EuCAP 2006 - European Conference on Antennas & Propagation

 
Session: Session 5A09P - Propagation for Radar and Navigation Systems (15i2)
Type: Oral Propagation
Date: Friday, November 10, 2006
Time: 08:30 - 12:20
Room: Gallieni 5
Chair:
Co-chair:
Remarks:


Seq   Time   Title   Abs No
 
1   08:30   Experimental Study and Modeling of HF Radio Wave Propagation in the Course of Substorm Event
Blagoveshchensky, D.1; Borisova, T.2; MacDougall, J.3; Sergeyeva, M.1
1St. Petersburg State University of Aerospace Instrumentation, RUSSIAN FEDERATION;
2Arctic and Antarctic Research Institute, St. Petersburg, RUSSIAN FEDERATION;
3University of Western Ontario, London, Ontario, CANADA

It is well known that the main ionospheric trough (MIT), and the auroral oval, sporadic structures, and belt of ionospheric inhomogeneities concentrated southward the oval impact on HF radio propagation on the paths located in the area of invariant latitudes 50-75o. Lateral signal reflections, backscatter, quick fading of signals at a receiving point, and unusual modes of propagation are observed. However, geomagnetic disturbances occurring in the auroral and subauroral ionosphere of the Earth, lead to even more complicated (anomalous) conditions of HF radio propagation in the subpolar regions. This happened because there are additional small- and large-scale irregularities of the ionosphere during magnetospheric storms and substorms. Also all parameters of the ionosphere and the large-scale structures in the subauroral region (MIT, gradients, sporadic ionization and so on) show more change in their morphology when the substorm/storm intensity is greater. The impact of the main ionospheric trough, sporadic structures, gradients and inhomogeneities of the subpolar ionosphere during substorms on the signal amplitude, azimuthal angles of arrival, and propagation modes for the HF radio path Ottawa (Canada) - St. Petersburg (Russia) was considered. This subauroral path with the length of about 6600 km has approximately an east-west orientation. Earlier, experimental investigations of the HF radio propagation on high-latitude paths were carried out by many authors. However, special measurements of signal amplitude and azimuths of arrival angles at the receiving point of paths and information about basic propagation modes during substorms are not enough to understand how this region affects radio propagation. A more detailed analysis of the propagation is necessary. This is important for questions of radio communication organization, over horizon location, direction finding, navigation and so on at high latitudes. The main goals are to carry out numerical modeling of radio propagation for the path and to compare the model calculations with experimental results. Wave absorption and effects of focusing and divergence of rays were taken into consideration in the radio wave modeling process. The following basic results were obtained: Substorm effects are manifested in the essential growth of the signal amplitude (up to 20-30 dB) 1-1.5 hour before the substorm expansion phase onset. At the same time the signal azimuthal deviates towards north of the great circle arc for the propagation path. Compared with quiet periods there are effects due to irregularities and gradients in the area of the polar edge of the main ionospheric trough on the passing signals. Propagation mechanisms also change during substorms. The growth of signal amplitude before the substorm can be physically explained by both a decrease of the F2-layer ionization and a growth of the F2-layer height that leads to a decrease of the signal field divergence and to a drop of the collision frequency. Ionospheric gradients are also important. This increase of signal level prior to a substorm could be used for forecasting of space weather disturbed conditions. This work was facilitated through financial support on grant NATO ESP/CLG No981604.

 
 
2   08:50   Ionospheric Clutter Cancellation and Wavelet Analysis
Jangal, F.1; Saillant, S.1; Helier, M.2
1ONERA, FRANCE;
2Universite Pierre et Marie Curie, FRANCE


Maritime surveillance of the Exclusive Economic Zone (EEZ) is a modern challenge for the High Frequency Surface Wave Radar (HFSWR). HFSRW is based on the ability of HF waves (30 MHz to 300 MHz) to propagate along the earth curvature. Consequently, the coverage range is not limited by the radioelectric horizon and it is possible to detect target up to few hundreds kilometers. However, the effect of sea clutter and the random behaviour of the ionospheric clutter can strongly limit detection capabilities. If the sea clutter can be used for remote sensing of sea state, the ionospheric clutter is always an unwanted signal. Ionospheric clutter results from a sky wave propagation mode excited by the transmitting antenna. If an ionisation instability is located along the path of the sky wave and if the wave vector is perpendicular to the earth magnetic field, a high strength signal will be backscattered. The dimension of the instability and the time variations of the refractive index along the path cause a spread distance and spread Doppler target mask.

