Monitoring techniques for phased-array antennas

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. A l - 3 3 , NO. 12, DECEMBER 1985 1313

Monitoring Techniques for Phased-Array Antennas JACOB RONEN, MEMBER, IEEE, AND RICHARD H. CLARKE

Abstract-The problem of monitoring phased-array antennas in gen- eral and microwave landing system (MU) in particular is considered. Various methods of monitoring phased-array antennas are suggested. One is based on changes in the far-field radiation pattern arising from defects in the array. Another method nses the near-field to far-field transformation, based on the concept of the plane-wave spectrum, for the detection of defects in the antenna. A third method is based on near-field measurements and uses the properties of the Fresnel integral. The methods were simulated on the computer and, where possible, were tested by experiment. A comparative assessment of the methods is given, and an operational monitoring system is suggested for the M U phased array.

I. INTRODUCTION

T HE MICROWAVE LANDING system (MU) which has been proposed to replace the present instrument landing

system (ILS) has presented an interesting challenge to phased- array antenna monitoring. This challenge is mainly to find a solution, on a noninterfering basis, to the problem of real-time monitoring where a decision is to be made within a fraction of a second, on the presence of defects in the array. The purpose of the present work is to look for monitoring methods based on the composite RF signal radiated from the array radiators.

Not much published work has been found that deals with this kind of composite signal monitoring. Blake, Schwartz- man, and Esposito [ l ] suggested a method for maintenance system check, which can best be described as a “perturba- tion” or “coding” technique. The necessary time stated for performing the tests over a 2165element array is 16 minutes. This method, although simple, is too lengthy.

Ransom and Mittra [2] suggested a method of locating defective elements in large arrays based on near field (Fresnel region) recording of phase and amplitude over a plane parallel to, and of the same size as, the aperture. The solution is based on the reconstruction of the aperture field by inversion of the recorded field, using the diffraction formula. This method which can be used in a near field antenna measurement is impractical in field-operated systems, such as the MLS, where such obstructions are not permitted. This is quite apart from the requirement of two Fourier transformations which might be found too lengthy, although probably shorter than the previous method [ 11.

A method for pattern measurement of phased-array anten- nas is suggested by Scharfman and August [3], by focusing the transmitting antenna into the near zone. It is also not desirable

Manuscript received September 19, 1984; revised June 26, 1985. Some of the material in this paper was presented at the 13th Convention of Electrical and Electronic Engineers in Tel-Aviv, Israel, March 22-23, 1983, and some of the material appears in CPEM-84, Delft Nederland, Aug. 1984.

J. Ronen is with Rafael Armament Development Authority, P. 0. Box 2250 Haifa, Israel.

R. H. Clarke is with Imperial College, London SW7, Ensland.

as it changes the original patterns and, in addition, interrupts the normal operation of the system.

An experimental investigation by a team from the Bendix Company [4] checked the degradation in the performance of MLS antenna patterns due to array elements failure, using two methods. The first was as in [3]. The second method used a waveguide line integral monitor. Both tests results showed good agreement with patterns measured previously on an antenna test range. It was found that about 10 percent of array components can fail before the sidelobe increases to 17 dB and the beam pointing error exceeds 0.02”. However, as in the previous paper [3], no specific proposal has been made for the inverse problem of identifying defective elements based on monitoring.

No other methods for the monitoring and detection of defects in operational phased array antennas are known to the authors. Therefore, alternative methods, or modification of present methods, will be sought in the present study.

The work reported here emphasizes the proposed “subtrac- tion method,” based on changes in the far-field radiation pattern arising from defects in the array. The “substitute element” technique based on familiar formulas for ideal antenna arrays is first presented, and the subtraction method for the detection of single defective elements in the array is described. A more realistic antenna model is then described by the inclusion of random phase errors (see Section HI) and interelement mutual coupling effects (see Section IV) to the ideal antenna model. The performance of the proposed technique in the presence of these effects is discussed. Two other methods briefly mentioned are the “angular spectrum method” which uses the near-field to far-field transformation based on the concept of the plane-wave spectrum for the detection of defects in the antenna, and the “near field focusing” method which uses properties of the Fresnel integral. The last method proposes an alternative technique for checking the far-field beam scanning from near-field monitor- ing. This is different from methods described earlier, for example in [3] and [4]. The benefit of all three methods stems from the fact that no modification of normal operation of the array is needed, and uses modes of the ordinary transmission (or reception) of the array.

The proposed methods were simulated on the computer and, where possible, were tested. by experiment. An operational monitoring system for the MLS phased array is described (see Section IX) .

II. THE SUBSTITUTE ELEMENT TECHNIQUE A method is described for the detection of defective

elements in antenna arrays, based on a simple idea which uses

0018-926X/85/1200-1313$01.00 O 1985 IEEE

13 14 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985

familiar array theory [lo], [20]. The method emphasizes the engineering significance of using rather simple formulas for accurately determining the location of defective elements in the array, based on changes in the far-field pattern. The idea of an “equivalent substitute element” is proposed in order to represent defective elements in an array. The “subtraction method,” based on the equivalent substitute element tech- nique, is presented, and the application of the method is discussed.

For simplicity, two-dimensional situations will be used throughout most of the work, as it is then easier to appreciate the underlying concepts and methods. In addition most results can be used almost directly for MLS phased arrays which are characterized by their two-dimensional beam scanning.

A . Patterns of Uniformly Illuminated Ideal Array The normalized far-field E,v of an N element, isotropic,

equally spaced, and uniformly illuminated array is given by [ 101 9 1201.

where 4 is the total phase difference as viewed from the far field, between successive elements of the array, and consists of the internal phase shift (Y introduced between the elements and the additional spatial phase shift due to differential free- space propagation delay between successive elements. Thus

+=kd sin O+a (2)

where d is the spacing between the elements and 6 is the angle of observation, measured to the broadside direction. The propagation constant is k = 2n/X, where h is the wavelength of the radiation. The variable s = sin 8 rather than 6 will be used, thus simplifying the analysis. It is the changes in the far- field patterns that leads to the detection of defective elements as follows.

