random motion of the sea surface that we see can be decomposed into component
waves with frequency and direction, as shown in Figure 2. Ocean HF radar uses the Bragg
resonance of the component waves of sea-surface motion relative to the radio wavelength,
and receives the reflected echoes of the sea surface that are scattered back to the radar, i.e.,
Bragg scattered waves.

Figure 2 Decomposition of Random Sea Surface Motion[6]Figure 3 is a schematic illustration of first-order Bragg scattering, in which reflected waves
from adjacent wave peaks are in phase with each other and strengthen and resonate witheach other. In other words, Bragg scattering occurs when the distance between thepeaks is half the radio wavelength 0 . In this figure, the sea surface is represented as if itwere stationary, but in reality, the sea surface moves in the right and left directions, i.e.,advancing wave and receding wave toward the radar. Therefore, the first-order Bragg
scattering in the received signal is observed as two Doppler frequency components with3

different signs.

Figure 3 First-order Bragg Backscatter
Mathematically, it can be expressed by the following equations.

k B = 2k 0
fB = g0(1)(2)

where k 0 and k B are the radio wavevector and the ocean wavevector corresponding tofirst-order Bragg scattering respectively.

f B and g are the first-order Bragg frequency

and the acceleration of gravity respectively. Figure 4 is given to confirm (1).

Figure 4 First-order Bragg Backscatter Condition

4

Second-order Bragg scattering results from a combination of electromagnetic andhydrodynamic effects. The former is the Bragg resonance due to two reflections at the sea
surface, and the latter is the Bragg resonance due to the synthesis of two wave components.
Second-order Bragg scattering due to electromagnetic effects occurs via two wave
components to produce an intermediate and twice scattered radio wave directed toward theradar. Figure 5 schematically illustrates the mechanism of this occurrence. Mathematically, it
can be expressed by the following equation.

k1 + k 2 = −2k 0(3)where k 1 and k 2 are the ocean wavevectors.

Figure 5 Second-order Bragg Scattering due to Electromagnetic Effects
Second-order Bragg scattering due to hydrodynamic effects occurs when the wavelengthof the interacted wave in the two intersecting wavenumber vectors is half the radio
wavelength in the radar line-of-sight direction, similar to the mechanism that generates firstorder Bragg scattering. This scattering process is expressed by (3).

5Figure 6 Second-order Bragg Scattering due to Hydrodynamic Effects
The Bragg scattering wave received over a predefined observation time, typically a few
minutes, is analyzed as a Doppler spectrum using the discrete Fourier transform of thereceived radar signal. A typical Doppler spectrum measured at certain range and angle isshown in Figure 7. In this figure, the Bragg peak is the Doppler spectrum due to first-order
Bragg scattering, and the Doppler frequency offset f is due to the ocean current velocity
observed in the radar line-of-sight direction.

Figure 7 A typical Doppler spectrum [7]The Doppler spectrum of Bragg scattering  ( )where  ( = 2 f )is the Doppler

frequency in radians per second is given by ( ) =  (1) ( ) +  ( 2) ( )6(4)where  (1) (  ) and  ( 2 ) ( ) are the Doppler spectrum of first- and second-order Bragg
scattering1.
The relationship between the Doppler spectrum of Bragg scattering and wave spectrum
has been studied theoretically[8]. The Doppler spectrum of first-order Bragg scattering isgiven by (1) ( ) = 26  k04  S ( −2mk 0 )  ( − mB )

(5)

m =1

where k0 = k 0 = 2  is radio wavenumber, S ( k ) is the wave spectrum for wavevector

k and  ( ) is the Dirac delta function.  B = 2 gk0 is known as the first-order Bragg

angular frequency. Clearly (5) is a mathematical expression of the first-order Bragg
scattering mechanism described above with Figure 4. In actual ocean HF radar operations,Bragg first-order scattering is used for ocean current velocity estimation by measuring theDoppler frequency offset f as seen in Figure 7.
The wave spectrum on which this project focuses are estimated based on the theoreticalequation for second-order Bragg scattering, which will be explained below. The Doppler
spectrum of second-order Bragg scattering is given by ( 2) ( ) = 26  k04    
m1 =1 m2 =1+− ( m1k1 , m2k 2 ) S ( m1k1 ) S ( m2k 2 )2()(6)   − m1 gk1 − m2 gk2 dpdq
where k1 = k1 = 2 1 and k2 = k 2 = 2 2 are the ocean wavenumbers respectivelyand  ( m1k1 , m2k 2 ) is the coupling coefficient. The integral variable p and q is thevariable associated with the radar and ocean wavenumber vectors by the following
relationshipk 0 = ( k0 , 0 ) , k 1 = ( p − k0 , q ) , k 2 = ( − p − k0 , − q )(7)

 ( m1k1 , m2k 2 ) is the sum of  E ( k1 , k 2 ) due toelectromagnetic effects and  H ( m1k1 , m2k 2 ) due to hydrodynamic effects, each given as
The coupling coefficientin (8) and (9).