One idea to minimize the ionospheric clutter is based on polarimetric considerations. Due to the boundary conditions, the surface wave is vertically polarized while propagation in the ionosphere modifies the polarization state. We are trying to sense only the horizontally polarized field component that will give us clutter without any target information. With such clutter caracterisation, we think to perform some subtractive processing.

A complementary signal processing approach on vertically polarized component is carried out. Since we work on deterministic target echoes and non-stationary ionospheric instability echoes, the wavelet analysis is expected to be well appropriate to decompose the signal and extract the ionospheric clutter. The result of a very simple decomposition of the signal on Daubechie's wavelet (fig.1) is very promising. Our aim is to find an efficient signal representation (e.g. before or after Doppler integration, data processing, etc.), the good wavelet space (e.g. real 1 D wavelet, complex 2 D, etc.) and the adequate wavelet (e.g. Daubechie, biorthogonal, etc).

Fig. 1 : a very simple wavelet analysis with fourth order Daubechie's wavelet.The ionospheric clutter is separate from a meteorite echo. a) The original image b) Fifth approximation on fourth order Daubechie's wavelet : ionospheric clutter c) Fifth detail on fourth order Daubechie's wavelet : meteorite echo

a) b) c)
 
 
3   09:10   Investigation of Signal Correlation or Spaced and Co-Located Antennas on Multipath HF Links and Implications for the Design of SIMO and MIMO Systems
Strangeways, H.J.
University of Leeds, UNITED KINGDOM

The significant multipath and diffraction by small-scale irregularities that exists for HF links would seem to be very suitable for MIMO (Multiple Input Multiple Output) techniques which employ antenna arrays at both transmitter and receiver locations and use space-time coding methods to utilize the increased capacity inherent in having a number of uncorrelated (or at least partially uncorrelated) paths. The capacity improvement which MIMO systems permit at UHF would be very desirable for HF links, permitting much higher data rates and perhaps also video or picture communication. However, it is not clear whether MIMO systems could be used to advantage for HF ionospherically reflected signals and there are significant differences between the UHF and HF scenarios. These include the geometrical difference in the multipath (particularly the variation in DOA generally being in elevation rather than azimuth) and the effect of time-varying ionospheric irregularities which, although decreasing the correlation at spaced antennas, will also lead to reduced channel stationarity. The wavelength is also much longer at HF (10 100m) implying large area arrays at the transmitting and receiving locations although the latter could be avoided using either Alamouti coding or co-located antenna e.g loops and dipoles in different planes.

A vital quantity in determining SIMO (Single Input Multiple Output) or MIMO capacity is the correlation between the signals at the receiving antennas. This correlation will be influenced by the fading effect of moving ionospheric irregularities and will be determined not only by the antenna spacing and modes present but also by the dimensions of these irregularities and their velocity and orientation with respect to the plane of propagation. This will also be true for co-located antennas where, in effect, polarization diversity is employed rather than space diversity.

These effects have been investigated for both co-located and spatially extended receiving antenna arrays. For co-located antennas, proper account is taken of the coupling of the transmitter signal to, and the receiving antennas from, the two magneto-ionic modes. This has been achieved using the Leeds/St. Petersburg HF simulator [1] which permits simulation of multipath HF links including the effect of small scale time-varying irregularities and both magneto-ionic modes. The irregularities are modeled as elongated along the direction of the geomagnetic field and are specified in terms of their spectral index, outer scale, aspect ratios, velocity and the variance of their electron density fluctuations.

Correlation results have been obtained which illustrate the effect of changing transmission frequency, mode structure, irregularity electron density variance etc. From these it can be seen that, although it might be anticipated that best conditions for MIMO would arise when there are many propagation modes, in actual fact this may often not be the case due to (i) the de-correlation introduced by the irregularities (ii) the poorer SNR achieved at the lower frequencies required for the multimoded propagation and (iii) the better correlation for signals reflected from the lower ionosphere layers.