B. The Concept of an Equivalent Substitute Array An “equivalent substitute array” is an array of “equivalent

substitute elements.” It is derived by considering the actual defective array to be the sum of an ideal array, which has no defective elements, and the equivalent substitute array. This decomposition is justified by the linear relation between the elements’ excitation and the radiation.

C. The Equivalent Substitute Field of a Defective Element in an N-Element Array

Expressions will now be developed for the equivalent substitute excitation and the resulting far-field radiation for defects of a static nature in a simple, though important, case. Combined amplitude and phase defects in a single element of the array (element K ) are assumed. The effect is conveniently demonstrated by the phasor representation of Fig. 1. (The analysis for a single defective element also applies to the case of many elements through the principle of superposition.)

Fig. 1 shows the ideal element of unit amplitude and phase &, referred to the array center reference phase, where, from ( 1 )

I /

b

I i ARRAY CENTRE REFEENCE PHPSE

Fig. 1. Phasor representation of phase and amplitude defect, the equivalent substitute element.

and K is the element number concerned. The defective Kth element has an amplitude ratio of a:l to the ideal, and is shifted A 4 radians in phase. The following expressions are derived for the normalized magnitude b and phase shift 6 of the substitute element,

b=(l +a2-2a cos A4)1/2

6 = r - arcsin (: sin A4) (4)

and the radiated normalized far field E of the defective array will, therefore, be a superposition of the good array and the substitute element far fields, giving

and

It can be seen immediately that information on the defective element location ( K ) and the nature of the defect (b, 6) is contained in (5). Use will now be made of this information in suggesting the subtraction method of monitoring, and in the simulation on the computer of defective array patterns. It also demonstrates a higher sensitivity of the far field pattern to defects in the far sidelobe region.

D. The Subtraction Method From (5) it is clear that subtraction of the ideal array from

the defective array field yields the field of the equivalent substitute element in the array. A method to extract a defective element location in an array can be performed by the “subtraction method” using the following procedure.

Measure the amplitude and phase in the far field of the defective array pattern in discrete steps of sin Oi:

Yi= Y(sin OJ, i= 1, 2, . e - , M ,

where A4 is the number of samples and Y is complex.

?

rt

&

I

d

RONEN AND CLARKE: PHASED-ARRAY ANTENNAS 1315

The corresponding values for the ideal array would be

Xi=X(sin OJ, i= 1, 2, ., M.

Subtract, giving

Zi= Yi-Xi , i = l , 2, * * a , M. (6)

These values will include the required information of the equivalent-substitute (defective) elements in the array and their location. This data will then contain the radiation field pattern of the substitute elements, sampled at M points in the angular range from Ol to OM. If a single element is missing in the array and the resulting phase ambiguity is resolved, two values Z1 and ZM are sufficient to give full identification of the defective element. For more than one missing element additional work will be required. Example: given an N- element isotropic uniform linear array where element number K is missing, the difference values Z; will have a magnitude ( ( Z ( ) and phases (& = arg Zi) given in Fig. 2. From (5)

Hence the missing element number will be

In practice the estimation of K , say K , is assumed, where is, e.g. the closest integer to the number K derived from (8).

Equation (8), although simple, is a powerful tool which is effective for practically any array aperture illumination. As will be shown in Sections III and N this method can give good results even in cases which are subject to random phase-shift excitation errors and mutual coupling effects.

The type of defect (for the above example) can be identified from the values of the phase shift error A$ and the magnitude ratio a, calculated from E ; and I Zi l . Hence, a full description of the defective element, namely its location and type can be achieved.

E. Some Computer Simulations Simulation on the computer of two types of defective

elements will now be given, an N = 99 elements linear uniform isotropic array is assumed with d = 0.61 h. In the first case element K = 47 (- 3d distant from the array center) is missing. In the second case element K = 56 (+ 6d from array center) is then simulated to have a pure phase defect of A+ = al4.

The far-field far sidelobe patterns (in dB) of the ideal, the defective and the substitute array are plotted in Fig. 3 and 5 for the two types of defect. The corresponding phase lines of the substitute element for these cases are shown in Figs. 4 and 6. I t can be seen that the linear phase lines are of opposite signs, for defects located, respectively, to the left and to the right of the array phase center. Also the slope is doubled for doubling the spacing between the defective element and the array center.

IZ' I

4 7 t - - - - - - - - - f l ;

I sinel sinel siney

S - r l n B

Fig. 2. Subtraction method, equivalent substitute element far-field values.

-24 1 -32

-40

- 48

- 56 .5 .6 .7 '8 sine

Fig. 3. Far-field far sidelobe region amplitude patterns N = 99 element array, missing element K = 47.

Fig. 4. Far-field far sidelobe region, phase pattern of substitute element N = 99, K = 41.

Any region can be used, however, the far sidelobe region enables the subtraction of magnitudes of the order of 1/N of the main lobe region. Hence the expected accuracy in the far sidelobe region will be greatly enhanced.

F. Nonnecessity of Measuring in the Far Field In the case of a single defective element, or of a single

defective subarray, the subtraction method does not require

1316 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985

N.99 K= 56 Atp=nl4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - ----

amplitude -- - - substitute - defectlve . . . I . . . . nondefectlve

-24

- 32 I

-56 I I I I .5 .6 -7 - -8 sm 8

Fig. 5. Far-field far sidelobe amplitude patterns N = 99 element array, r14 phase defect in element K = 56.

240, N=99 K.56 A l p = ~ / 4 , phase

(degrees) 60

0

-120 -60L \ -1 80 1 I

.5 .6 .7 sine .8

Fig. 6. Far-field far sidelobe phase pattern of substitute array, N = 99 element array, r14 phase defect in K = 56.

the measurement to be performed in the far field of the complete array. It is merely necessary to be in the far field of the element or the subarray (whichever is being sought), since the field due to the complete array is subtracted out.

G. Applicability of the Subtraction Method The subtraction method gives simple results in cases when a

single element of the array is defective. Due to the expected high reliability of present and future

solid state phased-array antennas, it is very unlikely that more than one element will fail at any one time. Hence, if the reference pattern is updated, and previously found failures are memorized, this modified subtraction method can be used sequentially for the identification of a sequence of defective elements in the array.

