Introduction

An Analysis of Helicopter RotorModulation Interference

IVAN KADAR, Senior Member, IEEEGrumman Aerospace CorporationBethpage, N.Y., 11714

Abstract

In satellite-to-helicopter communications, interference exists on theincoming signal when the receiving antenna is located below the

rotor blades. A bound is established for the performance of a

coherent fixed-tone ranging system operating at L band in this

interference environment.

The scalar diffracted field beneath the rotating blades, at L band

and above, is found to satisfy the criterion of Fresnel diffraction,

and is computed using the techniques of Fourier optics. The dif-

fracted field is expressed in terms of a narrow-band signal. The

amplitude and phase components are calculated from a Fourier

Series expansion using the F FT algorithm. The significant harmonics

of the phase component of the interference combine with the base-

band of the narrow-band, phase-modulated ranging signal. This re-

sults in CW interference, and in rearrangement of the first-order,sideband, ranging-tone channel powers.

The degradation in ranging accuracy is evaluated by computing

the signal-to-interference (SIR) ratio for a set of ranging tones. The

post-detection (SIR)pD at the output of the correlator is shown to

be a function of the amplitude of the phase harmonics of the inter-

ference, the relative difference between the ranging tone and inter-

ference center frequencies (a function of rotor speed), the range-

tone modulation indices, and the post-detection filter noise

bandwidth.

Manuscript received August 9, 1972.

In satellite-to-helicopter communications, interferenceexists on the incoming signal when the receiving antenna islocated below the rotor blades. The degree of interferenceand techniques of analysis depend upon the wavelength ofthe source, the dimensions of the blade, and the relativegeometry between the blade and the antenna location. Thispaper developes an analysis technique that allows boundingof this interference on the performance of communicationssystems operating in the interference environment. Inparticular, the effects of interference are evaluated for asatellite-to-helicopter fixed-tone ranging system operatingat L band.

The analysis used here to evaluate this interference isbased upon the premise that the techniques of Fourieroptics are applicable at L band and above for most helicoptergeometries examined [1]. In this case, the solution of theinhomogeneous wave equation with a harmonic source andspecified boundaries [2] allows the formulation of Kirch-hoff's approximation and satisfies the criterion for Fresneldiffraction [3].

Assuming a normally incident monochromatic planewavefront (CW), the field beneath the opaque blades isfound using Babinet's principle [31. The opaque rotorblades are replaced and approximated mathematically by anequivalent rectangular aperture of dimensions equal to themaximum blade width and length. The rotation of theblades (aperture) in this case becomes a one-to-one rotationof coordinate axes of Lhe diffracted field with respect tothe field point (antenna location). It is assumed that thereceiving antenna pattern is known with respect to theground plane (helicopter structure) and that the total fieldwill be merely weighted by the antenna pattern. Theweighting of the field by the antenna pattern is assumed tobe unity.

The scalar diffracted field is expressed in terms of anarrow-band signal by finding its envelope and phase com-ponents. Both the amplitude and phase components of thefield are expanded in a Fourier series, utilizing the FFTalgorithm [4], to assess the performance of systems suscepti-ble to the interference by finding the number of significantterms of the expansion for a particular geometry considered.

For the case of the fixed-tone ranging system examined,the significant harmonics and the interference combinewith the baseband of the narrow-band, phase-modulatedranging signal. This results in intermodulation interferenceand in rearrangement of the significant (first-order) sidebandsubcarrier tone channel powers [5], effecting the de-modulation process. The degradation in ranging accuracy isevaluated by computing the signal-to-interference (SIR)ratio for a set of ranging tones. An example is given forthe UH- lB helicopter, considering typical antenna locations.

Discussion

As we are interested in evaluating the relative variationof the total diffracted field, the scalar theory formulation

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-9, NO. 3 MAY 1973434

of the diffracted field is adequate. This approach assumesthat the incident field is unpolarized [61 ; i.e., it is made upof an assemblage of radiators which are randomly distributedin phase and polarization, or by a single random radiator.The results agree, for the case above, with the vectordiffraction field for the deterministic case, where thesource wave function is chosen to represent the scalarfield component of the incident vector field [7]. In thecase of the helicopter flying near the Earth's surface, thesource (satellite) is practically at infinity and the sourcewave function becomes a uniform harmonic plane wave.