[1] V. Gherm, N. N. Zernov and H.J. Strangeways, HF propagation in a wideband ionospheric fluctuating reflection channel: Physically based software simulator of the channel, Radio Science, Vol. 40, No. 1, doi 10.1029/2004RS003093, January 2005

 
 
4   09:30   Novel Digital Broadcast / Communication Systems and Groundwave Propagation Prediction Requirements
Sevgi, L.
DOGUS University, TURKEY

Ground wave propagation has long been one of the important options for short, medium and long range communication. In addition to the historical progress from LF to millimeter bands in broadcast and communication systems, emerging HF and VHF radar technologies, intelligent transportation systems, digital radio, etc., require to review and revisit investigations of propagation characteristics over the Earths surface along realistic propagation paths through inhomogeneous atmosphere in connection to the international standards like ITU, IEC and ETSI. The geometry of the generic problem is pictured in Fig. 1.

Groundwaves have three components; direct wave between the transmitter and receiver and the ground-reflected wave both of which exist within LOS (the sum of these two also referred to as the space wave), and the surface wave which couples to the ground and may reach ranges beyond the LOS into the shadow regions. At MF/HF frequencies, ground wave propagation is dominated by the surface wave. As long as the transmitter and receiver are close to surface direct and ground reflected waves cancel each other and only surface wave can propagate. The Earth's surface electrical parameters are important in reaching longer ranges. Sea surface is a good conductor, but ground is poor at these frequencies. A challenging problem is to predict surface wave path loss variations over mixed paths, such as sea-land or sea-land-sea transitions. At VHF, shadow regions may still be covered (up to a certain range) via the edge- and tip-diffracted waves. At MW, propagation is limited by the LOS and suffers atmospheric variations.

This presentation aims to review early analytical studies as well as novel time and frequency domain powerful numerical techniques together with characteristic examples including non-flat terrain and refractivity modeling, multi-mixed path propagation. Variety of Matlab-based virtual propagation prediction tools which can be used for educational purposes as well as research tools. A mixed-path groundwave field strength prediction tool GrMIX [1] automates path loss calculations along multi-mixed paths as included in ITU-R Rec. 386-7. The parabolic equation method based GrSSPE [2] takes all kind of refractivity as well as user-specified non-flat terrain profiles into account. The GrFDTD simulates propagation through the same scenarios directly in time domain [3], etc.

References
[1] L. Sevgi, "A Mixed-Path Groundwave Field Strength Prediction Virtual Tool for Digital Radio Broadcast Systems in Medium and Short Wave Bands", IEEE Antennas and Propagation Magazine, (scheduled for) Vol. 48, No.5, Oct 2006 [2] L. Sevgi, . Uluk, F. Akleman, "A Matlab-based Two-dimensional Parabolic Equation Radiowave Propagation Package", IEEE Antennas and Propagation Magazine, Vol. 47, No. 4, pp. 184-195, Aug. 2005 [3] Visit http://www3.dogus.edu.tr/lsevgi for these and all other virtual tools.

 
 
5   09:50   Radar Coverage Prediction over Ocean: Duct Mapping Using Least Squares Support Vector Machines
Douvenot, R.1; Fabbro, V.1; Bourlier, C.2; Saillard, J.2
1ONERA - CERT, FRANCE;
2IREENA, FRANCE

Keywords: Modified refractive index profile, inversion method, Least Squares Support Vector Machines, sea clutter, grazing angle, Refractivity From Clutter.

Sea environment is a complex and changing medium which causes important variations on shipborne radar coverage. Actually, the electromagnetic waves propagation sustains strong refractive effects due to the presence of ducts [1], and both reflexion and diffraction effects due to the sea surface. However, efficient two-dimensional prediction models for wave propagation based on Parabolic Equation (PE) [2] are available nowadays, but a relevant description of the refractive index profile is needed to feed these models.

The idea, first introduced by Rogers and Gerstoft [3] and known as Refractivity From Clutter (RFC), is to exploit the sea clutter in order to retrieve the refractive index profile. The aim of this paper is to propose a new inversion method to obtain the vertical variations of the modified refractive index from the knowledge of the range-dependant propagation losses. These latters can be deduced from the sea clutter collected by the radar. Whereas Rogers and Gerstoft used a Genetic Algorithm (GA) to find the modified refractive index profile parameters, Least Squares Support Vector Machines (LS-SVM), whose theory is exposed by Suykens et al. in [4], are used here. This method produces good results with the great advantage of quickness.