In comparison to the near-field method suggested by Ransom and Mittra [2], based on inverse diffraction, the subtraction method uses simple equations and does not require Fourier transformations. Also, in the subtraction method it is preferable to use the far sidelobe region, hence avoiding obstruction of the array radiation, which is required using Ransom and Mittra’s method. The subtraction method, in addition, enables one to identify the type of defect.

Application of the substitute element technique (i.e., the subtraction method) is further extended to more realistic models of antennas by the inclusion of effects of random phase-shift errors and mutual coupling effects, (see Sections III and IV).

III. ARRAY RANDOM PHASE ERROR EFFECTS We now show that the subtraction method works in

presence of random-phase excitation errors. Uniformly dis- tributed phase errors will be assumed in the excitation of the elements of a linear isotropic uniform array (a detailed discussion is given in [36]).

A . Performance of an Array of Isotropic Elements with Random Phase Errors

The random phase will reduce the mean, or “coherent,” far-field radiation pattern at the same time introducing a variance representing the fluctuating, or the “incoherent,” radiated power [21]. The far-field pattern can therefore be regarded as composed of its coherent and incoherent compo- nents.

Assume an N-element array, where random phase excita- tion errors of uniform distribution in the range kb, and assumed to be statistically independent, are attributed to its elements.

The mean far-field radiation (E(s)) is given by [21], [36]

(E(s)) = A ~ , ( S ) sine b (9)

where ( - ) is the expectation, A&) is the array factor and sinc b = sin b /b .

The variance of the far-field radiation, var [E(s)], is given by P11, 1361.

vx [E(s)] =N(1- sin C2b). (10)

The incoherent to coherent far-field radiation power ratio will be considered in two regions. In the main lobe maximum (s = 0 for broadside array) then

I A , v ( 0 ) 1 2 = ~ . (1 1)

In the far sidelobe (s = 1 for broadside array) then

I&(1)12= 1. (1 2)

Hence the main lobe incoherent to coherent ratio will be given by

var [E(s)] 1 (1 -sincl b) I (E(0))I 2=i sinc2 b ‘

The far sidelobe incoherent power ratio will be given by

var [E(s)] (1 - sinc2 b )

(13)

I (E(1)) I = N (14)

Values for these ratios for an N = 100 element array,

sinc2 b ’

function of the phase error range b, is as follows:

Range b [rad] d l 6 r18 r14 Main lobe ratio percent ((13)) 0.013 0.053 0.2 Far sidelobe [dbl ((14)) 1.1 7.2 13.7

c RONEN AND CLARKE: PHASED-ARRAY ANTENNAS

It can be concluded from this that a major effect of phase- shift errors is to mask and distort the sidelobe region of the array pattern, thereby complicating the monitoring method considered.

B. Computer Simulation of Defects in the Presence of Random Phase Excitation Errors

The subtraction method will be examined with similar parameters as in the simulation of Section 11, and will be repeated with two cases of random phase excitation. First, a defective missing element K = 47 in presence of random phase excitation b = f ?r/8 produced by a nonreset pseudoran- dom number generator (i.e., “dynamic” phase errors are produced).

Second, element K = 56 having a constant phase defect of A 4 = d 4 in the presence of random phase excitation error b = f n/8 produced by a reset pseudorandom number generator (i.e., “static” phase errors are produced).

The results are shown in Figs. 7-10. As expected (see [36]) the phase line in Fig. 8 fluctuates

around the correct mean slope line (dashed) which is repro- duced from Fig. 4. It is therefore possible to extract a defective element by a statistical estimation of a regression line. In Fig. 10, however, the phase line gives no variation about the mean slope line but is parallel to it (i.e., no phase slope error).

IV. MUTUAL COUPLING EFFECTS

Until now mutual coupling between array elements has been ignored. It is the purpose now to include these effects in the array model, thus leading to a more realistic analysis. The effect of mutual coupling on the performance of the subtrac- tion method will be discussed, for an infinite long array. Known formulas of the mutual coupling impedances due to Carter 191 will be used. The two extreme cases of defects in array elements will be considered, i.e., the open circuit (oc) and the short circuit (sc). Dipole radiators will be assumed, but by duality these formulas may be applied to slot radiators.

It can be shown [36] using the designations of Fig. 1 (in Section II) that in a two-element array a and A 4 are given by

and

for the case of an sc defect, and are given by

and

where

for the case of an oc defect.

(dB) N=99 K.47 b = + T / 8

- -- -substitute defective

amplitude

-16 ............. nondrfactive

I I I - 5 -6 -7 sin 8

Fig. 7. Far-field far sidelobe magnitude patterns in presence of random phase excitation (dynamic case).

O t

-180 - t .~ Fig. 8. Far-field far sidelobe phase pattern of substitute element in presence

of random phase (dynamic case)

amplitude ---- substitute

. . . . . . . . . . . . nondefective (dB) - daf ect iva

- 48k 1

Fig. 9. Far-field far sidelobe magnitude patterns in presence of random phase (static case).

Values of Z12 for several different array configurations can be calculated and/or found in the literature (e.g. [l l] , [19]).

In an infinitely long array a defect in one element will be felt also by the neighboring elements thus modifying their parame- ters. Ignoring second-order effects a simplification in the resulting effects can be assumed, using results of a two- element array.

1318 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985

phose h I

-90-

un v Fig. 10. Far-field far sidelobe phase pattern of substitute element in

presence of random phase (static case).

For example, assume element i is missing in an infinitely long array. Then the magnitudes aj of the substitute elements will be, approximately, given by

aj = I Z u / Z j I and the phase A+j

A computer simulation of an array with interelement mutual coupling effects to resemble an N = 8 element slot array, used in the experimental test, is given in Figs. 11 and 12 assuming element K = 4 is missing.

In Fig. 12 it can be seen that the simulated phase line varies around the expected correct phase line (i.e., if no mutual coupling effects have been included). 9

V. APPLICATION OF THE ANGULAR SPECTRUM METHOD Another monitoring method is described. This method is

more adequate for the detection of many elements failing at one time, although at the price of more complex processing than the previous method.