Considering a uniform harmonic plane wave with unity(normalized) amplitude normally incident on a transparentaperture, the diffracted field can be expressed as a solutionof Kirchhoff's formula (integral) subject to Kirchhoffsapproximation [3]. Kirchhoff's integral scalar wave func-tion for harmonic signals for every point in a source-freeregion, VO is given by [7]

g(r) = fs exp (Jr --r') (r)S0 L Ir .-r'j, exp (jkIr - r') ndsir -r'l (1

VO is a region of space containing the field point (r fromthe origin) and is bounded by a closed surface SO; thegradient operator is with respect to the source point (r'from the origin); k is the wave number in free space; andthe unit vector n is the surface outward normal. It is as-sumed that the time dependence is e-iwt in all equations,although not explicitly shown. The source wave function,g(r') in this case, is given by

g(r') = f(r')eikZ (2)

where f(r') is the two-dimensional aperture function.The foregoing formulation of the diffracted field has

assumed a transparent aperture in an opaque background.In the case of the rotor blade, the equivalent aperture isopaque and occupies a finite region in space; hence, thefield cannot be found directly using the above formulation.But we know that if the opaque aperture was not present,the total field would be equal to the incident field g1[given by (2)]. Applying Babinet's principle [3], the totalfield may be expressed as

g gi - g, (3)

wheregc is the diffracted field obtained from (1) by integrat-ing over the bounded region of the aperture.

In order to evaluate (1) in reference to the mathematicallyequivalent system geometry (see Fig. 1), let R = Ir - r'l anddefine r'2 = (aox + j3oy)2 + d2, following an approach usedby Papoulis [3]. With direction cosines ao, go, and y0defined as

I r I = roI''l = 'l

= o

rO=ao ryo-To

Fig. 1. Mathematically equivalentgeometry. Symbols with underbarscorrespond to boldface symbols inthe text.

where r = irl, (xo, yo, zo) are the coordinates of the fieldpoint, and a = aox + fo3y. It follows from inspection ofFig. 1 that

kR = k[r0 - (a0x+ 3y)]2 + d2

k[ro - (aox +30y)

d2 1 d42r0 8r3J3

0 o j

If r0 > X and r0 > rt, (4) can be further approximated by

(5)kR~~~~~~~~ + y2

kR k[ro - (aox + 0y) +

with an error term for the Fresnel approximation [3]

k[x2+y2 _ (aox + )21<y2

8 r3j/2 (6)

If we assume that an angle error of e = ir/6, 6 > 0, in (1)can be tolerated, then with the above approximations con-sidered, (6) requires

e5r' -r 3

-<4X r'

(7)

where the larger the value of 6, the better the approxima-tion becomes. Substituting (2) into (1), with the necessaryapproximations considered, (1) yields [3]

g(r) -+y° ) exp (jkzo)

[ f(x - y) exp [-jk(aOx + 00y)]

(4)

x[jk x2 y ] dxd (8)

KADAR: HELICOPTER ROTOR MODULATION INTERFERENCE

a0 =- (03 rrO rO ro

(1)

435

The Diffracted Field

The near-zone diffracted field beneath the stationaryrotor blade (aperture) is given by (3) and (8). In order toevaluate the field beneath the rotating aperture, certainproperties of (8) have to be examined.

Papoulis [3] has shown that the integral in (8) can beexpressed as the two-dimensional Fourier transform of thefunction

g(x, y) = f(x, y) exp(kXY)

g(xo,yo, zo, t)

(9)

F.Iu2 + v2'= exp(ikzo)j+ ii / exp 4(__

( U') ~2 V )

2( / I, 2I/

+ F( a - -~'F(b +vevaluated at u = (kxo/ro), v = (kyo/ro), wheref(x, y) is thetwo-dimensional aperture function, the exponential term isthe "Fresnel kernel," and u and v are the transform variableswhere the two-dimensional Fourier transform of the func-tion is defined as [3]:

00 00

G(u, v) = g(x, y) exp [-j(ux + vy)] dxdy.(10)

It is easy to see from theorems on Fourier transforms thatif f(x, y) is rotated by an angle 00, its transform F(u, v) isrotated by the same angle. It follows from the definitionof G(u, v) [Eq. (10)], by direct transformation, that1

g(a x + b 1y, a2x + b2y)

<a*b2 -a2b1 G(Alu+A2v,B,u+B2v) (11)

where

LA1 B1] [a1 b1LA2 2 La2 b2

If we introduce polar coordinates in (11), viz.,

x = rcos0, y = rsin0

u =wcos , v wsin 2,

then g(x, y) and G(u, v) become go(r, 0) and GO(w, 0),respectively. We then have, as shown in [3],

go(ar, 0 + 0 ) 1 G 0 0 ) (12)