First, the parameterization of the refractive index profile is presented. Thus will be quickly explained the LS-SVM process. At last, a comparison between the two methods (LS-SVM and GA) will be exposed in this paper. The final aim of the LS-SVM method is to provide a system able to give satisfying results in real-time, and usable in operational conditions.

References
[1] R. Paulus, "Evaporation Duct Effects on Sea Clutter", IEEE Transactions of Antennas and Propagation, Volume 38, Number 11, November 1990.
[2] V. Fabbro, C. Bourlier, P. F. Combes, "Forward Propagation Modeling Above Gaussian Rough Surfaces by the Parabolic Wave Equation: Introduction of the Shadowing Effect", Progress In Electromagnetic Research, PIER 58, pp 243-269, 2006.
[3] P. Gerstoft, L. T. Rogers, J. L. Krolik and W. S. Hodgkiss, "Inversion for Refractivity Parameters from Radar Sea Clutter", Radio Science, Volume 38, Number 3, April 2003.
[4] J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor and J. Vandewalle, "Least Squares Support Vector Machines", World Scientific, Singapore, 2002, (ISBN 981-238-151-1).

 
 
6   10:40   Signal Scintillations in the Equatorial Regions a Review
Bniguel, Y.; Adam, J.-P.
IEEA, FRANCE

This paper deals with the problem of signal scintillations due to propagation through ionosphere in the equatorial regions. A measurement campaign is on going in several locations in these regions in South America, Africa and Asia in the frame of an ESA / ESTEC contract and on the leadership of IEEA. A review of results obtained will be presented. This will include the values of the scintillation indices of intensity and phase, the fades characteristics and the correlation properties with respect to space and frequency.

We will report in addition on results obtained from the analysis of GPS signals received from three ground stations located in the vicinity of Sao Paulo, Brazil. Two additional informations can be obtained in that case from a simultaneous analysis : the extent of the ionosphere inhomogeneities region and the drift velocity of the medium which is of particular importance for this problem.

The scintillations activity is highly depending on the solar activity. The data from Brazil were recorded in the beginning of 2001 which was very near of the maximum of the solar cycle. The solar spot number was about 190 as compared to about 100 for 2006.

We will conclude in presenting the consequences of signal scintillations on the positioning accuracy for navigation purposes

 
 
7   11:00   Effect of Scintillations on the Correlation of Different Frequency L-band Satellite Navigation Signals on the Same Transionospheric Link
Gherm, V.E.1; Zernov, N.N.1; Strangeways, H.J.2
1University of St.Petersburg, RUSSIAN FEDERATION;
2University of Leeds, UNITED KINGDOM

To compensate for the background ionosphere in satellite positioning, a linear combination of signals is used, e.g. the L1 and L2 GPS signals. Further, in the future, both GPS and the Galileo system will broadcast 3 frequencies enabling more advanced 3 frequency correction methods. State-of-the-art semi-codeless techniques rely on cross-correlation of the signals received at L1 and L2 to improve the likelihood of acquiring and maintaining lock on the L2 signal. Thus it is important to determine how well these signals are correlated. Lack of correlation will also introduce range error in the 2-frequency correction. A significant factor in reducing this correlation is scintillation resulting from propagation through time-varying small-scale irregularities in the ionosphere. Such conditions are especially likely at polar, high and low latitudes.

In order to model severe scintillation effects on transionospheric propagation of GNSS signals, a suitable propagation model and simulator have been constructed [1]. This simulator contains a physical model which takes as input models of both the background and stochastic (time varying irregularities) ionosphere components. The electron density fluctuations are specified in terms of their magnitude, velocity, outer scale (independently in three dimensions, or 2 aspect ratios along and across the magnetic field lines and spectra index p of the inverse power law of their anisotropic spatial spectrum. The propagation model can treat scintillations even for very strong fluctuations of the electron density (up to 100% of the background) at L-band frequencies. This is by means of a hybrid model which is a combination of the complex phase method together with an appropriately placed random screen below the ionosphere. To further extend the scintillation propagation model to determine signal correlation at spaced frequencies, the program has been modified to generate 2 random screens below the ionosphere, corresponding to 2 GNSS frequencies. These random fields are generated taking into account the auto- and cross-correlation functions of phase and log-amplitude for the 2 frequencies. Then the fields of the both frequencies are simulated on the ground. This thus provides a method of simulating the stochastic fields at different frequencies which are properly correlated. Then any required correlations and cross correlations of these fields and of their phases and amplitudes can be calculated. This enables extraction of the phases and determination of the "ionosphere-free" combination. The correlation of phases at different frequencies which is quantitatively characterized by the correlation coefficient (normalized 2-frequency phase correlation) can be also determined.