A . Summary of the Angular Spectrum Concept L

The angular spectrum concept [ 121, [ 131, [ 141 enables one to resolve the aperture illumination of an antenna if its angular spectrum is known. The dual Fourier transform relationship between the aperture illumination and the an,dar spectrum is given by

F(s)= l / X Im f ( x ) exp (jksx) dx -m

A defect in one element of the array will cause symmetrical f ( x ) = 'jm ~ ( s ) exp ( - j k x ~ ) (20) effects in elements located on both sides of the defective elements, i.e., where F(s) is the angular spectrum with s = sin 8, and f (x) is

- m

ai+/=ai - / the aperture illumination with x the aperture coordinate. The far field of the antenna is asymptotically proportional to its

A+i+l=A+i-l (18) angular spectrum (see [13])

where I is the spacing in element number. E(r, s) 0: F(s) exp ( - jk r ) (21)

far field E may then be approximated, if element K is missing, where E(r, s) is the far field at distance r from the antenna. For a linear uniform array, the defective array normalized-

by Hence, the measurement of the far field of an antenna can, in I 1 sin (N4/2) N sin (9/2)

E = -

where P(K + i) is + 1 or - 1 according to whether the elements (for example the Kth and the (K + 1)) are of same or opposite hands (see Fig. 22).

Comparing (19) to (5) it can be concluded that the effect of the additional factor in the second term on the r.h.s. of (19) is to cause periodic variations of the resulting phase line around its expected mean value.

As in the case of random phase error excitation 0 it may be concluded that an estimation of a statistical regression line may lead to the correct value of the missing element.

~ ~ ~~~~ ~ ~~

principle, yield the aperture field illumination. The process of determining the aperture field from the far-field measurement will be used as a basis for the monitoring method.

3. Use of the Angular Spectrum Method to Locate Defects in Antenna Arrays

The monitoring method is based on a procedure for the detection of defective elements through their effect on the aperture illumination field. In practice, however, a procedure for achieving a close approximation to the aperture field is

RONEN AND CLARKE: PHASED-ARRAY ANTENNAS 1319

N=8 K.4 (C0w)LED +3 ELEMENTS) 20

MAGNllUDE SlsSnTUTE

(dB) /--.- / 0 ...... ---+e- -@I -- - - \__0- - . .

-.5 0 .5 S- sin 8

Fig. 1 1 . Mutual coupling effects, amplitude pattern (far field).

O'

S=sin 0 Fig. 12. Mutual coupling effects, phase pattern (far field).

limited due to the finite directioncosine range of the far-field measurements (and hence of the angular spectrum).

The procedure is as follows.

Measure the far field, in the direction-cosine range of S,, < s < S-. This will be a truncated version of the angular spectrum function of the radiating aperture. Perform a Fourier transform of this truncated angular spectrum function. This yields a smoothed version of the aperture distribution. Identify defects by checking for anomalies in this calculated aperture field distribution.

This modified calculated aperture distribution will in general have a different shape from the unmodified one. It depends on whether the part of the angular spectrum chosen for analysis is in the far sidelobe or main lobe regions. Both cases give information on defects in the antenna aperture distribution. But it will be demonstrated with the aid of simplified examples that, as with the subtraction method, the angular spectrum method also gives superior information in the far sidelobe region for monitoring purposes.

C. Demonstration of the Angular Spectrum Method Assume an ideal linear uniform broadside array of d 2: X12

spaced isotropic N elements, with missing elements in the antenna. The far sidelobe region of an ideal array pattern can be approximated by sin (?rNds/X), (see (1)). This is equivalent

to the interference pattern of the two edge elements of the array, with a distance (measured in wavelengths) of Nd/X in between, where all other elements have zero illumination.

The Fourier transform of this angular spectrum is given by two delta functions located at f (Nd/h)/2, i.e.,

Ea(x) = Eo[S(x - a/2) + &(x + a/2>] (22)

where E,(x) is the apparent aperture illumination field derived from the far-field far sidelobe region monitoring, therefore, representing the edges of the aperture. Missing elements in the array will be represented according to (5) and Fig. 3 by additional delta functions in accordance with their relative location in the array aperture. The magnitude ratios of the spectral components of the angular spectrum is given by their normalized amplitude ratio. Therefore the magnitude ratio is given by

E,/E/= 2 sin (.rrdSa/X) (23)

where E,/E/ the missing to edge-element illumination ampli- tude ratio, So is the mean direction cosine and sin (rdS,/h) is the reciprocal of the mean sidelobe level magnitude. For example, in the far sidelobe region

E,/E/=2. (24)

If measurements are performed in a region symmetrically placed in r - t the main lobe then the Fourier transform of the angular spectrum will give approximately constant illumina- tion over the aperture range. Missing elements will be identified by holes in the calculated illumination. Due to the finite direction-cosine range used the resulting illumination will spread outside the theoretical aperture, and the theoretical delta functions will be replaced by sin [k(x - xi)L]/k(x - xi) functions, where 2L is the direction cosine range (i.e., S,,, - S,,, in Fig. 13) and the xi are the locations of the peaks in the aperture plane. Qualitative results, when use is made of this technique, are presented in Fig. 13 for two cases: 1) the far sidelobe region (Fig. 13(a)), and 2 ) the main-lobe region (Fig.

In Fig. 13 h/xo is the range of the direction-cosine for one period of sin (.lrNds/X) given by X/x = (2X/Nd), 2L is the measurement range of the direction-cosine given by 2L = (S- - Sme). The location of the edge element will be given after Fourier transformation by X O / X and the width of the sin [k(x - xi)L]lk(x - xi) function by Ax/h = 1/L.

D. Computer Simulation

13(b)).

As an example assume that a N = 100 element linear uniform array with 0.61 X spacing between elements has element number 35 missing, and a phase error range (see HI) of f ~ 1 1 6 . The measurement range is about 30" to 90" (i.e., far sidelobe) in M = 100 equal direction-cosine steps. As seen in Fig. 14 the missing element is made prominent and the ratio EJE, is about 1.5, close to the value of two predicted in (24).