 ( m1k1 , m2k 2 ) =  E ( k1 , k 2 ) +  H ( m1k1 , m2k 2 )1(4), buy,ymy

Db.

7(8)

2

1  ( k1  k 0 )( k 2  k 0 ) k0 − 2k1  k 2  E ( k 1 , k 2 ) = 
2 k 1  k 2 − k0 
k1 k2 − k1  k 2 ) ( 2 + B2 ) (i H ( m1k1 , m2k 2 ) = − 2  k1 + k2 −22 −mmkkB)
1 2
12 ((9)where  is the average normalized impedance of the seawater and typical value is = 0.011 − 0.012i .
As shown in (6) through (9), two wavevectors k 1 and k 2 are involved in second-order
Bragg scattering. There are various combinations of k 1 and k 2 that yield a given Doppler()frequency that satisfy (3), subject to the Dirac delta function   − m1 gk1 − m2 gk2 = 1in (6). Other than S ( m1k1 ) S ( m2k 2 ) , which is determined by the combination of k 1 andk 2 , the other elements contributing to the Doppler spectrum are the coupling coefficient ( m1k1 , m2k 2 ) .
Given a Doppler frequency  , (6) implies that the Doppler spectrum  ( 2 ) ( ) isdetermined by the integral values of the integrating variables p and q . The integration
path follows a curve on the pq plane, as shown in Figure 8, that is determined for each of interest. Note that the Doppler frequencies in the figure arenormalized by the Doppler frequency  B of the first-order Bragg scattering.
Doppler frequency8(a)  B(b)  BFigure 8 Normalized constant Doppler frequency contours on pq plane [8] (Note thatsome edits were made to the original figure)
3. Directional Wave Spectrum Estimation from the Doppler Spectrum
In this project, we work on a method to estimate the wave spectrum S ( k ) contained in

the right-hand side of equation (6) from the measured Doppler spectrum  ( 2 ) ( )(left-hand side of equation (6)). Although many estimation methods have been proposed, suchas those described in [8]-[13] , only a few of them are feasible with a single ocean HF radar,which is the premise of this project.
The Barrick method [8] is a classical method for estimating wave spectrum using a single
radar. In this method, the wave spectrum is assumed to have a small directional dependence,9and the frequency spectrum of the ocean wave is obtained. Specifically, based on thisassumption, (6) is approximated as a linear integral, the measured Doppler spectrum ismultiplied by a weight function, normalized by the first-order Bragg scattering spectrum, andintegrated along the frequency axis. The Barrick method is widely known because it is arelatively simple estimation method, although the accuracy of the obtained frequency
spectrum and wave height which is estimated by the frequency spectrum may not be
sufficient because it ignores the directional dependence of the wave spectrum.
The Hisaki method [11][12][13] avoids the approximation to (6) as in the Barrick methodand directly solves the same equation. (6) is the integral of the wave spectrum along an isoDoppler frequency curve defined on a plane determined by the wave frequency and direction.
The Hisaki method interpolates the wave spectrum at any point on this curve with the wave
spectrum at surrounding grid points. This allows (6) to be rewritten with the wave spectrum
at each grid point. The objective function is then given by adding the energy balance equation,
foresight conditions on the wave spectrum, etc., and the wave spectrum is estimated bysolving an optimization problem. Although the Hisaki method has the problem of a large
number of unknowns, measurement data have shown that wave spectrum estimation ispossible using the Doppler spectrum of second-order Bragg scattering, which has highreceiver sensitivity.
Expectations
In this project, we expect you to propose a new estimation method for the wave spectra
described above. To validate the proposed method, Industrial Mentor will provide measured
Doppler spectral data and information on the significant wave height as a reference for theestimation results. The Doppler spectral data may contain signals other than Bragg scatteredwaves, such as ship reflection signals and radio wave interferences, which will be notified
when the Doppler spectral data is provided.
Requirements
We welcome students who are motivated to contribute to industry and achieve personal
growth by solving problems faced by radar systems that measure the real world. To solve theproblems, students should have basic knowledge of optimization and basic programmingskill (e.g. Python, MATLAB). In addition, it is desirable for the candidate to have knowledge
on statistical signal processing Note that knowledge of radar technology is not necessarily
required. Whatever knowledge is needed has been described above will be explained by theindustrial mentors at the beginning of this project.

10References[1] Fujii, S., Heron, M.L., Kim, K. et al. “An overview of developments and applications ofoceanographic radar networks in Asia and Oceania countries,” Ocean Sci. J. 48, 69–97(2013).
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:// u[5] High Frequency Radar – EuroGOOS (k. u/quym/)[6] Journée, J.; Massie, W. Offshore Hydromechanics; Delft University of Technology: Delft,The Netherlands, 2001; p. 153.
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[11] Y. Hisaki, “Ocean Wave Directional Spectra Estimation from an HF ocean radar with aSingle Antenna Array: Methodology,”J. Atomospheric and Oceanic Technology, vol.23,
issue 2, 2006.
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