Therefore, the rotation of the blade in the spatial domainbecomes a one-to-one coordinate transformation in thetransform domain. It is assumed that the rotor rotates at aconstant angular velocity, wrOtOr rad/s. Hence, 0 = 2wrotortWblade t.After some manipulations, the field (8) can be expressed

as

+ F( a t 2)F( b+ (13)

where f = N/(7r/Azj, and F(x) is the complex Fresnel inte-gral function, defined as

-2

F(x) =e2jy' dy. (14)i[rj14The primed variables, u' and v', are referred to the rotatedcoordinate system, and are given by

= usin0 + vcos0

v - ucos0 - vsin0. (15)

In order to facilitate the numerical evaluation of (13),utilizing a digital computer, F(x) is expanded into its realand imaginary parts, where, in terms of the definition of thestored Fresnel integrals in [8], the expression for F(x)becomes

F(x) = C(x2) + jS(x2) (16)

l cos tC(r) = J -I dt

(17)1

S(Tr) =N27J sin tJ-T dt.

Now, making the necessary substitutions in (13), the fieldis expressed as

g(xO, YO, zO, t) = exp (jkzo)*{l + IyeiW[a+IjB]} (18)

where

1 u2 + V2ly= -, W= 2 2rrk =2a

1 denotes a two-dimensional Fourier transform pair.

a = [C1 +C3]C2 - [S1 +S3]S2+ [C1 +C3]C4 - [SI +S3]S4

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS436 MAY 1973

Fig. 2. Typical helicopter (UH-1B) showing candi-date antenna locations.

o = 1s +S31 C2 + [Cl +C3]S2+ [C1 +C3]S4 + [Sl +S3]C4

and

C1 [(t 22 ]'

C2 = C -b- 2 ])

C3 = C [a+ 2]

C4= b

S1 = S (ta u4)]

S2 = v')b ]

S3 = S [(a + 2]

S4 = S (b + 2\

The magnitude of g(x0, yo, zo, t) is obtained by multiplying(18) by its complex conjugate and taking the square rootof the resulting expression:

Ig(xo,yO,ZO,t)l = [1 + 'y2(a2+ f2)- 2'y cos W- 2ya sin W] 1/2. (19)

The phase ofg(xo, yo, zo, t) is given by

¢(t) = tan1sin kz +'ya cos (kzo - W) - a: sin (kz0 - W)]

Lcos kzo -yo: cos (kzo - W) - Oya sin (kzo - ._

The total scalar diffracted field may be expressed as

Y(t)I(X0,YO0zO0t) = Ig(xo, yo, zo, t)l cos [¢(t)] . (21)This representation of the field allows the evaluation of theeffect on rotor interference of specific carrier modulation/demodulation techniques.

Fourier Series Expansion

Taking 2N sampled values in the period (0, ir) of both themagnitude and phase of the field, i.e., xj, j = 0, 1, 2, .

2N - 1, (19) and (20) can be represented by

N-1

= a+~j {akco[COSXi 2{& [ Nk=l

+ bR sin 7]4} + LaN(-I)i (22)

utilizing the IBM DRHARM subroutine [8] to compute thecoefficients ao0 l , bo b1, *, aNl, bN-l , aN, basedupon the Fast Fourier Transform algorithm [4].

Before the FFT algorithm can be applied, however, onehas to select N, the number of samples required to representa bandlimited function to a specified accuracy, which isgiven by the sampling theorem [3]. If the function is notbandlimited, the number of samples required to reconstructthe function from its sampled values is not defined. Theapproach in this case is to bandlimit the function prior tosampling. The amplitude and phase functions given in (19)and (20) are not bandlimited. Therefore, we examine thetime functions to assess the significant frequencies of interestand vary the sample size until the Fourier coefficients arestabilized, i.e., the aliasing error is made vanishingly small.

Applications

The results of the analysis are applied to a typicalhelicopter, e.g., UH-IB [1], with an on-board communica-tions system that uses the incoming signal to extract range,with candidate antenna locations as shown in Fig. 2.