E. Array Random Phase Error and Mutual Coupling Effects

The analysis presented in Sections III and IV apply to the angular spectrum method as well.

1320 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985 & ANGULAR SPECTRUM (A.S.) FOURIER TRAWORM OF THE A.S.

rdoa rlrmrnt

rpeclrum angular

miuing

S - L - 4

Smin S m x aprlure region [x/),] -. (b)

Fig. 13. (a) The angular spectrum method, far sidelobe region. (b) The a n g u l a r spectrum method, main lobe region.

N= 100 K= 35 I I I

4.0 -

2.0 -

O ' -I& -& ' 4 ' I

array 50 100

a p r t u n [X/Al

owtura coadimte Fig. 14. Simulation of detection of a missing element by the a n g u l a r

spectrum method.

Random phase excitation will spread out the line width of the resulting estimated defective element excitation peaks, function of the incoherent to coherent ratio (( 13), (14)) and A4 (direction steps). Hence, degrading aperture resolution of the

beam scanning, and the second with the application of the monitoring techniques described earlier in Sections II and V to very near-field monitoring. The first part of this section deals with near field monitor antenna focusing of array beam scanning, based on the properties of Fresnel integrals [25]. The last part of the chapter will describe an internal integral monitoring technique based on a beam forming network of the Blass [29] type.

A . A Focused Near-Field Monitoring Antenna The technique for focusing the transmitter antenna into the

near zone, to determine its far-field pattern, is widely used [3]. However, this technique requires modification of the transmit- ting (receiving) array phase excitation from linear to para- bolic. This means a monitoring in real time, which is not practical in some cases, such as M U . The present section is concerned with the problem of monitor antenna focusing without the need to modify the transmitting antenna phase excitation and hence enabling real-time main beam monitoring on a noninterference basis.

resulting defect location. B. Fresnel Diffraction in the Near Field Mutual coupling, as well, will effect the resulting aperture

illumination by introducing additional apparent defects charac- The apeflure field distribution f (4') Of the

teked by the normalized magnitudes of the equivalent antenna, assumed to be composed of Y-Pol&ed dipoles

substitute element. (hence isotropic in e), extends over the aperture a (see Fig. 15). The monitoring antenna of aperture b is parallel to the transmitting antenna, is assumed to have the same polariza-

Two further aspects of near field monitoring will now be tion, and senses the field distribution g(x) radiated by the presented. The first is concerned with monitoring of the array transmitting antenna. The parabolic phase approximation is

VI. MONITORING IN THE NEAR FIELD

a

f

?

RONEN AND CLARKE: PHASED-ARRAY ANTENNAS 1321

Fig. 15. The geometry of near-field monitoring.

assumed, hence (see for example [13])

g(x) U/hR)”2 exp ( - j k R ) 1 f ( E ) E = +a12

E = - a12

exp [- j k(:iE)2] d4 (25)

where R the distance of the monitor antenna (aperture b), from the transmitting antenna (aperture a). Assume now the transmitting antenna is of a unity amplitude uniform illumina- tion and has a linear phase scan corresponding to propagation in the direction s. Hence,

It can be shown [36] that

g(x, s) = (A) exp [ - jkR (1 - )]

where g(x, s) is the field distribution over the monitoring antenna when the transmitting antenna is scanned to direction s, and F [ - 1 is the Fresnel integral in the complex form. It is given by (see [ 131)

F[ . ]=C[ . ] - jS[ - ] (28)

where C[ - 1 and S[ - 1 are the cosine and sine Fresnel integrals (see [25]). Following the discussion on the above function [36] it can be shown that g(x) may be approximated over the range b < a for s Q 1 (i.e., the main beam region), by a uniform distribution having a linear phase scan like the radiation aperture field. Therefore, the unfocused beamwidth in the near-field is approximately proportional to a/R, as long as a/ R > h/a. Signal Vreceived by the monitor antenna, (i.e., the focused beam), given by integrating g(x) over the range - b/2 to b/2, can then be approximated over b < a, by

b/2 sin (1 /2 kbs) - b/2

V= g(x, s) dx2:const b 1 /2 kbs * (29)

If we choose the monitor antenna aperture to be of equal size ,

to the transmitting antenna (i.e., b = a), then

sin ( 1 /2 kas) 1 /2 kas

V2:const a

which is a similar expression to the far-field radiated from aperture a. Hence, it is scanning with the same directiodtime function and is having approximately the same beamwidth, i.e., about h/a.

It has been demonstrated (see [36]) that the length of the monitor antenna is not critical as long as b 2 a.

It is therefore proposed to use such a system for monitoring main beam scanning in the near field.

C. The Near-Fieid Monitoring Technique Summarizing, a technique for near field (Fresnel region)

monitoring of main beam pointing has been proposed. The technique, based on approximations to the Fresnel integral, is a simple one, and consists of a uniformly illuminated monitor antenna positioned in parallel with the transmitting antenna. It has been shown that the radiated beam is focused with no necessity to change its illumination phase function. No additional transformations are required beyond the linear response to signals of the sampling elements which are sparsely distributed over the monitoring aperture (see Fig. 16).

D. Computer Simulation The technique has been simulated numerically for several

types of illumination functions, for different R/a and b /a ratios and different number N of sampling elements distributed over the monitor antenna aperture (see Figs. 17-21). The results have been shown to be quite promising, when compared to the theoretical expected far-field pattern in the main-lobe region (for details see [36]). The unfocused near field is demonstrated by a single element sampling, N = 1 , in the monitor antenna aperture (see Figs. 17(a), 20(a) and 21(a)). There, the unfocused beamwidth in the near-field is approximately proportional to a/R (as long as a/R > Wa) . The focused beamwidth is approximately equal to Ma (i.e., the far-field beamwidth), for b 2 a (see Figs. 17(b), 18(b), 19, 20@) and 21(b)). However if b < a, then the focused beamwidth is approximately equal to h/b (see Fig. 18(a)). Note that thick (near field) and thin (far field) solid curves in Figs. 17-21 are all displaced from each other by about 10 dB.