In the paper the estimated errors of the 2-frequency range determination and the correlation coefficients of the phases at 2 different frequencies are presented depending on the strength of the electron density fluctuations for 3 different pairs of frequencies (L1/L2, L1/L3, L2/L3). The results show that their dependence on the variance of the electron density fluctuations diverges from a linear relationship, the stronger are scintillation effects. This needs to be taken into account when a choice of more than 2 frequencies is available for dual frequency ionospheric correction or other purposes in scintillation conditions.

[1]V.E. Gherm, N. N. Zernov and H.J. Strangeways, Radio Science, Vol. 40, RS1003, doi:10.1029/2004RS003097, 2005

 
 
8   11:20   Effects of Objects with Moving Parts Like Wind Turbines on Maritime RF Safety and Navigation Systems
Trappeniers, D.; Van Lil, E.; Van de Capelle, A.
K.U.Leuven, ESAT-Telemic, BELGIUM

Recently, in Europe, a large number of wind turbines of large size are being planned. The different effects of the wind turbine parks that are being planned offshore, near shore and onshore, specially on navigation systems (e.g. radar, VOR, RDF) and on navigation aids (e.g. (D)GPS) as well as on communications systems (both analog and digital), will be investigated in this paper. By using, depending on the wavelength, UTD or Moment Methods, the effects of the different parts (gondola, blades, tower) can be investigated in detail and recommendations made about how to minimise the adverse effects. This paper will focus on maritime applications.

The most important effects noted are on radar systems (both maritime with a frequency around 9 GHz and aeronautical approach radars with a frequency around 2.8 GHz). The most important factor is the influence of the attenuation of the wind turbine for radar signals. Indeed, a pyramid of deep shadow exists behind the turbine that extends at maritime frequencies (9.035 MHz) to about 100 meters behind the tower. The further extent depends on the size of the obstacle. Another, though temporary effect, is the occurrence of false echoes, which can be caused by different phenomena. However, their effect is only noticeable in a small area around them, so that the practical influence of those offshore parks on the working of navigation aids is negligible.

Since the frequency of the communication system (VHF) is much lower, the obstacles will be much smaller in terms of the wavelength, and also will be the shadowing effects. The deep shadowing zone now reduces to a few tens of meters behind the turbine. The effects on the RDF is more interesting to investigate, since there is no longer only the direct signal that determines the direction of the ship. Reflected signals will introduce an angular error in the determination of the direction of the target.

Since the ships mostly have (D)GPS on board, it became obvious to use this (very accurate) information to complement the radar systems. The channel delay spread has to be checked to verify the possibility of (slow rate: 9.6 kbps) data transmission. This turned out to be no problem, since the highest delay spread was about 300 nsec. The result of the shadowing effect is rather unexpected in that sense that the parks form an array increasing the fields behind the park, but only about half a dB, except in the immediate neighbourhood of the turbines themselves (note that here Moment Methods are required).

The adverse effects are usually very limited in space and magnitude, unless the targets or the origin/destination of the communication system, are very close (less than 1 km) from the wind turbines. Even then, some of the effects can be strongly reduced by using absorbing material, but making the installation at that particular site very costly.

 
 
9   11:40   Suppression of Multipath for the Instrument Landing System of Geneva Airport
Thain, A1; Peres, G1; Colignon, D1; Demule, H2
1EADS CCR, FRANCE;
2Skyguide, SWITZERLAND

The Instrument Landing System (ILS) is an airport radio-navigation system, which permits safe landings in low visibility conditions. It relies on producing a signal with a well defined spatial variation and so its performance can be severely degraded by the presence of multipath interference - notably from large neighbouring buildings.

In this paper we present numerical simulations of a real-life example of this problem encountered at Geneva Airport, where the construction of a building measuring 184 m (L) by 27 m (H) near a runway produced undesirable perturbations on the ILS. We also propose and simulate a number of solutions designed to direct the unwanted signal back towards its source, rather than specularly reflecting it towards the incoming aircraft.