The dimensions of the equivalent geometry, in referenceto Fig. 1, are: a = 1 foot, b = 24 feet, xo =O feet, yo = 4.5feet, zo = 6 feet, and the wavelength of the source is 0.6 feet(L band). Substituting the above parameters in (18), theamplitude and phase variation, respectively, of the dif-fracted field are evaluated and plotted in Figs. 3 and 4 as afunction of blade rotation angle at xo = 0 feet, yo = 4.5feet, and zo = 6 feet, using the IBM 360/67 time-sharingcomputer. Note that the magnitude and phase of the field

KADAR: HELICOPTER ROTOR MODULATION INTERFERENCE 437

...------ ........

s -.;-;--;-; ----;-----:---~~~~~~~~~~~~. -; -.- -!

-R -- ---,.

-r/4 3/2 3rJ4

BLA[E TATION 1E, RMD.

Fig. 3. Magnitude of the diffracted field at (0', 4.5', 6.') versus

blade rotation angle.

TABLE

Fourier Components of Amplitude of F ield

Cosine Coefficients Sine Coefficients

0.1018D+01 0.0-0.7736D-01 -0.5979D-040.917OD-02 0.1419D-04-0.1488D-02 -0. 3446D-04-0.1401D-01 -0.4328D-04-0.7249D-02 -0.2804D-040. 11 19D-00 0.5186D-03

-0.535 3D-01 -0.2895D-030.2635D-01 0.1628D-03

-0.1778D-01 -0.1236D-03-0.2438D-01 -0.1883D-030.1561D-01 0.1327D-030.7368D-02 0.6823D-04-0.3251D-02 -0. 3262D-04-0.6494D-02 -0.7018D-040.6614D-02 0.7659D-04

-0. 2060D-02 -0.2542D-040.4675D-03 0.6176D-05

-0.5823D-03 -0.8117D-05-0.3843D-03 -0.5653D-050.1367D-02 0.2112D-04

(monotonically decreasing)

O, -w/4 r/2 3-r/4 r

BLUIE ROTATION ANGLE, RPD,

Fig. 4. Phase of the diffracted field at (O', 4.5', 6.') versus bladerotation angle.

TABLE 11

Fourier Components of Phase of Field

Cosine Coefficients Sine Coefficients

-0.41 37D-00 0.0-0.4167D-01 -0.3223D-040.8665D-01 0.1339D-03

-0. 1732D-01 -0.4020D-040.2926D-01 0.90 31 D-040.6723D-01 0.2596D-03

-0.1005 D-00 -0.4656D-030.9194D-02 0.4985D-04-0.2664D-02 0.1643D-04-0.1811D-01 -0.1259D-030.3763D-01 0.2906D-030.4989D-03 0.4158D-05-0.2219D-01 -0.2056D-030.6596D-02 0.6628D-040.2327D-02 0.2511 D-04-0.2294D-02 -0. 265 3D-040.611OD-02 0.7551D-04-0.6250D-02 -0.8212D-040. 1819D-02 0.2532D-040.6415D-03 0.9438D-05

-0. 1699D-02 -0.2627D-04

(monotonically decreasing)

are periodic in (0, 'r) with even symmetry. The amplitudevariation is small, approximately 1.5 dB, and the phasevariation is in the range of 0.2 to 0.6 radians. The wave-

shapes are complex and are expected to contain highharmonics of the blade frequency.

Using 8196 sample values of the magnitude and phasefunction, to reduce aliasing, the significant harmonics of theblade frequency were computed and are summarized inTables I and II, corresponding to a typical fundamentalfrequency of 10.9 Hz of blade rotation (a rotor speed of324). Since the input data is real and even, the sinecoefficients should be theoretically zero. The data inTables I and LI show the bk vanishingly small, correspond-ing to the accuracy used in the computer program.

sine waves, each of which modulates the RF carrier. Bymeans of a series of phase measurements starting with thelowest frequency tone, the succeeding ambiguities of eachtone are resolved, ending with a precision phase measure-

ment of the highest frequency tone [9].The demodulator implementation in this case is assumed

to consist of a second-order carrier tracking loop, followedby coherent phase comparison of the ranging tones, as

shown in Fig. 5. The input signal in the absence of inter-ference and noise is given by

f(t) = cos 2rfot + i

i=1

mi sin 2irfit) (23)

Tone-Ranging System

A fixed-frequency, side tone-ranging system is considered, where fo is the carrier frequency in hertz, mi is the ithwhere the ranging signal consists of a group of coherent modulation index, mi < r/2 radians for all i, and f1 is the

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS

*-!

. *t----,-- --------i -- l. '''- 1;-

.t,i.., ,,1,;,,;', ib ..............