E. Internal/Integral Monitoring The far-field monitoring techniques described in Sections V

and I1 can be applied in the near field using internal/integral monitoring. The limitation, however, is that although the full array radiator excitation fields can be examined no actual radiation is checked.

Internal monitoring can be regarded as monitoring in the very near field of the antenna, i.e., as an extention of the previous technique to very small R / a ratio.

Using waveguide manifold samplers of different sizes and orientations leads to the possibility of monitoring different

1322 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985 4

110 M N G E L M H T S

8

(dB) 0 gain

-8

-1 6

-2 4

-32

- 4 0 -.25 0 .25

Wa=D

16

8

:dB) 0

-8

-1 6

-24

-32

-40

gain

0

(a) (b)

Fig. 17. Computer simulation of near field monitoring, a = 50 X, uniform illumination. (a) Single sampling element (no focusing). (b) N = 10 sampling elements monitoring.

16

8 gain

(dB)

-8

-16

-24

-32

-40 0 125 .25

(a) cb)

Fig. 18. Simulation of near-field monitoring, a = 50 X, uniform illumina- tion, b/a ratio effect.

7h Wa.2 N.25 Rk=O 1 7L bh=3 N=31 R/a=D 1 gain

(dB)-

0 gain 0 (dB) -7

-14

-21

-28

-3 5

-42

-14

-21

-28

-35

-42 0 0 ,125 .25

Gl,N e, N=l , bh=l R h . 4

Fig. 20. Simulation of near-field monitoring, a = 50 X cosine illumination. (a) Single sampling element (no focusing). (b) N = 15 sampling elements monitoring.

b h = I

(a) (b)

Fig. 21. Simulation of near field monitoring, a = 50 h sine illumination. (a) Single sampling element (no focusing). (b) N = 10 sampling elements monitoring.

main beam directions (for more details see [36]). An example of a proposed monitor sampler for four beams is given in Fig. 22. A possible way of integrating a serial manifold sampler into an array is shown in Fig. 23.

VII. MEASUREMENT ERROR EFFECTS Measurement errors can broadly be divided into two main

categories, short term and long term effects. Short term effects can mostly be related to additive noise effects. Long term effects, on the other hand, can mostly be related to instrumen- tational temporal bias errors and instabilities. It is assumed that bias errors may change between measurements, while noise errors are assumed to happen within measurements. A heuristic discussion will now be made on the effects of these two types of errors on the different monitoring techniques.

A . Additive Noke Errors Measurement errors are characterized by the amplitude and

phase variances of the monitored signal. The normalized mean square (ms) amplitude error of a

monitoring amplitude estimator, is inversely proportional to the signal-to-noise ratio (SNR) as follows:

((V-S)2)/((S)2)=((n)2)/((S)2)=1/SNR (31)

where the left term in (31) is the normalized ms error of the

RONEN AND CLARKE: PHASED-ARRAY ANTENNAS 1323

HAND ECGE-@.EM REPRowcTloN

Fig. 22. Description of internal monitor waveguide samplers.

POWER

/"-COLUMNS RADIATNG FEE0

UNE ~,

VIEW FROM \ -

REAR

REAR VIEW

W I F O U ) SAMPLER

tW.Gl

Fig. 23. Demonstration of a serial manifold waveguide sampler to be used in the MLS phased array.

measured signal amplitude, S is the theoretical signal to be monitored (i.e., before noise has been added in the monitoring system), Vis the signal actually monitored containing additive noise n, and where ( - ) designates the expectation.

The ms phase error of optimal phase measuring estimators is approximately proportional to 1/SNR, for high SNR. Then, the measured phase ms error a i is given by (see [28], [30])

6; & 2/SNR, for SNR % 1 (32)

Other phase estimators are assumed to have similar behavior although probably, with degraded performances. The assump- tion that S N R % 1 is justified in practical monitoring systems, since measurements are mostly performed near the antenna to be monitored.

The effect of additive noise will now be discussed for the different monitoring techniques.

B. The Subtraction Method Noise is assumed to be stationary, therefore have the same

variance in the different measurements. Hence, the subtraction used in this method doubles the resulting noise variance. Therefore, degrading the resulting S N R by a factor of two and similarly degrading the resulting phase variance. Assume a statistical regression line of m independent samples is used. Then, an improvement is expected in the resulting phase ms error. by about a factor of m, therefore

6; = 4/(m SNR). (33)

C. The Angular Spectrum Method Fast Fourier transform (FFT) processing used in this

method normally divides the effective noise bandwidth into m cells, where m is the number of proper samples used by the FFT processing. Thereby, reducing the noise variance by about l/m per cell. Hence, with the angular spectrum method

one can achieve a lower ms error than with the subtraction method, by a factor of about two.

In both techniques, the subtraction and the angular spectrum methods, the resulting SNR is proportional to the relative intensity of the aperture illumination of the relevant elements of the array to be monitored. Therefore, a tapered illumination results in a lower SNR for detecting elements displaced from array peak illumination center.

D. The Near-Field Method The near-field method is used mainly to sense main

beamwidth of the array. Then, the normalized ms error of the measured amplitude (i.e., the 1/SNR) is of importance. The combined signal power of the monitor sampling array is approximately proportional to W in the main beam region, where N the number of sampling elements in the monitoring array. Therefore, the resulting amplitude ms error, in the main beam region, is proportional to 1/(W SNR). Where SNR is the signal-to-noise ratio resulting from a single sampling element monitoring. If a tapered illumination is used in the transmitting array, then, an effective Neff should be used instead. Where Neff is the effective number of sampling elements to be taken into account for estimating the resulting SNR.

E. Bias Errors For simplicity small bias errors of amplitude or phase

between measurements will be assumed. It is clear that subtracting two phasors having identical magnitudes and a small phase error difference A4 yields a resultant which is approximately proportional to A 4 as follows

A V / V = 2 sin A4/2 & A$, for A 4 Q 1 (34)

where A V/ V is the resulting normalized magnitude error and V is the original phasor magnitude. This can be compared to the subtraction of phasors having identical phase but a small amplitude error difference AV. However, the resultant of a pure amplitude difference is orthogonal to that of a pure phase difference. It is, therefore, possible to compare the three monitoring methods in presence of small phase or amplitude bias errors.