One solution is to place shallow corrugations on the side of the building (figure 1). By carefully choosing their dimensions (here 23 cm by 28 cm) one can produce a diffraction grating with zero specular reflection [1] for a given incidence angle. This solution presents the advantage of being rather discrete.

A conceptually simpler solution is to install a single panel perpendicular to the building faade, creating a dihedral. As this panel would need to be 25 m in length, it is very important to keep its weight to a minimum. To this end it would consist of a horizontal wire array rather than a solid sheet. A subsidiary study was conducted to find the maximum spacing and minimum wire diameter tolerable for this application.

Although the reflection from the building faade alone is easy to model with asymptotic methods, our proposed solutions introduce complex scattering mechanisms, so a full-field approach is required. The building itself is electrically large (68 wavelengths long) leading to 250,000 unknowns; so we chose to adopt the Fast Multipole Method.

The quantity of interest for the ILS is the Difference of Depth of Modulation (DDM) (it is this value which is displayed in the cockpit to the pilot), so we also modelled the avionics system. Along the axis of the runway the DDM should be zero, and any perturbation would turn the aircraft from its correct course. In figure 3 we display the effect of the building with and without the wire panel. The results for the corrugations are similarly satisfactory.

[1] J. Heath and E. Jull. Total backscatter from conducting rectangular corrugations , IEEE Trans. Ant. Prop. 27, 95-97, (1988).

 
 
10   12:00   Ducted and Free-Space UWB Propagation of Transient Signals in Space Environments
E. Ferencz, O.1; Ferencz, C.2; Steinbach, P.2
1Eotvos University (ELTE), HUNGARY;
2MTA-ELTE Res. Group for Geoinformatics and Space Sciences, HUNGARY

In this paper a new solving method is presented, using the Method of Inhomogeneous Basic Modes (MIBM), that avoids all the former monochromatic ways of thinking in the description of UWB signals, in order to obtain the complete solution of Maxwell's equations for real impulses. The paper presents new and general solutions for ducted electromagnetic waves in wave-guides filled by vacuum or anisotropic plasma, and for free-space propagation in inhomogeneous media.

The theoretical results are presented in comparison with the data-base measured by DEMETER satellite.

One of the most important research topics is the investigation of (short) impulse propagation in waveguides. The known solutions are based upon the well-known monochromatic approaches, examining the different frequencies separately or building the model and the theory on a fundamentally monochromatic starting point (e.g. permittivity tensor, which is defined originally by assuming an type solution form).

By the application of a new theoretical model and solving method (MIBM), exact closed-formed solution of the UWB-problem can be yielded directly from Maxwell's equations, for free space propagation in inhomogeneous media, and for a rectangular waveguide filled by vacuum, or anisotropic, magnetized plasma, excited by an arbitrarily formed electromagnetic signal (Dirac, or real, short impulse). This method avoids the application of the former assumptions regarding the sinusoidal waveforms. The obtained closed-formed solution leads back to the former ones known for monochromatic excitation, for a sinusoidal excitation with a given frequency, but obviously the new formula results a general solution of the problem. The solution builds up the signal from basic (non-monochromatic, general) modes, which are not solutions of Maxwell's equations themselves, but their resultant sum fulfils the equations.

The theoretically deduced results are comparable to measured data registered by DEMETER satellite (SpW-phenomena, "spiky" whistlers) and some terrestrial stations (phenomenon of tweeks). This signals are excited by lightning discharge impulses in the Earth's (or other planets) atmosphere, and propagate in the Earth' surface-ionosphere wave-guide, or in guiding structures across the upper atmosphere.

The DEMETER-microsatellite developed by the CNES, started on 29 of June, 2004. The most important task of this experiment is monitoring the disturbances of the upper region of the ionosphere, especially regarding the relation between the electromagnetic phenomena and the seismic and volcanic activities on the surface. The description of the experiment can be found on the website http://demeter.cnrs-orleans.fr/dmt/.


Fig. 1. A measured and a calculated SpW signal (the excitation is a Dirac)


Fig. 2. Measured (DEMETER) and calculated UWB signals for wave-guide filled by anisotropic plasma.