,,

......::::: ....:"-:"" :::::: '::::: ':-:', l:;- -; ';,......

-- ----------

..........

438 MAY 1973

f(t)

AT IF ouTpur

FRltM KTH SUBCARRIERFILTER fo(t)' '

| I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

COS WKt

SIN WKt

F ig. 5. Range-tone demodulator-correlator implementation.

ith ranging-tone center frequency. The interference causesthe input signal to become modified as

M

(24)

i=1

where 4i(t) is the phase component of the interference,given by (20), with its Fourier coefficients given in Table II.

The phase-locked loop will follow the phase jump (doterm) and will tend to average out the phase variationcaused by the interference. Both the carrier power availableto the loop and the subcarrier channel power will be re-

duced, and the harmonics of the interference will combinewith the ranging tones, creating CW interference in thecoherent demodulation process.

Assuming K significant harmonics of the interferencepresent, (24) is expanded using the Jacobs-Anger expansionfor Bessel functions, considering only first-order terms withintermodulation neglected, following the approach used in[5]. The ratios of the carrier power and the kth ranging-tonepower, respectively, to the total incident power are givenin the presence of interference as [5]

M K-1Pc IJ 2(mi) IJ 2(aj)

i=l j=O

Pr(k)Pt

M2J(mk) 2 (m )

JO(mk)i="

(25)

where the a* are Fourier coefficients of the interference.Defining the predetection signal-to-interference ratio (SIR)as the desired ranging channel power for the kth tone tothe interference power,

M

2J2(mk) fJJ(mti)

SIR = i-lk-I

J0 (mk) IJJ0(aj)j=O

(27)

Note that SIR is not a function of the total incident power.

Range Error

It is easy to show that, for a fixed-tone ranging systemin additive white Gaussian noise, the range error for the ithranging tone is given by [9]

c

ORi = feet

2ifi(28)

where c is the speed of light,E = (Pr(k)IPt), No is the noisepower spectral density (W/Hz), and (2E/NO) A Q (capacityquotient). The range error in the presence of interferencebecomes

KADAR: HELICOPTER ROTOR MODULATION INIERFERENCE

K-1

Jj=O (aj=O

(26)

439

c

ORi = -27rf\/SN feet (29)

where

SNR= (SIR)(Q)SR SIR +Q + T

The above analysis of range error assumed that the inter-ference was out-of-band of the ranging tone predetectionfilter. If the interference falls in-band, in addition to thechange in the division of power, the interfering tone willcombine with the desired ranging tone, causing CW inter-ference.

The desired signal plus interference for the kth rangingtone at the output of the predetection filter (refer to Fig. 5)can be written as

fo(t) = B sin (wkt + VI) + A cos (wit + 0)

B2Pt

A2t-

i=1

K-1- 2JI(ai) JJJ (aj)

j 2(ai) =0

where B and A are range tone and interference amplitudes,respectively, after power division, 4 is the phase angle to bemeasured, and 0 is a random variable, uniformly distributedin (0, 2ir). In order to evaluate the post-detection SIR,(SIR)pD, at the output of the ideal low-pass filter followingthe quadrature demodulator, certain definitions and assump-tions have to be made.

Define noise bandwidth BL(Hz) for a filter with fre-quency response H(w) as

cc

BL=I IH(W)12 dw.

2lTIHmax,(w)JIo(31)

The ideal impulse response of the low-pass filter is given by

2BL j1 2 sin wTI12d22r (34)

-00

The ideal low-pass filter in this case becomes an ideal inte-grating filter with impulse response whose duration equalsthe reciprocal of the noise bandwidth.

Define (SIR)pD as

(SIR)pD = E{[y(T)12} E2{y()} (35)

where y(T) is the output of the low-pass filter with inputfo(t), and E{-} is the expected value [3] .

It is easy to see, by integrating y(t) =fo(t) cos wkt over(0, 7), that

2 + - [cos(wi - wk)t cos0

- sin (wi - wk)t sin eK-1

7j f2(aj)j=0

Mq 2(ml)

t1

(30)

(36)

where the sum frequency terms are assumed to be outsidethe cutoff of the post-detection filter.

Substituting (36) into (35) and taking expectations termby term, one easily obtains

2B2 sin2 4(SIR)PD = A2 (sin2 X/X2) (37)

where

(wi -wk)Tx 2-

The degree of interference in this case is a function of therange tone and interference amplitudes, the magnitude of thephase angle to be measured, the separation between therange tone and interference center frequencies, and theintegration time.