F. The Subtraction Method Assume a missing element in a uniform N element array. In

addition, a small bias error is assumed to be introduced by the measuring system. Then, checking carefully ( 5 ) , it can be shown that the resulting phase line will oscillate around the correct slope line with a maximum phase deviation error A 4 max, given by

sin (N4/2) sin (4/2)

A 4 max < A 4

where A 4 is either a pure phase bias error or an analogous normalized amplitude error according to (34), and 4 is the total phase-difference (see (2) in Section E). From (35) it is clear that the envelope of A 4 max is changing with the scan angle s, between a maximum value N A ~ J in the main lobe

1324 IEEE TRANSACTIONS OK ANTEhWAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985 i YI SUOLRS

Y M K m

1 LPS;;*F;R 7 r--

-7-

HP 1410 A 8413 A tw 70s B

Fig. 24. Schematic diagram of the experimental set-up.

region, and A 4 in the far sidelobe region. Therefore

NA4 2 A4 max 2 A+. (36)

G. The Angular Spectrum Method The effect of a phase error will not be noticed in the

angular-spectrum method, since no phasor subtraction is being used. However, a small normalized amplitude bias error will effect the resulting output magnitude proportionally, thereby, effecting the estimated aperture illumination.

H . The Near-Field Method As with the angular spectrum, the effect of a phase bias

error will not be noticed when the near-field method is being used for monitoring of main beamwidth fidelity. Again, a small normalized amplitude error will effect the resulting output magnitude proportionally. Thereby, proportionally effecting the estimated main beamwidth, if a comparison to a fixed threshold is being used.

VIII. EXPERIMENTAL INVESTIGATIOK An experimental setup was used for near-field measure-

ments of antenna characteristics before and after the antenna has been subjected to defects. These defects were introduced artificially by blocking slots of a slot waveguide antennas with a piece of metal tape.

The schematic diagram of the setup is given in Fig. 24. Few samples of the results are shown in Figs. 25-27. In Fig. 25 the subtraction method is tested in the side lobe

region with a N = 3 0 slot waveguide array where radiating slot K = 1 3 is missing (blocked). The measured phase line of the actual antenna is compared to that of the theoretical phase lines for a missing radiator K = 12, 13, 14 , 15 or 16. A test for the sensitivity to instability of the measurement system has

(DEGREES) PHASE

K=13 N.30

-I8O4 -L---..J .5 .6 .7 .8

Fig. 25. The subtraction method, missing element 13. sin 8

r)

u

also been carried out [36], with no practical affect on the phase slope line. In Figs. 26 and 27 the angular spectrum method is demonstrated with the same antenna in the main lobe region, with missing element K = 13 (Fig. 26) or K = 1 8 (Fig. 27). 4 The original smooth cos2 + pedestal illumination function is shown and the anomaly (Hole) in the illumination due to the defect is also shown.

It may be concluded that the experimental investigation has gone some way toward providing a practical test of part of the monitoring theories proposed and simulated earlier.

E. TENTATIVE MONITORING SYSTEhl FOR THE MLS ,

The monitoring is to perform two main tasks: the direct measurements giving the beam pointing error; the indirect measurements giving maintenance alarms in the presence of failed elements in the array. Using a preassigned number, for multielement failure, a downgrade or shut down alarm can be produced (see ICAO [6]).

A far-field monitoring system is assumed for the detection 1

RONEN AND CLARKE: PH4SED-ARR-4Y AiiTEiiNAS

.'""! normalized magnitude

*4g01 .420

1325

. . . . . . . . . . . . nondefective array

- _ _ _ _ _ equivalent substitute element defective array

N.30 K.13

- Fig. 26. The angular spectrum method, main lobe region missing element 13.

J

. . . . . . . . . . . . oondefective array

----- equivalent substitute defective array

axis

dement

Fig. 27. The angular spectrum method, main lobe region missing element 18.

1326 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-33, NO. 12, DECEMBER 1985 @

INTERNAL/ INTEGRAL MONITORING

P I R b N M L H O W FAR-FIELD MAIN BEAM YONITOR 4NTEWHb

ALARM AND

IDENTIFICTION DEFECT

r)

a

Fig. 28. Monitoring system simplified block diagram.

of defects using the subtraction method. However (see sections II-F and II-G) it is merely necessary to be in the far field of an element or of a subarray and not of the complete array (e.g. horn B in Fig. 28). Therefore, minimizing interference and multipath effects.

Internal integral monitoring is to be used for the detection of defects, in parallel with the above method. Then, in addition, other far-field methods (e.g. the angular spectrum method), can be used.

A far-field monitoring system might be required for pointing error measurement. (If a near-field real time beam pointing scheme is required, then a planar monitor antenna should be used, see Section VI.)

A simplified block diagram is given in Fig. 28. More details on the monitoring system, including a description of a wide dynamic range phase and amplitude receiver are given in [36].

X. SUMMARY AND CONCLUSION Far-field and near-field monitoring methods have been

suggested. The far-field methods included the subtraction method and the angular spectrum method.

These two different methods also correspond to two quite distinct levels of processing, in that they demand an increasing amount of processing time for their implementation.

The near-field methods included the near-field monitoring technique and the internal/integral monitoring.

The simulation models used in the work have been found very helpful in checking the theoretical methods and extending the ideal array model to a more realistic antenna model by the inclusion of random phase-shift errors and mutual coupling effects.

REFERENCES ?

C. S. Blake, L. Schwartzman, and F. J. Esposito, “Evaluation of large phased-amy antennas,” in Phased Arruy Antennas, A. A. Oliner and G. H. Knittel, Eds. Dedham, MA: Artech House, 1972. P. L. Ransom and R. Mittra, “A method of locating defective elements in large phased mays,’’ in Phased Array Antennas, A. A. Oliner and G. H. Knittel, Eds. Dedham, MA: Artech House, 1972. W. E. Scharfman and G. August, “Pattern measurements of phased- arrayed antennas by focusing into the near zone,” in Phased Array Antennas, A. A. Oliner and G. Knittel, Eds. Dedham, MA: Artech House, 1972. 1 Bendix Company, “MLS EL-1 antenna pattern monitor,” Bendix company technical note MU-BCD-TN082, 1973. J . Brown, “A theoretical analysis of some errors in aerial measure- ments,” Proc. Inst. Elec. Eng., vol. pt. C, pp. 343-351, 1958. International Committee for Aviation Organisation (ICAO) (1979): “Microwave Landing System (angle guidance documents)”, AWOP, WGM/2 report Appendix A revised 10 October 1979. W. H. Kummer, “Feeding and phase scanning” in Microwave Scanning Antennas, vol. 3 , R. C. Hansen, Ed. New York: Aca- # demic, 1966. P. J . Taylor, “MU beam forming,” Plessey internal report, 1979. P. S. Carter, “Circuit relations in radiating systems and applications to antenna problems,” Proc. IRE, vol. 20, pp. 1004-1041, 1932. J. D. Kraus, Antennas. New York: McGraw-HiU, 1950. A. A. Oliner and R. G. Malech, “Radiating elements and mutual coupling” in Microwave Scanning Antennas, vol. 2, R. C. Hansen, Ed. New York: Academic, 1966. H. G. Booker and P. C. Clemmow, “The concept of an angular spectrum of plane waves, and its relation to that of polar diagram and aperture distribution,” Proc. Inst. Elec. Eng., vol. 97, pt. ID, pp. 11- 17, 1950. R. H. Clarke and J. Brown, Diffraction Theory andAntennas New York: Wiley, 1980. J. A. Ratcliffe, “Some aspects of diffraction theory and their application to the ionosphere,” Reports on progress in physics, vol. 19,

D. T. Paris, W. M. Leach, and E. B. Joy, “Basic theory of probe-

Propagat., vol. AP-26, no. 3, pp. 373-379, 1978. compensated near-field measurements,” IEEE Trans. Antennas

j

pp. 188-267.

I

1 RONEN AND CLARKE: PHASED-ARRAY ANTENNAS 1327

A. Papoulis, The Fourier Integral and Its Applications. New York: McGraw-Hill, 1962. D. M. Kerns, “Corrections of near-field measurements made with an arbitrary but known measuring antenna,” ElectronicLett., vol. 6, no. 11, pp. 346-347, 1970. M. Born and E. Wolf, Principles of Optics, 5th ed. New York: Pergamon, 1975. S. A. Schelkunoff, Advanced Antenna Theory. New York: Wiley, 1952. E. C. Jordan and K. G . Balmain, Electromagnetic Waves and Radiating Systems. Englewood Cliffs, NJ: F’rentice-Hall, 1960. P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces. New York: Macmillan, 1963. W. Rotman and R. F. Turner, ”Wide-angle microwave lens for line source application,” IEEE Trans. Antennas Propagat., vol. AP-11, pp. 623-632, Nov. 1963. R. J . Chignell, “Slot loss coupling studies in stacked linear array application,” Ph.D. dissertation, University of London, 1975. S. A. Schelkunoff, Applied Mathematics for Engineers and Scien- tists. New York: Van Nostrand, 1948. M. Abramowitz and I. A. S t e p , “Handbook of mathematical functions, graphs, and mathematical tables,” Nat. Bur. Stand., U.S. Government Printing Office, 1964. E. Jahnke and F. Emde, Tables of Functions with Formulae and Curves, 4th ed., New York: Dover, 1945. A. A. Oliner and R. C. Malech, “Mutual coupling in infinite scanning arrays” in MicrowaveScanning Antennas, (Ed. Hansen, R. C.), vol. 2, New York: Academic, 1966. J. Ronen and M. Zakai, “The maximum likelihood estimator for a phase comparison angle measuring system,” Proc. ZEEE, vol. 51, no. 11, 1963. J. Blass, “Multidirectional antenna a new approach to stacked beams,” in IRE Nat. Conven. Rec., 1960. J. Ronen, “The influence of noise on the accuracy of interferometric angle measurements,” M.Sc. thesis, Technion-Israel Inst., Haifa, Israel, 1963.

1311 I. S. Gradsteyn and I. M. Ryzhik, Tables of Integrals, Series, and

1321 D. C. Champney, Fourier Transforms and Their Physical Applica-

[33] S. A. Schelkunoff and A. T. Friis, Antennas Theory and Practice.

1341 J . Ronen, “The monitoring of MLS phased-arrays,” Imperial College

[35] N. Williams, “Mutual coupling in waveguide slot arrays,” Ph.D.

1361 J. Ronen, “Techniques for monitoring the performance of phased-array

Products, 4th ed. New York: Academic, 1965.

tions. New York: Academic, 1973.

New York: Wiley, 1952.

London Rep. EWA 79-1, 1979.

dissertation, University of London, 1975.

antennas,” Ph.D. dissertation, University of London, 1981.

Jacob Ronen (A’59-M’74-S’78-M’80) received the B.Sc. and M.Sc. degrees in electrical engineering from the Technion, Haifa, Israel, in 1959 and 1963, respectively, and the Ph.D. degree in electrical engineering from Imperial College University of London in 1981.

He is with Rafael Armament Development, Authority of Israel M.O.D.

’, : ., Richard H. Clarke received the Ph.D. degree from University College, London, in 1960.

In 1962 he became an Assistant Professor in electrical engineering at the University of Califor-

’ _ nia, Berkeley. In 1964 he joined Bell Telephone j Laboratories, Crawford Hill, Holmdel, NJ, pursu-

ing research in mobile radio and coherent optics. From 1969 he was Deputy Group Leader in Theoretical Studies at the NATO Antisubmarine Warfare Research Centre, La Spezia, Italy, until 1974 when he took up his present appointment as a

Dr. Clarke is a coauthor of the book Diffraction Theory and Antennas Reader in electrical engineering at Imperial College, London.

(Ellis Honvood Ltd, 1980).