The range error in this case becomes

cUR. = i-rfi v/NR

(SR)pD(Q

(38)

h(t) = PT/2(t -T (32)

where

P - ,Itl >TPT=O, Itl>T

where

(SIR)PD + (Q) + 1

Conclusions

h(t) * H(w) = 2 sin wT/2 -jwT (33

It follows from the definition of noise bandwidth, by directsubstitution of (33) into (31) and by application of Parseval'stheorem [3] , that

The effects of helicopter rotor modulator interferenceon the performance of a coherent fixed-tone ranging sys-tem operating at L band have been computed. The equationsderived for the near-zone diffracted field are expressed in aform suitable for the evaluation of other geometrical con-figurations. In particular, the narrow-band representation

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS MAY 1973440

and FFT expansion of the diffracted field provide a basisfor the evaluation of systems susceptible to the interference.

The results of the analysis have been applied to a typical(UH-IB) helicopter. Numerical values of the interferenceare evaluated for a typical antenna location, assuming unityweighting by the antenna pattern.

The range error caused by the interference on a coherentfixed-tone ranging system has been computed in terms ofthe interference harmonics by evaluating the predetectionand post-detection signal-to-interference ratios. The rangeerror is clearly a function of the antenna placement androtor speed.

Numerical bounds on the ranging error have not beencomputed, since specific parameters needed would dependon the detailed design of the ranging system, which is notconsidered here. It is clear from Table II, however, that theinterference levels are small; nevertheless, they impose anupper bound on the performance of the ranging system.

As part of further work, it would be interesting tocompare the analytical results with actual or scaled-modelmeasurements. It is hoped that someone will undertake thisendeavor.

References

[1] K. Munson, Helicopters and Other Rotorcraft Since 190ZNew York: Macmillan, 1969.

121 M. Born and E. Wolf, Principles of Optics New York:Pergamon, 1964.

[3] A. Papoulis, Systems and Transforms with Applications toOptics. New York: MoGraw-HilL 1968

[4] J.W. Cooley and J.W. Turkey, "An algorithm for the machinecalculation of complex Fourier series," Math Computations,voL 19, April 1965.

[5] I. Kadar, "A simplified optimum selection of modulation in-dices for multitone phase modulation," Proc. NEC, paper68CP514-COM, 1968.

[6] M. Kline and L W. Kay, Electromagnetic Theory and Geometri-cal Optics New York: Interscience, 1965.

[7] C.C. Johnson, Field and Wave Electrodynamics. New York;McGraw-Hill, 1965

[81 Fifth Edition (1970) IBM Technical Publications Department,White Plains, N.Y.

[9] S.C. Martin and W.D.T. Davies, "A simplified correlationtechnique for position location using earth satellites,"presented at the AIAA 4th Communications Satellite Conf.Washington, D.C., 1972.

Ivan Kadar (S'61-M'62-SM'72) was born on August 1, 1937. He received the B.E.E.degree from The City College of New York, N.Y., in 1962 and the M.S.E.E. degree fromColumbia University, New York, in 1967. He has also been a part-time doctoral studentin communications at the Polytechnic Institute of Brooklyn, Brooklyn, N.Y.

He first worked, for Westrex Company, a division of Litton Industries, where heparticipated in the design of high-frequency SSB and AM subminiaturized communicationsmodules, transceivers, and dual-diversity frequency multiplexed systems. He has beenwith Grumman Aerospace Corporation, Bethpage, N.Y., since 1963. For the past sixyears he has worked on the analysis, design, and development of advanced satellite andterrestial communications and navigation systems. His recent responsibilities have encom-passed RF systems design and integration, the development of navigational algorithms,Kalnan filters, error modelling, simulations, and data processing and analysis. He ispresently engaged in the analysis of navigation satellite systems, signal processing, and theeffects of propagation, multipath interference, and signal distortion on time-of-arrivalestimation. From 1963 to 1967 he was responsible for analytical and empirical analysisand studies pertaining to modulation and detection schemes covering the communicationssystems for the Lunar Module (LM). He has also served as consultant for companies inthe area of communications theory and systems.

Mr. Kadar represents Grumman Aerospace Corporation on the AIAA Technical Com-mittee on Communications Systems, and he is an Associate Fellow of the AIAA. He is aregistered Professional Engineer in the State of New York.

KADAR: HELICOPTER ROTOR MODULATION INTERFERENCE 441